TSTP Solution File: SCT080-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT080-1 : 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 : n011.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 14:55:42 EDT 2024
% Result : Unsatisfiable 121.14s 17.74s
% Output : Refutation 121.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2093
% Syntax : Number of formulae : 5584 ( 727 unt; 0 def)
% Number of atoms : 17373 (2270 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 21338 (9549 ~;10243 |; 0 &)
% (1546 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 1568 (1566 usr;1547 prp; 0-9 aty)
% Number of functors : 83 ( 83 usr; 9 con; 0-6 aty)
% Number of variables : 15240 (15240 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f133398,plain,
$false,
inference(avatar_sat_refutation,[],[f1023,f1028,f1033,f1038,f1043,f1048,f1053,f1058,f1063,f1068,f1073,f1078,f1083,f1088,f1093,f1098,f1103,f1108,f1113,f1118,f1123,f1128,f1133,f1137,f1141,f1145,f1149,f1153,f1157,f1161,f1165,f1169,f1173,f1177,f1181,f1185,f1189,f1193,f1197,f1201,f1205,f1209,f1213,f1217,f1221,f1225,f1229,f1233,f1237,f1241,f1245,f1249,f1256,f1263,f1267,f1271,f1275,f1279,f1283,f1287,f1291,f1295,f1299,f1303,f1307,f1311,f1315,f1319,f1323,f1327,f1331,f1345,f1359,f1363,f1367,f1371,f1375,f1379,f1383,f1387,f1391,f1395,f1399,f1403,f1407,f1415,f1439,f1443,f1447,f1451,f1455,f1459,f1467,f1471,f1475,f1479,f1483,f1487,f1491,f1495,f1499,f1503,f1507,f1511,f1515,f1519,f1523,f1527,f1531,f1535,f1540,f1544,f1548,f1553,f1579,f1624,f1628,f1633,f1637,f1641,f1645,f1649,f1783,f1787,f1791,f1795,f1799,f1803,f1807,f1811,f1815,f1819,f1824,f1828,f1832,f1836,f1840,f1844,f1848,f1852,f1856,f1860,f1864,f1869,f1873,f1877,f1881,f1885,f2178,f2182,f2186,f2190,f2194,f2198,f2202,f2206,f2210,f2214,f2218,f2222,f2226,f2230,f2234,f2238,f2242,f2246,f2250,f2254,f2258,f2262,f2266,f2270,f2274,f2278,f2282,f2286,f2290,f2294,f2298,f2569,f2626,f2640,f2644,f2648,f2652,f2656,f2660,f2664,f2668,f2672,f2676,f2680,f2684,f2688,f2692,f2713,f2809,f2813,f2817,f2821,f2825,f2829,f2833,f2837,f2852,f2856,f2860,f2864,f2868,f2872,f2876,f2880,f2884,f2888,f3049,f3053,f3057,f3061,f3065,f3069,f3073,f3077,f3081,f3085,f3089,f3093,f3097,f3110,f3114,f3118,f3122,f3126,f3130,f3134,f3138,f3142,f3146,f3150,f3154,f3158,f3162,f3166,f3170,f3174,f3178,f3441,f3551,f3578,f3582,f3586,f3590,f3597,f3601,f3605,f3609,f3613,f3617,f3621,f3625,f3629,f3633,f3637,f3641,f3645,f3649,f3653,f3657,f3661,f3665,f3669,f3673,f3677,f3684,f3688,f3893,f4104,f4108,f4112,f4116,f4120,f4124,f4128,f4132,f4136,f4140,f4144,f4148,f4152,f4156,f4160,f4164,f4168,f4172,f4480,f4484,f4488,f4492,f4496,f4500,f4504,f4508,f4512,f4516,f4520,f4656,f4660,f4664,f4668,f4672,f4676,f4680,f4684,f4688,f4692,f4696,f4700,f4704,f5240,f5336,f5340,f5344,f5348,f5352,f5356,f5360,f5364,f5369,f5373,f5403,f5408,f5412,f5417,f5621,f5625,f5629,f5633,f5637,f5641,f5645,f5649,f5653,f5657,f5661,f5665,f5669,f5673,f5677,f5681,f5685,f5690,f5705,f6680,f6684,f6688,f6692,f6696,f6700,f6704,f6708,f6712,f6716,f6720,f6724,f6729,f6735,f6740,f6746,f6751,f7026,f7030,f7034,f7038,f7042,f7046,f7050,f7054,f7058,f7062,f7066,f7070,f7074,f7078,f7082,f7087,f7542,f7546,f7550,f7554,f7558,f7562,f7566,f7570,f7574,f7578,f7582,f7863,f7867,f7910,f7914,f7918,f7922,f7926,f7930,f7934,f7938,f8017,f8219,f8223,f8227,f8231,f8235,f8239,f8243,f8247,f8251,f8255,f8259,f8263,f8267,f8271,f8275,f8279,f8283,f8287,f8291,f8296,f8401,f8405,f8409,f8413,f8417,f8422,f8990,f9953,f9957,f9961,f9965,f9969,f9973,f10019,f10023,f10027,f10031,f10035,f10039,f10043,f10047,f10051,f10057,f10061,f10067,f10073,f10079,f10084,f10108,f10114,f10550,f10556,f10562,f10566,f10570,f10574,f10578,f10582,f10586,f10590,f10595,f10628,f10633,f10709,f10714,f10887,f10891,f10895,f10899,f10903,f10907,f10911,f10915,f10919,f10923,f10927,f10932,f10964,f10989,f11004,f11009,f11057,f11062,f11209,f11300,f11304,f11309,f11314,f11318,f11386,f11391,f11486,f11491,f11614,f11660,f11664,f11668,f11672,f11676,f11681,f11686,f11719,f11763,f11767,f11771,f11775,f11779,f11783,f11787,f11803,f11807,f11811,f11816,f11862,f11867,f11985,f11989,f11993,f11997,f12003,f12090,f12094,f12584,f12607,f12611,f12615,f12621,f12632,f12637,f12745,f12749,f12781,f12787,f12930,f12934,f12939,f12961,f12966,f13018,f13023,f13165,f13169,f13173,f13179,f13183,f13188,f13238,f13242,f13358,f13362,f13366,f13527,f13531,f13535,f13541,f13579,f13700,f13741,f13745,f13773,f13777,f13782,f13875,f13880,f13884,f13992,f13997,f14099,f14104,f14150,f14154,f14158,f14162,f14166,f14170,f14174,f14403,f14407,f14411,f14417,f14513,f14521,f14533,f14541,f14545,f14551,f14664,f14669,f14673,f14792,f14796,f14800,f14804,f14808,f14979,f15004,f15008,f15096,f15102,f15436,f15440,f15453,f15457,f15629,f15657,f15661,f15665,f15669,f15868,f15872,f15960,f16003,f16007,f16011,f16015,f16107,f16111,f16115,f16119,f16123,f16365,f16369,f16373,f16377,f16630,f16634,f16638,f16642,f16834,f16888,f16892,f16896,f16900,f16904,f16908,f17277,f17281,f17285,f17289,f17340,f17391,f17395,f17399,f17403,f17407,f17411,f17416,f17430,f17434,f17439,f17444,f17449,f17453,f17457,f17461,f17525,f17795,f17834,f17838,f17842,f17846,f17850,f17858,f17862,f17923,f17927,f17931,f17935,f17939,f17943,f17947,f17951,f18033,f18037,f18218,f18222,f18226,f18230,f18236,f18240,f18244,f18248,f18252,f18256,f18260,f18264,f18268,f18272,f18276,f18280,f18284,f18288,f18292,f18297,f18301,f18306,f18310,f18336,f18340,f18344,f18695,f19908,f19912,f19916,f19920,f19924,f19928,f19932,f19936,f19940,f19944,f19948,f19952,f19956,f19960,f19964,f19968,f19972,f19989,f19993,f19997,f20001,f20005,f20009,f20013,f20017,f20021,f20025,f20029,f20033,f20037,f20041,f20045,f20049,f20053,f20057,f20061,f20065,f20069,f20090,f20110,f20130,f20134,f20138,f20142,f20146,f20150,f20154,f20158,f20162,f20166,f20170,f20174,f20178,f20182,f20186,f20190,f20194,f20211,f20247,f21231,f22300,f23053,f23132,f23136,f23140,f23144,f23148,f23168,f23172,f23176,f23180,f23184,f23188,f23192,f23196,f23200,f23204,f23208,f23212,f23216,f23220,f23224,f23228,f23232,f23236,f23243,f23247,f23265,f23269,f23273,f23277,f23281,f23285,f23289,f23364,f25507,f25886,f25890,f25894,f26540,f26544,f26548,f26552,f26556,f26560,f26564,f26568,f26572,f26576,f26580,f26584,f26588,f26592,f26596,f26600,f26604,f26608,f26612,f26617,f26622,f26640,f26644,f26648,f26719,f26723,f26728,f26732,f26736,f26740,f26744,f26748,f26752,f26756,f26760,f26764,f26768,f26772,f26776,f26780,f26784,f26858,f26862,f26866,f26870,f26874,f26878,f26882,f26886,f26890,f26894,f26898,f26902,f26906,f26910,f26914,f26918,f26922,f26926,f26930,f26934,f26938,f26946,f26950,f26954,f26958,f26962,f26966,f26970,f26975,f26979,f26983,f26987,f27359,f30568,f31981,f32368,f32372,f32376,f32380,f32384,f32388,f32392,f32396,f32400,f32404,f32408,f32412,f32416,f32420,f32424,f32428,f32432,f32436,f32440,f32491,f32516,f32521,f32525,f32529,f32533,f32537,f32541,f32545,f32549,f32553,f32557,f32561,f32565,f32570,f32575,f32580,f32606,f32611,f32621,f32626,f32630,f32634,f32638,f32642,f32646,f32650,f32654,f32658,f32712,f32765,f32770,f32774,f32778,f32783,f32805,f32810,f32814,f32822,f32826,f32830,f32835,f32879,f32884,f32906,f32921,f32925,f33292,f35626,f36089,f36093,f36097,f36101,f36105,f36109,f36113,f36117,f36121,f36125,f36129,f36133,f36137,f36141,f36145,f36149,f36153,f36157,f36161,f36165,f36169,f36173,f36177,f36181,f36185,f36189,f36223,f36227,f36231,f36236,f36240,f36244,f36248,f36252,f36256,f36260,f36294,f36298,f36302,f36306,f36310,f36314,f36318,f36322,f36327,f36332,f36417,f36421,f36425,f36429,f36433,f36437,f36441,f36446,f36936,f36940,f36944,f36949,f36964,f36969,f36984,f36988,f36993,f38967,f40150,f41994,f41998,f42173,f42177,f42181,f42185,f42189,f42193,f42197,f42201,f42205,f42209,f42213,f42217,f42221,f42225,f42229,f42233,f42237,f42241,f42245,f42249,f42253,f42257,f42261,f42265,f42269,f42273,f42277,f42281,f42285,f42289,f42293,f42301,f42305,f42310,f42315,f42320,f42325,f42329,f42334,f42339,f42354,f42373,f42377,f42381,f42386,f42465,f42469,f42473,f42477,f42481,f42488,f42492,f42496,f42500,f42504,f42509,f42516,f42521,f42527,f42563,f43008,f43013,f43458,f43463,f43908,f43913,f43917,f44362,f44367,f44812,f44816,f44820,f44824,f44828,f44832,f44837,f44842,f44980,f44985,f44993,f44998,f45060,f45062,f45066,f45175,f45179,f45183,f45188,f45195,f45200,f45204,f45241,f45245,f45249,f45253,f45257,f45261,f45822,f48927,f49734,f51529,f52375,f52543,f52547,f52551,f52555,f52559,f52563,f52567,f52571,f52575,f52580,f52584,f52588,f52592,f52596,f52600,f52604,f52608,f52612,f52616,f52620,f52624,f52628,f52632,f52636,f52640,f52644,f52649,f52653,f52657,f52661,f52719,f52723,f52727,f52731,f52736,f52741,f52747,f52751,f52756,f52812,f52816,f52822,f52828,f52835,f55569,f55837,f57038,f57386,f57390,f58343,f59046,f59392,f59553,f59633,f59840,f60189,f60999,f61561,f61956,f61962,f62582,f62698,f62861,f62865,f63108,f64427,f64789,f65091,f65175,f65758,f65867,f67313,f68788,f69347,f69557,f69654,f69658,f70081,f70306,f70920,f71185,f71189,f71199,f72709,f73857,f73861,f74633,f76661,f77859,f77917,f77928,f78051,f78284,f79135,f79867,f81168,f81866,f82335,f82811,f82815,f83650,f89230,f89234,f91015,f91274,f93051,f94992,f95158,f95162,f95166,f98008,f100439,f102978,f102982,f102986,f102990,f103288,f103293,f103731,f103736,f103740,f104177,f104181,f104185,f104190,f104195,f104205,f104209,f104213,f104227,f104231,f104235,f104239,f104243,f104247,f104251,f104255,f104259,f104263,f105837,f106946,f108087,f108091,f109315,f110104,f110108,f110117,f110119,f110217,f110286,f110355,f110423,f110427,f110437,f110441,f110446,f110450,f110454,f110458,f110462,f110466,f110470,f110474,f110483,f110487,f110492,f110663,f110668,f110808,f110813,f110955,f110960,f110965,f110969,f110974,f111081,f111086,f111189,f111202,f111208,f111212,f111217,f111318,f111322,f111326,f111330,f111335,f111339,f111344,f111348,f111352,f111356,f111360,f111364,f111368,f111373,f111378,f111504,f111509,f111514,f111640,f111644,f111650,f111654,f111658,f111662,f111666,f111670,f111674,f111678,f111682,f111686,f111690,f111917,f116636,f117546,f117550,f117554,f117558,f117562,f117566,f117570,f117574,f117579,f117583,f117587,f117591,f117595,f117599,f117604,f117608,f117612,f117616,f117620,f117625,f117629,f117633,f117637,f117641,f117646,f117994,f117999,f118336,f118340,f118345,f118698,f118703,f119044,f119049,f119403,f119408,f119413,f119432,f119437,f119498,f119503,f119564,f119569,f119573,f119666,f119671,f119761,f119767,f119772,f119777,f119783,f119788,f119793,f119798,f119803,f119808,f119812,f119816,f119820,f119825,f119829,f119833,f119838,f119842,f120074,f120080,f120361,f120365,f120370,f120462,f120466,f120470,f120475,f120479,f120483,f120488,f120500,f120504,f120509,f120513,f120517,f120521,f120525,f120529,f120533,f120537,f120541,f120545,f120549,f120553,f120557,f120561,f120649,f120653,f120658,f120700,f120705,f120747,f120752,f120799,f120803,f120807,f120812,f120881,f120885,f120889,f120893,f120897,f120901,f120911,f120915,f121813,f123135,f129640,f130873,f130877,f130881,f130885,f130919,f130923,f130928,f130932,f130936,f130940,f130944,f130948,f130952,f130956,f130960,f130964,f130968,f130972,f130976,f130980,f130985,f131094,f131098,f131102,f131220,f131224,f131228,f131232,f131236,f131241,f131322,f131327,f131391,f131395,f131400,f131464,f131469,f131533,f131538,f131602,f131607,f131611,f131806,f131811,f131816,f131821,f131826,f131831,f131836,f131841,f131846,f131850,f131855,f131860,f131865,f131870,f131875,f131880,f131885,f131890,f131894,f132011,f132015,f132019,f132023,f132027,f132031,f132035,f132039,f132045,f132309,f132313,f132317,f132322,f132327,f132331,f132336,f132404,f132410,f132452,f132457,f132462,f132717,f132722,f132899,f132905,f132910,f132914,f132960,f132964,f132968,f132973,f133228,f133232,f133236,f133397]) ).
fof(f133397,plain,
( ~ spl0_144
| spl0_1214
| ~ spl0_1538 ),
inference(avatar_split_clause,[],[f132915,f132908,f78048,f1866]) ).
fof(f1866,plain,
( spl0_144
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f78048,plain,
( spl0_1214
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f132908,plain,
( spl0_1538
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f132915,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____))
| spl0_1214
| ~ spl0_1538 ),
inference(resolution,[],[f132909,f78050]) ).
fof(f78050,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))
| spl0_1214 ),
inference(avatar_component_clause,[],[f78048]) ).
fof(f132909,plain,
( ! [X0] :
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0)) )
| ~ spl0_1538 ),
inference(avatar_component_clause,[],[f132908]) ).
fof(f133236,plain,
( spl0_1546
| ~ spl0_29
| ~ spl0_192
| ~ spl0_401
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f66099,f18286,f7920,f2678,f1155,f133234]) ).
fof(f133234,plain,
( spl0_1546
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(X4)
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X1,c_COMBI(X0),X2,X3))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X1,c_COMBI(X0),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f1155,plain,
( spl0_29
<=> ! [X20,X0] : hAPP(c_COMBI(X0),X20) = X20 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f2678,plain,
( spl0_192
<=> ! [X18,X20,X0,X12,X16,X19] : hAPP(hAPP(c_COMBC(X20,X12,X18,X0),X19),X16) = hAPP(hAPP(X20,X16),X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f7920,plain,
( spl0_401
<=> ! [X19,X20,X0,X6,X49] :
( hBOOL(hAPP(X20,X49))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X49),X6))
| ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)))
| ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f18286,plain,
( spl0_699
<=> ! [X0,X1] : hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f66099,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(X4)
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X1,c_COMBI(X0),X2,X3))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X1,c_COMBI(X0),X2,X3))) )
| ~ spl0_29
| ~ spl0_192
| ~ spl0_401
| ~ spl0_699 ),
inference(forward_demodulation,[],[f66098,f1156]) ).
fof(f1156,plain,
( ! [X0,X20] : hAPP(c_COMBI(X0),X20) = X20
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f66098,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X1,c_COMBI(X0),X2,X3))
| hBOOL(hAPP(c_COMBI(X0),X4))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X1,c_COMBI(X0),X2,X3))) )
| ~ spl0_29
| ~ spl0_192
| ~ spl0_401
| ~ spl0_699 ),
inference(forward_demodulation,[],[f66087,f19417]) ).
fof(f19417,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_in(X0),X2),X1) = hAPP(X1,X2)
| ~ spl0_192
| ~ spl0_699 ),
inference(superposition,[],[f2679,f18287]) ).
fof(f18287,plain,
( ! [X0,X1] : hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X1) = X1
| ~ spl0_699 ),
inference(avatar_component_clause,[],[f18286]) ).
fof(f2679,plain,
( ! [X0,X18,X19,X16,X12,X20] : hAPP(hAPP(c_COMBC(X20,X12,X18,X0),X19),X16) = hAPP(hAPP(X20,X16),X19)
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f2678]) ).
fof(f66087,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X1,c_COMBI(X0),X2,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| hBOOL(hAPP(c_COMBI(X0),X4))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X1,c_COMBI(X0),X2,X3))) )
| ~ spl0_29
| ~ spl0_401 ),
inference(superposition,[],[f7921,f1156]) ).
fof(f7921,plain,
( ! [X0,X49,X6,X19,X20] :
( ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X49),X6))
| hBOOL(hAPP(X20,X49))
| ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0))) )
| ~ spl0_401 ),
inference(avatar_component_clause,[],[f7920]) ).
fof(f133232,plain,
( spl0_1545
| ~ spl0_29
| ~ spl0_1186 ),
inference(avatar_split_clause,[],[f62982,f62863,f1155,f133230]) ).
fof(f133230,plain,
( spl0_1545
<=> ! [X2,X0,X1] :
( hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X1,c_COMBI(X0),X2))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_COMBI(X0),tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f62863,plain,
( spl0_1186
<=> ! [X6,X0,X8] :
( hBOOL(hAPP(X8,c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X6,X8,X0)))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f62982,plain,
( ! [X2,X0,X1] :
( hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X1,c_COMBI(X0),X2))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_COMBI(X0),tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) )
| ~ spl0_29
| ~ spl0_1186 ),
inference(superposition,[],[f62864,f1156]) ).
fof(f62864,plain,
( ! [X0,X8,X6] :
( hBOOL(hAPP(X8,c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X6,X8,X0)))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) )
| ~ spl0_1186 ),
inference(avatar_component_clause,[],[f62863]) ).
fof(f133228,plain,
( spl0_1544
| ~ spl0_43
| ~ spl0_1182 ),
inference(avatar_split_clause,[],[f61968,f61960,f1211,f133226]) ).
fof(f133226,plain,
( spl0_1544
<=> ! [X3,X4,X0,X5,X2,X1] : c_Set_Oimage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3) = c_Set_Oimage(c_Fun_Ofun__upd(X0,X4,X5,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f1211,plain,
( spl0_43
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f61960,plain,
( spl0_1182
<=> ! [X2,X10,X0,X12,X6,X1] :
( hBOOL(hAPP(X6,X1))
| c_Set_Oimage(X10,X6,X12,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f61968,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_Set_Oimage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3) = c_Set_Oimage(c_Fun_Ofun__upd(X0,X4,X5,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3)
| ~ spl0_43
| ~ spl0_1182 ),
inference(resolution,[],[f61961,f1212]) ).
fof(f1212,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1))
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1211]) ).
fof(f61961,plain,
( ! [X2,X10,X0,X1,X6,X12] :
( hBOOL(hAPP(X6,X1))
| c_Set_Oimage(X10,X6,X12,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) )
| ~ spl0_1182 ),
inference(avatar_component_clause,[],[f61960]) ).
fof(f132973,plain,
( spl0_1543
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1542 ),
inference(avatar_split_clause,[],[f132969,f132966,f18286,f2678,f132971]) ).
fof(f132971,plain,
( spl0_1543
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X1,X2,X3,X0,X4)))
| c_lessequals(c_Set_Oimage(X3,X1,X0,X4),X2,tc_fun(X4,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f132966,plain,
( spl0_1542
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(c_Set_Oimage(X3,X1,X0,X4),X2,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X1,X2,X3,X0,X4)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f132969,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X1,X2,X3,X0,X4)))
| c_lessequals(c_Set_Oimage(X3,X1,X0,X4),X2,tc_fun(X4,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1542 ),
inference(forward_demodulation,[],[f132967,f19417]) ).
fof(f132967,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Set_Oimage(X3,X1,X0,X4),X2,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X1,X2,X3,X0,X4)),X1)) )
| ~ spl0_1542 ),
inference(avatar_component_clause,[],[f132966]) ).
fof(f132968,plain,
( spl0_1542
| ~ spl0_194
| ~ spl0_422
| ~ spl0_516 ),
inference(avatar_split_clause,[],[f12341,f11801,f8277,f2686,f132966]) ).
fof(f2686,plain,
( spl0_194
<=> ! [X10,X0,X12,X6] : c_Set_Oimage(X10,X6,X12,X0) = c_Set_Oimage(c_FuncSet_Orestrict(X10,X6,X12,X0),X6,X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f8277,plain,
( spl0_422
<=> ! [X10,X0,X12,X6,X7] :
( c_lessequals(c_Set_Oimage(X10,X6,X0,X12),X7,tc_fun(X12,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f11801,plain,
( spl0_516
<=> ! [X10,X0,X12,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f12341,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Set_Oimage(X3,X1,X0,X4),X2,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X1,X2,X3,X0,X4)),X1)) )
| ~ spl0_194
| ~ spl0_422
| ~ spl0_516 ),
inference(forward_demodulation,[],[f12310,f2687]) ).
fof(f2687,plain,
( ! [X10,X0,X6,X12] : c_Set_Oimage(X10,X6,X12,X0) = c_Set_Oimage(c_FuncSet_Orestrict(X10,X6,X12,X0),X6,X12,X0)
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2686]) ).
fof(f12310,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X1,X2,X3,X0,X4)),X1))
| c_lessequals(c_Set_Oimage(c_FuncSet_Orestrict(X3,X1,X0,X4),X1,X0,X4),X2,tc_fun(X4,tc_bool)) )
| ~ spl0_422
| ~ spl0_516 ),
inference(resolution,[],[f11802,f8278]) ).
fof(f8278,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| c_lessequals(c_Set_Oimage(X10,X6,X0,X12),X7,tc_fun(X12,tc_bool)) )
| ~ spl0_422 ),
inference(avatar_component_clause,[],[f8277]) ).
fof(f11802,plain,
( ! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X6,X7,X10,X0,X12)),X6)) )
| ~ spl0_516 ),
inference(avatar_component_clause,[],[f11801]) ).
fof(f132964,plain,
( spl0_1541
| ~ spl0_268
| ~ spl0_526 ),
inference(avatar_split_clause,[],[f12011,f12001,f3659,f132962]) ).
fof(f132962,plain,
( spl0_1541
<=> ! [X0,X3,X2,X1] :
( c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XballE__1__1(X0,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f3659,plain,
( spl0_268
<=> ! [X20,X0,X6,X1] :
( hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XballE__1__1(X6,X20,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f12001,plain,
( spl0_526
<=> ! [X6,X0,X1] :
( c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f12011,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XballE__1__1(X0,X3,X1))) )
| ~ spl0_268
| ~ spl0_526 ),
inference(resolution,[],[f12002,f3660]) ).
fof(f3660,plain,
( ! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XballE__1__1(X6,X20,X0))) )
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f3659]) ).
fof(f12002,plain,
( ! [X0,X1,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_526 ),
inference(avatar_component_clause,[],[f12001]) ).
fof(f132960,plain,
( spl0_1540
| ~ spl0_94
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f11908,f11865,f1469,f132958]) ).
fof(f132958,plain,
( spl0_1540
<=> ! [X4,X0,X3,X2,X1] : c_lessequals(hAPP(X0,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X3),X1),X2,tc_fun(X3,tc_bool)),X0,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f1469,plain,
( spl0_94
<=> ! [X6,X0,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f11865,plain,
( spl0_521
<=> ! [X0,X12,X6,X3,X7] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X12),X3),X6,tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f11908,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(hAPP(X0,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X3),X1),X2,tc_fun(X3,tc_bool)),X0,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ spl0_94
| ~ spl0_521 ),
inference(superposition,[],[f1470,f11866]) ).
fof(f11866,plain,
( ! [X3,X0,X6,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X12),X3),X6,tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool))
| ~ spl0_521 ),
inference(avatar_component_clause,[],[f11865]) ).
fof(f1470,plain,
( ! [X0,X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1469]) ).
fof(f132914,plain,
( spl0_1539
| ~ spl0_838
| ~ spl0_1451 ),
inference(avatar_split_clause,[],[f130907,f129638,f26738,f132912]) ).
fof(f132912,plain,
( spl0_1539
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X2,X3,tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f26738,plain,
( spl0_838
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f129638,plain,
( spl0_1451
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X0,X2,tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f130907,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X2,X3,tc_bool) )
| ~ spl0_838
| ~ spl0_1451 ),
inference(superposition,[],[f129639,f26739]) ).
fof(f26739,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool)
| ~ spl0_838 ),
inference(avatar_component_clause,[],[f26738]) ).
fof(f129639,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X0,X2,tc_bool) )
| ~ spl0_1451 ),
inference(avatar_component_clause,[],[f129638]) ).
fof(f132910,plain,
( spl0_1538
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1537 ),
inference(avatar_split_clause,[],[f132906,f132903,f18286,f2678,f132908]) ).
fof(f132903,plain,
( spl0_1537
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f132906,plain,
( ! [X0] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1537 ),
inference(forward_demodulation,[],[f132904,f19417]) ).
fof(f132904,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) )
| ~ spl0_1537 ),
inference(avatar_component_clause,[],[f132903]) ).
fof(f132905,plain,
( spl0_1537
| ~ spl0_113
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f11266,f10917,f1546,f132903]) ).
fof(f1546,plain,
( spl0_113
<=> ! [X0,X1,X28] :
( hBOOL(hAPP(X28,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f10917,plain,
( spl0_480
<=> ! [X37] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(X37,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f11266,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) )
| ~ spl0_113
| ~ spl0_480 ),
inference(resolution,[],[f10918,f1547]) ).
fof(f1547,plain,
( ! [X28,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X28))
| hBOOL(hAPP(X28,X1)) )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1546]) ).
fof(f10918,plain,
( ! [X37] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(X37,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_480 ),
inference(avatar_component_clause,[],[f10917]) ).
fof(f132899,plain,
( spl0_1536
| ~ spl0_52
| ~ spl0_358
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f11264,f10909,f6702,f1247,f132897]) ).
fof(f132897,plain,
( spl0_1536
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(X1,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| ~ c_Fun_Obij__betw(X1,X5,X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f1247,plain,
( spl0_52
<=> ! [X20,X0,X12,X19] : hAPP(c_COMBK(X20,X0,X12),X19) = X20 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f6702,plain,
( spl0_358
<=> ! [X10,X0,X12,X6,X7] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f10909,plain,
( spl0_478
<=> ! [X10,X0,X12,X6,X1,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X1)),hAPP(X7,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f11264,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(X1,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| ~ c_Fun_Obij__betw(X1,X5,X3,X4,X0) )
| ~ spl0_52
| ~ spl0_358
| ~ spl0_478 ),
inference(forward_demodulation,[],[f11247,f1248]) ).
fof(f1248,plain,
( ! [X0,X19,X12,X20] : hAPP(c_COMBK(X20,X0,X12),X19) = X20
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f11247,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(X1,X2)),hAPP(c_COMBK(X3,tc_fun(X0,tc_bool),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| ~ c_Fun_Obij__betw(X1,X5,X3,X4,X0) )
| ~ spl0_358
| ~ spl0_478 ),
inference(resolution,[],[f10910,f6703]) ).
fof(f6703,plain,
( ! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12) )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f6702]) ).
fof(f10910,plain,
( ! [X10,X0,X1,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12)))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X1)),hAPP(X7,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_478 ),
inference(avatar_component_clause,[],[f10909]) ).
fof(f132722,plain,
( spl0_1535
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1534 ),
inference(avatar_split_clause,[],[f132718,f132715,f18286,f2678,f132720]) ).
fof(f132720,plain,
( spl0_1535
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X1,X3))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(hAPP(c_fequal(X2),X3),X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f132715,plain,
( spl0_1534
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_lessequals(hAPP(c_fequal(X2),X3),X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f132718,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X1,X3))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(hAPP(c_fequal(X2),X3),X1,tc_fun(X2,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1534 ),
inference(forward_demodulation,[],[f132716,f19417]) ).
fof(f132716,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_lessequals(hAPP(c_fequal(X2),X3),X1,tc_fun(X2,tc_bool)) )
| ~ spl0_1534 ),
inference(avatar_component_clause,[],[f132715]) ).
fof(f132717,plain,
( spl0_1534
| ~ spl0_218
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f11011,f11007,f3059,f132715]) ).
fof(f3059,plain,
( spl0_218
<=> ! [X0,X6,X8,X7] :
( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f11007,plain,
( spl0_487
<=> ! [X0,X6,X1,X7] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f11011,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_lessequals(hAPP(c_fequal(X2),X3),X1,tc_fun(X2,tc_bool)) )
| ~ spl0_218
| ~ spl0_487 ),
inference(resolution,[],[f11008,f3060]) ).
fof(f3060,plain,
( ! [X0,X8,X6,X7] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool)) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f3059]) ).
fof(f11008,plain,
( ! [X0,X1,X6,X7] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f11007]) ).
fof(f132462,plain,
( spl0_1533
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1532 ),
inference(avatar_split_clause,[],[f132458,f132455,f18286,f2678,f132460]) ).
fof(f132460,plain,
( spl0_1533
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X3,X4,X2,X0,X1)))
| c_lessequals(c_Set_Oimage(X2,X3,X0,X1),X4,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f132455,plain,
( spl0_1532
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X3,X4,X2,X0,X1)),X3))
| c_lessequals(c_Set_Oimage(X2,X3,X0,X1),X4,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f132458,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X3,X4,X2,X0,X1)))
| c_lessequals(c_Set_Oimage(X2,X3,X0,X1),X4,tc_fun(X1,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1532 ),
inference(forward_demodulation,[],[f132456,f19417]) ).
fof(f132456,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X3,X4,X2,X0,X1)),X3))
| c_lessequals(c_Set_Oimage(X2,X3,X0,X1),X4,tc_fun(X1,tc_bool)) )
| ~ spl0_1532 ),
inference(avatar_component_clause,[],[f132455]) ).
fof(f132457,plain,
( spl0_1532
| ~ spl0_422
| ~ spl0_462 ),
inference(avatar_split_clause,[],[f10794,f10572,f8277,f132455]) ).
fof(f10572,plain,
( spl0_462
<=> ! [X10,X0,X12,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f10794,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X3,X4,X2,X0,X1)),X3))
| c_lessequals(c_Set_Oimage(X2,X3,X0,X1),X4,tc_fun(X1,tc_bool)) )
| ~ spl0_422
| ~ spl0_462 ),
inference(resolution,[],[f10573,f8278]) ).
fof(f10573,plain,
( ! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) )
| ~ spl0_462 ),
inference(avatar_component_clause,[],[f10572]) ).
fof(f132452,plain,
( spl0_1531
| ~ spl0_112
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f10091,f10082,f1542,f132450]) ).
fof(f132450,plain,
( spl0_1531
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| hBOOL(hAPP(hAPP(c_in(X2),X0),X3))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X2),X1),X3,tc_fun(X2,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f1542,plain,
( spl0_112
<=> ! [X0,X1,X28] :
( ~ hBOOL(hAPP(X28,X1))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f10082,plain,
( spl0_454
<=> ! [X4,X0,X6,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X4),X6,tc_fun(X0,tc_bool))))
| X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f10091,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| hBOOL(hAPP(hAPP(c_in(X2),X0),X3))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X2),X1),X3,tc_fun(X2,tc_bool)),X0)) )
| ~ spl0_112
| ~ spl0_454 ),
inference(resolution,[],[f10083,f1543]) ).
fof(f1543,plain,
( ! [X28,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X28))
| ~ hBOOL(hAPP(X28,X1)) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1542]) ).
fof(f10083,plain,
( ! [X3,X0,X6,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X4),X6,tc_fun(X0,tc_bool))))
| X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_454 ),
inference(avatar_component_clause,[],[f10082]) ).
fof(f132410,plain,
( spl0_1530
| ~ spl0_231
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f8321,f8294,f3120,f132408]) ).
fof(f132408,plain,
( spl0_1530
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X4,c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(X4,X3,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f3120,plain,
( spl0_231
<=> ! [X0,X6,X8,X7] :
( c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f8294,plain,
( spl0_426
<=> ! [X0,X6,X8,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f8321,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X4,c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(X4,X3,tc_fun(X2,tc_bool)) )
| ~ spl0_231
| ~ spl0_426 ),
inference(superposition,[],[f3121,f8295]) ).
fof(f8295,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ spl0_426 ),
inference(avatar_component_clause,[],[f8294]) ).
fof(f3121,plain,
( ! [X0,X8,X6,X7] :
( ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X8,X7,tc_fun(X0,tc_bool)) )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f3120]) ).
fof(f132404,plain,
( spl0_1529
| ~ spl0_112
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f8172,f7932,f1542,f132402]) ).
fof(f132402,plain,
( spl0_1529
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f7932,plain,
( spl0_404
<=> ! [X31,X0,X6,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X6),X31))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),X8))
| hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f8172,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(X3,X2)) )
| ~ spl0_112
| ~ spl0_404 ),
inference(resolution,[],[f7933,f1543]) ).
fof(f7933,plain,
( ! [X31,X0,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X6),X31))
| hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)))) )
| ~ spl0_404 ),
inference(avatar_component_clause,[],[f7932]) ).
fof(f132336,plain,
( spl0_1528
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1527 ),
inference(avatar_split_clause,[],[f132332,f132329,f18286,f2678,f132334]) ).
fof(f132334,plain,
( spl0_1528
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f132329,plain,
( spl0_1527
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f132332,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3,X0))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1527 ),
inference(forward_demodulation,[],[f132330,f19417]) ).
fof(f132330,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3,X0))) )
| ~ spl0_1527 ),
inference(avatar_component_clause,[],[f132329]) ).
fof(f132331,plain,
( spl0_1527
| ~ spl0_44
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f8122,f7916,f1215,f132329]) ).
fof(f1215,plain,
( spl0_44
<=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f7916,plain,
( spl0_400
<=> ! [X48,X0,X6,X19,X20] :
( hBOOL(hAPP(X19,X48))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X48),X6))
| ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)))
| ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f8122,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3,X0))) )
| ~ spl0_44
| ~ spl0_400 ),
inference(resolution,[],[f7917,f1216]) ).
fof(f1216,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1))
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f7917,plain,
( ! [X48,X0,X6,X19,X20] :
( ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X48),X6))
| hBOOL(hAPP(X19,X48))
| ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0))) )
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f7916]) ).
fof(f132327,plain,
( spl0_1526
| ~ spl0_71
| ~ spl0_222
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f8121,f7912,f3075,f1329,f132325]) ).
fof(f132325,plain,
( spl0_1526
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X0,tc_bool))
| c_lessequals(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X2,c_Set_OPow(X1,X0),X0),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f1329,plain,
( spl0_71
<=> ! [X6,X0] : c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X6,X0),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f3075,plain,
( spl0_222
<=> ! [X6,X0,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X6),c_Set_OPow(X7,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f7912,plain,
( spl0_399
<=> ! [X6,X0,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X6,X8,X0)),X8))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f8121,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X0,tc_bool))
| c_lessequals(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X2,c_Set_OPow(X1,X0),X0),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_71
| ~ spl0_222
| ~ spl0_399 ),
inference(forward_demodulation,[],[f8107,f1330]) ).
fof(f1330,plain,
( ! [X0,X6] : c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X6,X0),tc_fun(X0,tc_bool)) = X6
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1329]) ).
fof(f8107,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X1,X0),tc_fun(X0,tc_bool)),X2,tc_fun(X0,tc_bool))
| c_lessequals(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X2,c_Set_OPow(X1,X0),X0),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_222
| ~ spl0_399 ),
inference(resolution,[],[f7913,f3076]) ).
fof(f3076,plain,
( ! [X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X6),c_Set_OPow(X7,X0)))
| c_lessequals(X6,X7,tc_fun(X0,tc_bool)) )
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f3075]) ).
fof(f7913,plain,
( ! [X0,X8,X6] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X6,X8,X0)),X8))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) )
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f7912]) ).
fof(f132322,plain,
( spl0_1525
| ~ spl0_113
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f7384,f7056,f1546,f132320]) ).
fof(f132320,plain,
( spl0_1525
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X4)),X3),c_FuncSet_OPi(X1,X2,X0,X4)))
| hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X1,X2,X3,X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f7056,plain,
( spl0_377
<=> ! [X10,X0,X12,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f7384,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X4)),X3),c_FuncSet_OPi(X1,X2,X0,X4)))
| hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X1,X2,X3,X0,X4))) )
| ~ spl0_113
| ~ spl0_377 ),
inference(resolution,[],[f7057,f1547]) ).
fof(f7057,plain,
( ! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12))) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f7056]) ).
fof(f132317,plain,
( spl0_1524
| ~ spl0_113
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f7314,f7052,f1546,f132315]) ).
fof(f132315,plain,
( spl0_1524
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X4)),X3),c_FuncSet_OPi(X1,X2,X0,X4)))
| hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X1,X2,X3,X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f7052,plain,
( spl0_376
<=> ! [X10,X0,X12,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f7314,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X4)),X3),c_FuncSet_OPi(X1,X2,X0,X4)))
| hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X1,X2,X3,X0,X4))) )
| ~ spl0_113
| ~ spl0_376 ),
inference(resolution,[],[f7053,f1547]) ).
fof(f7053,plain,
( ! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12))) )
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f7052]) ).
fof(f132313,plain,
( spl0_1523
| ~ spl0_61
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f7140,f7024,f1289,f132311]) ).
fof(f132311,plain,
( spl0_1523
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f1289,plain,
( spl0_61
<=> ! [X6,X0] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f7024,plain,
( spl0_369
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X7,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f7140,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 )
| ~ spl0_61
| ~ spl0_369 ),
inference(resolution,[],[f7025,f1290]) ).
fof(f1290,plain,
( ! [X0,X6] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f1289]) ).
fof(f7025,plain,
( ! [X0,X8,X6,X7] :
( ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X7,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_369 ),
inference(avatar_component_clause,[],[f7024]) ).
fof(f132309,plain,
( spl0_1522
| ~ spl0_24
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f6953,f6714,f1135,f132307]) ).
fof(f132307,plain,
( spl0_1522
<=> ! [X0,X1] : hAPP(c_COMBC(c_COMBB(c_in(X0),c_COMBI(X0),X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X0),X0,tc_fun(X0,tc_bool),tc_bool),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f1135,plain,
( spl0_24
<=> ! [X20,X0] : c_Collect(X20,X0) = X20 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f6714,plain,
( spl0_361
<=> ! [X32,X0] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X0),c_COMBI(X0),X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X0),X0,tc_fun(X0,tc_bool),tc_bool),X32),X0) = X32 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f6953,plain,
( ! [X0,X1] : hAPP(c_COMBC(c_COMBB(c_in(X0),c_COMBI(X0),X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X0),X0,tc_fun(X0,tc_bool),tc_bool),X1) = X1
| ~ spl0_24
| ~ spl0_361 ),
inference(superposition,[],[f6715,f1136]) ).
fof(f1136,plain,
( ! [X0,X20] : c_Collect(X20,X0) = X20
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f1135]) ).
fof(f6715,plain,
( ! [X0,X32] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X0),c_COMBI(X0),X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X0),X0,tc_fun(X0,tc_bool),tc_bool),X32),X0) = X32
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f6714]) ).
fof(f132045,plain,
( spl0_1521
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1520 ),
inference(avatar_split_clause,[],[f132041,f132037,f18286,f2678,f132043]) ).
fof(f132043,plain,
( spl0_1521
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),hAPP(X2,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f132037,plain,
( spl0_1520
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),hAPP(X2,X4))),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f132041,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),hAPP(X2,X4)))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1520 ),
inference(forward_demodulation,[],[f132040,f19417]) ).
fof(f132040,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),hAPP(X2,X4))))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1520 ),
inference(forward_demodulation,[],[f132038,f19417]) ).
fof(f132038,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),hAPP(X2,X4))),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),X1)) )
| ~ spl0_1520 ),
inference(avatar_component_clause,[],[f132037]) ).
fof(f132039,plain,
( spl0_1520
| ~ spl0_303
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f6788,f6682,f4514,f132037]) ).
fof(f4514,plain,
( spl0_303
<=> ! [X10,X0,X12,X6,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X1)),c_Set_Oimage(X10,X6,X12,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f6682,plain,
( spl0_353
<=> ! [X10,X0,X12,X6,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Set_Oimage(X10,X6,X12,X0)))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),X1)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f6788,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),hAPP(X2,X4))),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),X1)) )
| ~ spl0_303
| ~ spl0_353 ),
inference(resolution,[],[f6683,f4515]) ).
fof(f4515,plain,
( ! [X10,X0,X1,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X1)),c_Set_Oimage(X10,X6,X12,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f4514]) ).
fof(f6683,plain,
( ! [X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Set_Oimage(X10,X6,X12,X0)))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),X1)),X6)) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f6682]) ).
fof(f132035,plain,
( spl0_1519
| ~ spl0_232
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f6461,f5663,f3124,f132033]) ).
fof(f132033,plain,
( spl0_1519
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X4,c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X4,X0,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f3124,plain,
( spl0_232
<=> ! [X0,X6,X8,X7] :
( c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f5663,plain,
( spl0_344
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ominus__class_Ominus(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f6461,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X4,c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X4,X0,tc_fun(X3,tc_bool)) )
| ~ spl0_232
| ~ spl0_344 ),
inference(superposition,[],[f3125,f5664]) ).
fof(f5664,plain,
( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ominus__class_Ominus(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f5663]) ).
fof(f3125,plain,
( ! [X0,X8,X6,X7] :
( ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X8,X6,tc_fun(X0,tc_bool)) )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f3124]) ).
fof(f132031,plain,
( spl0_1518
| ~ spl0_232
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f6345,f5659,f3124,f132029]) ).
fof(f132029,plain,
( spl0_1518
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X4,X0,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f5659,plain,
( spl0_343
<=> ! [X0,X6,X8,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f6345,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X4,X0,tc_fun(X3,tc_bool)) )
| ~ spl0_232
| ~ spl0_343 ),
inference(superposition,[],[f3125,f5660]) ).
fof(f5660,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f5659]) ).
fof(f132027,plain,
( spl0_1517
| ~ spl0_231
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f6245,f5655,f3120,f132025]) ).
fof(f132025,plain,
( spl0_1517
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(X4,X3,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f5655,plain,
( spl0_342
<=> ! [X0,X6,X8,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f6245,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(X4,X3,tc_fun(X2,tc_bool)) )
| ~ spl0_231
| ~ spl0_342 ),
inference(superposition,[],[f3121,f5656]) ).
fof(f5656,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f5655]) ).
fof(f132023,plain,
( spl0_1516
| ~ spl0_229
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f6024,f5635,f3112,f132021]) ).
fof(f132021,plain,
( spl0_1516
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f3112,plain,
( spl0_229
<=> ! [X6,X0,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X7
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f5635,plain,
( spl0_337
<=> ! [X0,X6,X8,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f6024,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X3 )
| ~ spl0_229
| ~ spl0_337 ),
inference(superposition,[],[f3113,f5636]) ).
fof(f5636,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f5635]) ).
fof(f3113,plain,
( ! [X0,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X7 )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f3112]) ).
fof(f132019,plain,
( spl0_1515
| ~ spl0_219
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f6023,f5635,f3063,f132017]) ).
fof(f132017,plain,
( spl0_1515
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| c_lessequals(X3,X4,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f3063,plain,
( spl0_219
<=> ! [X6,X0,X8,X7] :
( c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f6023,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| c_lessequals(X3,X4,tc_fun(X2,tc_bool)) )
| ~ spl0_219
| ~ spl0_337 ),
inference(superposition,[],[f3064,f5636]) ).
fof(f3064,plain,
( ! [X0,X8,X6,X7] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| c_lessequals(X7,X8,tc_fun(X0,tc_bool)) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f3063]) ).
fof(f132015,plain,
( spl0_1514
| ~ spl0_230
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5878,f5631,f3116,f132013]) ).
fof(f132013,plain,
( spl0_1514
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f3116,plain,
( spl0_230
<=> ! [X6,X0,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f5631,plain,
( spl0_336
<=> ! [X0,X6,X8,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f5878,plain,
( ! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X0 )
| ~ spl0_230
| ~ spl0_336 ),
inference(superposition,[],[f3117,f5632]) ).
fof(f5632,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f5631]) ).
fof(f3117,plain,
( ! [X0,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f3116]) ).
fof(f132011,plain,
( spl0_1513
| ~ spl0_218
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5875,f5631,f3059,f132009]) ).
fof(f132009,plain,
( spl0_1513
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X0,X4,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f5875,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X0,X4,tc_fun(X3,tc_bool)) )
| ~ spl0_218
| ~ spl0_336 ),
inference(superposition,[],[f3060,f5632]) ).
fof(f131894,plain,
( spl0_1512
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5817,f5627,f4702,f2288,f1445,f131892]) ).
fof(f131892,plain,
( spl0_1512
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_fequal(X1),X2),X0,X1,X3),hAPP(X0,X2)) = X2
| ~ c_Fun_Oinj__on(X0,hAPP(c_fequal(X1),X2),X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f1445,plain,
( spl0_89
<=> ! [X6,X0] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f2288,plain,
( spl0_177
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f4702,plain,
( spl0_317
<=> ! [X0,X3] : hAPP(c_fequal(X0),X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f5627,plain,
( spl0_335
<=> ! [X10,X0,X12,X6,X1] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),hAPP(X10,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f5817,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_fequal(X1),X2),X0,X1,X3),hAPP(X0,X2)) = X2
| ~ c_Fun_Oinj__on(X0,hAPP(c_fequal(X1),X2),X1,X3) )
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_335 ),
inference(forward_demodulation,[],[f5816,f5265]) ).
fof(f5265,plain,
( ! [X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1)
| ~ spl0_89
| ~ spl0_317 ),
inference(superposition,[],[f4703,f1446]) ).
fof(f1446,plain,
( ! [X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f4703,plain,
( ! [X3,X0] : hAPP(c_fequal(X0),X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f4702]) ).
fof(f5816,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Fun_Oinj__on(X0,hAPP(c_fequal(X1),X2),X1,X3)
| hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X0,X1,X3),hAPP(X0,X2)) = X2 )
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_335 ),
inference(forward_demodulation,[],[f5794,f5265]) ).
fof(f5794,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Fun_Oinj__on(X0,hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X1,X3)
| hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X0,X1,X3),hAPP(X0,X2)) = X2 )
| ~ spl0_177
| ~ spl0_335 ),
inference(resolution,[],[f5628,f2289]) ).
fof(f2289,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1)))
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f2288]) ).
fof(f5628,plain,
( ! [X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),hAPP(X10,X1)) = X1 )
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f5627]) ).
fof(f131890,plain,
( spl0_1511
| ~ spl0_139
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f5496,f5342,f1846,f131888]) ).
fof(f131888,plain,
( spl0_1511
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f1846,plain,
( spl0_139
<=> ! [X6,X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f5342,plain,
( spl0_321
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f5496,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) )
| ~ spl0_139
| ~ spl0_321 ),
inference(superposition,[],[f5343,f1847]) ).
fof(f1847,plain,
( ! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool))
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1846]) ).
fof(f5343,plain,
( ! [X0,X8,X6,X7] :
( ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) )
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f5342]) ).
fof(f131885,plain,
( spl0_1510
| ~ spl0_303
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f5420,f5334,f4514,f131883]) ).
fof(f131883,plain,
( spl0_1510
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X0,X4) = hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X1,X0,X2,X3),hAPP(X0,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f5334,plain,
( spl0_319
<=> ! [X10,X0,X12,X6,X2] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Oimage(X10,X6,X12,X0)))
| hAPP(X10,hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f5420,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X0,X4) = hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X1,X0,X2,X3),hAPP(X0,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1)) )
| ~ spl0_303
| ~ spl0_319 ),
inference(resolution,[],[f5335,f4515]) ).
fof(f5335,plain,
( ! [X2,X10,X0,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Oimage(X10,X6,X12,X0)))
| hAPP(X10,hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),X2)) = X2 )
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f5334]) ).
fof(f131880,plain,
( spl0_1509
| ~ spl0_114
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f5260,f4694,f1550,f131878]) ).
fof(f131878,plain,
( spl0_1509
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f1550,plain,
( spl0_114
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f4694,plain,
( spl0_315
<=> ! [X20,X0,X6,X1] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X6,X20,X0)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f5260,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_114
| ~ spl0_315 ),
inference(resolution,[],[f4695,f1552]) ).
fof(f1552,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin))
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1550]) ).
fof(f4695,plain,
( ! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X6,X20,X0)),X6)) )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f4694]) ).
fof(f131875,plain,
( spl0_1508
| ~ spl0_111
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f5259,f4694,f1537,f131873]) ).
fof(f131873,plain,
( spl0_1508
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f1537,plain,
( spl0_111
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f5259,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_111
| ~ spl0_315 ),
inference(resolution,[],[f4695,f1539]) ).
fof(f1539,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin))
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f131870,plain,
( spl0_1507
| ~ spl0_110
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f5251,f4694,f1533,f131868]) ).
fof(f131868,plain,
( spl0_1507
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f1533,plain,
( spl0_110
<=> ! [X6,X0] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X6),c_Set_OPow(X6,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f5251,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) )
| ~ spl0_110
| ~ spl0_315 ),
inference(resolution,[],[f4695,f1534]) ).
fof(f1534,plain,
( ! [X0,X6] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X6),c_Set_OPow(X6,X0)))
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f131865,plain,
( spl0_1506
| ~ spl0_114
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f5232,f4690,f1550,f131863]) ).
fof(f131863,plain,
( spl0_1506
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f4690,plain,
( spl0_314
<=> ! [X20,X0,X6,X1] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XbexE__1__1(X6,X20,X0)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f5232,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_114
| ~ spl0_314 ),
inference(resolution,[],[f4691,f1552]) ).
fof(f4691,plain,
( ! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XbexE__1__1(X6,X20,X0)),X6)) )
| ~ spl0_314 ),
inference(avatar_component_clause,[],[f4690]) ).
fof(f131860,plain,
( spl0_1505
| ~ spl0_111
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f5231,f4690,f1537,f131858]) ).
fof(f131858,plain,
( spl0_1505
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f5231,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_111
| ~ spl0_314 ),
inference(resolution,[],[f4691,f1539]) ).
fof(f131855,plain,
( spl0_1504
| ~ spl0_110
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f5223,f4690,f1533,f131853]) ).
fof(f131853,plain,
( spl0_1504
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f5223,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) )
| ~ spl0_110
| ~ spl0_314 ),
inference(resolution,[],[f4691,f1534]) ).
fof(f131850,plain,
( spl0_1503
| ~ spl0_114
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f5208,f4686,f1550,f131848]) ).
fof(f131848,plain,
( spl0_1503
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f4686,plain,
( spl0_313
<=> ! [X20,X0,X6,X1] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XbexI__1__1(X6,X20,X0)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f5208,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_114
| ~ spl0_313 ),
inference(resolution,[],[f4687,f1552]) ).
fof(f4687,plain,
( ! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XbexI__1__1(X6,X20,X0)),X6)) )
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f4686]) ).
fof(f131846,plain,
( spl0_1502
| ~ spl0_648
| ~ spl0_1466 ),
inference(avatar_split_clause,[],[f131164,f130958,f17393,f131844]) ).
fof(f131844,plain,
( spl0_1502
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_bool),X3,tc_bool)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f17393,plain,
( spl0_648
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f130958,plain,
( spl0_1466
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool),X3,tc_bool)
| ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f131164,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_bool),X3,tc_bool)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool) )
| ~ spl0_648
| ~ spl0_1466 ),
inference(superposition,[],[f130959,f17394]) ).
fof(f17394,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0
| ~ spl0_648 ),
inference(avatar_component_clause,[],[f17393]) ).
fof(f130959,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool),X3,tc_bool)
| ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) )
| ~ spl0_1466 ),
inference(avatar_component_clause,[],[f130958]) ).
fof(f131841,plain,
( spl0_1501
| ~ spl0_111
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f5207,f4686,f1537,f131839]) ).
fof(f131839,plain,
( spl0_1501
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f5207,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_111
| ~ spl0_313 ),
inference(resolution,[],[f4687,f1539]) ).
fof(f131836,plain,
( spl0_1500
| ~ spl0_110
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f5199,f4686,f1533,f131834]) ).
fof(f131834,plain,
( spl0_1500
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f5199,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) )
| ~ spl0_110
| ~ spl0_313 ),
inference(resolution,[],[f4687,f1534]) ).
fof(f131831,plain,
( spl0_1499
| ~ spl0_114
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f5184,f4682,f1550,f131829]) ).
fof(f131829,plain,
( spl0_1499
<=> ! [X0] :
( hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f4682,plain,
( spl0_312
<=> ! [X20,X0,X6,X1] :
( hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XballE__1__1(X6,X20,X0)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f5184,plain,
( ! [X0] :
( hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_114
| ~ spl0_312 ),
inference(resolution,[],[f4683,f1552]) ).
fof(f4683,plain,
( ! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XballE__1__1(X6,X20,X0)),X6)) )
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f4682]) ).
fof(f131826,plain,
( spl0_1498
| ~ spl0_111
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f5183,f4682,f1537,f131824]) ).
fof(f131824,plain,
( spl0_1498
<=> ! [X0] :
( hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f5183,plain,
( ! [X0] :
( hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_111
| ~ spl0_312 ),
inference(resolution,[],[f4683,f1539]) ).
fof(f131821,plain,
( spl0_1497
| ~ spl0_110
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f5175,f4682,f1533,f131819]) ).
fof(f131819,plain,
( spl0_1497
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f5175,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) )
| ~ spl0_110
| ~ spl0_312 ),
inference(resolution,[],[f4683,f1534]) ).
fof(f131816,plain,
( spl0_1496
| ~ spl0_114
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f5160,f4678,f1550,f131814]) ).
fof(f131814,plain,
( spl0_1496
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f4678,plain,
( spl0_311
<=> ! [X20,X0,X6,X3] :
( ~ hBOOL(hAPP(X20,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X6,X20,X0)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f5160,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_114
| ~ spl0_311 ),
inference(resolution,[],[f4679,f1552]) ).
fof(f4679,plain,
( ! [X3,X0,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(X20,X3))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X6,X20,X0)),X6)) )
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f4678]) ).
fof(f131811,plain,
( spl0_1495
| ~ spl0_111
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f5159,f4678,f1537,f131809]) ).
fof(f131809,plain,
( spl0_1495
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f5159,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_111
| ~ spl0_311 ),
inference(resolution,[],[f4679,f1539]) ).
fof(f131806,plain,
( spl0_1494
| ~ spl0_110
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f5151,f4678,f1533,f131804]) ).
fof(f131804,plain,
( spl0_1494
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f5151,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))) )
| ~ spl0_110
| ~ spl0_311 ),
inference(resolution,[],[f4679,f1534]) ).
fof(f131611,plain,
( spl0_1493
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1491 ),
inference(avatar_split_clause,[],[f131603,f131600,f18286,f2678,f131609]) ).
fof(f131609,plain,
( spl0_1493
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( ~ hBOOL(hAPP(X4,X3))
| c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f131600,plain,
( spl0_1491
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f131603,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(X4,X3))
| c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1491 ),
inference(forward_demodulation,[],[f131601,f19417]) ).
fof(f131601,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4)) )
| ~ spl0_1491 ),
inference(avatar_component_clause,[],[f131600]) ).
fof(f131607,plain,
( spl0_1492
| ~ spl0_841
| ~ spl0_1450 ),
inference(avatar_split_clause,[],[f127319,f123133,f26750,f131605]) ).
fof(f131605,plain,
( spl0_1492
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X0,X3,tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f26750,plain,
( spl0_841
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f123133,plain,
( spl0_1450
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X2,tc_bool)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f127319,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X0,X3,tc_bool) )
| ~ spl0_841
| ~ spl0_1450 ),
inference(superposition,[],[f123134,f26751]) ).
fof(f26751,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool)
| ~ spl0_841 ),
inference(avatar_component_clause,[],[f26750]) ).
fof(f123134,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X0,X2,tc_bool) )
| ~ spl0_1450 ),
inference(avatar_component_clause,[],[f123133]) ).
fof(f131602,plain,
( spl0_1491
| ~ spl0_52
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4938,f4662,f1247,f131600]) ).
fof(f4662,plain,
( spl0_307
<=> ! [X0,X12,X6,X3,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_lessequals(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f4938,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4)) )
| ~ spl0_52
| ~ spl0_307 ),
inference(superposition,[],[f4663,f1248]) ).
fof(f4663,plain,
( ! [X3,X0,X6,X7,X12] :
( c_lessequals(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f4662]) ).
fof(f131538,plain,
( spl0_1490
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1489 ),
inference(avatar_split_clause,[],[f131534,f131531,f18286,f2678,f131536]) ).
fof(f131536,plain,
( spl0_1490
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X4))
| ~ c_lessequals(c_SetInterval_Oord_OlessThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f131531,plain,
( spl0_1489
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_SetInterval_Oord_OlessThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f131534,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,X4))
| ~ c_lessequals(c_SetInterval_Oord_OlessThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1489 ),
inference(forward_demodulation,[],[f131532,f19417]) ).
fof(f131532,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_SetInterval_Oord_OlessThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) )
| ~ spl0_1489 ),
inference(avatar_component_clause,[],[f131531]) ).
fof(f131533,plain,
( spl0_1489
| ~ spl0_210
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4614,f4502,f2870,f131531]) ).
fof(f2870,plain,
( spl0_210
<=> ! [X42,X0,X27,X25] :
( ~ hBOOL(hAPP(hAPP(X42,X25),X27))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OlessThan(X42,X27,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f4502,plain,
( spl0_300
<=> ! [X0,X6,X29,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X29),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X29),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f4614,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_SetInterval_Oord_OlessThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) )
| ~ spl0_210
| ~ spl0_300 ),
inference(resolution,[],[f4503,f2871]) ).
fof(f2871,plain,
( ! [X0,X27,X25,X42] :
( hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OlessThan(X42,X27,X0)))
| ~ hBOOL(hAPP(hAPP(X42,X25),X27)) )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f2870]) ).
fof(f4503,plain,
( ! [X0,X29,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X29),X6))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X29),X7)) )
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f4502]) ).
fof(f131469,plain,
( spl0_1488
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1487 ),
inference(avatar_split_clause,[],[f131465,f131462,f18286,f2678,f131467]) ).
fof(f131467,plain,
( spl0_1488
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X4))
| ~ c_lessequals(c_SetInterval_Oord_OgreaterThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(X0,X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f131462,plain,
( spl0_1487
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_SetInterval_Oord_OgreaterThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(X0,X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f131465,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,X4))
| ~ c_lessequals(c_SetInterval_Oord_OgreaterThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(X0,X1),X4)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1487 ),
inference(forward_demodulation,[],[f131463,f19417]) ).
fof(f131463,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_SetInterval_Oord_OgreaterThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(X0,X1),X4)) )
| ~ spl0_1487 ),
inference(avatar_component_clause,[],[f131462]) ).
fof(f131464,plain,
( spl0_1487
| ~ spl0_208
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4613,f4502,f2862,f131462]) ).
fof(f2862,plain,
( spl0_208
<=> ! [X42,X0,X27,X25] :
( ~ hBOOL(hAPP(hAPP(X42,X27),X25))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThan(X42,X27,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f4613,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_SetInterval_Oord_OgreaterThan(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(X0,X1),X4)) )
| ~ spl0_208
| ~ spl0_300 ),
inference(resolution,[],[f4503,f2863]) ).
fof(f2863,plain,
( ! [X0,X27,X25,X42] :
( hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThan(X42,X27,X0)))
| ~ hBOOL(hAPP(hAPP(X42,X27),X25)) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f2862]) ).
fof(f131400,plain,
( spl0_1486
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1485 ),
inference(avatar_split_clause,[],[f131396,f131393,f18286,f2678,f131398]) ).
fof(f131398,plain,
( spl0_1486
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X4))
| ~ c_lessequals(c_SetInterval_Oord_OatMost(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f131393,plain,
( spl0_1485
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_SetInterval_Oord_OatMost(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f131396,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,X4))
| ~ c_lessequals(c_SetInterval_Oord_OatMost(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1485 ),
inference(forward_demodulation,[],[f131394,f19417]) ).
fof(f131394,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_SetInterval_Oord_OatMost(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) )
| ~ spl0_1485 ),
inference(avatar_component_clause,[],[f131393]) ).
fof(f131395,plain,
( spl0_1485
| ~ spl0_206
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4612,f4502,f2854,f131393]) ).
fof(f2854,plain,
( spl0_206
<=> ! [X41,X0,X27,X25] :
( ~ hBOOL(hAPP(hAPP(X41,X25),X27))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatMost(X41,X27,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f4612,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_SetInterval_Oord_OatMost(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(X0,X4),X1)) )
| ~ spl0_206
| ~ spl0_300 ),
inference(resolution,[],[f4503,f2855]) ).
fof(f2855,plain,
( ! [X41,X0,X27,X25] :
( hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatMost(X41,X27,X0)))
| ~ hBOOL(hAPP(hAPP(X41,X25),X27)) )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f2854]) ).
fof(f131391,plain,
( spl0_1484
| ~ spl0_846
| ~ spl0_1449 ),
inference(avatar_split_clause,[],[f125022,f121811,f26770,f131389]) ).
fof(f131389,plain,
( spl0_1484
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool),X3,tc_bool)
| ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f26770,plain,
( spl0_846
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f121811,plain,
( spl0_1449
<=> ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool),X2,tc_bool)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f125022,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool),X3,tc_bool)
| ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) )
| ~ spl0_846
| ~ spl0_1449 ),
inference(superposition,[],[f121812,f26771]) ).
fof(f26771,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool)
| ~ spl0_846 ),
inference(avatar_component_clause,[],[f26770]) ).
fof(f121812,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool),X2,tc_bool)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) )
| ~ spl0_1449 ),
inference(avatar_component_clause,[],[f121811]) ).
fof(f131327,plain,
( spl0_1483
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1482 ),
inference(avatar_split_clause,[],[f131323,f131320,f18286,f2678,f131325]) ).
fof(f131325,plain,
( spl0_1483
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f131320,plain,
( spl0_1482
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f131323,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1482 ),
inference(forward_demodulation,[],[f131321,f19417]) ).
fof(f131321,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)) )
| ~ spl0_1482 ),
inference(avatar_component_clause,[],[f131320]) ).
fof(f131322,plain,
( spl0_1482
| ~ spl0_167
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4602,f4502,f2248,f131320]) ).
fof(f2248,plain,
( spl0_167
<=> ! [X0,X7] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),c_Set_OPow(X7,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f4602,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)) )
| ~ spl0_167
| ~ spl0_300 ),
inference(resolution,[],[f4503,f2249]) ).
fof(f2249,plain,
( ! [X0,X7] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),c_Set_OPow(X7,X0)))
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f2248]) ).
fof(f131241,plain,
( spl0_1481
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1480 ),
inference(avatar_split_clause,[],[f131237,f131234,f18286,f2678,f131239]) ).
fof(f131239,plain,
( spl0_1481
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,hAPP(X0,X4)))
| ~ c_lessequals(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),X3,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f131234,plain,
( spl0_1480
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(X0,X4)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f131237,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,hAPP(X0,X4)))
| ~ c_lessequals(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),X3,tc_fun(X2,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1480 ),
inference(forward_demodulation,[],[f131235,f19417]) ).
fof(f131235,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(X0,X4)),X3)) )
| ~ spl0_1480 ),
inference(avatar_component_clause,[],[f131234]) ).
fof(f131236,plain,
( spl0_1480
| ~ spl0_203
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4598,f4502,f2831,f131234]) ).
fof(f2831,plain,
( spl0_203
<=> ! [X10,X0,X12,X1] : hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X1)),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool)),X12,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f4598,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(X0,X4)),X3)) )
| ~ spl0_203
| ~ spl0_300 ),
inference(resolution,[],[f4503,f2832]) ).
fof(f2832,plain,
( ! [X10,X0,X1,X12] : hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X1)),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool)),X12,X0)))
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2831]) ).
fof(f131232,plain,
( spl0_1479
| ~ spl0_152
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4581,f4490,f2188,f131230]) ).
fof(f131230,plain,
( spl0_1479
<=> ! [X4,X0,X3,X2,X1] :
( c_Set_Oimage(X3,X1,X2,X4) = c_Set_Oimage(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2,X4)
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f2188,plain,
( spl0_152
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f4490,plain,
( spl0_297
<=> ! [X10,X0,X12,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f4581,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Set_Oimage(X3,X1,X2,X4) = c_Set_Oimage(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2,X4)
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) )
| ~ spl0_152
| ~ spl0_297 ),
inference(forward_demodulation,[],[f4553,f93]) ).
fof(f93,axiom,
! [X10,X0,X6,X7,X12] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X10,X6,X12,X0),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
fof(f4553,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X3,X0,X2,X4),c_Set_Oimage(X3,X1,X2,X4),tc_fun(X4,tc_bool)) )
| ~ spl0_152
| ~ spl0_297 ),
inference(resolution,[],[f4491,f2189]) ).
fof(f2189,plain,
( ! [X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X7 )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f2188]) ).
fof(f4491,plain,
( ! [X10,X0,X6,X7,X12] :
( c_lessequals(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool)) )
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f4490]) ).
fof(f131228,plain,
( spl0_1478
| ~ spl0_150
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4580,f4490,f2180,f131226]) ).
fof(f131226,plain,
( spl0_1478
<=> ! [X4,X0,X3,X2,X1] :
( c_Set_Oimage(X3,X1,X2,X4) = c_Set_Oimage(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),X2,X4)
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f2180,plain,
( spl0_150
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f4580,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Set_Oimage(X3,X1,X2,X4) = c_Set_Oimage(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),X2,X4)
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) )
| ~ spl0_150
| ~ spl0_297 ),
inference(forward_demodulation,[],[f4552,f93]) ).
fof(f4552,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X3,X1,X2,X4),c_Set_Oimage(X3,X0,X2,X4),tc_fun(X4,tc_bool)) )
| ~ spl0_150
| ~ spl0_297 ),
inference(resolution,[],[f4491,f2181]) ).
fof(f2181,plain,
( ! [X0,X6,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f2180]) ).
fof(f131224,plain,
( spl0_1477
| ~ spl0_142
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4574,f4490,f1858,f131222]) ).
fof(f131222,plain,
( spl0_1477
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Set_Oimage(X0,X3,X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f1858,plain,
( spl0_142
<=> ! [X0,X12,X10] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f4574,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Set_Oimage(X0,X3,X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) )
| ~ spl0_142
| ~ spl0_297 ),
inference(superposition,[],[f4491,f1859]) ).
fof(f1859,plain,
( ! [X10,X0,X12] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12,X0)
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1858]) ).
fof(f131220,plain,
( spl0_1476
| ~ spl0_157
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4554,f4490,f2208,f131218]) ).
fof(f131218,plain,
( spl0_1476
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Set_Oimage(X3,X1,X2,X4),X5))
| ~ hBOOL(hAPP(c_Set_Oimage(X3,X0,X2,X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f2208,plain,
( spl0_157
<=> ! [X19,X20,X0,X1] :
( ~ hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(X19,X1))
| ~ c_lessequals(X20,X19,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f4554,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Set_Oimage(X3,X1,X2,X4),X5))
| ~ hBOOL(hAPP(c_Set_Oimage(X3,X0,X2,X4),X5)) )
| ~ spl0_157
| ~ spl0_297 ),
inference(resolution,[],[f4491,f2209]) ).
fof(f2209,plain,
( ! [X0,X1,X19,X20] :
( ~ c_lessequals(X20,X19,tc_fun(X0,tc_bool))
| hBOOL(hAPP(X19,X1))
| ~ hBOOL(hAPP(X20,X1)) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f2208]) ).
fof(f131102,plain,
( spl0_1475
| ~ spl0_159
| ~ spl0_203
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4550,f4486,f2831,f2216,f131100]) ).
fof(f131100,plain,
( spl0_1475
<=> ! [X5,X4,X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_in(X3),hAPP(X0,hAPP(X1,X5))),c_Set_Oimage(X0,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X2),X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f2216,plain,
( spl0_159
<=> ! [X18,X20,X0,X12,X16,X19] : hAPP(c_COMBB(X20,X19,X12,X0,X18),X16) = hAPP(X20,hAPP(X19,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f4486,plain,
( spl0_296
<=> ! [X18,X10,X0,X12,X6,X17] : c_Set_Oimage(X10,c_Set_Oimage(X17,X6,X18,X12),X12,X0) = c_Set_Oimage(c_COMBB(X10,X17,X12,X0,X18),X6,X18,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f4550,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_in(X3),hAPP(X0,hAPP(X1,X5))),c_Set_Oimage(X0,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X2),X2,X3)))
| ~ spl0_159
| ~ spl0_203
| ~ spl0_296 ),
inference(forward_demodulation,[],[f4546,f2217]) ).
fof(f2217,plain,
( ! [X0,X18,X19,X16,X12,X20] : hAPP(c_COMBB(X20,X19,X12,X0,X18),X16) = hAPP(X20,hAPP(X19,X16))
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f2216]) ).
fof(f4546,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_in(X3),hAPP(c_COMBB(X0,X1,X2,X3,X4),X5)),c_Set_Oimage(X0,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X2),X2,X3)))
| ~ spl0_203
| ~ spl0_296 ),
inference(superposition,[],[f2832,f4487]) ).
fof(f4487,plain,
( ! [X10,X0,X18,X6,X17,X12] : c_Set_Oimage(X10,c_Set_Oimage(X17,X6,X18,X12),X12,X0) = c_Set_Oimage(c_COMBB(X10,X17,X12,X0,X18),X6,X18,X0)
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f4486]) ).
fof(f131098,plain,
( spl0_1474
| ~ spl0_223
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4410,f4158,f3079,f131096]) ).
fof(f131096,plain,
( spl0_1474
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_OPow(X2,X3),X4,X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f3079,plain,
( spl0_223
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X6),c_Set_OPow(X7,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f4158,plain,
( spl0_290
<=> ! [X7,X20,X0,X6,X30] :
( ~ hBOOL(hAPP(X20,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X30),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f4410,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_OPow(X2,X3),X4,X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) )
| ~ spl0_223
| ~ spl0_290 ),
inference(resolution,[],[f4159,f3080]) ).
fof(f3080,plain,
( ! [X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X6),c_Set_OPow(X7,X0)))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool)) )
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f3079]) ).
fof(f4159,plain,
( ! [X0,X6,X7,X30,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X30),X6))
| ~ hBOOL(hAPP(X20,X30))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0))) )
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f4158]) ).
fof(f131094,plain,
( spl0_1473
| ~ spl0_223
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4389,f4150,f3079,f131092]) ).
fof(f131092,plain,
( spl0_1473
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,c_Set_OPow(X3,X4),X0,tc_fun(X4,tc_bool))))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f4150,plain,
( spl0_288
<=> ! [X20,X0,X6,X1,X7] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f4389,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,c_Set_OPow(X3,X4),X0,tc_fun(X4,tc_bool))))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) )
| ~ spl0_223
| ~ spl0_288 ),
inference(resolution,[],[f4151,f3080]) ).
fof(f4151,plain,
( ! [X0,X1,X6,X7,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| ~ hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0))) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f4150]) ).
fof(f130985,plain,
( spl0_1472
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1471 ),
inference(avatar_split_clause,[],[f130981,f130978,f18286,f2678,f130983]) ).
fof(f130983,plain,
( spl0_1472
<=> ! [X5,X3,X4,X2,X7,X0,X6,X1] :
( ~ hBOOL(hAPP(X5,X1))
| c_lessequals(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6,X7),X7)
| ~ class_Complete__Lattice_Ocomplete__lattice(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f130978,plain,
( spl0_1471
<=> ! [X2,X4,X7,X0,X6,X5,X3,X1] :
( c_lessequals(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6,X7),X7)
| ~ hBOOL(hAPP(hAPP(c_in(X6),X1),X5))
| ~ class_Complete__Lattice_Ocomplete__lattice(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f130981,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(X5,X1))
| c_lessequals(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6,X7),X7)
| ~ class_Complete__Lattice_Ocomplete__lattice(X7) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1471 ),
inference(forward_demodulation,[],[f130979,f19417]) ).
fof(f130979,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( c_lessequals(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6,X7),X7)
| ~ hBOOL(hAPP(hAPP(c_in(X6),X1),X5))
| ~ class_Complete__Lattice_Ocomplete__lattice(X7) )
| ~ spl0_1471 ),
inference(avatar_component_clause,[],[f130978]) ).
fof(f130980,plain,
( spl0_1471
| ~ spl0_73
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f4212,f4106,f1357,f130978]) ).
fof(f1357,plain,
( spl0_73
<=> ! [X11,X0,X10,X2,X1] : hAPP(c_Fun_Ofun__upd(X10,X1,X2,X0,X11),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f4106,plain,
( spl0_277
<=> ! [X0,X21,X12,X6,X25] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),X6))
| c_lessequals(hAPP(X21,X25),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X21,X0,X12),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f4212,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( c_lessequals(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6,X7),X7)
| ~ hBOOL(hAPP(hAPP(c_in(X6),X1),X5))
| ~ class_Complete__Lattice_Ocomplete__lattice(X7) )
| ~ spl0_73
| ~ spl0_277 ),
inference(superposition,[],[f4107,f1358]) ).
fof(f1358,plain,
( ! [X2,X10,X0,X11,X1] : hAPP(c_Fun_Ofun__upd(X10,X1,X2,X0,X11),X1) = X2
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1357]) ).
fof(f4107,plain,
( ! [X21,X0,X6,X25,X12] :
( c_lessequals(hAPP(X21,X25),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X21,X0,X12),X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X12) )
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f4106]) ).
fof(f130976,plain,
( spl0_1470
| ~ spl0_268
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f4091,f3682,f3659,f130974]) ).
fof(f130974,plain,
( spl0_1470
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| hBOOL(hAPP(X2,c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_Omktop(X3,X0),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f3682,plain,
( spl0_273
<=> ! [X37,X1,X30] :
( X1 = X30
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f4091,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| hBOOL(hAPP(X2,c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_Omktop(X3,X0),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) )
| ~ spl0_268
| ~ spl0_273 ),
inference(resolution,[],[f3683,f3660]) ).
fof(f3683,plain,
( ! [X1,X37,X30] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X1)))
| X1 = X30 )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f3682]) ).
fof(f130972,plain,
( spl0_1469
| ~ spl0_268
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f4081,f3675,f3659,f130970]) ).
fof(f130970,plain,
( spl0_1469
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| hBOOL(hAPP(X2,c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_Omkbot(X3,X0),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f3675,plain,
( spl0_272
<=> ! [X2,X37,X1] :
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f4081,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| hBOOL(hAPP(X2,c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_Omkbot(X3,X0),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) )
| ~ spl0_268
| ~ spl0_272 ),
inference(resolution,[],[f3676,f3660]) ).
fof(f3676,plain,
( ! [X2,X1,X37] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1)))
| X1 = X2 )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f3675]) ).
fof(f130968,plain,
( spl0_1468
| ~ spl0_258
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4045,f3659,f3619,f130966]) ).
fof(f130966,plain,
( spl0_1468
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f3619,plain,
( spl0_258
<=> ! [X4,X3] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f4045,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))
| X1 = X2 )
| ~ spl0_258
| ~ spl0_268 ),
inference(resolution,[],[f3660,f3620]) ).
fof(f3620,plain,
( ! [X3,X4] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X3,X4)))
| X3 = X4 )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f3619]) ).
fof(f130964,plain,
( spl0_1467
| ~ spl0_30
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3907,f3615,f1159,f130962]) ).
fof(f130962,plain,
( spl0_1467
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = 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_1467])]) ).
fof(f1159,plain,
( spl0_30
<=> ! [X59,X58] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X59)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f3615,plain,
( spl0_257
<=> ! [X0,X12,X6,X21] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X12)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X21,X12,X0),X0,X12) = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f3907,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = 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_30
| ~ spl0_257 ),
inference(resolution,[],[f3616,f1160]) ).
fof(f1160,plain,
( ! [X58,X59] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X58,X59))
| ~ class_Complete__Lattice_Ocomplete__lattice(X59) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f3616,plain,
( ! [X21,X0,X6,X12] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X12)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X21,X12,X0),X0,X12) = X21 )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f3615]) ).
fof(f130960,plain,
( spl0_1466
| ~ spl0_844
| ~ spl0_1418 ),
inference(avatar_split_clause,[],[f120623,f120519,f26762,f130958]) ).
fof(f26762,plain,
( spl0_844
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f120519,plain,
( spl0_1418
<=> ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f120623,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool),X3,tc_bool)
| ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) )
| ~ spl0_844
| ~ spl0_1418 ),
inference(superposition,[],[f120520,f26763]) ).
fof(f26763,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool)
| ~ spl0_844 ),
inference(avatar_component_clause,[],[f26762]) ).
fof(f120520,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) )
| ~ spl0_1418 ),
inference(avatar_component_clause,[],[f120519]) ).
fof(f130956,plain,
( spl0_1465
| ~ spl0_229
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3824,f3595,f3112,f130954]) ).
fof(f130954,plain,
( spl0_1465
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f3595,plain,
( spl0_252
<=> ! [X6,X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f3824,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)) )
| ~ spl0_229
| ~ spl0_252 ),
inference(superposition,[],[f3113,f3596]) ).
fof(f3596,plain,
( ! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f3595]) ).
fof(f130952,plain,
( spl0_1464
| ~ spl0_219
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3823,f3595,f3063,f130950]) ).
fof(f130950,plain,
( spl0_1464
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f3823,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) )
| ~ spl0_219
| ~ spl0_252 ),
inference(superposition,[],[f3064,f3596]) ).
fof(f130948,plain,
( spl0_1463
| ~ spl0_216
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3821,f3595,f3051,f130946]) ).
fof(f130946,plain,
( spl0_1463
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3))
| hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f3051,plain,
( spl0_216
<=> ! [X0,X6,X1,X7] :
( hBOOL(hAPP(X7,X1))
| hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f3821,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3))
| hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X3)) )
| ~ spl0_216
| ~ spl0_252 ),
inference(superposition,[],[f3052,f3596]) ).
fof(f3052,plain,
( ! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X1))
| hBOOL(hAPP(X6,X1))
| hBOOL(hAPP(X7,X1)) )
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f3051]) ).
fof(f130944,plain,
( spl0_1462
| ~ spl0_230
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3787,f3588,f3116,f130942]) ).
fof(f130942,plain,
( spl0_1462
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f3588,plain,
( spl0_251
<=> ! [X6,X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f3787,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) )
| ~ spl0_230
| ~ spl0_251 ),
inference(superposition,[],[f3117,f3589]) ).
fof(f3589,plain,
( ! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f3588]) ).
fof(f130940,plain,
( spl0_1461
| ~ spl0_218
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3784,f3588,f3059,f130938]) ).
fof(f130938,plain,
( spl0_1461
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f3784,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) )
| ~ spl0_218
| ~ spl0_251 ),
inference(superposition,[],[f3060,f3589]) ).
fof(f130936,plain,
( spl0_1460
| ~ spl0_216
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3783,f3588,f3051,f130934]) ).
fof(f130934,plain,
( spl0_1460
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3))
| hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3))
| hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f3783,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3))
| hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3))
| hBOOL(hAPP(X1,X3)) )
| ~ spl0_216
| ~ spl0_251 ),
inference(superposition,[],[f3052,f3589]) ).
fof(f130932,plain,
( spl0_1459
| ~ spl0_216
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3745,f3584,f3051,f130930]) ).
fof(f130930,plain,
( spl0_1459
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f3584,plain,
( spl0_250
<=> ! [X6,X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f3745,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3)) )
| ~ spl0_216
| ~ spl0_250 ),
inference(superposition,[],[f3052,f3585]) ).
fof(f3585,plain,
( ! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f3584]) ).
fof(f130928,plain,
( spl0_1458
| ~ spl0_78
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3700,f3580,f1377,f130926]) ).
fof(f130926,plain,
( spl0_1458
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f1377,plain,
( spl0_78
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f3580,plain,
( spl0_249
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f3700,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_249 ),
inference(resolution,[],[f3581,f1378]) ).
fof(f1378,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1377]) ).
fof(f3581,plain,
( ! [X0,X8,X6,X7] :
( ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool)) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f3580]) ).
fof(f130923,plain,
( spl0_1457
| ~ spl0_187
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f3380,f3079,f2658,f130921]) ).
fof(f130921,plain,
( spl0_1457
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(X1,X2),tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f2658,plain,
( spl0_187
<=> ! [X6,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,X0),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f3380,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(X1,X2),tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) )
| ~ spl0_187
| ~ spl0_223 ),
inference(resolution,[],[f3080,f2659]) ).
fof(f2659,plain,
( ! [X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f2658]) ).
fof(f130919,plain,
( spl0_1456
| ~ spl0_158
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2784,f2678,f2212,f130917]) ).
fof(f130917,plain,
( spl0_1456
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( ~ c_lessequals(hAPP(hAPP(X0,X5),X4),X5,X6)
| ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_COMBC(X0,X1,X2,X3),X4),X6),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f2212,plain,
( spl0_158
<=> ! [X6,X0,X10] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_lessequals(hAPP(X10,X6),X6,X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X10,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f2784,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_lessequals(hAPP(hAPP(X0,X5),X4),X5,X6)
| ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_COMBC(X0,X1,X2,X3),X4),X6),X5,X6) )
| ~ spl0_158
| ~ spl0_192 ),
inference(superposition,[],[f2213,f2679]) ).
fof(f2213,plain,
( ! [X10,X0,X6] :
( ~ c_lessequals(hAPP(X10,X6),X6,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X10,X0),X6,X0) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f2212]) ).
fof(f130885,plain,
( spl0_1455
| ~ spl0_158
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f2743,f2646,f2212,f130883]) ).
fof(f130883,plain,
( spl0_1455
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( ~ c_lessequals(hAPP(X0,X5),X5,X6)
| ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6),X5,X6)
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f2646,plain,
( spl0_184
<=> ! [X5,X2,X0,X12,X1,X10] :
( X1 = X5
| hAPP(X10,X5) = hAPP(c_Fun_Ofun__upd(X10,X1,X2,X0,X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f2743,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_lessequals(hAPP(X0,X5),X5,X6)
| ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6),X5,X6)
| X1 = X5 )
| ~ spl0_158
| ~ spl0_184 ),
inference(superposition,[],[f2213,f2647]) ).
fof(f2647,plain,
( ! [X2,X10,X0,X1,X5,X12] :
( hAPP(X10,X5) = hAPP(c_Fun_Ofun__upd(X10,X1,X2,X0,X12),X5)
| X1 = X5 )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f2646]) ).
fof(f130881,plain,
( spl0_1454
| ~ spl0_74
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2508,f2216,f1361,f130879]) ).
fof(f130879,plain,
( spl0_1454
<=> ! [X5,X3,X4,X2,X7,X0,X6,X1] : c_COMBB(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_COMBB(X0,X1,X2,X3,X4),X5,hAPP(X0,hAPP(X1,X5)),X6,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f1361,plain,
( spl0_74
<=> ! [X10,X0,X12,X1] : c_Fun_Ofun__upd(X10,X1,hAPP(X10,X1),X0,X12) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f2508,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_COMBB(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_COMBB(X0,X1,X2,X3,X4),X5,hAPP(X0,hAPP(X1,X5)),X6,X7)
| ~ spl0_74
| ~ spl0_159 ),
inference(superposition,[],[f1362,f2217]) ).
fof(f1362,plain,
( ! [X10,X0,X1,X12] : c_Fun_Ofun__upd(X10,X1,hAPP(X10,X1),X0,X12) = X10
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1361]) ).
fof(f130877,plain,
( spl0_1453
| ~ spl0_128
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2501,f2212,f1801,f130875]) ).
fof(f130875,plain,
( spl0_1453
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ c_lessequals(hAPP(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0)),X3,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f1801,plain,
( spl0_128
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X4,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f2501,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ c_lessequals(hAPP(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0)),X3,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_128
| ~ spl0_158 ),
inference(resolution,[],[f2213,f1802]) ).
fof(f1802,plain,
( ! [X3,X0,X1,X4] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0)
| ~ c_lessequals(X1,X4,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1801]) ).
fof(f130873,plain,
( spl0_1452
| ~ spl0_129
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2500,f2212,f1805,f130871]) ).
fof(f130871,plain,
( spl0_1452
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ c_lessequals(hAPP(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0)),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f1805,plain,
( spl0_129
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f2500,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ c_lessequals(hAPP(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0)),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_129
| ~ spl0_158 ),
inference(resolution,[],[f2213,f1806]) ).
fof(f1806,plain,
( ! [X3,X0,X1,X4] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0)
| ~ c_lessequals(X1,X3,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1805]) ).
fof(f129640,plain,
( spl0_1451
| ~ spl0_652
| ~ spl0_1450 ),
inference(avatar_split_clause,[],[f127315,f123133,f17409,f129638]) ).
fof(f17409,plain,
( spl0_652
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f127315,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X0,X2,tc_bool) )
| ~ spl0_652
| ~ spl0_1450 ),
inference(superposition,[],[f123134,f17410]) ).
fof(f17410,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool)
| ~ spl0_652 ),
inference(avatar_component_clause,[],[f17409]) ).
fof(f123135,plain,
( spl0_1450
| ~ spl0_648
| ~ spl0_1418 ),
inference(avatar_split_clause,[],[f120620,f120519,f17393,f123133]) ).
fof(f120620,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X2,tc_bool)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool) )
| ~ spl0_648
| ~ spl0_1418 ),
inference(superposition,[],[f120520,f17394]) ).
fof(f121813,plain,
( spl0_1449
| ~ spl0_655
| ~ spl0_1418 ),
inference(avatar_split_clause,[],[f120615,f120519,f17432,f121811]) ).
fof(f17432,plain,
( spl0_655
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f120615,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool),X2,tc_bool)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) )
| ~ spl0_655
| ~ spl0_1418 ),
inference(superposition,[],[f120520,f17433]) ).
fof(f17433,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool)
| ~ spl0_655 ),
inference(avatar_component_clause,[],[f17432]) ).
fof(f120915,plain,
( spl0_1448
| ~ spl0_177
| ~ spl0_192
| ~ spl0_473
| ~ spl0_699
| ~ spl0_764 ),
inference(avatar_split_clause,[],[f69499,f20188,f18286,f10889,f2678,f2288,f120913]) ).
fof(f120913,plain,
( spl0_1448
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(c_Relation_OImage(hAPP(c_fequal(tc_prod(X2,X0)),c_Pair(X3,X1,X2,X0)),X4,X2,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f10889,plain,
( spl0_473
<=> ! [X24,X4,X0,X12,X6,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(hAPP(c_in(X12),X4),c_Relation_OImage(X24,X6,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f20188,plain,
( spl0_764
<=> ! [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_764])]) ).
fof(f69499,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(c_Relation_OImage(hAPP(c_fequal(tc_prod(X2,X0)),c_Pair(X3,X1,X2,X0)),X4,X2,X0),X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_473
| ~ spl0_699
| ~ spl0_764 ),
inference(forward_demodulation,[],[f69498,f19417]) ).
fof(f69498,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Relation_OImage(hAPP(c_fequal(tc_prod(X2,X0)),c_Pair(X3,X1,X2,X0)),X4,X2,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X4)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_473
| ~ spl0_699
| ~ spl0_764 ),
inference(forward_demodulation,[],[f69497,f20189]) ).
fof(f20189,plain,
( ! [X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1)
| ~ spl0_764 ),
inference(avatar_component_clause,[],[f20188]) ).
fof(f69497,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Relation_OImage(hAPP(c_COMBC(c_fequal(tc_prod(X2,X0)),tc_prod(X2,X0),tc_prod(X2,X0),tc_bool),c_Pair(X3,X1,X2,X0)),X4,X2,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X4)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_473
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69469,f19417]) ).
fof(f69469,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(hAPP(c_COMBC(c_fequal(tc_prod(X2,X0)),tc_prod(X2,X0),tc_prod(X2,X0),tc_bool),c_Pair(X3,X1,X2,X0)),X4,X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X4)) )
| ~ spl0_177
| ~ spl0_473 ),
inference(resolution,[],[f10890,f2289]) ).
fof(f10890,plain,
( ! [X3,X0,X6,X4,X24,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),X24))
| hBOOL(hAPP(hAPP(c_in(X12),X4),c_Relation_OImage(X24,X6,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_473 ),
inference(avatar_component_clause,[],[f10889]) ).
fof(f120911,plain,
( spl0_1447
| ~ spl0_29
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f62931,f62859,f1155,f120909]) ).
fof(f120909,plain,
( spl0_1447
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( ~ hBOOL(X1)
| hAPP(X2,hAPP(X3,X1)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X2,X3,X4,X5,X6),c_COMBI(X0),X6,X5),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f62859,plain,
( spl0_1185
<=> ! [X18,X10,X0,X12,X6,X17,X1] :
( ~ hBOOL(hAPP(X6,X1))
| hAPP(X17,hAPP(X10,X1)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X17,X10,X18,X12,X0),X6,X0,X12),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f62931,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(X1)
| hAPP(X2,hAPP(X3,X1)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X2,X3,X4,X5,X6),c_COMBI(X0),X6,X5),X1) )
| ~ spl0_29
| ~ spl0_1185 ),
inference(superposition,[],[f62860,f1156]) ).
fof(f62860,plain,
( ! [X10,X0,X1,X18,X6,X17,X12] :
( ~ hBOOL(hAPP(X6,X1))
| hAPP(X17,hAPP(X10,X1)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X17,X10,X18,X12,X0),X6,X0,X12),X1) )
| ~ spl0_1185 ),
inference(avatar_component_clause,[],[f62859]) ).
fof(f120901,plain,
( spl0_1446
| ~ spl0_44
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f62872,f62859,f1215,f120899]) ).
fof(f120899,plain,
( spl0_1446
<=> ! [X5,X3,X4,X0,X6,X2,X1] : hAPP(X0,hAPP(X1,X2)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X0,X1,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool)),X5,X4),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f62872,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hAPP(X0,hAPP(X1,X2)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X0,X1,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool)),X5,X4),X2)
| ~ spl0_44
| ~ spl0_1185 ),
inference(resolution,[],[f62860,f1216]) ).
fof(f120897,plain,
( spl0_1445
| ~ spl0_45
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f62868,f62859,f1219,f120895]) ).
fof(f120895,plain,
( spl0_1445
<=> ! [X5,X3,X4,X0,X6,X2,X1] : hAPP(X0,hAPP(X1,X2)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X0,X1,X3,X4,X5),hAPP(c_fequal(X6),X2),X5,X4),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f1219,plain,
( spl0_45
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f62868,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hAPP(X0,hAPP(X1,X2)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X0,X1,X3,X4,X5),hAPP(c_fequal(X6),X2),X5,X4),X2)
| ~ spl0_45
| ~ spl0_1185 ),
inference(resolution,[],[f62860,f1220]) ).
fof(f1220,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1))
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1219]) ).
fof(f120893,plain,
( spl0_1444
| ~ spl0_183
| ~ spl0_192
| ~ spl0_280
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56383,f18286,f4118,f2678,f2642,f120891]) ).
fof(f120891,plain,
( spl0_1444
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| ~ c_lessequals(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f2642,plain,
( spl0_183
<=> ! [X6,X0,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f4118,plain,
( spl0_280
<=> ! [X6,X0,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X7),X6))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f56383,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| ~ c_lessequals(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_183
| ~ spl0_192
| ~ spl0_280
| ~ spl0_699 ),
inference(forward_demodulation,[],[f4246,f19417]) ).
fof(f4246,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| ~ c_lessequals(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_183
| ~ spl0_280 ),
inference(resolution,[],[f4119,f2643]) ).
fof(f2643,plain,
( ! [X0,X6,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| X6 = X7 )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f2642]) ).
fof(f4119,plain,
( ! [X0,X6,X7] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X7),X6)) )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f4118]) ).
fof(f120889,plain,
( spl0_1443
| ~ spl0_183
| ~ spl0_192
| ~ spl0_279
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56377,f18286,f4114,f2678,f2642,f120887]) ).
fof(f120887,plain,
( spl0_1443
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f4114,plain,
( spl0_279
<=> ! [X6,X0,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X7),X6))
| c_lessequals(X7,c_Complete__Lattice_OSup__class_OSup(X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f56377,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_183
| ~ spl0_192
| ~ spl0_279
| ~ spl0_699 ),
inference(forward_demodulation,[],[f4224,f19417]) ).
fof(f4224,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_183
| ~ spl0_279 ),
inference(resolution,[],[f4115,f2643]) ).
fof(f4115,plain,
( ! [X0,X6,X7] :
( c_lessequals(X7,c_Complete__Lattice_OSup__class_OSup(X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X7),X6)) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f4114]) ).
fof(f120885,plain,
( spl0_1442
| ~ spl0_192
| ~ spl0_300
| ~ spl0_526
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f55981,f18286,f12001,f4502,f2678,f120883]) ).
fof(f120883,plain,
( spl0_1442
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X2))
| c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| ~ c_lessequals(X0,X3,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f55981,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X3,X2))
| c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| ~ c_lessequals(X0,X3,tc_fun(X1,tc_bool)) )
| ~ spl0_192
| ~ spl0_300
| ~ spl0_526
| ~ spl0_699 ),
inference(forward_demodulation,[],[f12015,f19417]) ).
fof(f12015,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| ~ c_lessequals(X0,X3,tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) )
| ~ spl0_300
| ~ spl0_526 ),
inference(resolution,[],[f12002,f4503]) ).
fof(f120881,plain,
( spl0_1441
| ~ spl0_28
| ~ spl0_48
| ~ spl0_553 ),
inference(avatar_split_clause,[],[f13273,f13236,f1231,f1151,f120879]) ).
fof(f120879,plain,
( spl0_1441
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f1151,plain,
( spl0_28
<=> ! [X6,X0] : c_Fun_Oinj__on(c_COMBI(X0),X6,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1231,plain,
( spl0_48
<=> ! [X32,X0] : c_Set_Oimage(c_COMBI(X0),X32,X0,X0) = X32 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f13236,plain,
( spl0_553
<=> ! [X10,X0,X12,X6,X7] :
( ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12)
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),X0,X12),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f13273,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_28
| ~ spl0_48
| ~ spl0_553 ),
inference(forward_demodulation,[],[f13272,f1232]) ).
fof(f1232,plain,
( ! [X0,X32] : c_Set_Oimage(c_COMBI(X0),X32,X0,X0) = X32
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1231]) ).
fof(f13272,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(c_COMBI(X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X0,tc_bool)),X0,X0),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_28
| ~ spl0_48
| ~ spl0_553 ),
inference(forward_demodulation,[],[f13245,f1232]) ).
fof(f13245,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(c_COMBI(X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X0,tc_bool)),X0,X0),c_Set_Oimage(c_COMBI(X0),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),X0,X0),tc_fun(X0,tc_bool))
| ~ spl0_28
| ~ spl0_553 ),
inference(resolution,[],[f13237,f1152]) ).
fof(f1152,plain,
( ! [X0,X6] : c_Fun_Oinj__on(c_COMBI(X0),X6,X0,X0)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f13237,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12)
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),X0,X12),tc_fun(X12,tc_bool)) )
| ~ spl0_553 ),
inference(avatar_component_clause,[],[f13236]) ).
fof(f120812,plain,
( spl0_1440
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1439 ),
inference(avatar_split_clause,[],[f120808,f120805,f18286,f2678,f120810]) ).
fof(f120810,plain,
( spl0_1440
<=> ! [X2,X0,X1,X3] : hBOOL(hAPP(c_FuncSet_OPi(X3,c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool),X0),X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f120805,plain,
( spl0_1439
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X3,c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool),X0),X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f120808,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_FuncSet_OPi(X3,c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool),X0),X0,X1),X2))
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1439 ),
inference(forward_demodulation,[],[f120806,f19417]) ).
fof(f120806,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X3,c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool),X0),X0,X1)))
| ~ spl0_1439 ),
inference(avatar_component_clause,[],[f120805]) ).
fof(f120807,plain,
( spl0_1439
| ~ spl0_83
| ~ spl0_491 ),
inference(avatar_split_clause,[],[f11593,f11298,f1397,f120805]) ).
fof(f1397,plain,
( spl0_83
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f11298,plain,
( spl0_491
<=> ! [X6,X10,X0,X12,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X6,X7,X10,X0,X12))),X7))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f11593,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X3,c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool),X0),X0,X1)))
| ~ spl0_83
| ~ spl0_491 ),
inference(resolution,[],[f11299,f1398]) ).
fof(f1398,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1397]) ).
fof(f11299,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X6,X7,X10,X0,X12))),X7))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) )
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f11298]) ).
fof(f120803,plain,
( spl0_1438
| ~ spl0_203
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f11210,f10893,f2831,f120801]) ).
fof(f120801,plain,
( spl0_1438
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X1) = hAPP(X0,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(X0,X1),X0,X2,X3))
| ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f10893,plain,
( spl0_474
<=> ! [X4,X0,X12,X10] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| hAPP(X10,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X4,X10,X12,X0)) = X4
| ~ hBOOL(hAPP(hAPP(c_in(X12),X4),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f11210,plain,
( ! [X2,X3,X0,X1] :
( hAPP(X0,X1) = hAPP(X0,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(X0,X1),X0,X2,X3))
| ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X2) )
| ~ spl0_203
| ~ spl0_474 ),
inference(resolution,[],[f10894,f2832]) ).
fof(f10894,plain,
( ! [X10,X0,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X4),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)))
| hAPP(X10,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X4,X10,X12,X0)) = X4
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12) )
| ~ spl0_474 ),
inference(avatar_component_clause,[],[f10893]) ).
fof(f120799,plain,
( ~ spl0_1436
| spl0_1437
| ~ spl0_186
| ~ spl0_1418 ),
inference(avatar_split_clause,[],[f120622,f120519,f2654,f120797,f120793]) ).
fof(f120793,plain,
( spl0_1436
<=> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f120797,plain,
( spl0_1437
<=> ! [X0,X1] : c_lessequals(X0,X1,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f2654,plain,
( spl0_186
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f120622,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_bool)
| ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool) )
| ~ spl0_186
| ~ spl0_1418 ),
inference(superposition,[],[f120520,f2655]) ).
fof(f2655,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f2654]) ).
fof(f120752,plain,
( spl0_1435
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1434 ),
inference(avatar_split_clause,[],[f120748,f120745,f18286,f2678,f120750]) ).
fof(f120750,plain,
( spl0_1435
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(c_Equiv__Relations_Oquotient(X2,X3,X0),c_Relation_OImage(X3,hAPP(c_fequal(X0),X1),X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f120745,plain,
( spl0_1434
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Equiv__Relations_Oquotient(X2,X3,X0),c_Relation_OImage(X3,hAPP(c_fequal(X0),X1),X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f120748,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(c_Equiv__Relations_Oquotient(X2,X3,X0),c_Relation_OImage(X3,hAPP(c_fequal(X0),X1),X0,X0))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1434 ),
inference(forward_demodulation,[],[f120746,f19417]) ).
fof(f120746,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Equiv__Relations_Oquotient(X2,X3,X0),c_Relation_OImage(X3,hAPP(c_fequal(X0),X1),X0,X0))) )
| ~ spl0_1434 ),
inference(avatar_component_clause,[],[f120745]) ).
fof(f120747,plain,
( spl0_1434
| ~ spl0_113
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f10598,f10593,f1546,f120745]) ).
fof(f10593,plain,
( spl0_467
<=> ! [X24,X0,X6,X1] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Relation_OImage(X24,hAPP(c_fequal(X0),X1),X0,X0)),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f10598,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Equiv__Relations_Oquotient(X2,X3,X0),c_Relation_OImage(X3,hAPP(c_fequal(X0),X1),X0,X0))) )
| ~ spl0_113
| ~ spl0_467 ),
inference(resolution,[],[f10594,f1547]) ).
fof(f10594,plain,
( ! [X0,X1,X6,X24] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Relation_OImage(X24,hAPP(c_fequal(X0),X1),X0,X0)),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_467 ),
inference(avatar_component_clause,[],[f10593]) ).
fof(f120705,plain,
( spl0_1433
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1432 ),
inference(avatar_split_clause,[],[f120701,f120698,f18286,f2678,f120703]) ).
fof(f120703,plain,
( spl0_1433
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f120698,plain,
( spl0_1432
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f120701,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1432 ),
inference(forward_demodulation,[],[f120699,f19417]) ).
fof(f120699,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2))) )
| ~ spl0_1432 ),
inference(avatar_component_clause,[],[f120698]) ).
fof(f120700,plain,
( spl0_1432
| ~ spl0_113
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f9835,f8411,f1546,f120698]) ).
fof(f8411,plain,
( spl0_430
<=> ! [X2,X37,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X37,X1,X2)),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f9835,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2))) )
| ~ spl0_113
| ~ spl0_430 ),
inference(resolution,[],[f8412,f1547]) ).
fof(f8412,plain,
( ! [X2,X1,X37] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X37,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2 )
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f8411]) ).
fof(f120658,plain,
( spl0_1431
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1430 ),
inference(avatar_split_clause,[],[f120654,f120651,f18286,f2678,f120656]) ).
fof(f120656,plain,
( spl0_1431
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f120651,plain,
( spl0_1430
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f120654,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1430 ),
inference(forward_demodulation,[],[f120652,f19417]) ).
fof(f120652,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2))) )
| ~ spl0_1430 ),
inference(avatar_component_clause,[],[f120651]) ).
fof(f120653,plain,
( spl0_1430
| ~ spl0_113
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f9807,f8403,f1546,f120651]) ).
fof(f8403,plain,
( spl0_428
<=> ! [X2,X37,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X2)),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f9807,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2))) )
| ~ spl0_113
| ~ spl0_428 ),
inference(resolution,[],[f8404,f1547]) ).
fof(f8404,plain,
( ! [X2,X1,X37] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2 )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f8403]) ).
fof(f120649,plain,
( spl0_1429
| ~ spl0_94
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f9562,f8269,f1469,f120647]) ).
fof(f120647,plain,
( spl0_1429
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f8269,plain,
( spl0_420
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f9562,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_94
| ~ spl0_420 ),
inference(superposition,[],[f1470,f8270]) ).
fof(f8270,plain,
( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_420 ),
inference(avatar_component_clause,[],[f8269]) ).
fof(f120561,plain,
( spl0_1428
| ~ spl0_93
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f9561,f8269,f1465,f120559]) ).
fof(f120559,plain,
( spl0_1428
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f1465,plain,
( spl0_93
<=> ! [X6,X0,X7] : c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f9561,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_93
| ~ spl0_420 ),
inference(superposition,[],[f1466,f8270]) ).
fof(f1466,plain,
( ! [X0,X6,X7] : c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f120557,plain,
( spl0_1427
| ~ spl0_94
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f9447,f8261,f1469,f120555]) ).
fof(f120555,plain,
( spl0_1427
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f8261,plain,
( spl0_418
<=> ! [X0,X6,X8,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f9447,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_94
| ~ spl0_418 ),
inference(superposition,[],[f1470,f8262]) ).
fof(f8262,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_418 ),
inference(avatar_component_clause,[],[f8261]) ).
fof(f120553,plain,
( spl0_1426
| ~ spl0_93
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f9446,f8261,f1465,f120551]) ).
fof(f120551,plain,
( spl0_1426
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f9446,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_93
| ~ spl0_418 ),
inference(superposition,[],[f1466,f8262]) ).
fof(f120549,plain,
( spl0_1425
| ~ spl0_94
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f9312,f8257,f1469,f120547]) ).
fof(f120547,plain,
( spl0_1425
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f8257,plain,
( spl0_417
<=> ! [X0,X6,X8,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f9312,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_94
| ~ spl0_417 ),
inference(superposition,[],[f1470,f8258]) ).
fof(f8258,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_417 ),
inference(avatar_component_clause,[],[f8257]) ).
fof(f120545,plain,
( spl0_1424
| ~ spl0_93
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f9311,f8257,f1465,f120543]) ).
fof(f120543,plain,
( spl0_1424
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f9311,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_93
| ~ spl0_417 ),
inference(superposition,[],[f1466,f8258]) ).
fof(f120541,plain,
( spl0_1423
| ~ spl0_94
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f9185,f8253,f1469,f120539]) ).
fof(f120539,plain,
( spl0_1423
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f8253,plain,
( spl0_416
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f9185,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_94
| ~ spl0_416 ),
inference(superposition,[],[f1470,f8254]) ).
fof(f8254,plain,
( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_416 ),
inference(avatar_component_clause,[],[f8253]) ).
fof(f120537,plain,
( spl0_1422
| ~ spl0_93
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f9184,f8253,f1465,f120535]) ).
fof(f120535,plain,
( spl0_1422
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f9184,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_93
| ~ spl0_416 ),
inference(superposition,[],[f1466,f8254]) ).
fof(f120533,plain,
( spl0_1421
| ~ spl0_92
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f9078,f8249,f1457,f120531]) ).
fof(f120531,plain,
( spl0_1421
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f1457,plain,
( spl0_92
<=> ! [X6,X0,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f8249,plain,
( spl0_415
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f9078,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_92
| ~ spl0_415 ),
inference(superposition,[],[f1458,f8250]) ).
fof(f8250,plain,
( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_415 ),
inference(avatar_component_clause,[],[f8249]) ).
fof(f1458,plain,
( ! [X0,X6,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1457]) ).
fof(f120529,plain,
( spl0_1420
| ~ spl0_91
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f9077,f8249,f1453,f120527]) ).
fof(f120527,plain,
( spl0_1420
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f1453,plain,
( spl0_91
<=> ! [X6,X0,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f9077,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_91
| ~ spl0_415 ),
inference(superposition,[],[f1454,f8250]) ).
fof(f1454,plain,
( ! [X0,X6,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1453]) ).
fof(f120525,plain,
( spl0_1419
| ~ spl0_92
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f8763,f8233,f1457,f120523]) ).
fof(f120523,plain,
( spl0_1419
<=> ! [X2,X0,X1,X3] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f8233,plain,
( spl0_411
<=> ! [X0,X6,X8,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f8763,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_92
| ~ spl0_411 ),
inference(superposition,[],[f1458,f8234]) ).
fof(f8234,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f8233]) ).
fof(f120521,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_1418
| ~ spl0_820
| ~ spl0_1143 ),
inference(avatar_split_clause,[],[f52676,f52618,f26582,f120519,f1110,f1105]) ).
fof(f1105,plain,
( spl0_18
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1110,plain,
( spl0_19
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f26582,plain,
( spl0_820
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X1,X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f52618,plain,
( spl0_1143
<=> ! [X2,X0] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X0,X2,tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f52676,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool)
| ~ class_Orderings_Oorder(tc_bool)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_820
| ~ spl0_1143 ),
inference(resolution,[],[f52619,f26583]) ).
fof(f26583,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_820 ),
inference(avatar_component_clause,[],[f26582]) ).
fof(f52619,plain,
( ! [X2,X0] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X0,X2,tc_bool) )
| ~ spl0_1143 ),
inference(avatar_component_clause,[],[f52618]) ).
fof(f120517,plain,
( spl0_1417
| ~ spl0_91
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f8762,f8233,f1453,f120515]) ).
fof(f120515,plain,
( spl0_1417
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f8762,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_91
| ~ spl0_411 ),
inference(superposition,[],[f1454,f8234]) ).
fof(f120513,plain,
( spl0_1416
| ~ spl0_92
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8630,f8229,f1457,f120511]) ).
fof(f120511,plain,
( spl0_1416
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f8229,plain,
( spl0_410
<=> ! [X0,X6,X8,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f8630,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_92
| ~ spl0_410 ),
inference(superposition,[],[f1458,f8230]) ).
fof(f8230,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f8229]) ).
fof(f120509,plain,
( spl0_1415
| ~ spl0_91
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8629,f8229,f1453,f120507]) ).
fof(f120507,plain,
( spl0_1415
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f8629,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_91
| ~ spl0_410 ),
inference(superposition,[],[f1454,f8230]) ).
fof(f120504,plain,
( spl0_1414
| ~ spl0_214
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f8320,f8294,f2886,f120502]) ).
fof(f120502,plain,
( spl0_1414
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))))
| hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f2886,plain,
( spl0_214
<=> ! [X20,X0,X6,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Olower__semilattice__class_Oinf(X6,X20,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X20,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f8320,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))))
| hBOOL(hAPP(X3,X4)) )
| ~ spl0_214
| ~ spl0_426 ),
inference(superposition,[],[f2887,f8295]) ).
fof(f2887,plain,
( ! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Olower__semilattice__class_Oinf(X6,X20,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X20,X1)) )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2886]) ).
fof(f120500,plain,
( spl0_1413
| ~ spl0_91
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f8314,f8294,f1453,f120498]) ).
fof(f120498,plain,
( spl0_1413
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f8314,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_91
| ~ spl0_426 ),
inference(superposition,[],[f1454,f8295]) ).
fof(f120488,plain,
( spl0_1412
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1411 ),
inference(avatar_split_clause,[],[f120484,f120481,f18286,f2678,f120486]) ).
fof(f120486,plain,
( spl0_1412
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X2,X3),X1))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X4,X2,X5,X0),c_Pair(X3,X1,X5,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f120481,plain,
( spl0_1411
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X4,X2,X5,X0),c_Pair(X3,X1,X5,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f120484,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(X2,X3),X1))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X4,X2,X5,X0),c_Pair(X3,X1,X5,X0))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1411 ),
inference(forward_demodulation,[],[f120482,f19417]) ).
fof(f120482,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X4,X2,X5,X0),c_Pair(X3,X1,X5,X0))) )
| ~ spl0_1411 ),
inference(avatar_component_clause,[],[f120481]) ).
fof(f120483,plain,
( spl0_1411
| ~ spl0_112
| ~ spl0_393 ),
inference(avatar_split_clause,[],[f7786,f7572,f1542,f120481]) ).
fof(f7572,plain,
( spl0_393
<=> ! [X6,X4,X7,X0,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X12),X4),hAPP(X7,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Product__Type_OSigma(X6,X7,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f7786,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X4,X2,X5,X0),c_Pair(X3,X1,X5,X0))) )
| ~ spl0_112
| ~ spl0_393 ),
inference(resolution,[],[f7573,f1543]) ).
fof(f7573,plain,
( ! [X3,X0,X6,X7,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Product__Type_OSigma(X6,X7,X0,X12)))
| hBOOL(hAPP(hAPP(c_in(X12),X4),hAPP(X7,X3))) )
| ~ spl0_393 ),
inference(avatar_component_clause,[],[f7572]) ).
fof(f120479,plain,
( spl0_1410
| ~ spl0_125
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f7243,f7036,f1789,f120477]) ).
fof(f120477,plain,
( spl0_1410
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),X5))
| ~ hBOOL(hAPP(c_Relation_OImage(X0,X4,X2,X3),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f1789,plain,
( spl0_125
<=> ! [X6,X0,X1,X7] :
( ~ hBOOL(hAPP(X7,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f7036,plain,
( spl0_372
<=> ! [X6,X0,X12,X16,X7] : c_Relation_OImage(X16,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X16,X6,X12,X0),c_Relation_OImage(X16,X7,X12,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f7243,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),X5))
| ~ hBOOL(hAPP(c_Relation_OImage(X0,X4,X2,X3),X5)) )
| ~ spl0_125
| ~ spl0_372 ),
inference(superposition,[],[f1790,f7037]) ).
fof(f7037,plain,
( ! [X0,X6,X16,X7,X12] : c_Relation_OImage(X16,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X16,X6,X12,X0),c_Relation_OImage(X16,X7,X12,X0),tc_fun(X0,tc_bool))
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f7036]) ).
fof(f1790,plain,
( ! [X0,X1,X6,X7] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X1))
| ~ hBOOL(hAPP(X7,X1)) )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1789]) ).
fof(f120475,plain,
( spl0_1409
| ~ spl0_124
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f7242,f7036,f1785,f120473]) ).
fof(f120473,plain,
( spl0_1409
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),X5))
| ~ hBOOL(hAPP(c_Relation_OImage(X0,X1,X2,X3),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f1785,plain,
( spl0_124
<=> ! [X0,X6,X1,X7] :
( ~ hBOOL(hAPP(X6,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f7242,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),X5))
| ~ hBOOL(hAPP(c_Relation_OImage(X0,X1,X2,X3),X5)) )
| ~ spl0_124
| ~ spl0_372 ),
inference(superposition,[],[f1786,f7037]) ).
fof(f1786,plain,
( ! [X0,X1,X6,X7] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X1))
| ~ hBOOL(hAPP(X6,X1)) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1785]) ).
fof(f120470,plain,
( spl0_1408
| ~ spl0_1176
| ~ spl0_1205 ),
inference(avatar_split_clause,[],[f71889,f71197,f59838,f120468]) ).
fof(f120468,plain,
( spl0_1408
<=> ! [X0,X1] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f59838,plain,
( spl0_1176
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),X1,tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f71197,plain,
( spl0_1205
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f71889,plain,
( ! [X0,X1] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)
| ~ spl0_1176
| ~ spl0_1205 ),
inference(superposition,[],[f71198,f59839]) ).
fof(f59839,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),X1,tc_bool) = X1
| ~ spl0_1176 ),
inference(avatar_component_clause,[],[f59838]) ).
fof(f71198,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),tc_bool) = X0
| ~ spl0_1205 ),
inference(avatar_component_clause,[],[f71197]) ).
fof(f120466,plain,
( spl0_1407
| ~ spl0_125
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7192,f7032,f1789,f120464]) ).
fof(f120464,plain,
( spl0_1407
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),X5))
| ~ hBOOL(hAPP(c_Set_Oimage(X0,X4,X2,X3),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f7032,plain,
( spl0_371
<=> ! [X6,X10,X0,X12,X7] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X10,X6,X12,X0),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f7192,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),X5))
| ~ hBOOL(hAPP(c_Set_Oimage(X0,X4,X2,X3),X5)) )
| ~ spl0_125
| ~ spl0_371 ),
inference(superposition,[],[f1790,f7033]) ).
fof(f7033,plain,
( ! [X10,X0,X6,X7,X12] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X10,X6,X12,X0),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool))
| ~ spl0_371 ),
inference(avatar_component_clause,[],[f7032]) ).
fof(f120462,plain,
( spl0_1406
| ~ spl0_124
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7191,f7032,f1785,f120460]) ).
fof(f120460,plain,
( spl0_1406
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),X5))
| ~ hBOOL(hAPP(c_Set_Oimage(X0,X1,X2,X3),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f7191,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),X5))
| ~ hBOOL(hAPP(c_Set_Oimage(X0,X1,X2,X3),X5)) )
| ~ spl0_124
| ~ spl0_371 ),
inference(superposition,[],[f1786,f7033]) ).
fof(f120370,plain,
( spl0_1405
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1404 ),
inference(avatar_split_clause,[],[f120366,f120363,f18286,f2678,f120368]) ).
fof(f120368,plain,
( spl0_1405
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X3,X1))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X3,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f120363,plain,
( spl0_1404
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X3,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f120366,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X3,X1))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X3,tc_fun(X0,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1404 ),
inference(forward_demodulation,[],[f120364,f19417]) ).
fof(f120364,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X3,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X3)) )
| ~ spl0_1404 ),
inference(avatar_component_clause,[],[f120363]) ).
fof(f120365,plain,
( spl0_1404
| ~ spl0_139
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f7111,f7085,f1846,f120363]) ).
fof(f7085,plain,
( spl0_384
<=> ! [X0,X6,X1,X7] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f7111,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X3,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X3)) )
| ~ spl0_139
| ~ spl0_384 ),
inference(superposition,[],[f7086,f1847]) ).
fof(f7086,plain,
( ! [X0,X1,X6,X7] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_384 ),
inference(avatar_component_clause,[],[f7085]) ).
fof(f120361,plain,
( spl0_1403
| ~ spl0_113
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f6858,f6694,f1546,f120359]) ).
fof(f120359,plain,
( spl0_1403
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(hAPP(X3,X4),X1))
| hBOOL(hAPP(c_SetInterval_Oord_OatLeastLessThan(X3,X0,X4,X2,X5),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f6694,plain,
( spl0_356
<=> ! [X41,X47,X46,X0,X42,X25] :
( ~ hBOOL(hAPP(hAPP(X41,X46),X25))
| ~ hBOOL(hAPP(hAPP(X42,X25),X47))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastLessThan(X41,X42,X46,X47,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f6858,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(hAPP(X3,X4),X1))
| hBOOL(hAPP(c_SetInterval_Oord_OatLeastLessThan(X3,X0,X4,X2,X5),X1)) )
| ~ spl0_113
| ~ spl0_356 ),
inference(resolution,[],[f6695,f1547]) ).
fof(f6695,plain,
( ! [X41,X0,X46,X47,X25,X42] :
( hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastLessThan(X41,X42,X46,X47,X0)))
| ~ hBOOL(hAPP(hAPP(X42,X25),X47))
| ~ hBOOL(hAPP(hAPP(X41,X46),X25)) )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f6694]) ).
fof(f120080,plain,
( spl0_1402
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1401 ),
inference(avatar_split_clause,[],[f120076,f120072,f18286,f2678,f120078]) ).
fof(f120078,plain,
( spl0_1402
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2)))
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f120072,plain,
( spl0_1401
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f120076,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2)))
| ~ hBOOL(hAPP(X1,X2)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1401 ),
inference(forward_demodulation,[],[f120075,f19417]) ).
fof(f120075,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2)),X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1401 ),
inference(forward_demodulation,[],[f120073,f19417]) ).
fof(f120073,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2)),X1)) )
| ~ spl0_1401 ),
inference(avatar_component_clause,[],[f120072]) ).
fof(f120074,plain,
( spl0_1401
| ~ spl0_48
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f6799,f6682,f1231,f120072]) ).
fof(f6799,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2)),X1)) )
| ~ spl0_48
| ~ spl0_353 ),
inference(superposition,[],[f6683,f1232]) ).
fof(f119842,plain,
( spl0_1400
| ~ spl0_13
| ~ spl0_119
| ~ spl0_1194 ),
inference(avatar_split_clause,[],[f68176,f67311,f1635,f1080,f119840]) ).
fof(f119840,plain,
( spl0_1400
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X1,X2),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f1080,plain,
( spl0_13
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1635,plain,
( spl0_119
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f67311,plain,
( spl0_1194
<=> ! [X2,X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool),X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f68176,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X1,X2),tc_bool),tc_bool) = X0 )
| ~ spl0_119
| ~ spl0_1194 ),
inference(resolution,[],[f67312,f1636]) ).
fof(f1636,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1 )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1635]) ).
fof(f67312,plain,
( ! [X2,X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool),X2,tc_bool)
| ~ spl0_1194 ),
inference(avatar_component_clause,[],[f67311]) ).
fof(f119838,plain,
( spl0_1399
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1398 ),
inference(avatar_split_clause,[],[f119834,f119831,f18286,f2678,f119836]) ).
fof(f119836,plain,
( spl0_1399
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),X4)))
| ~ hBOOL(hAPP(c_Set_Oimage(X2,X1,X0,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f119831,plain,
( spl0_1398
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),X4)),X1))
| ~ hBOOL(hAPP(c_Set_Oimage(X2,X1,X0,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f119834,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),X4)))
| ~ hBOOL(hAPP(c_Set_Oimage(X2,X1,X0,X3),X4)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1398 ),
inference(forward_demodulation,[],[f119832,f19417]) ).
fof(f119832,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),X4)),X1))
| ~ hBOOL(hAPP(c_Set_Oimage(X2,X1,X0,X3),X4)) )
| ~ spl0_1398 ),
inference(avatar_component_clause,[],[f119831]) ).
fof(f119833,plain,
( spl0_1398
| ~ spl0_112
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f6791,f6682,f1542,f119831]) ).
fof(f6791,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X0,X3),X4)),X1))
| ~ hBOOL(hAPP(c_Set_Oimage(X2,X1,X0,X3),X4)) )
| ~ spl0_112
| ~ spl0_353 ),
inference(resolution,[],[f6683,f1543]) ).
fof(f119829,plain,
( spl0_1397
| ~ spl0_92
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f6454,f5663,f1457,f119827]) ).
fof(f119827,plain,
( spl0_1397
<=> ! [X2,X0,X1,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f6454,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ spl0_92
| ~ spl0_344 ),
inference(superposition,[],[f1458,f5664]) ).
fof(f119825,plain,
( spl0_1396
| ~ spl0_92
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f6338,f5659,f1457,f119823]) ).
fof(f119823,plain,
( spl0_1396
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f6338,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ spl0_92
| ~ spl0_343 ),
inference(superposition,[],[f1458,f5660]) ).
fof(f119820,plain,
( spl0_1395
| ~ spl0_214
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f6244,f5655,f2886,f119818]) ).
fof(f119818,plain,
( spl0_1395
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))))
| hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f6244,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))))
| hBOOL(hAPP(X3,X4)) )
| ~ spl0_214
| ~ spl0_342 ),
inference(superposition,[],[f2887,f5656]) ).
fof(f119816,plain,
( spl0_1394
| ~ spl0_91
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f6238,f5655,f1453,f119814]) ).
fof(f119814,plain,
( spl0_1394
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f6238,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_91
| ~ spl0_342 ),
inference(superposition,[],[f1454,f5656]) ).
fof(f119812,plain,
( spl0_1393
| ~ spl0_94
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f6013,f5635,f1469,f119810]) ).
fof(f119810,plain,
( spl0_1393
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f6013,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_94
| ~ spl0_337 ),
inference(superposition,[],[f1470,f5636]) ).
fof(f119808,plain,
( spl0_1392
| ~ spl0_93
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5865,f5631,f1465,f119806]) ).
fof(f119806,plain,
( spl0_1392
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f5865,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ spl0_93
| ~ spl0_336 ),
inference(superposition,[],[f1466,f5632]) ).
fof(f119803,plain,
( spl0_1391
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f5617,f5358,f4702,f2288,f1445,f119801]) ).
fof(f119801,plain,
( spl0_1391
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_fequal(X2),X1),X0,X3,X2)),hAPP(c_fequal(X2),X1)))
| hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f5358,plain,
( spl0_325
<=> ! [X54,X20,X0,X6,X19] :
( hBOOL(hAPP(X20,X54))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X54),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f5617,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_fequal(X2),X1),X0,X3,X2)),hAPP(c_fequal(X2),X1)))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_325 ),
inference(forward_demodulation,[],[f5596,f5265]) ).
fof(f5596,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X3,X2)),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1))) )
| ~ spl0_177
| ~ spl0_325 ),
inference(resolution,[],[f5359,f2289]) ).
fof(f5359,plain,
( ! [X0,X54,X6,X19,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X54),X6))
| hBOOL(hAPP(X20,X54))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)),X6)) )
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f5358]) ).
fof(f119798,plain,
( spl0_1390
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f5590,f5354,f4702,f2288,f1445,f119796]) ).
fof(f119796,plain,
( spl0_1390
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_fequal(X2),X1),X3,X0,X2)),hAPP(c_fequal(X2),X1)))
| hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f5354,plain,
( spl0_324
<=> ! [X53,X0,X6,X19,X20] :
( hBOOL(hAPP(X19,X53))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X53),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f5590,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_fequal(X2),X1),X3,X0,X2)),hAPP(c_fequal(X2),X1)))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_324 ),
inference(forward_demodulation,[],[f5569,f5265]) ).
fof(f5569,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X3,X0,X2)),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1))) )
| ~ spl0_177
| ~ spl0_324 ),
inference(resolution,[],[f5355,f2289]) ).
fof(f5355,plain,
( ! [X0,X6,X19,X53,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X53),X6))
| hBOOL(hAPP(X19,X53))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)),X6)) )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f5354]) ).
fof(f119793,plain,
( spl0_1389
| ~ spl0_13
| ~ spl0_119
| ~ spl0_1193 ),
inference(avatar_split_clause,[],[f66312,f65865,f1635,f1080,f119791]) ).
fof(f119791,plain,
( spl0_1389
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X1,X2),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f65865,plain,
( spl0_1193
<=> ! [X2,X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool),X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f66312,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X1,X2),tc_bool),tc_bool) = X0 )
| ~ spl0_119
| ~ spl0_1193 ),
inference(resolution,[],[f65866,f1636]) ).
fof(f65866,plain,
( ! [X2,X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool),X2,tc_bool)
| ~ spl0_1193 ),
inference(avatar_component_clause,[],[f65865]) ).
fof(f119788,plain,
( spl0_1388
| ~ spl0_94
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f5526,f5346,f1469,f119786]) ).
fof(f119786,plain,
( spl0_1388
<=> ! [X0,X3,X2,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f5346,plain,
( spl0_322
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f5526,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_94
| ~ spl0_322 ),
inference(resolution,[],[f5347,f1470]) ).
fof(f5347,plain,
( ! [X0,X8,X6,X7] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f5346]) ).
fof(f119783,plain,
( spl0_1387
| ~ spl0_93
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f5525,f5346,f1465,f119781]) ).
fof(f119781,plain,
( spl0_1387
<=> ! [X0,X3,X2,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f5525,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ spl0_93
| ~ spl0_322 ),
inference(resolution,[],[f5347,f1466]) ).
fof(f119777,plain,
( spl0_1386
| ~ spl0_95
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f5493,f5342,f1473,f119775]) ).
fof(f119775,plain,
( spl0_1386
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f1473,plain,
( spl0_95
<=> ! [X6,X0,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f5493,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| ~ spl0_95
| ~ spl0_321 ),
inference(resolution,[],[f5343,f1474]) ).
fof(f1474,plain,
( ! [X0,X6,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1473]) ).
fof(f119772,plain,
( spl0_1385
| ~ spl0_92
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f5483,f5342,f1457,f119770]) ).
fof(f119770,plain,
( spl0_1385
<=> ! [X2,X0,X1,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f5483,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ spl0_92
| ~ spl0_321 ),
inference(resolution,[],[f5343,f1458]) ).
fof(f119767,plain,
( spl0_1384
| ~ spl0_91
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f5482,f5342,f1453,f119765]) ).
fof(f119765,plain,
( spl0_1384
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f5482,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| ~ spl0_91
| ~ spl0_321 ),
inference(resolution,[],[f5343,f1454]) ).
fof(f119761,plain,
( spl0_1383
| ~ spl0_52
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4642,f4514,f1247,f119759]) ).
fof(f119759,plain,
( spl0_1383
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X4),X0),c_Set_Oimage(c_COMBK(X0,X1,X2),X5,X6,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X6),X3),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f4642,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X4),X0),c_Set_Oimage(c_COMBK(X0,X1,X2),X5,X6,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X6),X3),X5)) )
| ~ spl0_52
| ~ spl0_303 ),
inference(superposition,[],[f4515,f1248]) ).
fof(f119671,plain,
( spl0_1382
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1381 ),
inference(avatar_split_clause,[],[f119667,f119664,f18286,f2678,f119669]) ).
fof(f119669,plain,
( spl0_1382
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(X3,X2,X0,X4),X4),hAPP(X3,X1),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f119664,plain,
( spl0_1381
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(X3,X2,X0,X4),X4),hAPP(X3,X1),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f119667,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(X3,X2,X0,X4),X4),hAPP(X3,X1),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1381 ),
inference(forward_demodulation,[],[f119665,f19417]) ).
fof(f119665,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(X3,X2,X0,X4),X4),hAPP(X3,X1),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_1381 ),
inference(avatar_component_clause,[],[f119664]) ).
fof(f119666,plain,
( spl0_1381
| ~ spl0_187
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4627,f4514,f2658,f119664]) ).
fof(f4627,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(X3,X2,X0,X4),X4),hAPP(X3,X1),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_187
| ~ spl0_303 ),
inference(resolution,[],[f4515,f2659]) ).
fof(f119573,plain,
( spl0_1380
| ~ spl0_1187
| ~ spl0_1190 ),
inference(avatar_split_clause,[],[f65395,f65089,f63106,f119571]) ).
fof(f119571,plain,
( spl0_1380
<=> ! [X2,X0,X1] : c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f63106,plain,
( spl0_1187
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool),X2,tc_bool) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f65089,plain,
( spl0_1190
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f65395,plain,
( ! [X2,X0,X1] : c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool)
| ~ spl0_1187
| ~ spl0_1190 ),
inference(superposition,[],[f65090,f63107]) ).
fof(f63107,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool),X2,tc_bool) = X2
| ~ spl0_1187 ),
inference(avatar_component_clause,[],[f63106]) ).
fof(f65090,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool),tc_bool) = X0
| ~ spl0_1190 ),
inference(avatar_component_clause,[],[f65089]) ).
fof(f119569,plain,
( spl0_1379
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1378 ),
inference(avatar_split_clause,[],[f119565,f119562,f18286,f2678,f119567]) ).
fof(f119567,plain,
( spl0_1379
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(hAPP(X3,X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(X3,X2,X0,X4),X4),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f119562,plain,
( spl0_1378
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(hAPP(X3,X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(X3,X2,X0,X4),X4),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f119565,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(hAPP(X3,X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(X3,X2,X0,X4),X4),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1378 ),
inference(forward_demodulation,[],[f119563,f19417]) ).
fof(f119563,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(hAPP(X3,X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(X3,X2,X0,X4),X4),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_1378 ),
inference(avatar_component_clause,[],[f119562]) ).
fof(f119564,plain,
( spl0_1378
| ~ spl0_185
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4626,f4514,f2650,f119562]) ).
fof(f2650,plain,
( spl0_185
<=> ! [X6,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f4626,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(hAPP(X3,X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(X3,X2,X0,X4),X4),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_185
| ~ spl0_303 ),
inference(resolution,[],[f4515,f2651]) ).
fof(f2651,plain,
( ! [X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f2650]) ).
fof(f119503,plain,
( spl0_1377
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1376 ),
inference(avatar_split_clause,[],[f119499,f119496,f18286,f2678,f119501]) ).
fof(f119501,plain,
( spl0_1377
<=> ! [X0] :
( hBOOL(hAPP(X0,v_Lba____))
| ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f119496,plain,
( spl0_1376
<=> ! [X0] :
( ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f119499,plain,
( ! [X0] :
( hBOOL(hAPP(X0,v_Lba____))
| ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1376 ),
inference(forward_demodulation,[],[f119497,f19417]) ).
fof(f119497,plain,
( ! [X0] :
( ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),X0)) )
| ~ spl0_1376 ),
inference(avatar_component_clause,[],[f119496]) ).
fof(f119498,plain,
( spl0_1376
| ~ spl0_114
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4610,f4502,f1550,f119496]) ).
fof(f4610,plain,
( ! [X0] :
( ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),X0)) )
| ~ spl0_114
| ~ spl0_300 ),
inference(resolution,[],[f4503,f1552]) ).
fof(f119437,plain,
( spl0_1375
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1374 ),
inference(avatar_split_clause,[],[f119433,f119430,f18286,f2678,f119435]) ).
fof(f119435,plain,
( spl0_1375
<=> ! [X0] :
( hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f119430,plain,
( spl0_1374
<=> ! [X0] :
( ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f119433,plain,
( ! [X0] :
( hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1374 ),
inference(forward_demodulation,[],[f119431,f19417]) ).
fof(f119431,plain,
( ! [X0] :
( ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0)) )
| ~ spl0_1374 ),
inference(avatar_component_clause,[],[f119430]) ).
fof(f119432,plain,
( spl0_1374
| ~ spl0_111
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4609,f4502,f1537,f119430]) ).
fof(f4609,plain,
( ! [X0] :
( ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0)) )
| ~ spl0_111
| ~ spl0_300 ),
inference(resolution,[],[f4503,f1539]) ).
fof(f119413,plain,
( spl0_1373
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1371 ),
inference(avatar_split_clause,[],[f119404,f119401,f18286,f2678,f119411]) ).
fof(f119411,plain,
( spl0_1373
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f119401,plain,
( spl0_1371
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f119404,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X3)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1371 ),
inference(forward_demodulation,[],[f119402,f19417]) ).
fof(f119402,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X3)) )
| ~ spl0_1371 ),
inference(avatar_component_clause,[],[f119401]) ).
fof(f119408,plain,
( spl0_1372
| ~ spl0_1184
| ~ spl0_1190 ),
inference(avatar_split_clause,[],[f65394,f65089,f62696,f119406]) ).
fof(f119406,plain,
( spl0_1372
<=> ! [X2,X0,X1] : c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f62696,plain,
( spl0_1184
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool),X2,tc_bool) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f65394,plain,
( ! [X2,X0,X1] : c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool)
| ~ spl0_1184
| ~ spl0_1190 ),
inference(superposition,[],[f65090,f62697]) ).
fof(f62697,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool),X2,tc_bool) = X2
| ~ spl0_1184 ),
inference(avatar_component_clause,[],[f62696]) ).
fof(f119403,plain,
( spl0_1371
| ~ spl0_157
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f4243,f4118,f2208,f119401]) ).
fof(f4243,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X3)) )
| ~ spl0_157
| ~ spl0_280 ),
inference(resolution,[],[f4119,f2209]) ).
fof(f119049,plain,
( spl0_1370
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1369 ),
inference(avatar_split_clause,[],[f119045,f119042,f18286,f2678,f119047]) ).
fof(f119047,plain,
( spl0_1370
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f119042,plain,
( spl0_1369
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f119045,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1369 ),
inference(forward_demodulation,[],[f119043,f19417]) ).
fof(f119043,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_1369 ),
inference(avatar_component_clause,[],[f119042]) ).
fof(f119044,plain,
( spl0_1369
| ~ spl0_152
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f4242,f4118,f2188,f119042]) ).
fof(f4242,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_152
| ~ spl0_280 ),
inference(resolution,[],[f4119,f2189]) ).
fof(f118703,plain,
( spl0_1368
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1367 ),
inference(avatar_split_clause,[],[f118699,f118696,f18286,f2678,f118701]) ).
fof(f118701,plain,
( spl0_1368
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f118696,plain,
( spl0_1367
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f118699,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1367 ),
inference(forward_demodulation,[],[f118697,f19417]) ).
fof(f118697,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_1367 ),
inference(avatar_component_clause,[],[f118696]) ).
fof(f118698,plain,
( spl0_1367
| ~ spl0_150
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f4241,f4118,f2180,f118696]) ).
fof(f4241,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_150
| ~ spl0_280 ),
inference(resolution,[],[f4119,f2181]) ).
fof(f118345,plain,
( spl0_1366
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1365 ),
inference(avatar_split_clause,[],[f118341,f118338,f18286,f2678,f118343]) ).
fof(f118343,plain,
( spl0_1366
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f118338,plain,
( spl0_1365
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f118341,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1365 ),
inference(forward_demodulation,[],[f118339,f19417]) ).
fof(f118339,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_1365 ),
inference(avatar_component_clause,[],[f118338]) ).
fof(f118340,plain,
( spl0_1365
| ~ spl0_161
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f4223,f4114,f2224,f118338]) ).
fof(f2224,plain,
( spl0_161
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f4223,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_161
| ~ spl0_279 ),
inference(resolution,[],[f4115,f2225]) ).
fof(f2225,plain,
( ! [X0,X6,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X7 )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f2224]) ).
fof(f118336,plain,
( ~ spl0_17
| spl0_1337
| ~ spl0_156
| ~ spl0_1175 ),
inference(avatar_split_clause,[],[f59713,f59551,f2204,f116634,f1100]) ).
fof(f1100,plain,
( spl0_17
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f116634,plain,
( spl0_1337
<=> ! [X2,X0,X1] :
( c_lessequals(X2,X1,tc_bool)
| ~ c_lessequals(X2,c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f2204,plain,
( spl0_156
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X5,X0)
| c_lessequals(X1,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f59551,plain,
( spl0_1175
<=> ! [X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f59713,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool),tc_bool)
| ~ class_Orderings_Opreorder(tc_bool)
| c_lessequals(X0,X2,tc_bool) )
| ~ spl0_156
| ~ spl0_1175 ),
inference(resolution,[],[f59552,f2205]) ).
fof(f2205,plain,
( ! [X2,X0,X1,X5] :
( ~ c_lessequals(X2,X5,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X5,X0) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f2204]) ).
fof(f59552,plain,
( ! [X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool)
| ~ spl0_1175 ),
inference(avatar_component_clause,[],[f59551]) ).
fof(f117999,plain,
( spl0_1364
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1363 ),
inference(avatar_split_clause,[],[f117995,f117992,f18286,f2678,f117997]) ).
fof(f117997,plain,
( spl0_1364
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f117992,plain,
( spl0_1363
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f117995,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1363 ),
inference(forward_demodulation,[],[f117993,f19417]) ).
fof(f117993,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_1363 ),
inference(avatar_component_clause,[],[f117992]) ).
fof(f117994,plain,
( spl0_1363
| ~ spl0_160
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f4222,f4114,f2220,f117992]) ).
fof(f2220,plain,
( spl0_160
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f4222,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_160
| ~ spl0_279 ),
inference(resolution,[],[f4115,f2221]) ).
fof(f2221,plain,
( ! [X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f2220]) ).
fof(f117646,plain,
( spl0_1362
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1361 ),
inference(avatar_split_clause,[],[f117642,f117639,f18286,f2678,f117644]) ).
fof(f117644,plain,
( spl0_1362
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f117639,plain,
( spl0_1361
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f117642,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1361 ),
inference(forward_demodulation,[],[f117640,f19417]) ).
fof(f117640,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ spl0_1361 ),
inference(avatar_component_clause,[],[f117639]) ).
fof(f117641,plain,
( spl0_1361
| ~ spl0_157
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f4221,f4114,f2208,f117639]) ).
fof(f4221,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ spl0_157
| ~ spl0_279 ),
inference(resolution,[],[f4115,f2209]) ).
fof(f117637,plain,
( spl0_1360
| ~ spl0_142
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4192,f4102,f1858,f117635]) ).
fof(f117635,plain,
( spl0_1360
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0,X1,X2),X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f4102,plain,
( spl0_276
<=> ! [X6,X10,X0,X12,X7] :
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),X7,X0,X12)
| ~ c_lessequals(X7,c_Set_Oimage(X10,X6,X12,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f4192,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0,X1,X2),X3,X2,X1) )
| ~ spl0_142
| ~ spl0_276 ),
inference(superposition,[],[f4103,f1859]) ).
fof(f4103,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ c_lessequals(X7,c_Set_Oimage(X10,X6,X12,X0),tc_fun(X0,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),X7,X0,X12) )
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f4102]) ).
fof(f117633,plain,
( spl0_1359
| ~ spl0_223
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f4064,f3671,f3079,f117631]) ).
fof(f117631,plain,
( spl0_1359
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f3671,plain,
( spl0_271
<=> ! [X20,X0,X6,X1] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X6,X20,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f4064,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) )
| ~ spl0_223
| ~ spl0_271 ),
inference(resolution,[],[f3672,f3080]) ).
fof(f3672,plain,
( ! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X6,X20,X0))) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f3671]) ).
fof(f117629,plain,
( spl0_1358
| ~ spl0_223
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4043,f3659,f3079,f117627]) ).
fof(f117627,plain,
( spl0_1358
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f4043,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) )
| ~ spl0_223
| ~ spl0_268 ),
inference(resolution,[],[f3660,f3080]) ).
fof(f117625,plain,
( spl0_1357
| ~ spl0_239
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4035,f3659,f3152,f117623]) ).
fof(f117623,plain,
( spl0_1357
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X0,X3)))
| c_HOL_Oundefined(X5) = hAPP(c_FuncSet_Orestrict(X4,X2,X3,X5),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f3152,plain,
( spl0_239
<=> ! [X10,X0,X12,X6,X1] :
( hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hAPP(c_FuncSet_Orestrict(X10,X6,X12,X0),X1) = c_HOL_Oundefined(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f4035,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X0,X3)))
| c_HOL_Oundefined(X5) = hAPP(c_FuncSet_Orestrict(X4,X2,X3,X5),X1) )
| ~ spl0_239
| ~ spl0_268 ),
inference(resolution,[],[f3660,f3153]) ).
fof(f3153,plain,
( ! [X10,X0,X1,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hAPP(c_FuncSet_Orestrict(X10,X6,X12,X0),X1) = c_HOL_Oundefined(X0) )
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f3152]) ).
fof(f117620,plain,
( spl0_1356
| ~ spl0_151
| ~ spl0_1226 ),
inference(avatar_split_clause,[],[f91383,f91013,f2184,f117618]) ).
fof(f117618,plain,
( spl0_1356
<=> ! [X2,X4,X0,X3,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Set_OPow(X1,X2),X1),X3,X4),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f2184,plain,
( spl0_151
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_OPow(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f91013,plain,
( spl0_1226
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OInf__class_OInf(c_COMBK(X0,X1,X2),tc_bool),tc_bool) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f91383,plain,
( ! [X2,X3,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Set_OPow(X1,X2),X1),X3,X4),tc_bool),tc_bool) = X0
| ~ spl0_151
| ~ spl0_1226 ),
inference(resolution,[],[f91014,f2185]) ).
fof(f2185,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_OPow(X0,X1),X0))
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f2184]) ).
fof(f91014,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OInf__class_OInf(c_COMBK(X0,X1,X2),tc_bool),tc_bool) = X3 )
| ~ spl0_1226 ),
inference(avatar_component_clause,[],[f91013]) ).
fof(f117616,plain,
( spl0_1355
| ~ spl0_223
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f4026,f3655,f3079,f117614]) ).
fof(f117614,plain,
( spl0_1355
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f3655,plain,
( spl0_267
<=> ! [X20,X0,X6,X3] :
( ~ hBOOL(hAPP(X20,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X6,X20,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f4026,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) )
| ~ spl0_223
| ~ spl0_267 ),
inference(resolution,[],[f3656,f3080]) ).
fof(f3656,plain,
( ! [X3,X0,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(X20,X3))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X6,X20,X0))) )
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f3655]) ).
fof(f117612,plain,
( spl0_1354
| ~ spl0_223
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3953,f3631,f3079,f117610]) ).
fof(f117610,plain,
( spl0_1354
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f3631,plain,
( spl0_261
<=> ! [X20,X0,X6,X1] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XbexE__1__1(X6,X20,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f3953,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) )
| ~ spl0_223
| ~ spl0_261 ),
inference(resolution,[],[f3632,f3080]) ).
fof(f3632,plain,
( ! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XbexE__1__1(X6,X20,X0))) )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f3631]) ).
fof(f117608,plain,
( spl0_1353
| ~ spl0_223
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3936,f3627,f3079,f117606]) ).
fof(f117606,plain,
( spl0_1353
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f3627,plain,
( spl0_260
<=> ! [X20,X0,X6,X1] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XbexI__1__1(X6,X20,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f3936,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_OPow(X2,X3),X0,tc_fun(X3,tc_bool))))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) )
| ~ spl0_223
| ~ spl0_260 ),
inference(resolution,[],[f3628,f3080]) ).
fof(f3628,plain,
( ! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XbexI__1__1(X6,X20,X0))) )
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f3627]) ).
fof(f117604,plain,
( spl0_1352
| ~ spl0_223
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3919,f3623,f3079,f117602]) ).
fof(f117602,plain,
( spl0_1352
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,c_Set_OPow(X2,X3),tc_fun(X3,tc_bool),X4),X1)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f3623,plain,
( spl0_259
<=> ! [X10,X0,X12,X6,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hAPP(X10,X1) = hAPP(c_FuncSet_Orestrict(X10,X6,X12,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f3919,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,c_Set_OPow(X2,X3),tc_fun(X3,tc_bool),X4),X1)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) )
| ~ spl0_223
| ~ spl0_259 ),
inference(resolution,[],[f3624,f3080]) ).
fof(f3624,plain,
( ! [X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hAPP(X10,X1) = hAPP(c_FuncSet_Orestrict(X10,X6,X12,X0),X1) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f3623]) ).
fof(f117599,plain,
( spl0_1351
| ~ spl0_204
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3734,f3584,f2835,f117597]) ).
fof(f117597,plain,
( spl0_1351
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f2835,plain,
( spl0_204
<=> ! [X6,X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f3734,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0
| ~ spl0_204
| ~ spl0_250 ),
inference(superposition,[],[f3585,f2836]) ).
fof(f2836,plain,
( ! [X0,X6,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2835]) ).
fof(f117595,plain,
( spl0_1350
| ~ spl0_78
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f3494,f3124,f1377,f117593]) ).
fof(f117593,plain,
( spl0_1350
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f3494,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_232 ),
inference(resolution,[],[f3125,f1378]) ).
fof(f117591,plain,
( spl0_1349
| ~ spl0_78
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f3465,f3120,f1377,f117589]) ).
fof(f117589,plain,
( spl0_1349
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f3465,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_231 ),
inference(resolution,[],[f3121,f1378]) ).
fof(f117587,plain,
( spl0_1348
| ~ spl0_78
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f3270,f3063,f1377,f117585]) ).
fof(f117585,plain,
( spl0_1348
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f3270,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_219 ),
inference(resolution,[],[f3064,f1378]) ).
fof(f117583,plain,
( spl0_1347
| ~ spl0_78
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f3234,f3059,f1377,f117581]) ).
fof(f117581,plain,
( spl0_1347
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f3234,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_218 ),
inference(resolution,[],[f3060,f1378]) ).
fof(f117579,plain,
( spl0_1346
| ~ spl0_185
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2999,f2850,f2650,f117577]) ).
fof(f117577,plain,
( spl0_1346
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_FuncSet_Orestrict(X0,X1,X2,X3),c_Complete__Lattice_OSup__class_OSup(c_FuncSet_Oextensional(X1,X2,X3),tc_fun(X2,X3)),tc_fun(X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f2850,plain,
( spl0_205
<=> ! [X10,X0,X12,X6] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_Oextensional(X6,X0,X12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2999,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_FuncSet_Orestrict(X0,X1,X2,X3),c_Complete__Lattice_OSup__class_OSup(c_FuncSet_Oextensional(X1,X2,X3),tc_fun(X2,X3)),tc_fun(X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X3)) )
| ~ spl0_185
| ~ spl0_205 ),
inference(resolution,[],[f2851,f2651]) ).
fof(f2851,plain,
( ! [X10,X0,X6,X12] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_Oextensional(X6,X0,X12)))
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2850]) ).
fof(f117574,plain,
( spl0_1345
| ~ spl0_110
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1181 ),
inference(avatar_split_clause,[],[f62349,f61954,f18286,f2678,f1533,f117572]) ).
fof(f117572,plain,
( spl0_1345
<=> ! [X4,X0,X3,X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Set_OPow(X1,X0),X1),X2,X3),tc_bool),X4,tc_bool) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f61954,plain,
( spl0_1181
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(X0,X1,X2),tc_bool),X3,tc_bool) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f62349,plain,
( ! [X2,X3,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Set_OPow(X1,X0),X1),X2,X3),tc_bool),X4,tc_bool) = X4
| ~ spl0_110
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1181 ),
inference(forward_demodulation,[],[f62284,f19417]) ).
fof(f62284,plain,
( ! [X2,X3,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),c_Set_OPow(X1,X0)),X2,X3),tc_bool),X4,tc_bool) = X4
| ~ spl0_110
| ~ spl0_1181 ),
inference(resolution,[],[f61955,f1534]) ).
fof(f61955,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(X0,X1,X2),tc_bool),X3,tc_bool) = X3 )
| ~ spl0_1181 ),
inference(avatar_component_clause,[],[f61954]) ).
fof(f117570,plain,
( spl0_1344
| ~ spl0_187
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2998,f2850,f2658,f117568]) ).
fof(f117568,plain,
( spl0_1344
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_FuncSet_Oextensional(X0,X1,X2),tc_fun(X1,X2)),c_FuncSet_Orestrict(X3,X0,X1,X2),tc_fun(X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f2998,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_FuncSet_Oextensional(X0,X1,X2),tc_fun(X1,X2)),c_FuncSet_Orestrict(X3,X0,X1,X2),tc_fun(X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2)) )
| ~ spl0_187
| ~ spl0_205 ),
inference(resolution,[],[f2851,f2659]) ).
fof(f117566,plain,
( spl0_1343
| ~ spl0_121
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2990,f2835,f1643,f117564]) ).
fof(f117564,plain,
( spl0_1343
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != X0
| c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f1643,plain,
( spl0_121
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f2990,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != X0
| c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) )
| ~ spl0_121
| ~ spl0_204 ),
inference(superposition,[],[f1644,f2836]) ).
fof(f1644,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) != X1
| c_lessequals(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1643]) ).
fof(f117562,plain,
( spl0_1342
| ~ spl0_158
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2507,f2216,f2212,f117560]) ).
fof(f117560,plain,
( spl0_1342
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( ~ c_lessequals(hAPP(X0,hAPP(X1,X5)),X5,X6)
| ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBB(X0,X1,X2,X3,X4),X6),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f2507,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_lessequals(hAPP(X0,hAPP(X1,X5)),X5,X6)
| ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBB(X0,X1,X2,X3,X4),X6),X5,X6) )
| ~ spl0_158
| ~ spl0_159 ),
inference(superposition,[],[f2213,f2217]) ).
fof(f117558,plain,
( spl0_1341
| ~ spl0_123
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f2016,f1834,f1781,f117556]) ).
fof(f117556,plain,
( spl0_1341
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2) = X1
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f1781,plain,
( spl0_123
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1834,plain,
( spl0_136
<=> ! [X4,X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X1,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f2016,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2) = X1
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_123
| ~ spl0_136 ),
inference(resolution,[],[f1835,f1782]) ).
fof(f1782,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1781]) ).
fof(f1835,plain,
( ! [X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X1,X0)
| ~ c_lessequals(X4,X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1834]) ).
fof(f117554,plain,
( spl0_1340
| ~ spl0_123
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2004,f1830,f1781,f117552]) ).
fof(f117552,plain,
( spl0_1340
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2) = X1
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f1830,plain,
( spl0_135
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f2004,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2) = X1
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_123
| ~ spl0_135 ),
inference(resolution,[],[f1831,f1782]) ).
fof(f1831,plain,
( ! [X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X1,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1830]) ).
fof(f117550,plain,
( spl0_1339
| ~ spl0_123
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1930,f1805,f1781,f117548]) ).
fof(f117548,plain,
( spl0_1339
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) = X0
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f1930,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) = X0
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_123
| ~ spl0_129 ),
inference(resolution,[],[f1806,f1782]) ).
fof(f117546,plain,
( spl0_1338
| ~ spl0_123
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1918,f1801,f1781,f117544]) ).
fof(f117544,plain,
( spl0_1338
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) = X0
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f1918,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) = X0
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_123
| ~ spl0_128 ),
inference(resolution,[],[f1802,f1782]) ).
fof(f116636,plain,
( ~ spl0_13
| spl0_1337
| ~ spl0_129
| ~ spl0_1174 ),
inference(avatar_split_clause,[],[f59333,f59044,f1805,f116634,f1080]) ).
fof(f59044,plain,
( spl0_1174
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f59333,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,X1,tc_bool)
| ~ c_lessequals(X2,c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_129
| ~ spl0_1174 ),
inference(superposition,[],[f1806,f59045]) ).
fof(f59045,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool) = X1
| ~ spl0_1174 ),
inference(avatar_component_clause,[],[f59044]) ).
fof(f111917,plain,
( spl0_1336
| ~ spl0_213
| ~ spl0_764
| ~ spl0_1228 ),
inference(avatar_split_clause,[],[f94335,f93049,f20188,f2882,f111915]) ).
fof(f111915,plain,
( spl0_1336
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),X1,tc_fun(X0,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f2882,plain,
( spl0_213
<=> ! [X6,X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f93049,plain,
( spl0_1228
<=> ! [X0] :
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(X0,tc_bool)
| ~ hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f94335,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),X1,tc_fun(X0,tc_bool)),tc_bool)
| ~ spl0_213
| ~ spl0_764
| ~ spl0_1228 ),
inference(forward_demodulation,[],[f94302,f20189]) ).
fof(f94302,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1,tc_fun(X0,tc_bool)),tc_bool)
| ~ spl0_213
| ~ spl0_1228 ),
inference(resolution,[],[f93050,f2883]) ).
fof(f2883,plain,
( ! [X0,X1,X6] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X1))
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2882]) ).
fof(f93050,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_bool)))
| c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(X0,tc_bool) )
| ~ spl0_1228 ),
inference(avatar_component_clause,[],[f93049]) ).
fof(f111690,plain,
( spl0_1335
| ~ spl0_52
| ~ spl0_1186 ),
inference(avatar_split_clause,[],[f62981,f62863,f1247,f111688]) ).
fof(f111688,plain,
( spl0_1335
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_COMBK(X0,X1,X2),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f62981,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_COMBK(X0,X1,X2),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) )
| ~ spl0_52
| ~ spl0_1186 ),
inference(superposition,[],[f62864,f1248]) ).
fof(f111686,plain,
( spl0_1334
| ~ spl0_29
| ~ spl0_1182 ),
inference(avatar_split_clause,[],[f62011,f61960,f1155,f111684]) ).
fof(f111684,plain,
( spl0_1334
<=> ! [X5,X4,X2,X0,X3,X1] :
( hBOOL(X1)
| c_Set_Oimage(X2,c_COMBI(X0),X3,X4) = c_Set_Oimage(c_Fun_Ofun__upd(X2,X1,X5,X3,X4),c_COMBI(X0),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f62011,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(X1)
| c_Set_Oimage(X2,c_COMBI(X0),X3,X4) = c_Set_Oimage(c_Fun_Ofun__upd(X2,X1,X5,X3,X4),c_COMBI(X0),X3,X4) )
| ~ spl0_29
| ~ spl0_1182 ),
inference(superposition,[],[f61961,f1156]) ).
fof(f111682,plain,
( spl0_1333
| ~ spl0_107
| ~ spl0_192
| ~ spl0_529
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56822,f18286,f12582,f2678,f1521,f111680]) ).
fof(f111680,plain,
( spl0_1333
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Complete__Lattice_OSup__class_OSup(X0,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f1521,plain,
( spl0_107
<=> ! [X6,X0] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f12582,plain,
( spl0_529
<=> ! [X0,X8,X6,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X8))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X6,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f56822,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Complete__Lattice_OSup__class_OSup(X0,tc_fun(X1,tc_bool)) )
| ~ spl0_107
| ~ spl0_192
| ~ spl0_529
| ~ spl0_699 ),
inference(forward_demodulation,[],[f12602,f19417]) ).
fof(f12602,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Complete__Lattice_OSup__class_OSup(X0,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X0)) )
| ~ spl0_107
| ~ spl0_529 ),
inference(forward_demodulation,[],[f12595,f1522]) ).
fof(f1522,plain,
( ! [X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1521]) ).
fof(f12595,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Complete__Lattice_OSup__class_OSup(X0,tc_fun(X1,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X0)) )
| ~ spl0_107
| ~ spl0_529 ),
inference(superposition,[],[f12583,f1522]) ).
fof(f12583,plain,
( ! [X0,X1,X8,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X6,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X8)) )
| ~ spl0_529 ),
inference(avatar_component_clause,[],[f12582]) ).
fof(f111678,plain,
( spl0_1332
| ~ spl0_192
| ~ spl0_239
| ~ spl0_300
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56668,f18286,f4502,f3152,f2678,f111676]) ).
fof(f111676,plain,
( spl0_1332
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,X3))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_HOL_Oundefined(X5) = hAPP(c_FuncSet_Orestrict(X4,X0,X2,X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f56668,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X1,X3))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_HOL_Oundefined(X5) = hAPP(c_FuncSet_Orestrict(X4,X0,X2,X5),X3) )
| ~ spl0_192
| ~ spl0_239
| ~ spl0_300
| ~ spl0_699 ),
inference(forward_demodulation,[],[f4592,f19417]) ).
fof(f4592,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_HOL_Oundefined(X5) = hAPP(c_FuncSet_Orestrict(X4,X0,X2,X5),X3) )
| ~ spl0_239
| ~ spl0_300 ),
inference(resolution,[],[f4503,f3153]) ).
fof(f111674,plain,
( spl0_1331
| ~ spl0_161
| ~ spl0_192
| ~ spl0_280
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56385,f18286,f4118,f2678,f2224,f111672]) ).
fof(f111672,plain,
( spl0_1331
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f56385,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) )
| ~ spl0_161
| ~ spl0_192
| ~ spl0_280
| ~ spl0_699 ),
inference(forward_demodulation,[],[f4245,f19417]) ).
fof(f4245,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) )
| ~ spl0_161
| ~ spl0_280 ),
inference(resolution,[],[f4119,f2225]) ).
fof(f111670,plain,
( spl0_1330
| ~ spl0_904
| ~ spl0_1228 ),
inference(avatar_split_clause,[],[f94315,f93049,f32489,f111668]) ).
fof(f111668,plain,
( spl0_1330
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(X0,hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(X1,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f32489,plain,
( spl0_904
<=> ! [X2,X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f94315,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(X0,hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(X1,tc_bool)),tc_bool)
| ~ spl0_904
| ~ spl0_1228 ),
inference(resolution,[],[f93050,f32490]) ).
fof(f32490,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X1))
| ~ spl0_904 ),
inference(avatar_component_clause,[],[f32489]) ).
fof(f111666,plain,
( spl0_1329
| ~ spl0_160
| ~ spl0_192
| ~ spl0_280
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56384,f18286,f4118,f2678,f2220,f111664]) ).
fof(f111664,plain,
( spl0_1329
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f56384,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_160
| ~ spl0_192
| ~ spl0_280
| ~ spl0_699 ),
inference(forward_demodulation,[],[f4244,f19417]) ).
fof(f4244,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_160
| ~ spl0_280 ),
inference(resolution,[],[f4119,f2221]) ).
fof(f111662,plain,
( spl0_1328
| ~ spl0_152
| ~ spl0_192
| ~ spl0_279
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56379,f18286,f4114,f2678,f2188,f111660]) ).
fof(f111660,plain,
( spl0_1328
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f56379,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) )
| ~ spl0_152
| ~ spl0_192
| ~ spl0_279
| ~ spl0_699 ),
inference(forward_demodulation,[],[f4220,f19417]) ).
fof(f4220,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) )
| ~ spl0_152
| ~ spl0_279 ),
inference(resolution,[],[f4115,f2189]) ).
fof(f111658,plain,
( spl0_1327
| ~ spl0_150
| ~ spl0_192
| ~ spl0_279
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56378,f18286,f4114,f2678,f2180,f111656]) ).
fof(f111656,plain,
( spl0_1327
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f56378,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_150
| ~ spl0_192
| ~ spl0_279
| ~ spl0_699 ),
inference(forward_demodulation,[],[f4219,f19417]) ).
fof(f4219,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X2))
| c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_150
| ~ spl0_279 ),
inference(resolution,[],[f4115,f2181]) ).
fof(f111654,plain,
( spl0_1326
| ~ spl0_46
| ~ spl0_588 ),
inference(avatar_split_clause,[],[f14529,f14519,f1223,f111652]) ).
fof(f111652,plain,
( spl0_1326
<=> ! [X0,X3,X2,X1] :
( hAPP(c_fequal(X0),X1) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool))
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f1223,plain,
( spl0_46
<=> ! [X6,X0] : c_Lattices_Oupper__semilattice__class_Osup(X6,X6,tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f14519,plain,
( spl0_588
<=> ! [X4,X0,X14,X3,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X14),hAPP(c_fequal(X0),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f14529,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_fequal(X0),X1) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool))
| X1 = X3 )
| ~ spl0_46
| ~ spl0_588 ),
inference(duplicate_literal_removal,[],[f14522]) ).
fof(f14522,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_fequal(X0),X1) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool))
| X1 = X3
| X1 = X3 )
| ~ spl0_46
| ~ spl0_588 ),
inference(superposition,[],[f14520,f1224]) ).
fof(f1224,plain,
( ! [X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(X6,X6,tc_fun(X0,tc_bool)) = X6
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f1223]) ).
fof(f14520,plain,
( ! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X14),hAPP(c_fequal(X0),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 )
| ~ spl0_588 ),
inference(avatar_component_clause,[],[f14519]) ).
fof(f111650,plain,
( spl0_1325
| ~ spl0_89
| ~ spl0_533 ),
inference(avatar_split_clause,[],[f12622,f12619,f1445,f111648]) ).
fof(f111648,plain,
( spl0_1325
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f12619,plain,
( spl0_533
<=> ! [X4,X0,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f12622,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X1 = X2 )
| ~ spl0_89
| ~ spl0_533 ),
inference(superposition,[],[f12620,f1446]) ).
fof(f12620,plain,
( ! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X3 = X4 )
| ~ spl0_533 ),
inference(avatar_component_clause,[],[f12619]) ).
fof(f111644,plain,
( spl0_1324
| ~ spl0_281
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f10086,f10082,f4122,f111642]) ).
fof(f111642,plain,
( spl0_1324
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| hBOOL(hAPP(hAPP(c_in(X2),X0),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X0),hAPP(c_fequal(X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f4122,plain,
( spl0_281
<=> ! [X0,X14,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f10086,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| hBOOL(hAPP(hAPP(c_in(X2),X0),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X0),hAPP(c_fequal(X2),X1))) )
| ~ spl0_281
| ~ spl0_454 ),
inference(resolution,[],[f10083,f4123]) ).
fof(f4123,plain,
( ! [X0,X6,X7,X14] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X6)) )
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f4122]) ).
fof(f111640,plain,
( spl0_1323
| ~ spl0_25
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f7662,f7556,f1139,f111638]) ).
fof(f111638,plain,
( spl0_1323
<=> ! [X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X0,X1,X2,X3)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X0,X2,X3),c_Set_Oimage(X0,X1,X2,X3),X3,X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f1139,plain,
( spl0_25
<=> ! [X0,X1] : c_lessequals(X1,X1,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f7556,plain,
( spl0_389
<=> ! [X10,X0,X12,X6,X28] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_lessequals(X28,X6,tc_fun(X0,tc_bool))
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),c_Set_Oimage(X10,X28,X0,X12),X12,X0) = X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f7662,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Fun_Oinj__on(X0,X1,X2,X3)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X0,X2,X3),c_Set_Oimage(X0,X1,X2,X3),X3,X2) = X1 )
| ~ spl0_25
| ~ spl0_389 ),
inference(resolution,[],[f7557,f1140]) ).
fof(f1140,plain,
( ! [X0,X1] : c_lessequals(X1,X1,tc_fun(X0,tc_bool))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f7557,plain,
( ! [X28,X10,X0,X6,X12] :
( ~ c_lessequals(X28,X6,tc_fun(X0,tc_bool))
| ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),c_Set_Oimage(X10,X28,X0,X12),X12,X0) = X28 )
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f7556]) ).
fof(f111514,plain,
( spl0_1322
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f111510,f111507,f18286,f2678,f111512]) ).
fof(f111512,plain,
( spl0_1322
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X0,X1)))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f111507,plain,
( spl0_1321
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X0,X1)),X3))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f111510,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X0,X1)))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1321 ),
inference(forward_demodulation,[],[f111508,f19417]) ).
fof(f111508,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X0,X1)),X3))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) )
| ~ spl0_1321 ),
inference(avatar_component_clause,[],[f111507]) ).
fof(f111509,plain,
( spl0_1321
| ~ spl0_113
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f7428,f7056,f1546,f111507]) ).
fof(f7428,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X0,X1)),X3))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) )
| ~ spl0_113
| ~ spl0_377 ),
inference(resolution,[],[f7057,f1547]) ).
fof(f111504,plain,
( spl0_1320
| ~ spl0_947
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f89709,f89228,f32882,f111502]) ).
fof(f111502,plain,
( spl0_1320
<=> ! [X0,X3,X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f32882,plain,
( spl0_947
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X3),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f89228,plain,
( spl0_1224
<=> ! [X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(X1,tc_bool),tc_bool) = X0
| ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f89709,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3),tc_bool),tc_bool) = X0
| ~ spl0_947
| ~ spl0_1224 ),
inference(resolution,[],[f89229,f32883]) ).
fof(f32883,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X3),X2))
| ~ spl0_947 ),
inference(avatar_component_clause,[],[f32882]) ).
fof(f89229,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool)))
| c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(X1,tc_bool),tc_bool) = X0 )
| ~ spl0_1224 ),
inference(avatar_component_clause,[],[f89228]) ).
fof(f111378,plain,
( spl0_1319
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1318 ),
inference(avatar_split_clause,[],[f111374,f111371,f18286,f2678,f111376]) ).
fof(f111376,plain,
( spl0_1319
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X0,X1)))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f111371,plain,
( spl0_1318
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X0,X1)),X3))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f111374,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X0,X1)))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1318 ),
inference(forward_demodulation,[],[f111372,f19417]) ).
fof(f111372,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X0,X1)),X3))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) )
| ~ spl0_1318 ),
inference(avatar_component_clause,[],[f111371]) ).
fof(f111373,plain,
( spl0_1318
| ~ spl0_113
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f7358,f7052,f1546,f111371]) ).
fof(f7358,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X0,X1)),X3))
| hBOOL(hAPP(c_FuncSet_OPi(X3,X4,X0,X1),X2)) )
| ~ spl0_113
| ~ spl0_376 ),
inference(resolution,[],[f7053,f1547]) ).
fof(f111368,plain,
( spl0_1317
| ~ spl0_113
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f6642,f5703,f1546,f111366]) ).
fof(f111366,plain,
( spl0_1317
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X3))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,tc_fun(X2,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f5703,plain,
( spl0_351
<=> ! [X20,X0,X6,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Olower__semilattice__class_Oinf(X6,X20,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f6642,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X3))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,tc_fun(X2,tc_bool)),X1)) )
| ~ spl0_113
| ~ spl0_351 ),
inference(resolution,[],[f5704,f1547]) ).
fof(f5704,plain,
( ! [X0,X1,X6,X20] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Olower__semilattice__class_Oinf(X6,X20,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f5703]) ).
fof(f111364,plain,
( spl0_1316
| ~ spl0_114
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f6534,f5667,f1550,f111362]) ).
fof(f111362,plain,
( spl0_1316
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,v_Lba____),X1))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(X2,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f5667,plain,
( spl0_345
<=> ! [X4,X7,X0,X12,X6,X1] :
( ~ hBOOL(hAPP(hAPP(X7,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f6534,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,v_Lba____),X1))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(X2,tc_bool)),X1)) )
| ~ spl0_114
| ~ spl0_345 ),
inference(resolution,[],[f5668,f1552]) ).
fof(f5668,plain,
( ! [X0,X1,X6,X7,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(hAPP(X7,X1),X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_bool)),X4)) )
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f5667]) ).
fof(f111360,plain,
( spl0_1315
| ~ spl0_111
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f6533,f5667,f1537,f111358]) ).
fof(f111358,plain,
( spl0_1315
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X1))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(X2,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f6533,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X1))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(X2,tc_bool)),X1)) )
| ~ spl0_111
| ~ spl0_345 ),
inference(resolution,[],[f5668,f1539]) ).
fof(f111356,plain,
( spl0_1314
| ~ spl0_110
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f6525,f5667,f1533,f111354]) ).
fof(f111354,plain,
( spl0_1314
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_OPow(X1,X3),X0,tc_fun(X3,tc_bool),tc_fun(X4,tc_bool)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f6525,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_OPow(X1,X3),X0,tc_fun(X3,tc_bool),tc_fun(X4,tc_bool)),X2)) )
| ~ spl0_110
| ~ spl0_345 ),
inference(resolution,[],[f5668,f1534]) ).
fof(f111352,plain,
( spl0_1313
| ~ spl0_112
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f6516,f5667,f1542,f111350]) ).
fof(f111350,plain,
( spl0_1313
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X0,X4,tc_fun(X5,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f6516,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X0,X4,tc_fun(X5,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_112
| ~ spl0_345 ),
inference(resolution,[],[f5668,f1543]) ).
fof(f111348,plain,
( spl0_1312
| ~ spl0_113
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f6199,f5651,f1546,f111346]) ).
fof(f111346,plain,
( spl0_1312
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(hAPP(X0,X3),X1))
| hBOOL(hAPP(c_SetInterval_Oord_OgreaterThanLessThan(X0,X3,X2,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f5651,plain,
( spl0_341
<=> ! [X42,X47,X46,X0,X25] :
( ~ hBOOL(hAPP(hAPP(X42,X46),X25))
| ~ hBOOL(hAPP(hAPP(X42,X25),X47))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThanLessThan(X42,X46,X47,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f6199,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(hAPP(X0,X3),X1))
| hBOOL(hAPP(c_SetInterval_Oord_OgreaterThanLessThan(X0,X3,X2,X4),X1)) )
| ~ spl0_113
| ~ spl0_341 ),
inference(resolution,[],[f5652,f1547]) ).
fof(f5652,plain,
( ! [X0,X46,X47,X25,X42] :
( hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThanLessThan(X42,X46,X47,X0)))
| ~ hBOOL(hAPP(hAPP(X42,X25),X47))
| ~ hBOOL(hAPP(hAPP(X42,X46),X25)) )
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f5651]) ).
fof(f111344,plain,
( spl0_1311
| ~ spl0_113
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f6176,f5647,f1546,f111342]) ).
fof(f111342,plain,
( spl0_1311
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(hAPP(X0,X3),X1))
| hBOOL(hAPP(c_SetInterval_Oord_OatLeastAtMost(X0,X3,X2,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f5647,plain,
( spl0_340
<=> ! [X41,X47,X46,X0,X25] :
( ~ hBOOL(hAPP(hAPP(X41,X46),X25))
| ~ hBOOL(hAPP(hAPP(X41,X25),X47))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastAtMost(X41,X46,X47,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f6176,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(hAPP(X0,X3),X1))
| hBOOL(hAPP(c_SetInterval_Oord_OatLeastAtMost(X0,X3,X2,X4),X1)) )
| ~ spl0_113
| ~ spl0_340 ),
inference(resolution,[],[f5648,f1547]) ).
fof(f5648,plain,
( ! [X41,X0,X46,X47,X25] :
( hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastAtMost(X41,X46,X47,X0)))
| ~ hBOOL(hAPP(hAPP(X41,X25),X47))
| ~ hBOOL(hAPP(hAPP(X41,X46),X25)) )
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f5647]) ).
fof(f111339,plain,
( spl0_1310
| ~ spl0_947
| ~ spl0_1173 ),
inference(avatar_split_clause,[],[f78036,f58341,f32882,f111337]) ).
fof(f111337,plain,
( spl0_1310
<=> ! [X0,X3,X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X2),tc_bool),X3,tc_bool) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f58341,plain,
( spl0_1173
<=> ! [X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(X0,tc_bool),X1,tc_bool) = X1
| ~ hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f78036,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X2),tc_bool),X3,tc_bool) = X3
| ~ spl0_947
| ~ spl0_1173 ),
inference(resolution,[],[f32883,f58342]) ).
fof(f58342,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_bool)))
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(X0,tc_bool),X1,tc_bool) = X1 )
| ~ spl0_1173 ),
inference(avatar_component_clause,[],[f58341]) ).
fof(f111335,plain,
( spl0_1309
| ~ spl0_188
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f6019,f5635,f2662,f111333]) ).
fof(f111333,plain,
( spl0_1309
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X4,c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X2,X5)
| c_Fun_Oinj__on(X4,X3,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f2662,plain,
( spl0_188
<=> ! [X6,X10,X0,X12,X7] :
( c_Fun_Oinj__on(X10,X7,X0,X12)
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f6019,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X2,X5)
| c_Fun_Oinj__on(X4,X3,X2,X5) )
| ~ spl0_188
| ~ spl0_337 ),
inference(superposition,[],[f2663,f5636]) ).
fof(f2663,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12)
| c_Fun_Oinj__on(X10,X7,X0,X12) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f2662]) ).
fof(f111330,plain,
( spl0_1308
| ~ spl0_89
| ~ spl0_292
| ~ spl0_317
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5971,f5631,f4702,f4166,f1445,f111328]) ).
fof(f111328,plain,
( spl0_1308
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f4166,plain,
( spl0_292
<=> ! [X0,X1,X7] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X7,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f5971,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))))
| ~ spl0_89
| ~ spl0_292
| ~ spl0_317
| ~ spl0_336 ),
inference(forward_demodulation,[],[f5899,f5265]) ).
fof(f5899,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))))
| ~ spl0_292
| ~ spl0_336 ),
inference(superposition,[],[f4167,f5632]) ).
fof(f4167,plain,
( ! [X0,X1,X7] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X7,tc_fun(X0,tc_bool))))
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f4166]) ).
fof(f111326,plain,
( spl0_1307
| ~ spl0_189
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5873,f5631,f2666,f111324]) ).
fof(f111324,plain,
( spl0_1307
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X3,X5)
| c_Fun_Oinj__on(X4,X0,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f2666,plain,
( spl0_189
<=> ! [X10,X0,X12,X6,X7] :
( c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f5873,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X3,X5)
| c_Fun_Oinj__on(X4,X0,X3,X5) )
| ~ spl0_189
| ~ spl0_336 ),
inference(superposition,[],[f2667,f5632]) ).
fof(f2667,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12)
| c_Fun_Oinj__on(X10,X6,X0,X12) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f2666]) ).
fof(f111322,plain,
( spl0_1306
| ~ spl0_112
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5790,f5627,f1542,f111320]) ).
fof(f111320,plain,
( spl0_1306
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X0,X1,X2,X3)
| hAPP(c_Hilbert__Choice_Oinv__into(X1,X0,X2,X3),hAPP(X0,X4)) = X4
| ~ hBOOL(hAPP(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f5790,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X0,X1,X2,X3)
| hAPP(c_Hilbert__Choice_Oinv__into(X1,X0,X2,X3),hAPP(X0,X4)) = X4
| ~ hBOOL(hAPP(X1,X4)) )
| ~ spl0_112
| ~ spl0_335 ),
inference(resolution,[],[f5628,f1543]) ).
fof(f111318,plain,
( spl0_1305
| ~ spl0_138
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4953,f4666,f1842,f111316]) ).
fof(f111316,plain,
( spl0_1305
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f1842,plain,
( spl0_138
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X5,X0)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f4666,plain,
( spl0_308
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f4953,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_138
| ~ spl0_308 ),
inference(resolution,[],[f4667,f1843]) ).
fof(f1843,plain,
( ! [X2,X0,X1,X5] :
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0)
| c_lessequals(X1,X5,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1842]) ).
fof(f4667,plain,
( ! [X2,X0,X1,X5] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f4666]) ).
fof(f111217,plain,
( spl0_1304
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1303 ),
inference(avatar_split_clause,[],[f111213,f111210,f18286,f2678,f111215]) ).
fof(f111215,plain,
( spl0_1304
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f111210,plain,
( spl0_1303
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f111213,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1303 ),
inference(forward_demodulation,[],[f111211,f19417]) ).
fof(f111211,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) )
| ~ spl0_1303 ),
inference(avatar_component_clause,[],[f111210]) ).
fof(f111212,plain,
( spl0_1303
| ~ spl0_29
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4939,f4662,f1155,f111210]) ).
fof(f4939,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) )
| ~ spl0_29
| ~ spl0_307 ),
inference(superposition,[],[f4663,f1156]) ).
fof(f111208,plain,
( spl0_1302
| ~ spl0_130
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4706,f4658,f1809,f111206]) ).
fof(f111206,plain,
( spl0_1302
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X0),X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f1809,plain,
( spl0_130
<=> ! [X4,X0,X1,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X4,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f4658,plain,
( spl0_306
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f4706,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X0),X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_130
| ~ spl0_306 ),
inference(resolution,[],[f4659,f1810]) ).
fof(f1810,plain,
( ! [X3,X0,X1,X4] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X1,X0)
| c_lessequals(X4,X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1809]) ).
fof(f4659,plain,
( ! [X2,X0,X1,X5] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f4658]) ).
fof(f111202,plain,
( spl0_1301
| ~ spl0_177
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4597,f4502,f2288,f111200]) ).
fof(f111200,plain,
( spl0_1301
<=> ! [X2,X0,X1] :
( ~ c_lessequals(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X2,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f4597,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X2,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) )
| ~ spl0_177
| ~ spl0_300 ),
inference(resolution,[],[f4503,f2289]) ).
fof(f111189,plain,
( spl0_1300
| ~ spl0_202
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4543,f4486,f2827,f111187]) ).
fof(f111187,plain,
( spl0_1300
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X0,c_Set_Oimage(X1,X5,X4,X2),X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f2827,plain,
( spl0_202
<=> ! [X10,X0,X12,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X10,X6,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f4543,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X0,c_Set_Oimage(X1,X5,X4,X2),X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = X5 )
| ~ spl0_202
| ~ spl0_296 ),
inference(superposition,[],[f2828,f4487]) ).
fof(f2828,plain,
( ! [X10,X0,X6,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X10,X6,X12,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6 )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2827]) ).
fof(f111086,plain,
( spl0_1299
| ~ spl0_764
| ~ spl0_1298 ),
inference(avatar_split_clause,[],[f111082,f111079,f20188,f111084]) ).
fof(f111084,plain,
( spl0_1299
<=> ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f111079,plain,
( spl0_1298
<=> ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X2,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f111082,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_764
| ~ spl0_1298 ),
inference(forward_demodulation,[],[f111080,f20189]) ).
fof(f111080,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X2,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_1298 ),
inference(avatar_component_clause,[],[f111079]) ).
fof(f111081,plain,
( spl0_1298
| ~ spl0_187
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4434,f4166,f2658,f111079]) ).
fof(f4434,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X2,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_187
| ~ spl0_292 ),
inference(resolution,[],[f4167,f2659]) ).
fof(f110974,plain,
( spl0_1297
| ~ spl0_764
| ~ spl0_1296 ),
inference(avatar_split_clause,[],[f110970,f110967,f20188,f110972]) ).
fof(f110972,plain,
( spl0_1297
<=> ! [X2,X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X1),X0),X2,tc_fun(X1,tc_bool)),X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f110967,plain,
( spl0_1296
<=> ! [X2,X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X0),X2,tc_fun(X1,tc_bool)),X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f110970,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X1),X0),X2,tc_fun(X1,tc_bool)),X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_764
| ~ spl0_1296 ),
inference(forward_demodulation,[],[f110968,f20189]) ).
fof(f110968,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X0),X2,tc_fun(X1,tc_bool)),X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_1296 ),
inference(avatar_component_clause,[],[f110967]) ).
fof(f110969,plain,
( spl0_1296
| ~ spl0_185
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4433,f4166,f2650,f110967]) ).
fof(f4433,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X0),X2,tc_fun(X1,tc_bool)),X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_185
| ~ spl0_292 ),
inference(resolution,[],[f4167,f2651]) ).
fof(f110965,plain,
( spl0_1295
| ~ spl0_106
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f4334,f4130,f1517,f110963]) ).
fof(f110963,plain,
( spl0_1295
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1517,plain,
( spl0_106
<=> ! [X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f4130,plain,
( spl0_283
<=> ! [X6,X0,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f4334,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_106
| ~ spl0_283 ),
inference(superposition,[],[f4131,f1518]) ).
fof(f1518,plain,
( ! [X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1517]) ).
fof(f4131,plain,
( ! [X0,X6,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f4130]) ).
fof(f110960,plain,
( spl0_1294
| ~ spl0_187
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f4288,f4126,f2658,f110958]) ).
fof(f110958,plain,
( spl0_1294
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f4126,plain,
( spl0_282
<=> ! [X0,X14,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f4288,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_187
| ~ spl0_282 ),
inference(resolution,[],[f4127,f2659]) ).
fof(f4127,plain,
( ! [X0,X6,X7,X14] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X7)) )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f4126]) ).
fof(f110955,plain,
( spl0_1293
| ~ spl0_185
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f4287,f4126,f2650,f110953]) ).
fof(f110953,plain,
( spl0_1293
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X0,tc_bool)),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f4287,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X0,tc_bool)),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_185
| ~ spl0_282 ),
inference(resolution,[],[f4127,f2651]) ).
fof(f110813,plain,
( spl0_1292
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f110809,f110806,f18286,f2678,f110811]) ).
fof(f110811,plain,
( spl0_1292
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f110806,plain,
( spl0_1291
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f110809,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1291 ),
inference(forward_demodulation,[],[f110807,f19417]) ).
fof(f110807,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_1291 ),
inference(avatar_component_clause,[],[f110806]) ).
fof(f110808,plain,
( spl0_1291
| ~ spl0_187
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f4265,f4122,f2658,f110806]) ).
fof(f4265,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_187
| ~ spl0_281 ),
inference(resolution,[],[f4123,f2659]) ).
fof(f110668,plain,
( spl0_1290
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f110664,f110661,f18286,f2678,f110666]) ).
fof(f110666,plain,
( spl0_1290
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f110661,plain,
( spl0_1289
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f110664,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1289 ),
inference(forward_demodulation,[],[f110662,f19417]) ).
fof(f110662,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_1289 ),
inference(avatar_component_clause,[],[f110661]) ).
fof(f110663,plain,
( spl0_1289
| ~ spl0_185
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f4264,f4122,f2650,f110661]) ).
fof(f4264,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_185
| ~ spl0_281 ),
inference(resolution,[],[f4123,f2651]) ).
fof(f110492,plain,
( spl0_1288
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1287 ),
inference(avatar_split_clause,[],[f110488,f110485,f18286,f2678,f110490]) ).
fof(f110490,plain,
( spl0_1288
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( ~ hBOOL(hAPP(X4,X3))
| c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,X6),X6)
| ~ class_Complete__Lattice_Ocomplete__lattice(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f110485,plain,
( spl0_1287
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,X6),X6)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f110488,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(X4,X3))
| c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,X6),X6)
| ~ class_Complete__Lattice_Ocomplete__lattice(X6) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1287 ),
inference(forward_demodulation,[],[f110486,f19417]) ).
fof(f110486,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,X6),X6)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X6) )
| ~ spl0_1287 ),
inference(avatar_component_clause,[],[f110485]) ).
fof(f110487,plain,
( spl0_1287
| ~ spl0_52
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f4216,f4106,f1247,f110485]) ).
fof(f4216,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_lessequals(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBK(X0,X1,X2),X5,X6),X6)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X6) )
| ~ spl0_52
| ~ spl0_277 ),
inference(superposition,[],[f4107,f1248]) ).
fof(f110483,plain,
( spl0_1286
| ~ spl0_210
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4051,f3659,f2870,f110481]) ).
fof(f110481,plain,
( spl0_1286
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_SetInterval_Oord_OlessThan(X2,X3,X4),X0,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f4051,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_SetInterval_Oord_OlessThan(X2,X3,X4),X0,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X1),X3)) )
| ~ spl0_210
| ~ spl0_268 ),
inference(resolution,[],[f3660,f2871]) ).
fof(f110474,plain,
( spl0_1285
| ~ spl0_208
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4050,f3659,f2862,f110472]) ).
fof(f110472,plain,
( spl0_1285
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_SetInterval_Oord_OgreaterThan(X2,X3,X4),X0,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f4050,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_SetInterval_Oord_OgreaterThan(X2,X3,X4),X0,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X3),X1)) )
| ~ spl0_208
| ~ spl0_268 ),
inference(resolution,[],[f3660,f2863]) ).
fof(f110470,plain,
( spl0_1284
| ~ spl0_206
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4049,f3659,f2854,f110468]) ).
fof(f110468,plain,
( spl0_1284
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_SetInterval_Oord_OatMost(X2,X3,X4),X0,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f4049,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_SetInterval_Oord_OatMost(X2,X3,X4),X0,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X1),X3)) )
| ~ spl0_206
| ~ spl0_268 ),
inference(resolution,[],[f3660,f2855]) ).
fof(f110466,plain,
( spl0_1283
| ~ spl0_212
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4048,f3659,f2878,f110464]) ).
fof(f110464,plain,
( spl0_1283
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f2878,plain,
( spl0_212
<=> ! [X4,X3] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X3,X4)),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f4048,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))
| X1 = X2 )
| ~ spl0_212
| ~ spl0_268 ),
inference(resolution,[],[f3660,f2879]) ).
fof(f2879,plain,
( ! [X3,X4] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X3,X4)),c_Arrow__Order__Mirabelle_OLin))
| X3 = X4 )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2878]) ).
fof(f110462,plain,
( spl0_1282
| ~ spl0_205
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4044,f3659,f2850,f110460]) ).
fof(f110460,plain,
( spl0_1282
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,c_FuncSet_Orestrict(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_FuncSet_Oextensional(X2,X3,X4),X0,tc_fun(X3,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f4044,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,c_FuncSet_Orestrict(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_FuncSet_Oextensional(X2,X3,X4),X0,tc_fun(X3,X4)))) )
| ~ spl0_205
| ~ spl0_268 ),
inference(resolution,[],[f3660,f2851]) ).
fof(f110458,plain,
( spl0_1281
| ~ spl0_203
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4038,f3659,f2831,f110456]) ).
fof(f110456,plain,
( spl0_1281
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,hAPP(X1,X2)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f4038,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,hAPP(X1,X2)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) )
| ~ spl0_203
| ~ spl0_268 ),
inference(resolution,[],[f3660,f2832]) ).
fof(f110454,plain,
( spl0_1280
| ~ spl0_188
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3819,f3595,f2662,f110452]) ).
fof(f110452,plain,
( spl0_1280
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2,X4)
| c_Fun_Oinj__on(X3,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f3819,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2,X4)
| c_Fun_Oinj__on(X3,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X2,X4) )
| ~ spl0_188
| ~ spl0_252 ),
inference(superposition,[],[f2663,f3596]) ).
fof(f110450,plain,
( spl0_1279
| ~ spl0_189
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3782,f3588,f2666,f110448]) ).
fof(f110448,plain,
( spl0_1279
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2,X4)
| c_Fun_Oinj__on(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f3782,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2,X4)
| c_Fun_Oinj__on(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X2,X4) )
| ~ spl0_189
| ~ spl0_251 ),
inference(superposition,[],[f2667,f3589]) ).
fof(f110446,plain,
( spl0_1278
| ~ spl0_184
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3691,f3576,f2646,f110444]) ).
fof(f110444,plain,
( spl0_1278
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( hAPP(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6) = hAPP(c_Fun_Ofun__upd(X0,X1,X5,X3,X4),X6)
| X1 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f3576,plain,
( spl0_248
<=> ! [X2,X10,X0,X12,X5,X1] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X10,X1,X2,X0,X12),X1,X5,X0,X12) = c_Fun_Ofun__upd(X10,X1,X5,X0,X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3691,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6) = hAPP(c_Fun_Ofun__upd(X0,X1,X5,X3,X4),X6)
| X1 = X6 )
| ~ spl0_184
| ~ spl0_248 ),
inference(superposition,[],[f2647,f3577]) ).
fof(f3577,plain,
( ! [X2,X10,X0,X1,X5,X12] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X10,X1,X2,X0,X12),X1,X5,X0,X12) = c_Fun_Ofun__upd(X10,X1,X5,X0,X12)
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f3576]) ).
fof(f110441,plain,
( spl0_1277
| ~ spl0_239
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3572,f3176,f3152,f110439]) ).
fof(f110439,plain,
( spl0_1277
<=> ! [X2,X4,X0,X3,X1] :
( X0 = X1
| c_HOL_Oundefined(X4) = hAPP(c_FuncSet_Orestrict(X2,hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X0),X3,X4),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f3176,plain,
( spl0_245
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)))
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f3572,plain,
( ! [X2,X3,X0,X1,X4] :
( X0 = X1
| c_HOL_Oundefined(X4) = hAPP(c_FuncSet_Orestrict(X2,hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X0),X3,X4),X1) )
| ~ spl0_239
| ~ spl0_245 ),
inference(resolution,[],[f3177,f3153]) ).
fof(f3177,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)))
| X3 = X4 )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f3176]) ).
fof(f110437,plain,
( spl0_1276
| ~ spl0_78
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2934,f2815,f1377,f110435]) ).
fof(f110435,plain,
( spl0_1276
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X3,X2),X0)
| c_lessequals(X3,X1,tc_fun(X4,X0))
| ~ class_Orderings_Olinorder(tc_fun(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f2815,plain,
( spl0_199
<=> ! [X17,X10,X0,X12,X1] :
( ~ class_HOL_Oord(X12)
| ~ c_lessequals(X10,X17,tc_fun(X0,X12))
| c_lessequals(hAPP(X10,X1),hAPP(X17,X1),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f2934,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X3,X2),X0)
| c_lessequals(X3,X1,tc_fun(X4,X0))
| ~ class_Orderings_Olinorder(tc_fun(X4,X0)) )
| ~ spl0_78
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1378]) ).
fof(f2816,plain,
( ! [X10,X0,X1,X17,X12] :
( ~ c_lessequals(X10,X17,tc_fun(X0,X12))
| ~ class_HOL_Oord(X12)
| c_lessequals(hAPP(X10,X1),hAPP(X17,X1),X12) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f2815]) ).
fof(f110427,plain,
( spl0_1275
| ~ spl0_78
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2905,f2807,f1377,f110425]) ).
fof(f110425,plain,
( spl0_1275
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,X4,X2,X3)
| c_lessequals(X4,X1,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f2807,plain,
( spl0_197
<=> ! [X6,X10,X0,X12,X7] :
( ~ c_Fun_Oinj__on(X10,X7,X0,X12)
| c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f2905,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,X4,X2,X3)
| c_lessequals(X4,X1,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_197 ),
inference(resolution,[],[f2808,f1378]) ).
fof(f2808,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_Fun_Oinj__on(X10,X7,X0,X12) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2807]) ).
fof(f110423,plain,
( spl0_1274
| ~ spl0_142
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2789,f2682,f1858,f110421]) ).
fof(f110421,plain,
( spl0_1274
<=> ! [X2,X0,X1] :
( c_Fun_Obij__betw(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,X2)
| ~ c_Fun_Oinj__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f2682,plain,
( spl0_193
<=> ! [X10,X0,X12,X6] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Obij__betw(X10,X6,c_Set_Oimage(X10,X6,X0,X12),X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f2789,plain,
( ! [X2,X0,X1] :
( c_Fun_Obij__betw(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,X2)
| ~ c_Fun_Oinj__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2) )
| ~ spl0_142
| ~ spl0_193 ),
inference(superposition,[],[f2683,f1859]) ).
fof(f2683,plain,
( ! [X10,X0,X6,X12] :
( c_Fun_Obij__betw(X10,X6,c_Set_Oimage(X10,X6,X0,X12),X0,X12)
| ~ c_Fun_Oinj__on(X10,X6,X0,X12) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2682]) ).
fof(f110355,plain,
( ~ spl0_1269
| spl0_1273
| ~ spl0_114
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2759,f2658,f1550,f110352,f110110]) ).
fof(f110110,plain,
( spl0_1269
<=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f110352,plain,
( spl0_1273
<=> c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f2759,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_114
| ~ spl0_187 ),
inference(resolution,[],[f2659,f1552]) ).
fof(f110286,plain,
( ~ spl0_1269
| spl0_1272
| ~ spl0_111
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2758,f2658,f1537,f110283,f110110]) ).
fof(f110283,plain,
( spl0_1272
<=> c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f2758,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_111
| ~ spl0_187 ),
inference(resolution,[],[f2659,f1539]) ).
fof(f110217,plain,
( ~ spl0_1269
| spl0_1271
| ~ spl0_114
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2751,f2650,f1550,f110214,f110110]) ).
fof(f110214,plain,
( spl0_1271
<=> c_lessequals(v_Lba____,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f2751,plain,
( c_lessequals(v_Lba____,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_114
| ~ spl0_185 ),
inference(resolution,[],[f2651,f1552]) ).
fof(f110119,plain,
( ~ spl0_12
| ~ spl0_30
| spl0_1269 ),
inference(avatar_split_clause,[],[f110118,f110110,f1159,f1075]) ).
fof(f1075,plain,
( spl0_12
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f110118,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| ~ spl0_30
| spl0_1269 ),
inference(resolution,[],[f110112,f1160]) ).
fof(f110112,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| spl0_1269 ),
inference(avatar_component_clause,[],[f110110]) ).
fof(f110117,plain,
( ~ spl0_1269
| spl0_1270
| ~ spl0_111
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2750,f2650,f1537,f110114,f110110]) ).
fof(f110114,plain,
( spl0_1270
<=> c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f2750,plain,
( c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_111
| ~ spl0_185 ),
inference(resolution,[],[f2651,f1539]) ).
fof(f110108,plain,
( spl0_1268
| ~ spl0_36
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2619,f2264,f1183,f110106]) ).
fof(f110106,plain,
( spl0_1268
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3))
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f1183,plain,
( spl0_36
<=> ! [X59,X58] :
( ~ class_Lattices_Olattice(X59)
| class_Lattices_Olattice(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f2264,plain,
( spl0_171
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f2619,plain,
( ! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3))
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_36
| ~ spl0_171 ),
inference(resolution,[],[f2265,f1184]) ).
fof(f1184,plain,
( ! [X58,X59] :
( class_Lattices_Olattice(tc_fun(X58,X59))
| ~ class_Lattices_Olattice(X59) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1183]) ).
fof(f2265,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f2264]) ).
fof(f110104,plain,
( spl0_1267
| ~ spl0_31
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2565,f2228,f1163,f110102]) ).
fof(f110102,plain,
( spl0_1267
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3))
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f1163,plain,
( spl0_31
<=> ! [X59,X58] :
( ~ class_Lattices_Olattice(X59)
| class_Lattices_Oupper__semilattice(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f2228,plain,
( spl0_162
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f2565,plain,
( ! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3))
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_31
| ~ spl0_162 ),
inference(resolution,[],[f2229,f1164]) ).
fof(f1164,plain,
( ! [X58,X59] :
( class_Lattices_Oupper__semilattice(tc_fun(X58,X59))
| ~ class_Lattices_Olattice(X59) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f2229,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f2228]) ).
fof(f109315,plain,
( spl0_1266
| ~ spl0_114
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1243 ),
inference(avatar_split_clause,[],[f104652,f103738,f18286,f2678,f1550,f109313]) ).
fof(f109313,plain,
( spl0_1266
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Fun_Ofun__upd(X0,c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X1,X2),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f103738,plain,
( spl0_1243
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(X1)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Fun_Ofun__upd(X0,c_Orderings_Obot__class_Obot(tc_bool),X1,X2,X3),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f104652,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Fun_Ofun__upd(X0,c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X1,X2),tc_bool)
| ~ spl0_114
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1243 ),
inference(forward_demodulation,[],[f104387,f19417]) ).
fof(f104387,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Fun_Ofun__upd(X0,c_Orderings_Obot__class_Obot(tc_bool),hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin),X1,X2),tc_bool)
| ~ spl0_114
| ~ spl0_1243 ),
inference(resolution,[],[f103739,f1552]) ).
fof(f103739,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(X1)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Fun_Ofun__upd(X0,c_Orderings_Obot__class_Obot(tc_bool),X1,X2,X3),tc_bool) )
| ~ spl0_1243 ),
inference(avatar_component_clause,[],[f103738]) ).
fof(f108091,plain,
( spl0_1265
| ~ spl0_111
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1243 ),
inference(avatar_split_clause,[],[f104651,f103738,f18286,f2678,f1537,f108089]) ).
fof(f108089,plain,
( spl0_1265
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Fun_Ofun__upd(X0,c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X1,X2),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f104651,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Fun_Ofun__upd(X0,c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X1,X2),tc_bool)
| ~ spl0_111
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1243 ),
inference(forward_demodulation,[],[f104386,f19417]) ).
fof(f104386,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Fun_Ofun__upd(X0,c_Orderings_Obot__class_Obot(tc_bool),hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin),X1,X2),tc_bool)
| ~ spl0_111
| ~ spl0_1243 ),
inference(resolution,[],[f103739,f1539]) ).
fof(f108087,plain,
( spl0_1264
| ~ spl0_52
| ~ spl0_192
| ~ spl0_462
| ~ spl0_478
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f69583,f18286,f10909,f10572,f2678,f1247,f108085]) ).
fof(f108085,plain,
( spl0_1264
<=> ! [X5,X4,X2,X0,X3,X1] :
( hBOOL(hAPP(X5,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X5,X3,X1,X4,X0)))
| ~ hBOOL(hAPP(X5,X2))
| hBOOL(hAPP(X3,hAPP(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f69583,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X5,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X5,X3,X1,X4,X0)))
| ~ hBOOL(hAPP(X5,X2))
| hBOOL(hAPP(X3,hAPP(X1,X2))) )
| ~ spl0_52
| ~ spl0_192
| ~ spl0_462
| ~ spl0_478
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69582,f19417]) ).
fof(f69582,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(X5,X2))
| hBOOL(hAPP(X3,hAPP(X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X4),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X5,X3,X1,X4,X0)),X5)) )
| ~ spl0_52
| ~ spl0_192
| ~ spl0_462
| ~ spl0_478
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69581,f19417]) ).
fof(f69581,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X3,hAPP(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| hBOOL(hAPP(hAPP(c_in(X4),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X5,X3,X1,X4,X0)),X5)) )
| ~ spl0_52
| ~ spl0_192
| ~ spl0_462
| ~ spl0_478
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69580,f1248]) ).
fof(f69580,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_COMBK(X3,tc_fun(X0,tc_bool),X4),X2),hAPP(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| hBOOL(hAPP(hAPP(c_in(X4),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X5,X3,X1,X4,X0)),X5)) )
| ~ spl0_192
| ~ spl0_462
| ~ spl0_478
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69559,f19417]) ).
fof(f69559,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(X1,X2)),hAPP(c_COMBK(X3,tc_fun(X0,tc_bool),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| hBOOL(hAPP(hAPP(c_in(X4),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X5,X3,X1,X4,X0)),X5)) )
| ~ spl0_462
| ~ spl0_478 ),
inference(resolution,[],[f10910,f10573]) ).
fof(f106946,plain,
( spl0_1263
| ~ spl0_44
| ~ spl0_1229 ),
inference(avatar_split_clause,[],[f95642,f94990,f1215,f106944]) ).
fof(f106944,plain,
( spl0_1263
<=> ! [X2,X0,X1,X3] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1),X2,X3),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f94990,plain,
( spl0_1229
<=> ! [X2,X0,X1] :
( ~ hBOOL(X0)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(X0,X1,X2),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f95642,plain,
( ! [X2,X3,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1),X2,X3),tc_bool)
| ~ spl0_44
| ~ spl0_1229 ),
inference(resolution,[],[f94991,f1216]) ).
fof(f94991,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(X0)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(X0,X1,X2),tc_bool) )
| ~ spl0_1229 ),
inference(avatar_component_clause,[],[f94990]) ).
fof(f105837,plain,
( spl0_1262
| ~ spl0_45
| ~ spl0_1229 ),
inference(avatar_split_clause,[],[f95638,f94990,f1219,f105835]) ).
fof(f105835,plain,
( spl0_1262
<=> ! [X2,X0,X1,X3] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(hAPP(c_fequal(X0),X1),X1),X2,X3),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f95638,plain,
( ! [X2,X3,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(hAPP(c_fequal(X0),X1),X1),X2,X3),tc_bool)
| ~ spl0_45
| ~ spl0_1229 ),
inference(resolution,[],[f94991,f1220]) ).
fof(f104263,plain,
( spl0_1261
| ~ spl0_187
| ~ spl0_526 ),
inference(avatar_split_clause,[],[f12006,f12001,f2658,f104261]) ).
fof(f104261,plain,
( spl0_1261
<=> ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,X1),X2,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f12006,plain,
( ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,X1),X2,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_187
| ~ spl0_526 ),
inference(resolution,[],[f12002,f2659]) ).
fof(f104259,plain,
( spl0_1260
| ~ spl0_185
| ~ spl0_526 ),
inference(avatar_split_clause,[],[f12005,f12001,f2650,f104257]) ).
fof(f104257,plain,
( spl0_1260
<=> ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X0,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f12005,plain,
( ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X0,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_185
| ~ spl0_526 ),
inference(resolution,[],[f12002,f2651]) ).
fof(f104255,plain,
( spl0_1259
| ~ spl0_12
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f10074,f10071,f1075,f104253]) ).
fof(f104253,plain,
( spl0_1259
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_bool),X0),hAPP(c_fequal(tc_bool),X1),tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f10071,plain,
( spl0_452
<=> ! [X4,X0,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f10074,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_bool),X0),hAPP(c_fequal(tc_bool),X1),tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_12
| ~ spl0_452 ),
inference(resolution,[],[f10072,f1077]) ).
fof(f1077,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f1075]) ).
fof(f10072,plain,
( ! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)),X0) )
| ~ spl0_452 ),
inference(avatar_component_clause,[],[f10071]) ).
fof(f104251,plain,
( spl0_1258
| ~ spl0_12
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f10062,f10055,f1075,f104249]) ).
fof(f104249,plain,
( spl0_1258
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_bool),X0),hAPP(c_fequal(tc_bool),X1),tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f10055,plain,
( spl0_449
<=> ! [X4,X0,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f10062,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_bool),X0),hAPP(c_fequal(tc_bool),X1),tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_12
| ~ spl0_449 ),
inference(resolution,[],[f10056,f1077]) ).
fof(f10056,plain,
( ! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)),X0) )
| ~ spl0_449 ),
inference(avatar_component_clause,[],[f10055]) ).
fof(f104247,plain,
( spl0_1257
| ~ spl0_231
| ~ spl0_413 ),
inference(avatar_split_clause,[],[f8905,f8241,f3120,f104245]) ).
fof(f104245,plain,
( spl0_1257
<=> ! [X4,X0,X3,X2,X1] : c_lessequals(c_Set_Oimage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Set_Oimage(X0,X2,X3,X4),tc_fun(X4,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f8241,plain,
( spl0_413
<=> ! [X6,X10,X0,X12,X7] : c_lessequals(c_Set_Oimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool)),X12,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,X6,X12,X0),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f8905,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(c_Set_Oimage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Set_Oimage(X0,X2,X3,X4),tc_fun(X4,tc_bool))
| ~ spl0_231
| ~ spl0_413 ),
inference(resolution,[],[f8242,f3121]) ).
fof(f8242,plain,
( ! [X10,X0,X6,X7,X12] : c_lessequals(c_Set_Oimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool)),X12,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,X6,X12,X0),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_413 ),
inference(avatar_component_clause,[],[f8241]) ).
fof(f104243,plain,
( spl0_1256
| ~ spl0_232
| ~ spl0_413 ),
inference(avatar_split_clause,[],[f8904,f8241,f3124,f104241]) ).
fof(f104241,plain,
( spl0_1256
<=> ! [X2,X4,X0,X3,X1] : c_lessequals(c_Set_Oimage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Set_Oimage(X0,X1,X3,X4),tc_fun(X4,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f8904,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(c_Set_Oimage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Set_Oimage(X0,X1,X3,X4),tc_fun(X4,tc_bool))
| ~ spl0_232
| ~ spl0_413 ),
inference(resolution,[],[f8242,f3125]) ).
fof(f104239,plain,
( spl0_1255
| ~ spl0_231
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f8534,f8225,f3120,f104237]) ).
fof(f104237,plain,
( spl0_1255
<=> ! [X4,X0,X3,X2,X1] : c_lessequals(c_Relation_OImage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Relation_OImage(X0,X2,X3,X4),tc_fun(X4,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f8225,plain,
( spl0_409
<=> ! [X6,X0,X12,X16,X7] : c_lessequals(c_Relation_OImage(X16,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool)),X12,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X16,X6,X12,X0),c_Relation_OImage(X16,X7,X12,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f8534,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(c_Relation_OImage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Relation_OImage(X0,X2,X3,X4),tc_fun(X4,tc_bool))
| ~ spl0_231
| ~ spl0_409 ),
inference(resolution,[],[f8226,f3121]) ).
fof(f8226,plain,
( ! [X0,X6,X16,X7,X12] : c_lessequals(c_Relation_OImage(X16,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool)),X12,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X16,X6,X12,X0),c_Relation_OImage(X16,X7,X12,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_409 ),
inference(avatar_component_clause,[],[f8225]) ).
fof(f104235,plain,
( spl0_1254
| ~ spl0_232
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f8533,f8225,f3124,f104233]) ).
fof(f104233,plain,
( spl0_1254
<=> ! [X2,X4,X0,X3,X1] : c_lessequals(c_Relation_OImage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Relation_OImage(X0,X1,X3,X4),tc_fun(X4,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f8533,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(c_Relation_OImage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Relation_OImage(X0,X1,X3,X4),tc_fun(X4,tc_bool))
| ~ spl0_232
| ~ spl0_409 ),
inference(resolution,[],[f8226,f3125]) ).
fof(f104231,plain,
( spl0_1253
| ~ spl0_94
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f7241,f7036,f1469,f104229]) ).
fof(f104229,plain,
( spl0_1253
<=> ! [X4,X0,X3,X2,X1] : c_lessequals(c_Relation_OImage(X0,X1,X2,X3),c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f7241,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(c_Relation_OImage(X0,X1,X2,X3),c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool))
| ~ spl0_94
| ~ spl0_372 ),
inference(superposition,[],[f1470,f7037]) ).
fof(f104227,plain,
( spl0_1252
| ~ spl0_93
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f7240,f7036,f1465,f104225]) ).
fof(f104225,plain,
( spl0_1252
<=> ! [X4,X0,X3,X2,X1] : c_lessequals(c_Relation_OImage(X0,X4,X2,X3),c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f7240,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(c_Relation_OImage(X0,X4,X2,X3),c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool))
| ~ spl0_93
| ~ spl0_372 ),
inference(superposition,[],[f1466,f7037]) ).
fof(f104213,plain,
( spl0_1251
| ~ spl0_94
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7190,f7032,f1469,f104211]) ).
fof(f104211,plain,
( spl0_1251
<=> ! [X4,X0,X3,X2,X1] : c_lessequals(c_Set_Oimage(X0,X1,X2,X3),c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f7190,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(c_Set_Oimage(X0,X1,X2,X3),c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool))
| ~ spl0_94
| ~ spl0_371 ),
inference(superposition,[],[f1470,f7033]) ).
fof(f104209,plain,
( spl0_1250
| ~ spl0_93
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7189,f7032,f1465,f104207]) ).
fof(f104207,plain,
( spl0_1250
<=> ! [X4,X0,X3,X2,X1] : c_lessequals(c_Set_Oimage(X0,X4,X2,X3),c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f7189,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(c_Set_Oimage(X0,X4,X2,X3),c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool))
| ~ spl0_93
| ~ spl0_371 ),
inference(superposition,[],[f1466,f7033]) ).
fof(f104205,plain,
( spl0_1249
| ~ spl0_113
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f6882,f6702,f1546,f104203]) ).
fof(f104203,plain,
( spl0_1249
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4)
| hBOOL(hAPP(c_FuncSet_OPi(X1,c_COMBK(X2,tc_fun(X4,tc_bool),X3),X3,X4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f6882,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4)
| hBOOL(hAPP(c_FuncSet_OPi(X1,c_COMBK(X2,tc_fun(X4,tc_bool),X3),X3,X4),X0)) )
| ~ spl0_113
| ~ spl0_358 ),
inference(resolution,[],[f6703,f1547]) ).
fof(f104195,plain,
( spl0_1248
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1247 ),
inference(avatar_split_clause,[],[f104191,f104188,f18286,f2678,f104193]) ).
fof(f104193,plain,
( spl0_1248
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X2,X3,X0,X4),c_Pair(X1,X5,X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f104188,plain,
( spl0_1247
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X2,X3,X0,X4),c_Pair(X1,X5,X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f104191,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X2,X3,X0,X4),c_Pair(X1,X5,X0,X4))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1247 ),
inference(forward_demodulation,[],[f104189,f19417]) ).
fof(f104189,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X2,X3,X0,X4),c_Pair(X1,X5,X0,X4))) )
| ~ spl0_1247 ),
inference(avatar_component_clause,[],[f104188]) ).
fof(f104190,plain,
( spl0_1247
| ~ spl0_112
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f6855,f6690,f1542,f104188]) ).
fof(f6690,plain,
( spl0_355
<=> ! [X4,X0,X12,X6,X3,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Product__Type_OSigma(X6,X7,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f6855,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X2,X3,X0,X4),c_Pair(X1,X5,X0,X4))) )
| ~ spl0_112
| ~ spl0_355 ),
inference(resolution,[],[f6691,f1543]) ).
fof(f6691,plain,
( ! [X3,X0,X6,X7,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Product__Type_OSigma(X6,X7,X0,X12)))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_355 ),
inference(avatar_component_clause,[],[f6690]) ).
fof(f104185,plain,
( spl0_1246
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f6544,f5667,f4702,f2288,f1445,f104183]) ).
fof(f104183,plain,
( spl0_1246
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X3),X1),X0,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(hAPP(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f6544,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X3),X1),X0,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(hAPP(X0,X1),X2)) )
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_345 ),
inference(forward_demodulation,[],[f6520,f5265]) ).
fof(f6520,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X0,X3,tc_fun(X4,tc_bool)),X2)) )
| ~ spl0_177
| ~ spl0_345 ),
inference(resolution,[],[f5668,f2289]) ).
fof(f104181,plain,
( spl0_1245
| ~ spl0_83
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f6524,f5667,f1397,f104179]) ).
fof(f104179,plain,
( spl0_1245
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X0,X3,tc_fun(X4,tc_bool)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f6524,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X0,X3,tc_fun(X4,tc_bool)),X2)) )
| ~ spl0_83
| ~ spl0_345 ),
inference(resolution,[],[f5668,f1398]) ).
fof(f104177,plain,
( spl0_1244
| ~ spl0_139
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5695,f5688,f1846,f104175]) ).
fof(f104175,plain,
( spl0_1244
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X3))
| X1 = X3
| hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f5688,plain,
( spl0_350
<=> ! [X0,X6,X2,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),X6,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X6,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f5695,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X3))
| X1 = X3
| hBOOL(hAPP(X2,X3)) )
| ~ spl0_139
| ~ spl0_350 ),
inference(superposition,[],[f5689,f1847]) ).
fof(f5689,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),X6,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X6,X1)) )
| ~ spl0_350 ),
inference(avatar_component_clause,[],[f5688]) ).
fof(f103740,plain,
( spl0_1243
| ~ spl0_73
| ~ spl0_1228 ),
inference(avatar_split_clause,[],[f94328,f93049,f1357,f103738]) ).
fof(f94328,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(X1)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Fun_Ofun__upd(X0,c_Orderings_Obot__class_Obot(tc_bool),X1,X2,X3),tc_bool) )
| ~ spl0_73
| ~ spl0_1228 ),
inference(superposition,[],[f93050,f1358]) ).
fof(f103736,plain,
( spl0_1242
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1241 ),
inference(avatar_split_clause,[],[f103732,f103729,f18286,f2678,f103734]) ).
fof(f103734,plain,
( spl0_1242
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X0,X4,X2)))
| hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f103729,plain,
( spl0_1241
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X0,X4,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f103732,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X0,X4,X2)))
| hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1241 ),
inference(forward_demodulation,[],[f103730,f19417]) ).
fof(f103730,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X0,X4,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_1241 ),
inference(avatar_component_clause,[],[f103729]) ).
fof(f103731,plain,
( spl0_1241
| ~ spl0_112
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f5592,f5358,f1542,f103729]) ).
fof(f5592,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X0,X4,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_112
| ~ spl0_325 ),
inference(resolution,[],[f5359,f1543]) ).
fof(f103293,plain,
( spl0_1240
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1239 ),
inference(avatar_split_clause,[],[f103289,f103286,f18286,f2678,f103291]) ).
fof(f103291,plain,
( spl0_1240
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X4,X0,X2)))
| hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f103286,plain,
( spl0_1239
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X4,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f103289,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X4,X0,X2)))
| hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1239 ),
inference(forward_demodulation,[],[f103287,f19417]) ).
fof(f103287,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X4,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_1239 ),
inference(avatar_component_clause,[],[f103286]) ).
fof(f103288,plain,
( spl0_1239
| ~ spl0_112
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f5565,f5354,f1542,f103286]) ).
fof(f5565,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X3,X4,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_112
| ~ spl0_324 ),
inference(resolution,[],[f5355,f1543]) ).
fof(f102990,plain,
( spl0_1238
| ~ spl0_43
| ~ spl0_1186 ),
inference(avatar_split_clause,[],[f62952,f62863,f1211,f102988]) ).
fof(f102988,plain,
( spl0_1238
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X0,tc_bool)),X2,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f62952,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X0,tc_bool)),X2,tc_fun(X0,tc_bool))
| ~ spl0_43
| ~ spl0_1186 ),
inference(resolution,[],[f62864,f1212]) ).
fof(f102986,plain,
( spl0_1237
| ~ spl0_177
| ~ spl0_192
| ~ spl0_325
| ~ spl0_699
| ~ spl0_764 ),
inference(avatar_split_clause,[],[f62856,f20188,f18286,f5358,f2678,f2288,f102984]) ).
fof(f102984,plain,
( spl0_1237
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_fequal(X2),X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_fequal(X2),X1),X0,X3,X2)))
| hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f62856,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal(X2),X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_fequal(X2),X1),X0,X3,X2)))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_325
| ~ spl0_699
| ~ spl0_764 ),
inference(forward_demodulation,[],[f62855,f20189]) ).
fof(f62855,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal(X2),X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X3,X2)))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_325
| ~ spl0_699
| ~ spl0_764 ),
inference(forward_demodulation,[],[f62854,f22361]) ).
fof(f22361,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_fequal(X0),X1),X2) = hAPP(hAPP(c_fequal(X0),X2),X1)
| ~ spl0_192
| ~ spl0_764 ),
inference(superposition,[],[f2679,f20189]) ).
fof(f62854,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X3,X2)),X1))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_325
| ~ spl0_699 ),
inference(forward_demodulation,[],[f62853,f2679]) ).
fof(f62853,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X3,X2)))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_325
| ~ spl0_699 ),
inference(forward_demodulation,[],[f62820,f19417]) ).
fof(f62820,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X3,X2)),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1))) )
| ~ spl0_177
| ~ spl0_325 ),
inference(resolution,[],[f5359,f2289]) ).
fof(f102982,plain,
( spl0_1236
| ~ spl0_112
| ~ spl0_1228 ),
inference(avatar_split_clause,[],[f94312,f93049,f1542,f102980]) ).
fof(f102980,plain,
( spl0_1236
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(hAPP(c_in(X0),X1),tc_bool)
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f94312,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(hAPP(c_in(X0),X1),tc_bool)
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),X1)) )
| ~ spl0_112
| ~ spl0_1228 ),
inference(resolution,[],[f93050,f1543]) ).
fof(f102978,plain,
( spl0_1235
| ~ spl0_177
| ~ spl0_192
| ~ spl0_324
| ~ spl0_699
| ~ spl0_764 ),
inference(avatar_split_clause,[],[f62807,f20188,f18286,f5354,f2678,f2288,f102976]) ).
fof(f102976,plain,
( spl0_1235
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_fequal(X2),X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_fequal(X2),X1),X3,X0,X2)))
| hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f62807,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal(X2),X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_fequal(X2),X1),X3,X0,X2)))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_324
| ~ spl0_699
| ~ spl0_764 ),
inference(forward_demodulation,[],[f62806,f20189]) ).
fof(f62806,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal(X2),X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X3,X0,X2)))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_324
| ~ spl0_699
| ~ spl0_764 ),
inference(forward_demodulation,[],[f62805,f22361]) ).
fof(f62805,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X3,X0,X2)),X1))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_324
| ~ spl0_699 ),
inference(forward_demodulation,[],[f62804,f2679]) ).
fof(f62804,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X3,X0,X2)))
| hBOOL(hAPP(X0,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_324
| ~ spl0_699 ),
inference(forward_demodulation,[],[f62771,f19417]) ).
fof(f62771,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X3,X0,X2)),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1))) )
| ~ spl0_177
| ~ spl0_324 ),
inference(resolution,[],[f5355,f2289]) ).
fof(f100439,plain,
( spl0_1234
| ~ spl0_151
| ~ spl0_1229 ),
inference(avatar_split_clause,[],[f95630,f94990,f2184,f100437]) ).
fof(f100437,plain,
( spl0_1234
<=> ! [X0,X3,X2,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Set_OPow(X0,X1),X0),X2,X3),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f95630,plain,
( ! [X2,X3,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Set_OPow(X0,X1),X0),X2,X3),tc_bool)
| ~ spl0_151
| ~ spl0_1229 ),
inference(resolution,[],[f94991,f2185]) ).
fof(f98008,plain,
( spl0_1233
| ~ spl0_947
| ~ spl0_1228 ),
inference(avatar_split_clause,[],[f94321,f93049,f32882,f98006]) ).
fof(f98006,plain,
( spl0_1233
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X2),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f94321,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X2),tc_bool)
| ~ spl0_947
| ~ spl0_1228 ),
inference(resolution,[],[f93050,f32883]) ).
fof(f95166,plain,
( spl0_1232
| ~ spl0_177
| ~ spl0_192
| ~ spl0_404
| ~ spl0_699
| ~ spl0_764 ),
inference(avatar_split_clause,[],[f66172,f20188,f18286,f7932,f2678,f2288,f95164]) ).
fof(f95164,plain,
( spl0_1232
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(hAPP(c_fequal(tc_fun(X0,tc_bool)),X2),tc_fun(X0,tc_bool)),X1))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f66172,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(hAPP(c_fequal(tc_fun(X0,tc_bool)),X2),tc_fun(X0,tc_bool)),X1))
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_404
| ~ spl0_699
| ~ spl0_764 ),
inference(forward_demodulation,[],[f66171,f20189]) ).
fof(f66171,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),tc_bool),X2),tc_fun(X0,tc_bool)),X1))
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_404
| ~ spl0_699 ),
inference(forward_demodulation,[],[f66170,f19417]) ).
fof(f66170,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),tc_bool),X2),tc_fun(X0,tc_bool)))) )
| ~ spl0_177
| ~ spl0_192
| ~ spl0_404
| ~ spl0_699 ),
inference(forward_demodulation,[],[f66127,f19417]) ).
fof(f66127,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),tc_bool),X2),tc_fun(X0,tc_bool)))) )
| ~ spl0_177
| ~ spl0_404 ),
inference(resolution,[],[f7933,f2289]) ).
fof(f95162,plain,
( spl0_1231
| ~ spl0_182
| ~ spl0_192
| ~ spl0_280
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f57035,f18286,f4118,f2678,f2638,f95160]) ).
fof(f95160,plain,
( spl0_1231
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Complete__Lattice_OInf__class_OInf(X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f2638,plain,
( spl0_182
<=> ! [X6,X0] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f57035,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Complete__Lattice_OInf__class_OInf(X1,tc_fun(X0,tc_bool)) )
| ~ spl0_182
| ~ spl0_192
| ~ spl0_280
| ~ spl0_699 ),
inference(forward_demodulation,[],[f4251,f19417]) ).
fof(f4251,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Complete__Lattice_OInf__class_OInf(X1,tc_fun(X0,tc_bool)) )
| ~ spl0_182
| ~ spl0_280 ),
inference(resolution,[],[f4119,f2639]) ).
fof(f2639,plain,
( ! [X0,X6] :
( ~ c_lessequals(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f2638]) ).
fof(f95158,plain,
( spl0_1230
| ~ spl0_112
| ~ spl0_192
| ~ spl0_378
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f55971,f18286,f7060,f2678,f1542,f95156]) ).
fof(f95156,plain,
( spl0_1230
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X2,X1))
| hAPP(X3,X1) = c_HOL_Oundefined(X4)
| ~ hBOOL(hAPP(c_FuncSet_Oextensional(X2,X0,X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f7060,plain,
( spl0_378
<=> ! [X10,X0,X12,X6,X1] :
( hAPP(X10,X1) = c_HOL_Oundefined(X12)
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f55971,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X2,X1))
| hAPP(X3,X1) = c_HOL_Oundefined(X4)
| ~ hBOOL(hAPP(c_FuncSet_Oextensional(X2,X0,X4),X3)) )
| ~ spl0_112
| ~ spl0_192
| ~ spl0_378
| ~ spl0_699 ),
inference(forward_demodulation,[],[f7461,f19417]) ).
fof(f7461,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hAPP(X3,X1) = c_HOL_Oundefined(X4)
| ~ hBOOL(hAPP(c_FuncSet_Oextensional(X2,X0,X4),X3)) )
| ~ spl0_112
| ~ spl0_378 ),
inference(resolution,[],[f7061,f1543]) ).
fof(f7061,plain,
( ! [X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12)))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hAPP(X10,X1) = c_HOL_Oundefined(X12) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f7060]) ).
fof(f94992,plain,
( spl0_1229
| ~ spl0_52
| ~ spl0_1228 ),
inference(avatar_split_clause,[],[f94333,f93049,f1247,f94990]) ).
fof(f94333,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(X0)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(X0,X1,X2),tc_bool) )
| ~ spl0_52
| ~ spl0_1228 ),
inference(superposition,[],[f93050,f1248]) ).
fof(f93051,plain,
( ~ spl0_21
| ~ spl0_19
| spl0_1228
| ~ spl0_729
| ~ spl0_1163 ),
inference(avatar_split_clause,[],[f79355,f52810,f19999,f93049,f1110,f1120]) ).
fof(f1120,plain,
( spl0_21
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f19999,plain,
( spl0_729
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f52810,plain,
( spl0_1163
<=> ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,tc_bool),X1,tc_bool)
| ~ hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f79355,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(X0,tc_bool)
| ~ class_Orderings_Oorder(tc_bool)
| ~ class_Orderings_Obot(tc_bool)
| ~ hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_bool))) )
| ~ spl0_729
| ~ spl0_1163 ),
inference(resolution,[],[f20000,f52811]) ).
fof(f52811,plain,
( ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,tc_bool),X1,tc_bool)
| ~ hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_bool))) )
| ~ spl0_1163 ),
inference(avatar_component_clause,[],[f52810]) ).
fof(f20000,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
| c_Orderings_Obot__class_Obot(X1) = X0
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_729 ),
inference(avatar_component_clause,[],[f19999]) ).
fof(f91274,plain,
( spl0_1227
| ~ spl0_52
| ~ spl0_192
| ~ spl0_358
| ~ spl0_478
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f69586,f18286,f10909,f6702,f2678,f1247,f91272]) ).
fof(f91272,plain,
( spl0_1227
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(X5,X2))
| hBOOL(hAPP(X3,hAPP(X1,X2)))
| ~ c_Fun_Obij__betw(X1,X5,X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f69586,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(X5,X2))
| hBOOL(hAPP(X3,hAPP(X1,X2)))
| ~ c_Fun_Obij__betw(X1,X5,X3,X4,X0) )
| ~ spl0_52
| ~ spl0_192
| ~ spl0_358
| ~ spl0_478
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69585,f19417]) ).
fof(f69585,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X3,hAPP(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| ~ c_Fun_Obij__betw(X1,X5,X3,X4,X0) )
| ~ spl0_52
| ~ spl0_192
| ~ spl0_358
| ~ spl0_478
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69584,f1248]) ).
fof(f69584,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_COMBK(X3,tc_fun(X0,tc_bool),X4),X2),hAPP(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| ~ c_Fun_Obij__betw(X1,X5,X3,X4,X0) )
| ~ spl0_192
| ~ spl0_358
| ~ spl0_478
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69560,f19417]) ).
fof(f69560,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),hAPP(X1,X2)),hAPP(c_COMBK(X3,tc_fun(X0,tc_bool),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| ~ c_Fun_Obij__betw(X1,X5,X3,X4,X0) )
| ~ spl0_358
| ~ spl0_478 ),
inference(resolution,[],[f10910,f6703]) ).
fof(f91015,plain,
( spl0_1226
| ~ spl0_52
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f89721,f89228,f1247,f91013]) ).
fof(f89721,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OInf__class_OInf(c_COMBK(X0,X1,X2),tc_bool),tc_bool) = X3 )
| ~ spl0_52
| ~ spl0_1224 ),
inference(superposition,[],[f89229,f1248]) ).
fof(f89234,plain,
( spl0_1225
| spl0_23
| ~ spl0_1200 ),
inference(avatar_split_clause,[],[f70153,f70079,f1130,f89232]) ).
fof(f89232,plain,
( spl0_1225
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),c_Arrow__Order__Mirabelle_OLin),X1,tc_fun(X0,tc_bool)),hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),c_Arrow__Order__Mirabelle_OLin),c_HOL_Ominus__class_Ominus(X1,hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f1130,plain,
( spl0_23
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f70079,plain,
( spl0_1200
<=> ! [X0,X6,X1,X7] :
( hBOOL(hAPP(X7,X1))
| c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f70153,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),c_Arrow__Order__Mirabelle_OLin),X1,tc_fun(X0,tc_bool)),hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),c_Arrow__Order__Mirabelle_OLin),c_HOL_Ominus__class_Ominus(X1,hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| spl0_23
| ~ spl0_1200 ),
inference(resolution,[],[f70080,f1132]) ).
fof(f1132,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin))
| spl0_23 ),
inference(avatar_component_clause,[],[f1130]) ).
fof(f70080,plain,
( ! [X0,X1,X6,X7] :
( hBOOL(hAPP(X7,X1))
| c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) )
| ~ spl0_1200 ),
inference(avatar_component_clause,[],[f70079]) ).
fof(f89230,plain,
( spl0_1224
| ~ spl0_13
| ~ spl0_119
| ~ spl0_1163 ),
inference(avatar_split_clause,[],[f58020,f52810,f1635,f1080,f89228]) ).
fof(f58020,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(X1,tc_bool),tc_bool) = X0
| ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool))) )
| ~ spl0_119
| ~ spl0_1163 ),
inference(resolution,[],[f1636,f52811]) ).
fof(f83650,plain,
( spl0_1223
| ~ spl0_701
| ~ spl0_1163 ),
inference(avatar_split_clause,[],[f77079,f52810,f18295,f83648]) ).
fof(f83648,plain,
( spl0_1223
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_bool)
| ~ hBOOL(hAPP(hAPP(c_fequal(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f18295,plain,
( spl0_701
<=> ! [X0] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(tc_bool),X0),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f77079,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_bool)
| ~ hBOOL(hAPP(hAPP(c_fequal(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool))) )
| ~ spl0_701
| ~ spl0_1163 ),
inference(superposition,[],[f52811,f18296]) ).
fof(f18296,plain,
( ! [X0] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(tc_bool),X0),tc_bool) = X0
| ~ spl0_701 ),
inference(avatar_component_clause,[],[f18295]) ).
fof(f82815,plain,
( spl0_1222
| ~ spl0_30
| ~ spl0_178
| ~ spl0_764 ),
inference(avatar_split_clause,[],[f56391,f20188,f2292,f1159,f82813]) ).
fof(f82813,plain,
( spl0_1222
<=> ! [X2,X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(tc_fun(X0,X1)),X2),tc_fun(X0,X1)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f2292,plain,
( spl0_178
<=> ! [X0,X3] :
( c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f56391,plain,
( ! [X2,X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(tc_fun(X0,X1)),X2),tc_fun(X0,X1)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_30
| ~ spl0_178
| ~ spl0_764 ),
inference(forward_demodulation,[],[f2634,f20189]) ).
fof(f2634,plain,
( ! [X2,X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(tc_fun(X0,X1)),tc_fun(X0,X1),tc_fun(X0,X1),tc_bool),X2),tc_fun(X0,X1)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_30
| ~ spl0_178 ),
inference(resolution,[],[f2293,f1160]) ).
fof(f2293,plain,
( ! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = X3 )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f2292]) ).
fof(f82811,plain,
( spl0_1221
| ~ spl0_30
| ~ spl0_179
| ~ spl0_764 ),
inference(avatar_split_clause,[],[f56376,f20188,f2296,f1159,f82809]) ).
fof(f82809,plain,
( spl0_1221
<=> ! [X2,X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(hAPP(c_fequal(tc_fun(X0,X1)),X2),tc_fun(X0,X1)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f2296,plain,
( spl0_179
<=> ! [X0,X3] :
( c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f56376,plain,
( ! [X2,X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(hAPP(c_fequal(tc_fun(X0,X1)),X2),tc_fun(X0,X1)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_30
| ~ spl0_179
| ~ spl0_764 ),
inference(forward_demodulation,[],[f2636,f20189]) ).
fof(f2636,plain,
( ! [X2,X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(tc_fun(X0,X1)),tc_fun(X0,X1),tc_fun(X0,X1),tc_bool),X2),tc_fun(X0,X1)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_30
| ~ spl0_179 ),
inference(resolution,[],[f2297,f1160]) ).
fof(f2297,plain,
( ! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = X3 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f2296]) ).
fof(f82335,plain,
( spl0_1220
| ~ spl0_181
| ~ spl0_1187 ),
inference(avatar_split_clause,[],[f76665,f63106,f2624,f82333]) ).
fof(f82333,plain,
( spl0_1220
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f2624,plain,
( spl0_181
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f76665,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool)
| ~ spl0_181
| ~ spl0_1187 ),
inference(superposition,[],[f2625,f63107]) ).
fof(f2625,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f2624]) ).
fof(f81866,plain,
( spl0_1219
| ~ spl0_181
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f76664,f62696,f2624,f81864]) ).
fof(f81864,plain,
( spl0_1219
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f76664,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool)
| ~ spl0_181
| ~ spl0_1184 ),
inference(superposition,[],[f2625,f62697]) ).
fof(f81168,plain,
( spl0_1218
| ~ spl0_652
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f79165,f79133,f17409,f81166]) ).
fof(f81166,plain,
( spl0_1218
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(c_Orderings_Obot__class_Obot(tc_bool),X0),tc_bool),tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f79133,plain,
( spl0_1216
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(c_Orderings_Obot__class_Obot(tc_bool),X0),tc_bool),X1,tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f79165,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(c_Orderings_Obot__class_Obot(tc_bool),X0),tc_bool),tc_bool) = X1
| ~ spl0_652
| ~ spl0_1216 ),
inference(superposition,[],[f79134,f17410]) ).
fof(f79134,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(c_Orderings_Obot__class_Obot(tc_bool),X0),tc_bool),X1,tc_bool) = X1
| ~ spl0_1216 ),
inference(avatar_component_clause,[],[f79133]) ).
fof(f79867,plain,
( spl0_1217
| ~ spl0_181
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f79168,f79133,f2624,f79865]) ).
fof(f79865,plain,
( spl0_1217
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(c_Orderings_Obot__class_Obot(tc_bool),X0),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f79168,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(c_Orderings_Obot__class_Obot(tc_bool),X0),tc_bool)
| ~ spl0_181
| ~ spl0_1216 ),
inference(superposition,[],[f79134,f2625]) ).
fof(f79135,plain,
( spl0_1216
| ~ spl0_151
| ~ spl0_1173 ),
inference(avatar_split_clause,[],[f76594,f58341,f2184,f79133]) ).
fof(f76594,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(c_Orderings_Obot__class_Obot(tc_bool),X0),tc_bool),X1,tc_bool) = X1
| ~ spl0_151
| ~ spl0_1173 ),
inference(resolution,[],[f2185,f58342]) ).
fof(f78284,plain,
( spl0_1215
| spl0_23
| ~ spl0_1182 ),
inference(avatar_split_clause,[],[f61992,f61960,f1130,f78282]) ).
fof(f78282,plain,
( spl0_1215
<=> ! [X0,X3,X2,X1] : c_Set_Oimage(X0,hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X1,X2) = c_Set_Oimage(c_Fun_Ofun__upd(X0,c_Arrow__Order__Mirabelle_OLin,X3,X1,X2),hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f61992,plain,
( ! [X2,X3,X0,X1] : c_Set_Oimage(X0,hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X1,X2) = c_Set_Oimage(c_Fun_Ofun__upd(X0,c_Arrow__Order__Mirabelle_OLin,X3,X1,X2),hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X1,X2)
| spl0_23
| ~ spl0_1182 ),
inference(resolution,[],[f61961,f1132]) ).
fof(f78051,plain,
( ~ spl0_1214
| spl0_118
| ~ spl0_1212 ),
inference(avatar_split_clause,[],[f77918,f77915,f1630,f78048]) ).
fof(f1630,plain,
( spl0_118
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f77915,plain,
( spl0_1212
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X0))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f77918,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))
| spl0_118
| ~ spl0_1212 ),
inference(resolution,[],[f77916,f1632]) ).
fof(f1632,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))))
| spl0_118 ),
inference(avatar_component_clause,[],[f1630]) ).
fof(f77916,plain,
( ! [X0] :
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,X0)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X0)) )
| ~ spl0_1212 ),
inference(avatar_component_clause,[],[f77915]) ).
fof(f77928,plain,
( spl0_1213
| spl0_23
| ~ spl0_1199 ),
inference(avatar_split_clause,[],[f69849,f69656,f1130,f77926]) ).
fof(f77926,plain,
( spl0_1213
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X1),c_COMBK(c_Arrow__Order__Mirabelle_OLin,X1,X0),X1,tc_fun(tc_fun(X1,tc_bool),tc_bool),X0),X0,tc_fun(X1,tc_bool),tc_bool),hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f69656,plain,
( spl0_1199
<=> ! [X0,X14,X12,X6] :
( hBOOL(hAPP(X6,X14))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f69849,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X1),c_COMBK(c_Arrow__Order__Mirabelle_OLin,X1,X0),X1,tc_fun(tc_fun(X1,tc_bool),tc_bool),X0),X0,tc_fun(X1,tc_bool),tc_bool),hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))))
| spl0_23
| ~ spl0_1199 ),
inference(resolution,[],[f69657,f1132]) ).
fof(f69657,plain,
( ! [X0,X6,X14,X12] :
( hBOOL(hAPP(X6,X14))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6) )
| ~ spl0_1199 ),
inference(avatar_component_clause,[],[f69656]) ).
fof(f77917,plain,
( spl0_1212
| ~ spl0_52
| ~ spl0_192
| ~ spl0_478
| ~ spl0_594
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f69596,f18286,f14666,f10909,f2678,f1247,f77915]) ).
fof(f14666,plain,
( spl0_594
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f69596,plain,
( ! [X0] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X0))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,X0))) )
| ~ spl0_52
| ~ spl0_192
| ~ spl0_478
| ~ spl0_594
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69595,f19417]) ).
fof(f69595,plain,
( ! [X0] :
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X0),c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl0_52
| ~ spl0_192
| ~ spl0_478
| ~ spl0_594
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69594,f1248]) ).
fof(f69594,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X0),hAPP(v_F,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X0),c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl0_192
| ~ spl0_478
| ~ spl0_594
| ~ spl0_699 ),
inference(forward_demodulation,[],[f69566,f19417]) ).
fof(f69566,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,X0)),hAPP(c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X0),c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl0_478
| ~ spl0_594 ),
inference(resolution,[],[f10910,f14668]) ).
fof(f14668,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))
| ~ spl0_594 ),
inference(avatar_component_clause,[],[f14666]) ).
fof(f77859,plain,
( spl0_1211
| ~ spl0_180
| ~ spl0_1205 ),
inference(avatar_split_clause,[],[f76597,f71197,f2567,f77857]) ).
fof(f77857,plain,
( spl0_1211
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f2567,plain,
( spl0_180
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f76597,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)
| ~ spl0_180
| ~ spl0_1205 ),
inference(superposition,[],[f2568,f71198]) ).
fof(f2568,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f2567]) ).
fof(f76661,plain,
( spl0_1210
| ~ spl0_180
| ~ spl0_1190 ),
inference(avatar_split_clause,[],[f76596,f65089,f2567,f76659]) ).
fof(f76659,plain,
( spl0_1210
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f76596,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool)
| ~ spl0_180
| ~ spl0_1190 ),
inference(superposition,[],[f2568,f65090]) ).
fof(f74633,plain,
( spl0_1209
| ~ spl0_1201
| ~ spl0_1206 ),
inference(avatar_split_clause,[],[f73170,f72707,f70304,f74631]) ).
fof(f74631,plain,
( spl0_1209
<=> ! [X2,X1,X3] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),tc_bool),X3,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f70304,plain,
( spl0_1201
<=> ! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool),tc_bool),X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f72707,plain,
( spl0_1206
<=> ! [X0,X1] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f73170,plain,
( ! [X2,X3,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),tc_bool),X3,tc_bool)
| ~ spl0_1201
| ~ spl0_1206 ),
inference(superposition,[],[f70305,f72708]) ).
fof(f72708,plain,
( ! [X0,X1] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool)
| ~ spl0_1206 ),
inference(avatar_component_clause,[],[f72707]) ).
fof(f70305,plain,
( ! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool),tc_bool),X2,tc_bool)
| ~ spl0_1201 ),
inference(avatar_component_clause,[],[f70304]) ).
fof(f73861,plain,
( spl0_1208
| ~ spl0_192
| ~ spl0_617
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56438,f18286,f15958,f2678,f73859]) ).
fof(f73859,plain,
( spl0_1208
<=> ! [X56,X10,X0,X18,X8,X6,X55,X7,X17,X9,X12] :
( ~ hBOOL(hAPP(c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12),X10))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18),X17))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X8,c_COMBK(X9,tc_fun(X56,tc_bool),X18),X18,X56),X55))
| c_FuncSet_Orestrict(c_COMBB(X55,c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X18,X56,X0),X6,X0,X56) = c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBB(X55,X17,X18,X56,X12),X7,X12,X56),X10,X12,X56,X0),X6,X0,X56) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f15958,plain,
( spl0_617
<=> ! [X56,X10,X0,X55,X18,X8,X6,X9,X7,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X12,X18)),X17),c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X18,X56)),X55),c_FuncSet_OPi(X8,c_COMBK(X9,tc_fun(X56,tc_bool),X18),X18,X56)))
| c_FuncSet_Orestrict(c_COMBB(X55,c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X18,X56,X0),X6,X0,X56) = c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBB(X55,X17,X18,X56,X12),X7,X12,X56),X10,X12,X56,X0),X6,X0,X56) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f56438,plain,
( ! [X10,X0,X18,X8,X6,X9,X7,X56,X55,X17,X12] :
( ~ hBOOL(hAPP(c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12),X10))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18),X17))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X8,c_COMBK(X9,tc_fun(X56,tc_bool),X18),X18,X56),X55))
| c_FuncSet_Orestrict(c_COMBB(X55,c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X18,X56,X0),X6,X0,X56) = c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBB(X55,X17,X18,X56,X12),X7,X12,X56),X10,X12,X56,X0),X6,X0,X56) )
| ~ spl0_192
| ~ spl0_617
| ~ spl0_699 ),
inference(forward_demodulation,[],[f56437,f19417]) ).
fof(f56437,plain,
( ! [X10,X0,X18,X8,X56,X9,X7,X55,X6,X17,X12] :
( ~ hBOOL(hAPP(c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18),X17))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X8,c_COMBK(X9,tc_fun(X56,tc_bool),X18),X18,X56),X55))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| c_FuncSet_Orestrict(c_COMBB(X55,c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X18,X56,X0),X6,X0,X56) = c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBB(X55,X17,X18,X56,X12),X7,X12,X56),X10,X12,X56,X0),X6,X0,X56) )
| ~ spl0_192
| ~ spl0_617
| ~ spl0_699 ),
inference(forward_demodulation,[],[f56436,f19417]) ).
fof(f56436,plain,
( ! [X10,X0,X56,X8,X18,X9,X55,X7,X6,X17,X12] :
( ~ hBOOL(hAPP(c_FuncSet_OPi(X8,c_COMBK(X9,tc_fun(X56,tc_bool),X18),X18,X56),X55))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X12,X18)),X17),c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| c_FuncSet_Orestrict(c_COMBB(X55,c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X18,X56,X0),X6,X0,X56) = c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBB(X55,X17,X18,X56,X12),X7,X12,X56),X10,X12,X56,X0),X6,X0,X56) )
| ~ spl0_192
| ~ spl0_617
| ~ spl0_699 ),
inference(forward_demodulation,[],[f15959,f19417]) ).
fof(f15959,plain,
( ! [X10,X0,X18,X56,X8,X55,X9,X7,X6,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X18,X56)),X55),c_FuncSet_OPi(X8,c_COMBK(X9,tc_fun(X56,tc_bool),X18),X18,X56)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X12,X18)),X17),c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| c_FuncSet_Orestrict(c_COMBB(X55,c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X18,X56,X0),X6,X0,X56) = c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBB(X55,X17,X18,X56,X12),X7,X12,X56),X10,X12,X56,X0),X6,X0,X56) )
| ~ spl0_617 ),
inference(avatar_component_clause,[],[f15958]) ).
fof(f73857,plain,
( spl0_1207
| ~ spl0_1197
| ~ spl0_1206 ),
inference(avatar_split_clause,[],[f73169,f72707,f69555,f73855]) ).
fof(f73855,plain,
( spl0_1207
<=> ! [X2,X1,X3] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),X2,tc_bool),X3,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f69555,plain,
( spl0_1197
<=> ! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool),X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f73169,plain,
( ! [X2,X3,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),X2,tc_bool),X3,tc_bool)
| ~ spl0_1197
| ~ spl0_1206 ),
inference(superposition,[],[f69556,f72708]) ).
fof(f69556,plain,
( ! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool),X2,tc_bool)
| ~ spl0_1197 ),
inference(avatar_component_clause,[],[f69555]) ).
fof(f72709,plain,
( spl0_1206
| ~ spl0_1176
| ~ spl0_1190 ),
inference(avatar_split_clause,[],[f65393,f65089,f59838,f72707]) ).
fof(f65393,plain,
( ! [X0,X1] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool)
| ~ spl0_1176
| ~ spl0_1190 ),
inference(superposition,[],[f65090,f59839]) ).
fof(f71199,plain,
( spl0_1205
| ~ spl0_13
| ~ spl0_119
| ~ spl0_1180 ),
inference(avatar_split_clause,[],[f61751,f61559,f1635,f1080,f71197]) ).
fof(f61559,plain,
( spl0_1180
<=> ! [X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),X1,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f61751,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),tc_bool) = X0 )
| ~ spl0_119
| ~ spl0_1180 ),
inference(resolution,[],[f61560,f1636]) ).
fof(f61560,plain,
( ! [X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),X1,tc_bool)
| ~ spl0_1180 ),
inference(avatar_component_clause,[],[f61559]) ).
fof(f71189,plain,
( spl0_1204
| ~ spl0_192
| ~ spl0_584
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56408,f18286,f14405,f2678,f71187]) ).
fof(f71187,plain,
( spl0_1204
<=> ! [X10,X0,X12,X6,X7] :
( ~ hBOOL(hAPP(c_FuncSet_Oextensional(X6,X0,X12),X10))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12),X10))
| c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBI(X12),X7,X12,X12),X10,X12,X12,X0),X6,X0,X12) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f14405,plain,
( spl0_584
<=> ! [X10,X0,X12,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12)))
| c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBI(X12),X7,X12,X12),X10,X12,X12,X0),X6,X0,X12) = X10
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f56408,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(c_FuncSet_Oextensional(X6,X0,X12),X10))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12),X10))
| c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBI(X12),X7,X12,X12),X10,X12,X12,X0),X6,X0,X12) = X10 )
| ~ spl0_192
| ~ spl0_584
| ~ spl0_699 ),
inference(forward_demodulation,[],[f56407,f19417]) ).
fof(f56407,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12),X10))
| c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBI(X12),X7,X12,X12),X10,X12,X12,X0),X6,X0,X12) = X10
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12))) )
| ~ spl0_192
| ~ spl0_584
| ~ spl0_699 ),
inference(forward_demodulation,[],[f14406,f19417]) ).
fof(f14406,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBI(X12),X7,X12,X12),X10,X12,X12,X0),X6,X0,X12) = X10
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12))) )
| ~ spl0_584 ),
inference(avatar_component_clause,[],[f14405]) ).
fof(f71185,plain,
( spl0_1203
| ~ spl0_192
| ~ spl0_583
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56395,f18286,f14401,f2678,f71183]) ).
fof(f71183,plain,
( spl0_1203
<=> ! [X17,X0,X12,X6,X7] :
( ~ hBOOL(hAPP(c_FuncSet_Oextensional(X6,X0,X12),X17))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12),X17))
| c_FuncSet_Orestrict(c_COMBB(X17,c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0),X0,X12,X0),X6,X0,X12) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f14401,plain,
( spl0_583
<=> ! [X17,X0,X12,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_Oextensional(X6,X0,X12)))
| c_FuncSet_Orestrict(c_COMBB(X17,c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0),X0,X12,X0),X6,X0,X12) = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f56395,plain,
( ! [X0,X6,X7,X17,X12] :
( ~ hBOOL(hAPP(c_FuncSet_Oextensional(X6,X0,X12),X17))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12),X17))
| c_FuncSet_Orestrict(c_COMBB(X17,c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0),X0,X12,X0),X6,X0,X12) = X17 )
| ~ spl0_192
| ~ spl0_583
| ~ spl0_699 ),
inference(forward_demodulation,[],[f56394,f19417]) ).
fof(f56394,plain,
( ! [X0,X6,X7,X17,X12] :
( ~ hBOOL(hAPP(c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12),X17))
| c_FuncSet_Orestrict(c_COMBB(X17,c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0),X0,X12,X0),X6,X0,X12) = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_Oextensional(X6,X0,X12))) )
| ~ spl0_192
| ~ spl0_583
| ~ spl0_699 ),
inference(forward_demodulation,[],[f14402,f19417]) ).
fof(f14402,plain,
( ! [X0,X6,X7,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| c_FuncSet_Orestrict(c_COMBB(X17,c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0),X0,X12,X0),X6,X0,X12) = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_Oextensional(X6,X0,X12))) )
| ~ spl0_583 ),
inference(avatar_component_clause,[],[f14401]) ).
fof(f70920,plain,
( spl0_1202
| ~ spl0_192
| ~ spl0_586
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56170,f18286,f14415,f2678,f70918]) ).
fof(f70918,plain,
( spl0_1202
<=> ! [X2,X10,X0,X12,X6,X1] :
( ~ hBOOL(hAPP(X6,X1))
| c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X12),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f14415,plain,
( spl0_586
<=> ! [X2,X10,X0,X12,X6,X1] :
( c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X12),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f56170,plain,
( ! [X2,X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(X6,X1))
| c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X12),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)) )
| ~ spl0_192
| ~ spl0_586
| ~ spl0_699 ),
inference(forward_demodulation,[],[f14416,f19417]) ).
fof(f14416,plain,
( ! [X2,X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X12),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)) )
| ~ spl0_586 ),
inference(avatar_component_clause,[],[f14415]) ).
fof(f70306,plain,
( spl0_1201
| ~ spl0_14
| ~ spl0_896
| ~ spl0_1175 ),
inference(avatar_split_clause,[],[f59723,f59551,f32410,f1085,f70304]) ).
fof(f1085,plain,
( spl0_14
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f32410,plain,
( spl0_896
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f59723,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_bool)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool),tc_bool),X2,tc_bool) )
| ~ spl0_896
| ~ spl0_1175 ),
inference(resolution,[],[f59552,f32411]) ).
fof(f32411,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2) )
| ~ spl0_896 ),
inference(avatar_component_clause,[],[f32410]) ).
fof(f70081,plain,
( spl0_1200
| ~ spl0_192
| ~ spl0_573
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56047,f18286,f13995,f2678,f70079]) ).
fof(f13995,plain,
( spl0_573
<=> ! [X0,X6,X1,X7] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f56047,plain,
( ! [X0,X1,X6,X7] :
( hBOOL(hAPP(X7,X1))
| c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) )
| ~ spl0_192
| ~ spl0_573
| ~ spl0_699 ),
inference(forward_demodulation,[],[f13996,f19417]) ).
fof(f13996,plain,
( ! [X0,X1,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) )
| ~ spl0_573 ),
inference(avatar_component_clause,[],[f13995]) ).
fof(f69658,plain,
( spl0_1199
| ~ spl0_192
| ~ spl0_523
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56883,f18286,f11987,f2678,f69656]) ).
fof(f11987,plain,
( spl0_523
<=> ! [X0,X14,X12,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6)
| hBOOL(hAPP(hAPP(c_in(X12),X14),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f56883,plain,
( ! [X0,X6,X14,X12] :
( hBOOL(hAPP(X6,X14))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6) )
| ~ spl0_192
| ~ spl0_523
| ~ spl0_699 ),
inference(forward_demodulation,[],[f11988,f19417]) ).
fof(f11988,plain,
( ! [X0,X6,X14,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),X14),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6) )
| ~ spl0_523 ),
inference(avatar_component_clause,[],[f11987]) ).
fof(f69654,plain,
( spl0_1198
| ~ spl0_192
| ~ spl0_522
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56286,f18286,f11983,f2678,f69652]) ).
fof(f69652,plain,
( spl0_1198
<=> ! [X0,X14,X12,X6] :
( ~ hBOOL(hAPP(X6,X14))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f11983,plain,
( spl0_522
<=> ! [X0,X14,X12,X6] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6)
| ~ hBOOL(hAPP(hAPP(c_in(X12),X14),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f56286,plain,
( ! [X0,X6,X14,X12] :
( ~ hBOOL(hAPP(X6,X14))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6) )
| ~ spl0_192
| ~ spl0_522
| ~ spl0_699 ),
inference(forward_demodulation,[],[f11984,f19417]) ).
fof(f11984,plain,
( ! [X0,X6,X14,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X14),X6))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6) )
| ~ spl0_522 ),
inference(avatar_component_clause,[],[f11983]) ).
fof(f69557,plain,
( spl0_1197
| ~ spl0_14
| ~ spl0_895
| ~ spl0_1175 ),
inference(avatar_split_clause,[],[f59722,f59551,f32406,f1085,f69555]) ).
fof(f32406,plain,
( spl0_895
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f59722,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_bool)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool),X2,tc_bool) )
| ~ spl0_895
| ~ spl0_1175 ),
inference(resolution,[],[f59552,f32407]) ).
fof(f32407,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2) )
| ~ spl0_895 ),
inference(avatar_component_clause,[],[f32406]) ).
fof(f69347,plain,
( spl0_1196
| ~ spl0_192
| ~ spl0_529
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56825,f18286,f12582,f2678,f69345]) ).
fof(f69345,plain,
( spl0_1196
<=> ! [X0,X8,X6,X1] :
( ~ hBOOL(hAPP(X8,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f56825,plain,
( ! [X0,X1,X8,X6] :
( ~ hBOOL(hAPP(X8,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X6,tc_fun(X0,tc_bool)) )
| ~ spl0_192
| ~ spl0_529
| ~ spl0_699 ),
inference(forward_demodulation,[],[f12583,f19417]) ).
fof(f68788,plain,
( spl0_1195
| ~ spl0_1174
| ~ spl0_1190 ),
inference(avatar_split_clause,[],[f65392,f65089,f59044,f68786]) ).
fof(f68786,plain,
( spl0_1195
<=> ! [X0,X1] : c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f65392,plain,
( ! [X0,X1] : c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool)
| ~ spl0_1174
| ~ spl0_1190 ),
inference(superposition,[],[f65090,f59045]) ).
fof(f67313,plain,
( ~ spl0_13
| spl0_1194
| ~ spl0_63
| ~ spl0_1187 ),
inference(avatar_split_clause,[],[f64578,f63106,f1297,f67311,f1080]) ).
fof(f1297,plain,
( spl0_63
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f64578,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool),X2,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_63
| ~ spl0_1187 ),
inference(superposition,[],[f1298,f63107]) ).
fof(f1298,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1297]) ).
fof(f65867,plain,
( ~ spl0_13
| spl0_1193
| ~ spl0_63
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f64164,f62696,f1297,f65865,f1080]) ).
fof(f64164,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool),X2,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_63
| ~ spl0_1184 ),
inference(superposition,[],[f1298,f62697]) ).
fof(f65758,plain,
( spl0_1192
| ~ spl0_192
| ~ spl0_437
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56335,f18286,f9963,f2678,f65756]) ).
fof(f65756,plain,
( spl0_1192
<=> ! [X6,X0,X12,X27,X26] :
( ~ hBOOL(hAPP(X26,X27))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X6,X27),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f9963,plain,
( spl0_437
<=> ! [X6,X0,X12,X27,X26] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X27),X26))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X6,X27),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f56335,plain,
( ! [X0,X6,X26,X27,X12] :
( ~ hBOOL(hAPP(X26,X27))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X6,X27),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) )
| ~ spl0_192
| ~ spl0_437
| ~ spl0_699 ),
inference(forward_demodulation,[],[f9964,f19417]) ).
fof(f9964,plain,
( ! [X0,X6,X26,X27,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X27),X26))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X6,X27),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) )
| ~ spl0_437 ),
inference(avatar_component_clause,[],[f9963]) ).
fof(f65175,plain,
( spl0_1191
| ~ spl0_192
| ~ spl0_495
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56007,f18286,f11316,f2678,f65173]) ).
fof(f65173,plain,
( spl0_1191
<=> ! [X0,X6,X1,X7] :
( ~ hBOOL(hAPP(X7,X1))
| c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f11316,plain,
( spl0_495
<=> ! [X0,X6,X1,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f56007,plain,
( ! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(X7,X1))
| c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) )
| ~ spl0_192
| ~ spl0_495
| ~ spl0_699 ),
inference(forward_demodulation,[],[f11317,f19417]) ).
fof(f11317,plain,
( ! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) )
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f11316]) ).
fof(f65091,plain,
( spl0_1190
| ~ spl0_13
| ~ spl0_119
| ~ spl0_1175 ),
inference(avatar_split_clause,[],[f59708,f59551,f1635,f1080,f65089]) ).
fof(f59708,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_bool),tc_bool) = X0 )
| ~ spl0_119
| ~ spl0_1175 ),
inference(resolution,[],[f59552,f1636]) ).
fof(f64789,plain,
( spl0_1189
| ~ spl0_192
| ~ spl0_402
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56881,f18286,f7924,f2678,f64787]) ).
fof(f64787,plain,
( spl0_1189
<=> ! [X0,X12,X6,X1,X7] :
( ~ hBOOL(hAPP(X6,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X7,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f7924,plain,
( spl0_402
<=> ! [X7,X0,X12,X6,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X7,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f56881,plain,
( ! [X0,X1,X6,X7,X12] :
( ~ hBOOL(hAPP(X6,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X7,X1) )
| ~ spl0_192
| ~ spl0_402
| ~ spl0_699 ),
inference(forward_demodulation,[],[f7925,f19417]) ).
fof(f7925,plain,
( ! [X0,X1,X6,X7,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X7,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f7924]) ).
fof(f64427,plain,
( spl0_1188
| ~ spl0_192
| ~ spl0_469
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56487,f18286,f10631,f2678,f64425]) ).
fof(f64425,plain,
( spl0_1188
<=> ! [X10,X0,X6,X3] :
( hBOOL(hAPP(X6,X3))
| c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f10631,plain,
( spl0_469
<=> ! [X10,X0,X6,X3] :
( c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f56487,plain,
( ! [X3,X10,X0,X6] :
( hBOOL(hAPP(X6,X3))
| c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,tc_nat) )
| ~ spl0_192
| ~ spl0_469
| ~ spl0_699 ),
inference(forward_demodulation,[],[f10632,f19417]) ).
fof(f10632,plain,
( ! [X3,X10,X0,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,tc_nat) )
| ~ spl0_469 ),
inference(avatar_component_clause,[],[f10631]) ).
fof(f63108,plain,
( spl0_1187
| ~ spl0_114
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1181 ),
inference(avatar_split_clause,[],[f62372,f61954,f18286,f2678,f1550,f63106]) ).
fof(f62372,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),X0,X1),tc_bool),X2,tc_bool) = X2
| ~ spl0_114
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1181 ),
inference(forward_demodulation,[],[f62304,f19417]) ).
fof(f62304,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin),X0,X1),tc_bool),X2,tc_bool) = X2
| ~ spl0_114
| ~ spl0_1181 ),
inference(resolution,[],[f61955,f1552]) ).
fof(f62865,plain,
( spl0_1186
| ~ spl0_192
| ~ spl0_399
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56833,f18286,f7912,f2678,f62863]) ).
fof(f56833,plain,
( ! [X0,X8,X6] :
( hBOOL(hAPP(X8,c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X6,X8,X0)))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) )
| ~ spl0_192
| ~ spl0_399
| ~ spl0_699 ),
inference(forward_demodulation,[],[f7913,f19417]) ).
fof(f62861,plain,
( spl0_1185
| ~ spl0_192
| ~ spl0_381
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f55853,f18286,f7072,f2678,f62859]) ).
fof(f7072,plain,
( spl0_381
<=> ! [X18,X10,X0,X12,X6,X17,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hAPP(X17,hAPP(X10,X1)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X17,X10,X18,X12,X0),X6,X0,X12),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f55853,plain,
( ! [X10,X0,X1,X18,X6,X17,X12] :
( ~ hBOOL(hAPP(X6,X1))
| hAPP(X17,hAPP(X10,X1)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X17,X10,X18,X12,X0),X6,X0,X12),X1) )
| ~ spl0_192
| ~ spl0_381
| ~ spl0_699 ),
inference(forward_demodulation,[],[f7073,f19417]) ).
fof(f7073,plain,
( ! [X10,X0,X1,X18,X6,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hAPP(X17,hAPP(X10,X1)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X17,X10,X18,X12,X0),X6,X0,X12),X1) )
| ~ spl0_381 ),
inference(avatar_component_clause,[],[f7072]) ).
fof(f62698,plain,
( spl0_1184
| ~ spl0_111
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1181 ),
inference(avatar_split_clause,[],[f62371,f61954,f18286,f2678,f1537,f62696]) ).
fof(f62371,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),X0,X1),tc_bool),X2,tc_bool) = X2
| ~ spl0_111
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1181 ),
inference(forward_demodulation,[],[f62303,f19417]) ).
fof(f62303,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin),X0,X1),tc_bool),X2,tc_bool) = X2
| ~ spl0_111
| ~ spl0_1181 ),
inference(resolution,[],[f61955,f1539]) ).
fof(f62582,plain,
( spl0_1183
| ~ spl0_192
| ~ spl0_471
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56278,f18286,f10712,f2678,f62580]) ).
fof(f62580,plain,
( spl0_1183
<=> ! [X24,X0,X31,X6] :
( ~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(X6,X24,X0),X31))
| c_Relation_OImage(X24,hAPP(c_fequal(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0,X0) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f10712,plain,
( spl0_471
<=> ! [X24,X0,X31,X6] :
( c_Relation_OImage(X24,hAPP(c_fequal(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0,X0) = X31
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f56278,plain,
( ! [X31,X0,X6,X24] :
( ~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(X6,X24,X0),X31))
| c_Relation_OImage(X24,hAPP(c_fequal(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0,X0) = X31 )
| ~ spl0_192
| ~ spl0_471
| ~ spl0_699 ),
inference(forward_demodulation,[],[f10713,f19417]) ).
fof(f10713,plain,
( ! [X31,X0,X6,X24] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| c_Relation_OImage(X24,hAPP(c_fequal(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0,X0) = X31 )
| ~ spl0_471 ),
inference(avatar_component_clause,[],[f10712]) ).
fof(f61962,plain,
( spl0_1182
| ~ spl0_192
| ~ spl0_334
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56148,f18286,f5623,f2678,f61960]) ).
fof(f5623,plain,
( spl0_334
<=> ! [X2,X10,X0,X12,X6,X1] :
( hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| c_Set_Oimage(X10,X6,X12,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f56148,plain,
( ! [X2,X10,X0,X1,X6,X12] :
( hBOOL(hAPP(X6,X1))
| c_Set_Oimage(X10,X6,X12,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) )
| ~ spl0_192
| ~ spl0_334
| ~ spl0_699 ),
inference(forward_demodulation,[],[f5624,f19417]) ).
fof(f5624,plain,
( ! [X2,X10,X0,X1,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| c_Set_Oimage(X10,X6,X12,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) )
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f5623]) ).
fof(f61956,plain,
( spl0_1181
| ~ spl0_52
| ~ spl0_1173 ),
inference(avatar_split_clause,[],[f58645,f58341,f1247,f61954]) ).
fof(f58645,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBK(X0,X1,X2),tc_bool),X3,tc_bool) = X3 )
| ~ spl0_52
| ~ spl0_1173 ),
inference(superposition,[],[f58342,f1248]) ).
fof(f61561,plain,
( ~ spl0_13
| spl0_1180
| ~ spl0_63
| ~ spl0_1176 ),
inference(avatar_split_clause,[],[f60632,f59838,f1297,f61559,f1080]) ).
fof(f60632,plain,
( ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),X1,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_63
| ~ spl0_1176 ),
inference(superposition,[],[f1298,f59839]) ).
fof(f60999,plain,
( ~ spl0_18
| spl0_1179
| ~ spl0_306
| ~ spl0_655
| ~ spl0_1070
| ~ spl0_1174 ),
inference(avatar_split_clause,[],[f59382,f59044,f42475,f17432,f4658,f60997,f1105]) ).
fof(f60997,plain,
( spl0_1179
<=> ! [X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f42475,plain,
( spl0_1070
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f59382,plain,
( ! [X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_306
| ~ spl0_655
| ~ spl0_1070
| ~ spl0_1174 ),
inference(forward_demodulation,[],[f59381,f59045]) ).
fof(f59381,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),tc_bool),tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_306
| ~ spl0_655
| ~ spl0_1070
| ~ spl0_1174 ),
inference(forward_demodulation,[],[f59366,f49867]) ).
fof(f49867,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool)
| ~ spl0_655
| ~ spl0_1070 ),
inference(superposition,[],[f42476,f17433]) ).
fof(f42476,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool)
| ~ spl0_1070 ),
inference(avatar_component_clause,[],[f42475]) ).
fof(f59366,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X2,tc_bool),tc_bool),tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_306
| ~ spl0_1174 ),
inference(superposition,[],[f4659,f59045]) ).
fof(f60189,plain,
( spl0_1177
| ~ spl0_1178
| ~ spl0_29
| ~ spl0_1173 ),
inference(avatar_split_clause,[],[f58646,f58341,f1155,f60186,f60183]) ).
fof(f60183,plain,
( spl0_1177
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBI(X0),tc_bool),X1,tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f60186,plain,
( spl0_1178
<=> hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f58646,plain,
( ! [X0,X1] :
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_COMBI(X0),tc_bool),X1,tc_bool) = X1 )
| ~ spl0_29
| ~ spl0_1173 ),
inference(superposition,[],[f58342,f1156]) ).
fof(f59840,plain,
( spl0_1176
| ~ spl0_45
| ~ spl0_1173 ),
inference(avatar_split_clause,[],[f58630,f58341,f1219,f59838]) ).
fof(f58630,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),X1,tc_bool) = X1
| ~ spl0_45
| ~ spl0_1173 ),
inference(resolution,[],[f58342,f1220]) ).
fof(f59633,plain,
( spl0_879
| ~ spl0_192
| ~ spl0_526
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f55980,f18286,f12001,f2678,f26977]) ).
fof(f26977,plain,
( spl0_879
<=> ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| hBOOL(hAPP(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f55980,plain,
( ! [X0,X1,X6] :
( hBOOL(hAPP(X6,X1))
| c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_192
| ~ spl0_526
| ~ spl0_699 ),
inference(forward_demodulation,[],[f12002,f19417]) ).
fof(f59553,plain,
( ~ spl0_13
| spl0_1175
| ~ spl0_63
| ~ spl0_1174 ),
inference(avatar_split_clause,[],[f59327,f59044,f1297,f59551,f1080]) ).
fof(f59327,plain,
( ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_63
| ~ spl0_1174 ),
inference(superposition,[],[f1298,f59045]) ).
fof(f59392,plain,
( spl0_785
| ~ spl0_192
| ~ spl0_239
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f55969,f18286,f3152,f2678,f23202]) ).
fof(f23202,plain,
( spl0_785
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_FuncSet_Orestrict(X0,X1,X2,X3),X4) = c_HOL_Oundefined(X3)
| hBOOL(hAPP(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f55969,plain,
( ! [X10,X0,X1,X6,X12] :
( hBOOL(hAPP(X6,X1))
| hAPP(c_FuncSet_Orestrict(X10,X6,X12,X0),X1) = c_HOL_Oundefined(X0) )
| ~ spl0_192
| ~ spl0_239
| ~ spl0_699 ),
inference(forward_demodulation,[],[f3153,f19417]) ).
fof(f59046,plain,
( spl0_1174
| ~ spl0_44
| ~ spl0_1173 ),
inference(avatar_split_clause,[],[f58634,f58341,f1215,f59044]) ).
fof(f58634,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool) = X1
| ~ spl0_44
| ~ spl0_1173 ),
inference(resolution,[],[f58342,f1216]) ).
fof(f58343,plain,
( spl0_1173
| ~ spl0_13
| ~ spl0_116
| ~ spl0_1163 ),
inference(avatar_split_clause,[],[f57920,f52810,f1622,f1080,f58341]) ).
fof(f1622,plain,
( spl0_116
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f57920,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(X0,tc_bool),X1,tc_bool) = X1
| ~ hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_bool))) )
| ~ spl0_116
| ~ spl0_1163 ),
inference(resolution,[],[f1623,f52811]) ).
fof(f1623,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2 )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1622]) ).
fof(f57390,plain,
( spl0_1172
| ~ spl0_178
| ~ spl0_764 ),
inference(avatar_split_clause,[],[f56390,f20188,f2292,f57388]) ).
fof(f57388,plain,
( spl0_1172
<=> ! [X0,X3] :
( c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),X3),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f56390,plain,
( ! [X3,X0] :
( c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(X0),X3),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_178
| ~ spl0_764 ),
inference(forward_demodulation,[],[f2293,f20189]) ).
fof(f57386,plain,
( spl0_1171
| ~ spl0_179
| ~ spl0_764 ),
inference(avatar_split_clause,[],[f56373,f20188,f2296,f57384]) ).
fof(f57384,plain,
( spl0_1171
<=> ! [X0,X3] :
( c_Complete__Lattice_OSup__class_OSup(hAPP(c_fequal(X0),X3),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f56373,plain,
( ! [X3,X0] :
( c_Complete__Lattice_OSup__class_OSup(hAPP(c_fequal(X0),X3),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_179
| ~ spl0_764 ),
inference(forward_demodulation,[],[f2297,f20189]) ).
fof(f57038,plain,
( spl0_24
| ~ spl0_176
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f56485,f18286,f2284,f1135]) ).
fof(f2284,plain,
( spl0_176
<=> ! [X6,X0] : c_Collect(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X6),X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f56485,plain,
( ! [X0,X6] : c_Collect(X6,X0) = X6
| ~ spl0_176
| ~ spl0_699 ),
inference(forward_demodulation,[],[f2285,f18287]) ).
fof(f2285,plain,
( ! [X0,X6] : c_Collect(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X6),X0) = X6
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f2284]) ).
fof(f55837,plain,
( spl0_1170
| ~ spl0_1089
| ~ spl0_1167 ),
inference(avatar_split_clause,[],[f52880,f52830,f43915,f55835]) ).
fof(f55835,plain,
( spl0_1170
<=> ! [X2,X1] : c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X1,tc_bool),X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f43915,plain,
( spl0_1089
<=> ! [X2,X5] : c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_bool),X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f52830,plain,
( spl0_1167
<=> ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f52880,plain,
( ! [X2,X1] : c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X1,tc_bool),X2,tc_bool)
| ~ spl0_1089
| ~ spl0_1167 ),
inference(superposition,[],[f43916,f52831]) ).
fof(f52831,plain,
( ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X3
| ~ spl0_1167 ),
inference(avatar_component_clause,[],[f52830]) ).
fof(f43916,plain,
( ! [X2,X5] : c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_bool),X2,tc_bool)
| ~ spl0_1089 ),
inference(avatar_component_clause,[],[f43915]) ).
fof(f55569,plain,
( spl0_1169
| ~ spl0_89
| ~ spl0_274
| ~ spl0_317
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5972,f5631,f4702,f3686,f1445,f55567]) ).
fof(f55567,plain,
( spl0_1169
<=> ! [X0,X3,X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f3686,plain,
( spl0_274
<=> ! [X6,X0,X3] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f5972,plain,
( ! [X2,X3,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_89
| ~ spl0_274
| ~ spl0_317
| ~ spl0_336 ),
inference(forward_demodulation,[],[f5900,f5265]) ).
fof(f5900,plain,
( ! [X2,X3,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_274
| ~ spl0_336 ),
inference(superposition,[],[f3687,f5632]) ).
fof(f3687,plain,
( ! [X3,X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool))
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f3686]) ).
fof(f52835,plain,
( spl0_1167
| spl0_1168
| ~ spl0_52
| ~ spl0_293
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f5430,f5334,f4170,f1247,f52833,f52830]) ).
fof(f52833,plain,
( spl0_1168
<=> ! [X4,X0,X1] :
( X0 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),hAPP(c_fequal(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f4170,plain,
( spl0_293
<=> ! [X0,X14,X12,X6] :
( c_Set_Oimage(c_COMBK(X14,X0,X12),X6,X12,X0) = hAPP(c_fequal(X0),X14)
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f5430,plain,
( ! [X2,X3,X0,X1,X4] :
( X0 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),hAPP(c_fequal(X1),X0)))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X3 )
| ~ spl0_52
| ~ spl0_293
| ~ spl0_319 ),
inference(forward_demodulation,[],[f5427,f1248]) ).
fof(f5427,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),hAPP(c_fequal(X1),X0)))
| hAPP(c_COMBK(X0,X1,X2),hAPP(c_Hilbert__Choice_Oinv__into(X3,c_COMBK(X0,X1,X2),X2,X1),X4)) = X4
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X3 )
| ~ spl0_293
| ~ spl0_319 ),
inference(superposition,[],[f5335,f4171]) ).
fof(f4171,plain,
( ! [X0,X6,X14,X12] :
( c_Set_Oimage(c_COMBK(X14,X0,X12),X6,X12,X0) = hAPP(c_fequal(X0),X14)
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6 )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f4170]) ).
fof(f52828,plain,
( spl0_1166
| ~ spl0_112
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f5422,f5334,f1542,f52826]) ).
fof(f52826,plain,
( spl0_1166
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X1,X0,X2,X3),X4)) = X4
| ~ hBOOL(hAPP(c_Set_Oimage(X0,X1,X2,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f5422,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X1,X0,X2,X3),X4)) = X4
| ~ hBOOL(hAPP(c_Set_Oimage(X0,X1,X2,X3),X4)) )
| ~ spl0_112
| ~ spl0_319 ),
inference(resolution,[],[f5335,f1543]) ).
fof(f52822,plain,
( spl0_1165
| ~ spl0_71
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f5138,f4670,f1329,f52820]) ).
fof(f52820,plain,
( spl0_1165
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X0))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,c_Set_OPow(X0,X1),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f4670,plain,
( spl0_309
<=> ! [X6,X0,X8] :
( hBOOL(hAPP(hAPP(c_in(X0),X6),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X6,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f5138,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X0))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,c_Set_OPow(X0,X1),X1))) )
| ~ spl0_71
| ~ spl0_309 ),
inference(superposition,[],[f4671,f1330]) ).
fof(f4671,plain,
( ! [X0,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X0),X6),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X6,X8,X0))) )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f4670]) ).
fof(f52816,plain,
( spl0_1164
| ~ spl0_29
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4643,f4514,f1155,f52814]) ).
fof(f52814,plain,
( spl0_1164
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X2),X1),c_Set_Oimage(c_COMBI(X0),X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f4643,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X2),X1),c_Set_Oimage(c_COMBI(X0),X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X1),X3)) )
| ~ spl0_29
| ~ spl0_303 ),
inference(superposition,[],[f4515,f1156]) ).
fof(f52812,plain,
( ~ spl0_12
| spl0_1163
| ~ spl0_705
| ~ spl0_1143 ),
inference(avatar_split_clause,[],[f52696,f52618,f18334,f52810,f1075]) ).
fof(f18334,plain,
( spl0_705
<=> ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,X1),X2,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f52696,plain,
( ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,tc_bool),X1,tc_bool)
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| ~ hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_bool))) )
| ~ spl0_705
| ~ spl0_1143 ),
inference(resolution,[],[f52619,f18335]) ).
fof(f18335,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,X1),X2,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(X0,X2)) )
| ~ spl0_705 ),
inference(avatar_component_clause,[],[f18334]) ).
fof(f52756,plain,
( spl0_1162
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1161 ),
inference(avatar_split_clause,[],[f52752,f52749,f18286,f2678,f52754]) ).
fof(f52754,plain,
( spl0_1162
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,X0))
| ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f52749,plain,
( spl0_1161
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f52752,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X2,X0))
| ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1161 ),
inference(forward_demodulation,[],[f52750,f19417]) ).
fof(f52750,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X0),X2)) )
| ~ spl0_1161 ),
inference(avatar_component_clause,[],[f52749]) ).
fof(f52751,plain,
( spl0_1161
| ~ spl0_110
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4601,f4502,f1533,f52749]) ).
fof(f4601,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Set_OPow(X0,X1),X2,tc_fun(tc_fun(X1,tc_bool),tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X0),X2)) )
| ~ spl0_110
| ~ spl0_300 ),
inference(resolution,[],[f4503,f1534]) ).
fof(f52747,plain,
( spl0_1160
| ~ spl0_276
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4551,f4490,f4102,f52745]) ).
fof(f52745,plain,
( spl0_1160
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,X3,X2,X4),c_Set_Oimage(X3,X0,X2,X4),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f4551,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,X3,X2,X4),c_Set_Oimage(X3,X0,X2,X4),X4,X2) )
| ~ spl0_276
| ~ spl0_297 ),
inference(resolution,[],[f4491,f4103]) ).
fof(f52741,plain,
( spl0_1159
| ~ spl0_139
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4444,f4166,f1846,f52739]) ).
fof(f52739,plain,
( spl0_1159
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f4444,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool))))
| ~ spl0_139
| ~ spl0_292 ),
inference(superposition,[],[f4167,f1847]) ).
fof(f52736,plain,
( spl0_1158
| ~ spl0_177
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4404,f4158,f2288,f52734]) ).
fof(f52734,plain,
( spl0_1158
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X3,X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f4404,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X3,X0,X2))) )
| ~ spl0_177
| ~ spl0_290 ),
inference(resolution,[],[f4159,f2289]) ).
fof(f52731,plain,
( spl0_1157
| ~ spl0_177
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4383,f4150,f2288,f52729]) ).
fof(f52729,plain,
( spl0_1157
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f4383,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X0,X3))) )
| ~ spl0_177
| ~ spl0_288 ),
inference(resolution,[],[f4151,f2289]) ).
fof(f52727,plain,
( spl0_1156
| ~ spl0_141
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f4328,f4130,f1854,f52725]) ).
fof(f52725,plain,
( spl0_1156
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f1854,plain,
( spl0_141
<=> ! [X6,X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f4328,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = X0 )
| ~ spl0_141
| ~ spl0_283 ),
inference(superposition,[],[f4131,f1855]) ).
fof(f1855,plain,
( ! [X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool))
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1854]) ).
fof(f52723,plain,
( spl0_1155
| ~ spl0_149
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3780,f3588,f2176,f52721]) ).
fof(f52721,plain,
( spl0_1155
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) != X1
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f2176,plain,
( spl0_149
<=> ! [X6,X0,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f3780,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) != X1
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) )
| ~ spl0_149
| ~ spl0_251 ),
inference(superposition,[],[f2177,f3589]) ).
fof(f2177,plain,
( ! [X0,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != X7
| c_lessequals(X6,X7,tc_fun(X0,tc_bool)) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f2176]) ).
fof(f52719,plain,
( spl0_1154
| ~ spl0_106
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3736,f3584,f1517,f52717]) ).
fof(f52717,plain,
( spl0_1154
<=> ! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f3736,plain,
( ! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| ~ spl0_106
| ~ spl0_250 ),
inference(superposition,[],[f3585,f1518]) ).
fof(f52661,plain,
( spl0_1153
| ~ spl0_116
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f3435,f3108,f1622,f52659]) ).
fof(f52659,plain,
( spl0_1153
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,X2),X1,X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f3108,plain,
( spl0_228
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X1,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f3435,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,X2),X1,X2) = X1 )
| ~ spl0_116
| ~ spl0_228 ),
inference(duplicate_literal_removal,[],[f3398]) ).
fof(f3398,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,X2),X1,X2) = X1 )
| ~ spl0_116
| ~ spl0_228 ),
inference(resolution,[],[f3109,f1623]) ).
fof(f3109,plain,
( ! [X2,X0,X1,X5] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X1,X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f3108]) ).
fof(f52657,plain,
( spl0_1152
| ~ spl0_119
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f3434,f3108,f1635,f52655]) ).
fof(f52655,plain,
( spl0_1152
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X3,X2),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f3434,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X3,X2),X2) = X1 )
| ~ spl0_119
| ~ spl0_228 ),
inference(duplicate_literal_removal,[],[f3399]) ).
fof(f3399,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X3,X2),X2) = X1 )
| ~ spl0_119
| ~ spl0_228 ),
inference(resolution,[],[f3109,f1636]) ).
fof(f52653,plain,
( spl0_1151
| ~ spl0_120
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f3217,f3047,f1639,f52651]) ).
fof(f52651,plain,
( spl0_1151
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X0,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f1639,plain,
( spl0_120
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f3047,plain,
( spl0_215
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X1,X4,X0)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f3217,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X0,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2),X2) = X0 )
| ~ spl0_120
| ~ spl0_215 ),
inference(duplicate_literal_removal,[],[f3181]) ).
fof(f3181,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X0,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2),X2) = X0 )
| ~ spl0_120
| ~ spl0_215 ),
inference(resolution,[],[f3048,f1640]) ).
fof(f1640,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X1 )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1639]) ).
fof(f3048,plain,
( ! [X3,X0,X1,X4] :
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X1,X4,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f3047]) ).
fof(f52649,plain,
( spl0_1150
| ~ spl0_122
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f3216,f3047,f1647,f52647]) ).
fof(f52647,plain,
( spl0_1150
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X0,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2),X0,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f1647,plain,
( spl0_122
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f3216,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X0,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2),X0,X2) = X0 )
| ~ spl0_122
| ~ spl0_215 ),
inference(duplicate_literal_removal,[],[f3182]) ).
fof(f3182,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X0,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2),X0,X2) = X0 )
| ~ spl0_122
| ~ spl0_215 ),
inference(resolution,[],[f3048,f1648]) ).
fof(f1648,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X2 )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1647]) ).
fof(f52644,plain,
( spl0_1149
| ~ spl0_73
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2970,f2831,f1357,f52642]) ).
fof(f52642,plain,
( spl0_1149
<=> ! [X5,X4,X2,X0,X6,X3,X1] : hBOOL(hAPP(hAPP(c_in(X5),X2),c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool)),X6,X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f2970,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(hAPP(hAPP(c_in(X5),X2),c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool)),X6,X5)))
| ~ spl0_73
| ~ spl0_203 ),
inference(superposition,[],[f2832,f1358]) ).
fof(f52640,plain,
( spl0_1148
| ~ spl0_193
| ~ spl0_194
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2958,f2819,f2686,f2682,f52638]) ).
fof(f52638,plain,
( spl0_1148
<=> ! [X0,X3,X2,X1] :
( c_Fun_Obij__betw(X0,X1,c_Set_Oimage(X0,X1,X2,X3),X2,X3)
| ~ c_Fun_Oinj__on(c_FuncSet_Orestrict(X0,X1,X2,X3),X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f2819,plain,
( spl0_200
<=> ! [X10,X0,X12,X6,X7] :
( c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| ~ c_Fun_Obij__betw(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X7,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2958,plain,
( ! [X2,X3,X0,X1] :
( c_Fun_Obij__betw(X0,X1,c_Set_Oimage(X0,X1,X2,X3),X2,X3)
| ~ c_Fun_Oinj__on(c_FuncSet_Orestrict(X0,X1,X2,X3),X1,X2,X3) )
| ~ spl0_193
| ~ spl0_194
| ~ spl0_200 ),
inference(forward_demodulation,[],[f2957,f2687]) ).
fof(f2957,plain,
( ! [X2,X3,X0,X1] :
( c_Fun_Obij__betw(X0,X1,c_Set_Oimage(c_FuncSet_Orestrict(X0,X1,X2,X3),X1,X2,X3),X2,X3)
| ~ c_Fun_Oinj__on(c_FuncSet_Orestrict(X0,X1,X2,X3),X1,X2,X3) )
| ~ spl0_193
| ~ spl0_200 ),
inference(resolution,[],[f2820,f2683]) ).
fof(f2820,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Obij__betw(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X7,X0,X12)
| c_Fun_Obij__betw(X10,X6,X7,X0,X12) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2819]) ).
fof(f52636,plain,
( spl0_1147
| ~ spl0_55
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2951,f2815,f1265,f52634]) ).
fof(f52634,plain,
( spl0_1147
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,X0)),X4),hAPP(X2,X4),X0)
| ~ class_Lattices_Olower__semilattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f1265,plain,
( spl0_55
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f2951,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,X0)),X4),hAPP(X2,X4),X0)
| ~ class_Lattices_Olower__semilattice(tc_fun(X3,X0)) )
| ~ spl0_55
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1266]) ).
fof(f1266,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1265]) ).
fof(f52632,plain,
( spl0_1146
| ~ spl0_56
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2950,f2815,f1269,f52630]) ).
fof(f52630,plain,
( spl0_1146
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,X0)),X4),hAPP(X2,X4),X0)
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f1269,plain,
( spl0_56
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f2950,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,X0)),X4),hAPP(X2,X4),X0)
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) )
| ~ spl0_56
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1270]) ).
fof(f1270,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1269]) ).
fof(f52628,plain,
( spl0_1145
| ~ spl0_54
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2949,f2815,f1261,f52626]) ).
fof(f52626,plain,
( spl0_1145
<=> ! [X2,X4,X0,X3,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,X0)),X4),hAPP(X1,X4),X0)
| ~ class_Lattices_Olower__semilattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f1261,plain,
( spl0_54
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f2949,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,X0)),X4),hAPP(X1,X4),X0)
| ~ class_Lattices_Olower__semilattice(tc_fun(X3,X0)) )
| ~ spl0_54
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1262]) ).
fof(f1262,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1261]) ).
fof(f52624,plain,
( spl0_1144
| ~ spl0_57
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2948,f2815,f1273,f52622]) ).
fof(f52622,plain,
( spl0_1144
<=> ! [X2,X4,X0,X3,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,X0)),X4),hAPP(X1,X4),X0)
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f1273,plain,
( spl0_57
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f2948,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,X0)),X4),hAPP(X1,X4),X0)
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) )
| ~ spl0_57
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1274]) ).
fof(f1274,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f52620,plain,
( spl0_1143
| ~ spl0_1119
| ~ spl0_1132 ),
inference(avatar_split_clause,[],[f52576,f52573,f45820,f52618]) ).
fof(f45820,plain,
( spl0_1119
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f52573,plain,
( spl0_1132
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),tc_bool)
| c_lessequals(X0,X2,tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f52576,plain,
( ! [X2,X0] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X0,X2,tc_bool) )
| ~ spl0_1119
| ~ spl0_1132 ),
inference(forward_demodulation,[],[f52574,f45821]) ).
fof(f45821,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_bool)
| ~ spl0_1119 ),
inference(avatar_component_clause,[],[f45820]) ).
fof(f52574,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),tc_bool)
| c_lessequals(X0,X2,tc_bool) )
| ~ spl0_1132 ),
inference(avatar_component_clause,[],[f52573]) ).
fof(f52616,plain,
( spl0_1142
| ~ spl0_64
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2941,f2815,f1301,f52614]) ).
fof(f52614,plain,
( spl0_1142
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,X0)),X2),X0)
| ~ class_Lattices_Oupper__semilattice(tc_fun(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f1301,plain,
( spl0_64
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f2941,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,X0)),X2),X0)
| ~ class_Lattices_Oupper__semilattice(tc_fun(X4,X0)) )
| ~ spl0_64
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1302]) ).
fof(f1302,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1301]) ).
fof(f52612,plain,
( spl0_1141
| ~ spl0_65
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2940,f2815,f1305,f52610]) ).
fof(f52610,plain,
( spl0_1141
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,X0)),X2),X0)
| ~ class_Lattices_Olattice(tc_fun(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f1305,plain,
( spl0_65
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f2940,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,X0)),X2),X0)
| ~ class_Lattices_Olattice(tc_fun(X4,X0)) )
| ~ spl0_65
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1306]) ).
fof(f1306,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1305]) ).
fof(f52608,plain,
( spl0_1140
| ~ spl0_63
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2939,f2815,f1297,f52606]) ).
fof(f52606,plain,
( spl0_1140
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,X0)),X2),X0)
| ~ class_Lattices_Oupper__semilattice(tc_fun(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f2939,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,X0)),X2),X0)
| ~ class_Lattices_Oupper__semilattice(tc_fun(X4,X0)) )
| ~ spl0_63
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1298]) ).
fof(f52604,plain,
( spl0_1139
| ~ spl0_66
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2938,f2815,f1309,f52602]) ).
fof(f52602,plain,
( spl0_1139
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,X0)),X2),X0)
| ~ class_Lattices_Olattice(tc_fun(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f1309,plain,
( spl0_66
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f2938,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,X0)),X2),X0)
| ~ class_Lattices_Olattice(tc_fun(X4,X0)) )
| ~ spl0_66
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1310]) ).
fof(f1310,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1309]) ).
fof(f52600,plain,
( spl0_1138
| ~ spl0_167
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2757,f2658,f2248,f52598]) ).
fof(f52598,plain,
( spl0_1138
<=> ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(X0,X1),tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f2757,plain,
( ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(X0,X1),tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) )
| ~ spl0_167
| ~ spl0_187 ),
inference(resolution,[],[f2659,f2249]) ).
fof(f52596,plain,
( spl0_1137
| ~ spl0_95
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2740,f2642,f1473,f52594]) ).
fof(f52594,plain,
( spl0_1137
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f2740,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = X0 )
| ~ spl0_95
| ~ spl0_183 ),
inference(resolution,[],[f2643,f1474]) ).
fof(f52592,plain,
( spl0_1136
| ~ spl0_92
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2731,f2642,f1457,f52590]) ).
fof(f52590,plain,
( spl0_1136
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f2731,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)) = X0 )
| ~ spl0_92
| ~ spl0_183 ),
inference(resolution,[],[f2643,f1458]) ).
fof(f52588,plain,
( spl0_1135
| ~ spl0_91
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2730,f2642,f1453,f52586]) ).
fof(f52586,plain,
( spl0_1135
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f2730,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X0 )
| ~ spl0_91
| ~ spl0_183 ),
inference(resolution,[],[f2643,f1454]) ).
fof(f52584,plain,
( spl0_1134
| ~ spl0_94
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2721,f2642,f1469,f52582]) ).
fof(f52582,plain,
( spl0_1134
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f2721,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X0 )
| ~ spl0_94
| ~ spl0_183 ),
inference(resolution,[],[f2643,f1470]) ).
fof(f52580,plain,
( spl0_1133
| ~ spl0_93
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2720,f2642,f1465,f52578]) ).
fof(f52578,plain,
( spl0_1133
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f2720,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X1 )
| ~ spl0_93
| ~ spl0_183 ),
inference(resolution,[],[f2643,f1466]) ).
fof(f52575,plain,
( ~ spl0_17
| spl0_1132
| ~ spl0_156
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f45215,f43915,f2204,f52573,f1100]) ).
fof(f45215,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),tc_bool)
| ~ class_Orderings_Opreorder(tc_bool)
| c_lessequals(X0,X2,tc_bool) )
| ~ spl0_156
| ~ spl0_1089 ),
inference(resolution,[],[f43916,f2205]) ).
fof(f52571,plain,
( spl0_1131
| ~ spl0_135
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2464,f2204,f1830,f52569]) ).
fof(f52569,plain,
( spl0_1131
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X4,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f2464,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X4,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_135
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1831]) ).
fof(f52567,plain,
( spl0_1130
| ~ spl0_136
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2463,f2204,f1834,f52565]) ).
fof(f52565,plain,
( spl0_1130
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f2463,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_136
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1835]) ).
fof(f52563,plain,
( spl0_1129
| ~ spl0_128
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2456,f2204,f1801,f52561]) ).
fof(f52561,plain,
( spl0_1129
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2),X2)
| ~ c_lessequals(X1,X4,X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f2456,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2),X2)
| ~ c_lessequals(X1,X4,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_128
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1802]) ).
fof(f52559,plain,
( spl0_1128
| ~ spl0_129
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2455,f2204,f1805,f52557]) ).
fof(f52557,plain,
( spl0_1128
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2),X2)
| ~ c_lessequals(X1,X3,X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f2455,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2),X2)
| ~ c_lessequals(X1,X3,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_129
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1806]) ).
fof(f52555,plain,
( spl0_1127
| ~ spl0_135
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2434,f2200,f1830,f52553]) ).
fof(f52553,plain,
( spl0_1127
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X1,X2)
| ~ c_lessequals(X3,X0,X2)
| ~ class_Lattices_Olower__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f2200,plain,
( spl0_155
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X2,X0)
| c_lessequals(X5,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f2434,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X1,X2)
| ~ c_lessequals(X3,X0,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_135
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1831]) ).
fof(f2201,plain,
( ! [X2,X0,X1,X5] :
( ~ c_lessequals(X5,X2,X0)
| ~ c_lessequals(X2,X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X1,X0) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f2200]) ).
fof(f52551,plain,
( spl0_1126
| ~ spl0_136
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2433,f2200,f1834,f52549]) ).
fof(f52549,plain,
( spl0_1126
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X1,X2)
| ~ c_lessequals(X4,X0,X2)
| ~ class_Lattices_Olower__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f2433,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X1,X2)
| ~ c_lessequals(X4,X0,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_136
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1835]) ).
fof(f52547,plain,
( spl0_1125
| ~ spl0_128
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2426,f2200,f1801,f52545]) ).
fof(f52545,plain,
( spl0_1125
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X4,X3,X2)
| ~ c_lessequals(X4,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f2426,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X4,X3,X2)
| ~ c_lessequals(X4,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_128
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1802]) ).
fof(f52543,plain,
( spl0_1124
| ~ spl0_129
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2425,f2200,f1805,f52541]) ).
fof(f52541,plain,
( spl0_1124
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X4,X3,X2)
| ~ c_lessequals(X4,X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f2425,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X4,X3,X2)
| ~ c_lessequals(X4,X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_129
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1806]) ).
fof(f52375,plain,
( spl0_1123
| ~ spl0_14
| ~ spl0_896
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f45235,f43915,f32410,f1085,f52373]) ).
fof(f52373,plain,
( spl0_1123
<=> ! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),tc_bool),X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f45235,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_bool)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),tc_bool),X2,tc_bool) )
| ~ spl0_896
| ~ spl0_1089 ),
inference(resolution,[],[f43916,f32411]) ).
fof(f51529,plain,
( spl0_1122
| ~ spl0_14
| ~ spl0_895
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f45234,f43915,f32406,f1085,f51527]) ).
fof(f51527,plain,
( spl0_1122
<=> ! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool),X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f45234,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_bool)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool),X2,tc_bool) )
| ~ spl0_895
| ~ spl0_1089 ),
inference(resolution,[],[f43916,f32407]) ).
fof(f49734,plain,
( spl0_1121
| ~ spl0_13
| ~ spl0_119
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f45210,f43915,f1635,f1080,f49732]) ).
fof(f49732,plain,
( spl0_1121
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f45210,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(X0,c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),tc_bool) = X0 )
| ~ spl0_119
| ~ spl0_1089 ),
inference(resolution,[],[f43916,f1636]) ).
fof(f48927,plain,
( spl0_1120
| ~ spl0_13
| ~ spl0_116
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f45209,f43915,f1622,f1080,f48925]) ).
fof(f48925,plain,
( spl0_1120
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f45209,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_bool),X1,tc_bool) = X1 )
| ~ spl0_116
| ~ spl0_1089 ),
inference(resolution,[],[f43916,f1623]) ).
fof(f45822,plain,
( ~ spl0_21
| ~ spl0_19
| spl0_1119
| ~ spl0_729
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f45207,f43915,f19999,f45820,f1110,f1120]) ).
fof(f45207,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_bool) = c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_bool)
| ~ class_Orderings_Oorder(tc_bool)
| ~ class_Orderings_Obot(tc_bool) )
| ~ spl0_729
| ~ spl0_1089 ),
inference(resolution,[],[f43916,f20000]) ).
fof(f45261,plain,
( spl0_1118
| ~ spl0_89
| ~ spl0_100
| ~ spl0_142
| ~ spl0_177
| ~ spl0_317
| ~ spl0_586 ),
inference(avatar_split_clause,[],[f14508,f14415,f4702,f2288,f1858,f1493,f1445,f45259]) ).
fof(f45259,plain,
( spl0_1118
<=> ! [X4,X0,X3,X2,X1] : hAPP(c_fequal(X4),X2) = c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),hAPP(c_fequal(X3),X1),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f1493,plain,
( spl0_100
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f14508,plain,
( ! [X2,X3,X0,X1,X4] : hAPP(c_fequal(X4),X2) = c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),hAPP(c_fequal(X3),X1),X3,X4)
| ~ spl0_89
| ~ spl0_100
| ~ spl0_142
| ~ spl0_177
| ~ spl0_317
| ~ spl0_586 ),
inference(forward_demodulation,[],[f14507,f1446]) ).
fof(f14507,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),hAPP(c_fequal(X3),X1),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ spl0_89
| ~ spl0_100
| ~ spl0_142
| ~ spl0_177
| ~ spl0_317
| ~ spl0_586 ),
inference(forward_demodulation,[],[f14506,f1859]) ).
fof(f14506,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),hAPP(c_fequal(X3),X1),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X4),X2),c_Set_Oimage(X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool))
| ~ spl0_89
| ~ spl0_100
| ~ spl0_177
| ~ spl0_317
| ~ spl0_586 ),
inference(forward_demodulation,[],[f14505,f1494]) ).
fof(f1494,plain,
( ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X0,tc_bool))
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f14505,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),hAPP(c_fequal(X3),X1),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X4),X2),c_Set_Oimage(X0,c_HOL_Ominus__class_Ominus(hAPP(c_fequal(X3),X1),hAPP(c_fequal(X3),X1),tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool))
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_586 ),
inference(forward_demodulation,[],[f14442,f5265]) ).
fof(f14442,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X4),X2),c_Set_Oimage(X0,c_HOL_Ominus__class_Ominus(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),hAPP(c_fequal(X3),X1),tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool))
| ~ spl0_177
| ~ spl0_586 ),
inference(resolution,[],[f14416,f2289]) ).
fof(f45257,plain,
( spl0_1117
| ~ spl0_194
| ~ spl0_422
| ~ spl0_509 ),
inference(avatar_split_clause,[],[f12134,f11761,f8277,f2686,f45255]) ).
fof(f45255,plain,
( spl0_1117
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2),X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f11761,plain,
( spl0_509
<=> ! [X10,X0,X12,X6] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),c_Set_Oimage(X10,X6,X12,X0),X0,X12)),c_FuncSet_OPi(c_Set_Oimage(X10,X6,X12,X0),c_COMBK(X6,tc_fun(X12,tc_bool),X0),X0,X12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f12134,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2),X0,tc_fun(X2,tc_bool))
| ~ spl0_194
| ~ spl0_422
| ~ spl0_509 ),
inference(forward_demodulation,[],[f12095,f2687]) ).
fof(f12095,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Set_Oimage(c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2),c_Set_Oimage(X1,X0,X2,X3),X3,X2),X0,tc_fun(X2,tc_bool))
| ~ spl0_422
| ~ spl0_509 ),
inference(resolution,[],[f11762,f8278]) ).
fof(f11762,plain,
( ! [X10,X0,X6,X12] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),c_Set_Oimage(X10,X6,X12,X0),X0,X12)),c_FuncSet_OPi(c_Set_Oimage(X10,X6,X12,X0),c_COMBK(X6,tc_fun(X12,tc_bool),X0),X0,X12)))
| ~ spl0_509 ),
inference(avatar_component_clause,[],[f11761]) ).
fof(f45253,plain,
( spl0_1116
| ~ spl0_89
| ~ spl0_100
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f9613,f8269,f1493,f1445,f45251]) ).
fof(f45251,plain,
( spl0_1116
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X2,X0,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f9613,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X2,X0,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))
| ~ spl0_89
| ~ spl0_100
| ~ spl0_420 ),
inference(forward_demodulation,[],[f9550,f1446]) ).
fof(f9550,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X2,X0,tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_420 ),
inference(superposition,[],[f8270,f1494]) ).
fof(f45249,plain,
( spl0_1115
| ~ spl0_90
| ~ spl0_100
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f9606,f8269,f1493,f1449,f45247]) ).
fof(f45247,plain,
( spl0_1115
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X2,X0,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f1449,plain,
( spl0_90
<=> ! [X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f9606,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X2,X0,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))
| ~ spl0_90
| ~ spl0_100
| ~ spl0_420 ),
inference(forward_demodulation,[],[f9544,f1450]) ).
fof(f1450,plain,
( ! [X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f9544,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_420 ),
inference(superposition,[],[f8270,f1494]) ).
fof(f45245,plain,
( spl0_1114
| ~ spl0_89
| ~ spl0_100
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f9239,f8253,f1493,f1445,f45243]) ).
fof(f45243,plain,
( spl0_1114
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f9239,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_89
| ~ spl0_100
| ~ spl0_416 ),
inference(forward_demodulation,[],[f9171,f1446]) ).
fof(f9171,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_416 ),
inference(superposition,[],[f8254,f1494]) ).
fof(f45241,plain,
( spl0_1113
| ~ spl0_90
| ~ spl0_100
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f9230,f8253,f1493,f1449,f45239]) ).
fof(f45239,plain,
( spl0_1113
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f9230,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_90
| ~ spl0_100
| ~ spl0_416 ),
inference(forward_demodulation,[],[f9165,f1450]) ).
fof(f9165,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_416 ),
inference(superposition,[],[f8254,f1494]) ).
fof(f45204,plain,
( spl0_1112
| ~ spl0_143
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f8318,f8294,f1862,f45202]) ).
fof(f45202,plain,
( spl0_1112
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),X4))
| hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f1862,plain,
( spl0_143
<=> ! [X6,X0,X1,X7] :
( hBOOL(hAPP(X7,X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f8318,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),X4))
| hBOOL(hAPP(X3,X4)) )
| ~ spl0_143
| ~ spl0_426 ),
inference(superposition,[],[f1863,f8295]) ).
fof(f1863,plain,
( ! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X1))
| hBOOL(hAPP(X7,X1)) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1862]) ).
fof(f45200,plain,
( spl0_1111
| ~ spl0_73
| ~ spl0_385 ),
inference(avatar_split_clause,[],[f7597,f7540,f1357,f45198]) ).
fof(f45198,plain,
( spl0_1111
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( hAPP(c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X5,X6,X3,X4),X1,X2,X3,X4),X5) = X6
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f7540,plain,
( spl0_385
<=> ! [X4,X0,X14,X12,X3,X13,X15] :
( X3 = X14
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X13,X3,X4,X0,X12),X14,X15,X0,X12) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X13,X14,X15,X0,X12),X3,X4,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f7597,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X5,X6,X3,X4),X1,X2,X3,X4),X5) = X6
| X1 = X5 )
| ~ spl0_73
| ~ spl0_385 ),
inference(superposition,[],[f1358,f7541]) ).
fof(f7541,plain,
( ! [X3,X0,X14,X4,X15,X12,X13] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X13,X3,X4,X0,X12),X14,X15,X0,X12) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X13,X14,X15,X0,X12),X3,X4,X0,X12)
| X3 = X14 )
| ~ spl0_385 ),
inference(avatar_component_clause,[],[f7540]) ).
fof(f45195,plain,
( spl0_1110
| ~ spl0_113
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f7467,f7068,f1546,f45193]) ).
fof(f45193,plain,
( spl0_1110
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f7068,plain,
( spl0_380
<=> ! [X37] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X37,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f7467,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_113
| ~ spl0_380 ),
inference(resolution,[],[f7069,f1547]) ).
fof(f7069,plain,
( ! [X37] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X37,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_380 ),
inference(avatar_component_clause,[],[f7068]) ).
fof(f45188,plain,
( spl0_1109
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1108 ),
inference(avatar_split_clause,[],[f45184,f45181,f18286,f2678,f45186]) ).
fof(f45186,plain,
( spl0_1109
<=> ! [X0] :
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f45181,plain,
( spl0_1108
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f45184,plain,
( ! [X0] :
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1108 ),
inference(forward_demodulation,[],[f45182,f19417]) ).
fof(f45182,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_1108 ),
inference(avatar_component_clause,[],[f45181]) ).
fof(f45183,plain,
( spl0_1108
| ~ spl0_112
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f7464,f7064,f1542,f45181]) ).
fof(f7064,plain,
( spl0_379
<=> ! [X37] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X37,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f7464,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_112
| ~ spl0_379 ),
inference(resolution,[],[f7065,f1543]) ).
fof(f7065,plain,
( ! [X37] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X37,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_379 ),
inference(avatar_component_clause,[],[f7064]) ).
fof(f45179,plain,
( spl0_1107
| ~ spl0_12
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f6741,f6738,f1075,f45177]) ).
fof(f45177,plain,
( spl0_1107
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OSup__class_OSup(X1,tc_bool),tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_bool),X0),X1,tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f6738,plain,
( spl0_366
<=> ! [X6,X0,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f6741,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OSup__class_OSup(X1,tc_bool),tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_bool),X0),X1,tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_12
| ~ spl0_366 ),
inference(resolution,[],[f6739,f1077]) ).
fof(f6739,plain,
( ! [X3,X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f6738]) ).
fof(f45175,plain,
( spl0_1106
| ~ spl0_12
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f6730,f6727,f1075,f45173]) ).
fof(f45173,plain,
( spl0_1106
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Complete__Lattice_OInf__class_OInf(X1,tc_bool),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_bool),X0),X1,tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f6727,plain,
( spl0_364
<=> ! [X6,X0,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Complete__Lattice_OInf__class_OInf(X6,X0),X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f6730,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Complete__Lattice_OInf__class_OInf(X1,tc_bool),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_bool),X0),X1,tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_12
| ~ spl0_364 ),
inference(resolution,[],[f6728,f1077]) ).
fof(f6728,plain,
( ! [X3,X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Complete__Lattice_OInf__class_OInf(X6,X0),X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f6727]) ).
fof(f45066,plain,
( spl0_1105
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1104 ),
inference(avatar_split_clause,[],[f45061,f45058,f18286,f2678,f45064]) ).
fof(f45064,plain,
( spl0_1105
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X1,c_List_Osko__Equiv__Relations__XquotientE__1__1(X1,X2,X3,X0)))
| ~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(X1,X3,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f45058,plain,
( spl0_1104
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X1,X2,X3,X0)),X1))
| ~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(X1,X3,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f45061,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X1,c_List_Osko__Equiv__Relations__XquotientE__1__1(X1,X2,X3,X0)))
| ~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(X1,X3,X0),X2)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1104 ),
inference(forward_demodulation,[],[f45059,f19417]) ).
fof(f45059,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X1,X2,X3,X0)),X1))
| ~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(X1,X3,X0),X2)) )
| ~ spl0_1104 ),
inference(avatar_component_clause,[],[f45058]) ).
fof(f45062,plain,
( ~ spl0_21
| ~ spl0_39
| ~ spl0_1073 ),
inference(avatar_split_clause,[],[f44833,f42486,f1195,f1120]) ).
fof(f1195,plain,
( spl0_39
<=> ! [X59,X58] :
( ~ class_Orderings_Obot(X59)
| class_Orderings_Obot(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f42486,plain,
( spl0_1073
<=> ! [X0] : ~ class_Orderings_Obot(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f44833,plain,
( ~ class_Orderings_Obot(tc_bool)
| ~ spl0_39
| ~ spl0_1073 ),
inference(resolution,[],[f42487,f1196]) ).
fof(f1196,plain,
( ! [X58,X59] :
( class_Orderings_Obot(tc_fun(X58,X59))
| ~ class_Orderings_Obot(X59) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f42487,plain,
( ! [X0] : ~ class_Orderings_Obot(tc_fun(X0,tc_bool))
| ~ spl0_1073 ),
inference(avatar_component_clause,[],[f42486]) ).
fof(f45060,plain,
( spl0_1104
| ~ spl0_112
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f6638,f5679,f1542,f45058]) ).
fof(f5679,plain,
( spl0_348
<=> ! [X24,X0,X31,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f6638,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X1,X2,X3,X0)),X1))
| ~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(X1,X3,X0),X2)) )
| ~ spl0_112
| ~ spl0_348 ),
inference(resolution,[],[f5680,f1543]) ).
fof(f5680,plain,
( ! [X31,X0,X6,X24] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X6)) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f5679]) ).
fof(f44998,plain,
( spl0_1103
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1102 ),
inference(avatar_split_clause,[],[f44994,f44991,f18286,f2678,f44996]) ).
fof(f44996,plain,
( spl0_1103
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,c_Set_OPow(X2,X0),X0),X2,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f44991,plain,
( spl0_1102
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,c_Set_OPow(X2,X0),X0),X2,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f44994,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,c_Set_OPow(X2,X0),X0),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1102 ),
inference(forward_demodulation,[],[f44992,f19417]) ).
fof(f44992,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,c_Set_OPow(X2,X0),X0),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_1102 ),
inference(avatar_component_clause,[],[f44991]) ).
fof(f44993,plain,
( spl0_1102
| ~ spl0_71
| ~ spl0_222
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f6633,f5675,f3075,f1329,f44991]) ).
fof(f5675,plain,
( spl0_347
<=> ! [X6,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X6,X8,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f6633,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| c_lessequals(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,c_Set_OPow(X2,X0),X0),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_71
| ~ spl0_222
| ~ spl0_347 ),
inference(forward_demodulation,[],[f6620,f1330]) ).
fof(f6620,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X2,X0),tc_fun(X0,tc_bool))))
| c_lessequals(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,c_Set_OPow(X2,X0),X0),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_222
| ~ spl0_347 ),
inference(resolution,[],[f5676,f3076]) ).
fof(f5676,plain,
( ! [X0,X8,X6] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X6,X8,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)))) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f5675]) ).
fof(f44985,plain,
( spl0_1101
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1100 ),
inference(avatar_split_clause,[],[f44981,f44978,f18286,f2678,f44983]) ).
fof(f44983,plain,
( spl0_1101
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f44978,plain,
( spl0_1100
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f44981,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1100 ),
inference(forward_demodulation,[],[f44979,f19417]) ).
fof(f44979,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0))) )
| ~ spl0_1100 ),
inference(avatar_component_clause,[],[f44978]) ).
fof(f44980,plain,
( spl0_1100
| ~ spl0_113
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f6589,f5675,f1546,f44978]) ).
fof(f6589,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0))) )
| ~ spl0_113
| ~ spl0_347 ),
inference(resolution,[],[f5676,f1547]) ).
fof(f44842,plain,
( spl0_1099
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1098 ),
inference(avatar_split_clause,[],[f44838,f44835,f18286,f2678,f44840]) ).
fof(f44840,plain,
( spl0_1099
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f44835,plain,
( spl0_1098
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f44838,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1098 ),
inference(forward_demodulation,[],[f44836,f19417]) ).
fof(f44836,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0))) )
| ~ spl0_1098 ),
inference(avatar_component_clause,[],[f44835]) ).
fof(f44837,plain,
( spl0_1098
| ~ spl0_113
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f6545,f5671,f1546,f44835]) ).
fof(f5671,plain,
( spl0_346
<=> ! [X6,X0,X8] :
( hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X6,X8,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f6545,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0))) )
| ~ spl0_113
| ~ spl0_346 ),
inference(resolution,[],[f5672,f1547]) ).
fof(f5672,plain,
( ! [X0,X8,X6] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X6,X8,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X0,tc_bool)))) )
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f5671]) ).
fof(f44832,plain,
( spl0_1097
| ~ spl0_145
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f6458,f5663,f1871,f44830]) ).
fof(f44830,plain,
( spl0_1097
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1871,plain,
( spl0_145
<=> ! [X0,X6,X1,X7] :
( hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f6458,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X0,X4)) )
| ~ spl0_145
| ~ spl0_344 ),
inference(superposition,[],[f1872,f5664]) ).
fof(f1872,plain,
( ! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X1))
| hBOOL(hAPP(X6,X1)) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1871]) ).
fof(f44828,plain,
( spl0_1096
| ~ spl0_145
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f6342,f5659,f1871,f44826]) ).
fof(f44826,plain,
( spl0_1096
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f6342,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X0,X4)) )
| ~ spl0_145
| ~ spl0_343 ),
inference(superposition,[],[f1872,f5660]) ).
fof(f44824,plain,
( spl0_1095
| ~ spl0_143
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f6242,f5655,f1862,f44822]) ).
fof(f44822,plain,
( spl0_1095
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X4))
| hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f6242,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X4))
| hBOOL(hAPP(X3,X4)) )
| ~ spl0_143
| ~ spl0_342 ),
inference(superposition,[],[f1863,f5656]) ).
fof(f44820,plain,
( spl0_1094
| ~ spl0_125
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f6015,f5635,f1789,f44818]) ).
fof(f44818,plain,
( spl0_1094
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X4))
| ~ hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f6015,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X4))
| ~ hBOOL(hAPP(X3,X4)) )
| ~ spl0_125
| ~ spl0_337 ),
inference(superposition,[],[f1790,f5636]) ).
fof(f44816,plain,
( spl0_1093
| ~ spl0_124
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5867,f5631,f1785,f44814]) ).
fof(f44814,plain,
( spl0_1093
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f5867,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X0,X4)) )
| ~ spl0_124
| ~ spl0_336 ),
inference(superposition,[],[f1786,f5632]) ).
fof(f44812,plain,
( spl0_1092
| ~ spl0_203
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f5418,f5334,f2831,f44810]) ).
fof(f44810,plain,
( spl0_1092
<=> ! [X0,X3,X2,X1] : hAPP(X0,X3) = hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X0,X1,X2),hAPP(X0,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f5418,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X3) = hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X0,X1,X2),hAPP(X0,X3)))
| ~ spl0_203
| ~ spl0_319 ),
inference(resolution,[],[f5335,f2832]) ).
fof(f44367,plain,
( spl0_1091
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1090 ),
inference(avatar_split_clause,[],[f44363,f44360,f18286,f2678,f44365]) ).
fof(f44365,plain,
( spl0_1091
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X0,X2)))
| ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f44360,plain,
( spl0_1090
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f44363,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X0,X2)))
| ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1090 ),
inference(forward_demodulation,[],[f44361,f19417]) ).
fof(f44361,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_1090 ),
inference(avatar_component_clause,[],[f44360]) ).
fof(f44362,plain,
( spl0_1090
| ~ spl0_112
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f5242,f4694,f1542,f44360]) ).
fof(f5242,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_112
| ~ spl0_315 ),
inference(resolution,[],[f4695,f1543]) ).
fof(f43917,plain,
( spl0_1089
| ~ spl0_73
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f42551,f42483,f1357,f43915]) ).
fof(f42483,plain,
( spl0_1072
<=> ! [X2,X1,X3] : c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),hAPP(X2,X3),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f42551,plain,
( ! [X2,X5] : c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_bool),X2,tc_bool)
| ~ spl0_73
| ~ spl0_1072 ),
inference(superposition,[],[f42484,f1358]) ).
fof(f42484,plain,
( ! [X2,X3,X1] : c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),hAPP(X2,X3),tc_bool)
| ~ spl0_1072 ),
inference(avatar_component_clause,[],[f42483]) ).
fof(f43913,plain,
( spl0_1088
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1087 ),
inference(avatar_split_clause,[],[f43909,f43906,f18286,f2678,f43911]) ).
fof(f43911,plain,
( spl0_1088
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X0,X2)))
| ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f43906,plain,
( spl0_1087
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f43909,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X0,X2)))
| ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1087 ),
inference(forward_demodulation,[],[f43907,f19417]) ).
fof(f43907,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_1087 ),
inference(avatar_component_clause,[],[f43906]) ).
fof(f43908,plain,
( spl0_1087
| ~ spl0_112
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f5214,f4690,f1542,f43906]) ).
fof(f5214,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_112
| ~ spl0_314 ),
inference(resolution,[],[f4691,f1543]) ).
fof(f43463,plain,
( spl0_1086
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1085 ),
inference(avatar_split_clause,[],[f43459,f43456,f18286,f2678,f43461]) ).
fof(f43461,plain,
( spl0_1086
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XbexI__1__1(X3,X0,X2)))
| ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f43456,plain,
( spl0_1085
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XbexI__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f43459,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XbexI__1__1(X3,X0,X2)))
| ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1085 ),
inference(forward_demodulation,[],[f43457,f19417]) ).
fof(f43457,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XbexI__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_1085 ),
inference(avatar_component_clause,[],[f43456]) ).
fof(f43458,plain,
( spl0_1085
| ~ spl0_112
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f5190,f4686,f1542,f43456]) ).
fof(f5190,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XbexI__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_112
| ~ spl0_313 ),
inference(resolution,[],[f4687,f1543]) ).
fof(f43013,plain,
( spl0_1084
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1083 ),
inference(avatar_split_clause,[],[f43009,f43006,f18286,f2678,f43011]) ).
fof(f43011,plain,
( spl0_1084
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XballE__1__1(X3,X0,X2)))
| hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f43006,plain,
( spl0_1083
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XballE__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f43009,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XballE__1__1(X3,X0,X2)))
| hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1083 ),
inference(forward_demodulation,[],[f43007,f19417]) ).
fof(f43007,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XballE__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_1083 ),
inference(avatar_component_clause,[],[f43006]) ).
fof(f43008,plain,
( spl0_1083
| ~ spl0_112
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f5166,f4682,f1542,f43006]) ).
fof(f5166,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XballE__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_112
| ~ spl0_312 ),
inference(resolution,[],[f4683,f1543]) ).
fof(f42563,plain,
( spl0_1082
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1081 ),
inference(avatar_split_clause,[],[f42528,f42525,f18286,f2678,f42561]) ).
fof(f42561,plain,
( spl0_1082
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X0,X2)))
| ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f42525,plain,
( spl0_1081
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f42528,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X0,X2)))
| ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1081 ),
inference(forward_demodulation,[],[f42526,f19417]) ).
fof(f42526,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_1081 ),
inference(avatar_component_clause,[],[f42525]) ).
fof(f42527,plain,
( spl0_1081
| ~ spl0_112
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f5142,f4678,f1542,f42525]) ).
fof(f5142,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X0,X2)),X3))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_112
| ~ spl0_311 ),
inference(resolution,[],[f4679,f1543]) ).
fof(f42521,plain,
( spl0_1080
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1079 ),
inference(avatar_split_clause,[],[f42517,f42514,f18286,f2678,f42519]) ).
fof(f42519,plain,
( spl0_1080
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1))
| ~ hBOOL(hAPP(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f42514,plain,
( spl0_1079
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f42517,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool)),X1))
| ~ hBOOL(hAPP(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0),X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1079 ),
inference(forward_demodulation,[],[f42515,f19417]) ).
fof(f42515,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0),X1)) )
| ~ spl0_1079 ),
inference(avatar_component_clause,[],[f42514]) ).
fof(f42516,plain,
( spl0_1079
| ~ spl0_112
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f5140,f4674,f1542,f42514]) ).
fof(f4674,plain,
( spl0_310
<=> ! [X6,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X6,X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f5140,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X0),X1)) )
| ~ spl0_112
| ~ spl0_310 ),
inference(resolution,[],[f4675,f1543]) ).
fof(f4675,plain,
( ! [X0,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X6,X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X0,tc_bool)))) )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f4674]) ).
fof(f42509,plain,
( spl0_1078
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1077 ),
inference(avatar_split_clause,[],[f42505,f42502,f18286,f2678,f42507]) ).
fof(f42507,plain,
( spl0_1078
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0),X1))
| ~ hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f42502,plain,
( spl0_1077
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0)))
| ~ hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f42505,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0),X1))
| ~ hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1077 ),
inference(forward_demodulation,[],[f42503,f19417]) ).
fof(f42503,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0)))
| ~ hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_1077 ),
inference(avatar_component_clause,[],[f42502]) ).
fof(f42504,plain,
( spl0_1077
| ~ spl0_112
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f5137,f4670,f1542,f42502]) ).
fof(f5137,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X0)))
| ~ hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_112
| ~ spl0_309 ),
inference(resolution,[],[f4671,f1543]) ).
fof(f42500,plain,
( spl0_1076
| ~ spl0_15
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f4590,f4498,f1090,f42498]) ).
fof(f42498,plain,
( spl0_1076
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f1090,plain,
( spl0_15
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f4498,plain,
( spl0_299
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),c_Lattices_Olower__semilattice__class_Oinf(X5,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f4590,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool)
| ~ spl0_15
| ~ spl0_299 ),
inference(resolution,[],[f4499,f1092]) ).
fof(f1092,plain,
( class_Lattices_Odistrib__lattice(tc_bool)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f4499,plain,
( ! [X2,X0,X1,X5] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),c_Lattices_Olower__semilattice__class_Oinf(X5,X1,X0),X0) )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f4498]) ).
fof(f42496,plain,
( spl0_1075
| ~ spl0_5
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f4589,f4498,f1040,f42494]) ).
fof(f42494,plain,
( spl0_1075
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f1040,plain,
( spl0_5
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f4589,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat)
| ~ spl0_5
| ~ spl0_299 ),
inference(resolution,[],[f4499,f1042]) ).
fof(f1042,plain,
( class_Lattices_Odistrib__lattice(tc_nat)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f42492,plain,
( spl0_1074
| ~ spl0_15
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f4587,f4494,f1090,f42490]) ).
fof(f42490,plain,
( spl0_1074
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f4494,plain,
( spl0_298
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f4587,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool)
| ~ spl0_15
| ~ spl0_298 ),
inference(resolution,[],[f4495,f1092]) ).
fof(f4495,plain,
( ! [X2,X0,X1,X5] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0) )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f4494]) ).
fof(f42488,plain,
( spl0_1072
| ~ spl0_12
| spl0_1073
| ~ spl0_22
| ~ spl0_883
| ~ spl0_979 ),
inference(avatar_split_clause,[],[f39101,f36187,f30566,f1125,f42486,f1075,f42483]) ).
fof(f1125,plain,
( spl0_22
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f30566,plain,
( spl0_883
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X1,X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X4),X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f36187,plain,
( spl0_979
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2),hAPP(X3,X2),X0)
| ~ class_Orderings_Obot(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f39101,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| ~ class_Orderings_Obot(tc_fun(X0,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_bool),hAPP(X2,X3),tc_bool) )
| ~ spl0_883
| ~ spl0_979 ),
inference(resolution,[],[f36188,f30567]) ).
fof(f30567,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X1,X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X4),X1,X4) )
| ~ spl0_883 ),
inference(avatar_component_clause,[],[f30566]) ).
fof(f36188,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2),hAPP(X3,X2),X0)
| ~ class_HOL_Oord(X0)
| ~ class_Orderings_Obot(tc_fun(X1,X0)) )
| ~ spl0_979 ),
inference(avatar_component_clause,[],[f36187]) ).
fof(f42481,plain,
( spl0_1071
| ~ spl0_5
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f4586,f4494,f1040,f42479]) ).
fof(f42479,plain,
( spl0_1071
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f4586,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),tc_nat)
| ~ spl0_5
| ~ spl0_298 ),
inference(resolution,[],[f4495,f1042]) ).
fof(f42477,plain,
( spl0_1070
| ~ spl0_15
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4525,f4482,f1090,f42475]) ).
fof(f4482,plain,
( spl0_295
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f4525,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool)
| ~ spl0_15
| ~ spl0_295 ),
inference(resolution,[],[f4483,f1092]) ).
fof(f4483,plain,
( ! [X2,X0,X1,X5] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f4482]) ).
fof(f42473,plain,
( spl0_1069
| ~ spl0_5
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4524,f4482,f1040,f42471]) ).
fof(f42471,plain,
( spl0_1069
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f4524,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),tc_nat)
| ~ spl0_5
| ~ spl0_295 ),
inference(resolution,[],[f4483,f1042]) ).
fof(f42469,plain,
( spl0_1068
| ~ spl0_15
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f4522,f4478,f1090,f42467]) ).
fof(f42467,plain,
( spl0_1068
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f4478,plain,
( spl0_294
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X5,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f4522,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool)
| ~ spl0_15
| ~ spl0_294 ),
inference(resolution,[],[f4479,f1092]) ).
fof(f4479,plain,
( ! [X2,X0,X1,X5] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X5,X1,X0),X0) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f4478]) ).
fof(f42465,plain,
( spl0_1067
| ~ spl0_5
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f4521,f4478,f1040,f42463]) ).
fof(f42463,plain,
( spl0_1067
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f4521,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat)
| ~ spl0_5
| ~ spl0_294 ),
inference(resolution,[],[f4479,f1042]) ).
fof(f42386,plain,
( spl0_1066
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1065 ),
inference(avatar_split_clause,[],[f42382,f42379,f18286,f2678,f42384]) ).
fof(f42384,plain,
( spl0_1066
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,X4),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f42379,plain,
( spl0_1065
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f42382,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X2,X1))
| c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,X4),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1065 ),
inference(forward_demodulation,[],[f42380,f19417]) ).
fof(f42380,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_1065 ),
inference(avatar_component_clause,[],[f42379]) ).
fof(f42381,plain,
( spl0_1065
| ~ spl0_29
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f4217,f4106,f1155,f42379]) ).
fof(f4217,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBI(X0),X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_29
| ~ spl0_277 ),
inference(superposition,[],[f4107,f1156]) ).
fof(f42377,plain,
( spl0_1064
| ~ spl0_95
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4190,f4102,f1473,f42375]) ).
fof(f42375,plain,
( spl0_1064
<=> ! [X4,X0,X3,X2,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X0,X2,X3),X4,tc_fun(X3,tc_bool)),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f4190,plain,
( ! [X2,X3,X0,X1,X4] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X0,X2,X3),X4,tc_fun(X3,tc_bool)),X3,X2)
| ~ spl0_95
| ~ spl0_276 ),
inference(resolution,[],[f4103,f1474]) ).
fof(f42373,plain,
( spl0_1063
| ~ spl0_92
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4180,f4102,f1457,f42371]) ).
fof(f42371,plain,
( spl0_1063
<=> ! [X4,X0,X3,X2,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X4,c_Set_Oimage(X1,X0,X2,X3),tc_fun(X3,tc_bool)),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f4180,plain,
( ! [X2,X3,X0,X1,X4] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X4,c_Set_Oimage(X1,X0,X2,X3),tc_fun(X3,tc_bool)),X3,X2)
| ~ spl0_92
| ~ spl0_276 ),
inference(resolution,[],[f4103,f1458]) ).
fof(f42354,plain,
( spl0_1062
| ~ spl0_91
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4179,f4102,f1453,f42352]) ).
fof(f42352,plain,
( spl0_1062
<=> ! [X4,X0,X3,X2,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X0,X2,X3),X4,tc_fun(X3,tc_bool)),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f4179,plain,
( ! [X2,X3,X0,X1,X4] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X0,X2,X3),X4,tc_fun(X3,tc_bool)),X3,X2)
| ~ spl0_91
| ~ spl0_276 ),
inference(resolution,[],[f4103,f1454]) ).
fof(f42339,plain,
( spl0_1061
| ~ spl0_764
| ~ spl0_1060 ),
inference(avatar_split_clause,[],[f42335,f42332,f20188,f42337]) ).
fof(f42337,plain,
( spl0_1061
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f42332,plain,
( spl0_1060
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f42335,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool))
| ~ spl0_764
| ~ spl0_1060 ),
inference(forward_demodulation,[],[f42333,f20189]) ).
fof(f42333,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool))
| ~ spl0_1060 ),
inference(avatar_component_clause,[],[f42332]) ).
fof(f42334,plain,
( spl0_1060
| ~ spl0_139
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f4094,f3686,f1846,f42332]) ).
fof(f4094,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool))
| ~ spl0_139
| ~ spl0_274 ),
inference(superposition,[],[f3687,f1847]) ).
fof(f42329,plain,
( spl0_1059
| ~ spl0_177
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f4058,f3671,f2288,f42327]) ).
fof(f42327,plain,
( spl0_1059
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f4058,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) )
| ~ spl0_177
| ~ spl0_271 ),
inference(resolution,[],[f3672,f2289]) ).
fof(f42325,plain,
( spl0_1058
| ~ spl0_167
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4042,f3659,f2248,f42323]) ).
fof(f42323,plain,
( spl0_1058
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_OPow(X2,X1),X0,tc_fun(X1,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f4042,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_OPow(X2,X1),X0,tc_fun(X1,tc_bool)))) )
| ~ spl0_167
| ~ spl0_268 ),
inference(resolution,[],[f3660,f2249]) ).
fof(f42320,plain,
( spl0_1057
| ~ spl0_177
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4037,f3659,f2288,f42318]) ).
fof(f42318,plain,
( spl0_1057
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f4037,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) )
| ~ spl0_177
| ~ spl0_268 ),
inference(resolution,[],[f3660,f2289]) ).
fof(f42315,plain,
( spl0_1056
| ~ spl0_177
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f4020,f3655,f2288,f42313]) ).
fof(f42313,plain,
( spl0_1056
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f4020,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) )
| ~ spl0_177
| ~ spl0_267 ),
inference(resolution,[],[f3656,f2289]) ).
fof(f42310,plain,
( spl0_1055
| ~ spl0_177
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3947,f3631,f2288,f42308]) ).
fof(f42308,plain,
( spl0_1055
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f3947,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) )
| ~ spl0_177
| ~ spl0_261 ),
inference(resolution,[],[f3632,f2289]) ).
fof(f42305,plain,
( spl0_1054
| ~ spl0_177
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3930,f3627,f2288,f42303]) ).
fof(f42303,plain,
( spl0_1054
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f3930,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X0,X2))) )
| ~ spl0_177
| ~ spl0_260 ),
inference(resolution,[],[f3628,f2289]) ).
fof(f42301,plain,
( spl0_1052
| spl0_1053
| ~ spl0_29
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f36922,f31979,f1155,f42299,f42296]) ).
fof(f42296,plain,
( spl0_1052
<=> ! [X5,X4,X2,X0,X6,X3] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_COMBI(X0),X3,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f42299,plain,
( spl0_1053
<=> ! [X1] : ~ hBOOL(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f31979,plain,
( spl0_884
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,X6,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f36922,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(X1)
| hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_COMBI(X0),X3,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6))) )
| ~ spl0_29
| ~ spl0_884 ),
inference(superposition,[],[f31980,f1156]) ).
fof(f31980,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,X6,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))) )
| ~ spl0_884 ),
inference(avatar_component_clause,[],[f31979]) ).
fof(f42293,plain,
( spl0_1051
| ~ spl0_177
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3913,f3623,f2288,f42291]) ).
fof(f42291,plain,
( spl0_1051
<=> ! [X0,X3,X2,X1] : hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X2,X3),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f3913,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X2,X3),X1)
| ~ spl0_177
| ~ spl0_259 ),
inference(resolution,[],[f3624,f2289]) ).
fof(f42289,plain,
( spl0_1050
| ~ spl0_125
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3817,f3595,f1789,f42287]) ).
fof(f42287,plain,
( spl0_1050
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f3817,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X3)) )
| ~ spl0_125
| ~ spl0_252 ),
inference(superposition,[],[f1790,f3596]) ).
fof(f42285,plain,
( spl0_1049
| ~ spl0_124
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3776,f3588,f1785,f42283]) ).
fof(f42283,plain,
( spl0_1049
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f3776,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3)) )
| ~ spl0_124
| ~ spl0_251 ),
inference(superposition,[],[f1786,f3589]) ).
fof(f42281,plain,
( spl0_1048
| ~ spl0_139
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3769,f3588,f1846,f42279]) ).
fof(f42279,plain,
( spl0_1048
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f3769,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_139
| ~ spl0_251 ),
inference(superposition,[],[f3589,f1847]) ).
fof(f42277,plain,
( spl0_1047
| ~ spl0_141
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3731,f3584,f1854,f42275]) ).
fof(f42275,plain,
( spl0_1047
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f3731,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0
| ~ spl0_141
| ~ spl0_250 ),
inference(superposition,[],[f3585,f1855]) ).
fof(f42273,plain,
( spl0_1046
| ~ spl0_185
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3537,f3152,f2650,f42271]) ).
fof(f42271,plain,
( spl0_1046
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_FuncSet_Orestrict(X0,X1,X2,X3),X4) = c_HOL_Oundefined(X3)
| c_lessequals(X4,c_Complete__Lattice_OSup__class_OSup(X1,X2),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f3537,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(c_FuncSet_Orestrict(X0,X1,X2,X3),X4) = c_HOL_Oundefined(X3)
| c_lessequals(X4,c_Complete__Lattice_OSup__class_OSup(X1,X2),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_185
| ~ spl0_239 ),
inference(resolution,[],[f3153,f2651]) ).
fof(f42269,plain,
( spl0_1045
| ~ spl0_187
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3536,f3152,f2658,f42267]) ).
fof(f42267,plain,
( spl0_1045
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_FuncSet_Orestrict(X0,X1,X2,X3),X4) = c_HOL_Oundefined(X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X1,X2),X4,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f3536,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(c_FuncSet_Orestrict(X0,X1,X2,X3),X4) = c_HOL_Oundefined(X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X1,X2),X4,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_187
| ~ spl0_239 ),
inference(resolution,[],[f3153,f2659]) ).
fof(f42265,plain,
( spl0_1044
| ~ spl0_95
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2562,f2224,f1473,f42263]) ).
fof(f42263,plain,
( spl0_1044
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f2562,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_95
| ~ spl0_161 ),
inference(resolution,[],[f2225,f1474]) ).
fof(f42261,plain,
( spl0_1043
| ~ spl0_92
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2553,f2224,f1457,f42259]) ).
fof(f42259,plain,
( spl0_1043
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f2553,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_92
| ~ spl0_161 ),
inference(resolution,[],[f2225,f1458]) ).
fof(f42257,plain,
( spl0_1042
| ~ spl0_78
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2540,f2224,f1377,f42255]) ).
fof(f42255,plain,
( spl0_1042
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X1
| c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f2540,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X1
| c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_161 ),
inference(resolution,[],[f2225,f1378]) ).
fof(f42253,plain,
( spl0_1041
| ~ spl0_679
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f36851,f31979,f17949,f42251]) ).
fof(f42251,plain,
( spl0_1041
<=> ! [X5,X4,X2,X7,X0,X6,X3,X1] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_FuncSet_Oextensional(X1,X2,X3),X4,X5),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f17949,plain,
( spl0_679
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_FuncSet_Oextensional(X0,X1,X2),c_FuncSet_Orestrict(X3,X0,X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f36851,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_FuncSet_Oextensional(X1,X2,X3),X4,X5),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X7)))
| ~ spl0_679
| ~ spl0_884 ),
inference(resolution,[],[f31980,f17950]) ).
fof(f17950,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_FuncSet_Oextensional(X0,X1,X2),c_FuncSet_Orestrict(X3,X0,X1,X2)))
| ~ spl0_679 ),
inference(avatar_component_clause,[],[f17949]) ).
fof(f42249,plain,
( spl0_1040
| ~ spl0_95
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2535,f2220,f1473,f42247]) ).
fof(f42247,plain,
( spl0_1040
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f2535,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ spl0_95
| ~ spl0_160 ),
inference(resolution,[],[f2221,f1474]) ).
fof(f42245,plain,
( spl0_1039
| ~ spl0_92
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2526,f2220,f1457,f42243]) ).
fof(f42243,plain,
( spl0_1039
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f2526,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| ~ spl0_92
| ~ spl0_160 ),
inference(resolution,[],[f2221,f1458]) ).
fof(f42241,plain,
( spl0_1038
| ~ spl0_91
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2525,f2220,f1453,f42239]) ).
fof(f42239,plain,
( spl0_1038
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f2525,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ spl0_91
| ~ spl0_160 ),
inference(resolution,[],[f2221,f1454]) ).
fof(f42237,plain,
( spl0_1037
| ~ spl0_78
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2513,f2220,f1377,f42235]) ).
fof(f42235,plain,
( spl0_1037
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X0
| c_lessequals(X1,X0,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f2513,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X0
| c_lessequals(X1,X0,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_160 ),
inference(resolution,[],[f2221,f1378]) ).
fof(f42233,plain,
( spl0_1036
| ~ spl0_78
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2475,f2208,f1377,f42231]) ).
fof(f42231,plain,
( spl0_1036
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X2,X1))
| c_lessequals(X0,X2,tc_fun(X3,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f2475,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X2,X1))
| c_lessequals(X0,X2,tc_fun(X3,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X3,tc_bool)) )
| ~ spl0_78
| ~ spl0_157 ),
inference(resolution,[],[f2209,f1378]) ).
fof(f42229,plain,
( spl0_1035
| ~ spl0_93
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2339,f2188,f1465,f42227]) ).
fof(f42227,plain,
( spl0_1035
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f2339,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_93
| ~ spl0_152 ),
inference(resolution,[],[f2189,f1466]) ).
fof(f42225,plain,
( spl0_1034
| ~ spl0_78
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2337,f2188,f1377,f42223]) ).
fof(f42223,plain,
( spl0_1034
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X1
| c_lessequals(X1,X0,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f2337,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X1
| c_lessequals(X1,X0,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_152 ),
inference(resolution,[],[f2189,f1378]) ).
fof(f42221,plain,
( spl0_1033
| ~ spl0_94
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f2313,f2180,f1469,f42219]) ).
fof(f42219,plain,
( spl0_1033
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f2313,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ spl0_94
| ~ spl0_150 ),
inference(resolution,[],[f2181,f1470]) ).
fof(f42217,plain,
( spl0_1032
| ~ spl0_93
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f2312,f2180,f1465,f42215]) ).
fof(f42215,plain,
( spl0_1032
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f2312,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| ~ spl0_93
| ~ spl0_150 ),
inference(resolution,[],[f2181,f1466]) ).
fof(f42213,plain,
( spl0_1031
| ~ spl0_78
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f2310,f2180,f1377,f42211]) ).
fof(f42211,plain,
( spl0_1031
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X0
| c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f2310,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X0
| c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_78
| ~ spl0_150 ),
inference(resolution,[],[f2181,f1378]) ).
fof(f42209,plain,
( spl0_1030
| ~ spl0_292
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f36806,f31979,f4166,f42207]) ).
fof(f42207,plain,
( spl0_1030
<=> ! [X5,X4,X2,X0,X6,X3,X1] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),hAPP(c_in(X1),X2),X3,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f36806,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),hAPP(c_in(X1),X2),X3,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6)))
| ~ spl0_292
| ~ spl0_884 ),
inference(resolution,[],[f31980,f4167]) ).
fof(f42205,plain,
( spl0_1029
| ~ spl0_122
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f2027,f1834,f1647,f42203]) ).
fof(f42203,plain,
( spl0_1029
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f2027,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2) )
| ~ spl0_122
| ~ spl0_136 ),
inference(duplicate_literal_removal,[],[f2017]) ).
fof(f2017,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2) )
| ~ spl0_122
| ~ spl0_136 ),
inference(resolution,[],[f1835,f1648]) ).
fof(f42201,plain,
( spl0_1028
| ~ spl0_120
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f2026,f1834,f1639,f42199]) ).
fof(f42199,plain,
( spl0_1028
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f2026,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X1,X2) )
| ~ spl0_120
| ~ spl0_136 ),
inference(duplicate_literal_removal,[],[f2018]) ).
fof(f2018,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X1,X2) )
| ~ spl0_120
| ~ spl0_136 ),
inference(resolution,[],[f1835,f1640]) ).
fof(f42197,plain,
( spl0_1027
| ~ spl0_122
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2015,f1830,f1647,f42195]) ).
fof(f42195,plain,
( spl0_1027
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f2015,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2) )
| ~ spl0_122
| ~ spl0_135 ),
inference(duplicate_literal_removal,[],[f2005]) ).
fof(f2005,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2) )
| ~ spl0_122
| ~ spl0_135 ),
inference(resolution,[],[f1831,f1648]) ).
fof(f42193,plain,
( spl0_1026
| ~ spl0_120
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2014,f1830,f1639,f42191]) ).
fof(f42191,plain,
( spl0_1026
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f2014,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X1,X2) )
| ~ spl0_120
| ~ spl0_135 ),
inference(duplicate_literal_removal,[],[f2006]) ).
fof(f2006,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X1,X2) )
| ~ spl0_120
| ~ spl0_135 ),
inference(resolution,[],[f1831,f1640]) ).
fof(f42189,plain,
( spl0_1025
| ~ spl0_119
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1941,f1805,f1635,f42187]) ).
fof(f42187,plain,
( spl0_1025
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f1941,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2) )
| ~ spl0_119
| ~ spl0_129 ),
inference(duplicate_literal_removal,[],[f1933]) ).
fof(f1933,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2) )
| ~ spl0_119
| ~ spl0_129 ),
inference(resolution,[],[f1806,f1636]) ).
fof(f42185,plain,
( spl0_1024
| ~ spl0_116
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1940,f1805,f1622,f42183]) ).
fof(f42183,plain,
( spl0_1024
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f1940,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X2) )
| ~ spl0_116
| ~ spl0_129 ),
inference(duplicate_literal_removal,[],[f1934]) ).
fof(f1934,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X2) )
| ~ spl0_116
| ~ spl0_129 ),
inference(resolution,[],[f1806,f1623]) ).
fof(f42181,plain,
( spl0_1023
| ~ spl0_119
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1929,f1801,f1635,f42179]) ).
fof(f42179,plain,
( spl0_1023
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f1929,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2) )
| ~ spl0_119
| ~ spl0_128 ),
inference(duplicate_literal_removal,[],[f1921]) ).
fof(f1921,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2) )
| ~ spl0_119
| ~ spl0_128 ),
inference(resolution,[],[f1802,f1636]) ).
fof(f42177,plain,
( spl0_1022
| ~ spl0_116
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1928,f1801,f1622,f42175]) ).
fof(f42175,plain,
( spl0_1022
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f1928,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X2) )
| ~ spl0_116
| ~ spl0_128 ),
inference(duplicate_literal_removal,[],[f1922]) ).
fof(f1922,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X2) )
| ~ spl0_116
| ~ spl0_128 ),
inference(resolution,[],[f1802,f1623]) ).
fof(f42173,plain,
( spl0_1021
| ~ spl0_73
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1418,f1361,f1357,f42171]) ).
fof(f42171,plain,
( spl0_1021
<=> ! [X5,X3,X4,X0,X6,X2,X1] : c_Fun_Ofun__upd(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X1,X2,X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f1418,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : c_Fun_Ofun__upd(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X1,X2,X5,X6)
| ~ spl0_73
| ~ spl0_74 ),
inference(superposition,[],[f1362,f1358]) ).
fof(f41998,plain,
( spl0_1020
| ~ spl0_44
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f36778,f31979,f1215,f41996]) ).
fof(f41996,plain,
( spl0_1020
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X3),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f36778,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X3),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5)))
| ~ spl0_44
| ~ spl0_884 ),
inference(resolution,[],[f31980,f1216]) ).
fof(f41994,plain,
( spl0_1019
| spl0_23
| ~ spl0_573 ),
inference(avatar_split_clause,[],[f14076,f13995,f1130,f41992]) ).
fof(f41992,plain,
( spl0_1019
<=> ! [X0] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_HOL_Ominus__class_Ominus(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f14076,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_HOL_Ominus__class_Ominus(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| spl0_23
| ~ spl0_573 ),
inference(resolution,[],[f13996,f1132]) ).
fof(f40150,plain,
( spl0_1018
| ~ spl0_45
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f36774,f31979,f1219,f40148]) ).
fof(f40148,plain,
( spl0_1018
<=> ! [X5,X4,X2,X0,X6,X3,X1] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),hAPP(c_fequal(X1),X2),X3,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f36774,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),hAPP(c_fequal(X1),X2),X3,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6)))
| ~ spl0_45
| ~ spl0_884 ),
inference(resolution,[],[f31980,f1220]) ).
fof(f38967,plain,
( spl0_1017
| ~ spl0_151
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f36770,f31979,f2184,f38965]) ).
fof(f38965,plain,
( spl0_1017
<=> ! [X5,X4,X2,X0,X6,X3,X1] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Set_OPow(X1,X2),X3,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f36770,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Set_OPow(X1,X2),X3,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6)))
| ~ spl0_151
| ~ spl0_884 ),
inference(resolution,[],[f31980,f2185]) ).
fof(f36993,plain,
( spl0_1016
| ~ spl0_133
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f36907,f31979,f1821,f36991]) ).
fof(f36991,plain,
( spl0_1016
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Arrow__Order__Mirabelle_OLin,X1,X2),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1821,plain,
( spl0_133
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f36907,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Arrow__Order__Mirabelle_OLin,X1,X2),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4)))
| ~ spl0_133
| ~ spl0_884 ),
inference(resolution,[],[f31980,f1823]) ).
fof(f1823,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1821]) ).
fof(f36988,plain,
( spl0_1015
| ~ spl0_527
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f12941,f12937,f12088,f36986]) ).
fof(f36986,plain,
( spl0_1015
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X1) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X0,X1)),hAPP(c_fequal(X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f12088,plain,
( spl0_527
<=> ! [X10,X0,X12,X3,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f12937,plain,
( spl0_542
<=> ! [X4,X0,X12,X3,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),hAPP(c_fequal(X12),X4))))
| hAPP(X10,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f12941,plain,
( ! [X2,X3,X0,X1] :
( hAPP(X0,X1) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X0,X1)),hAPP(c_fequal(X3),X2))) )
| ~ spl0_527
| ~ spl0_542 ),
inference(resolution,[],[f12938,f12089]) ).
fof(f12089,plain,
( ! [X3,X10,X0,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),X7)) )
| ~ spl0_527 ),
inference(avatar_component_clause,[],[f12088]) ).
fof(f12938,plain,
( ! [X3,X10,X0,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),hAPP(c_fequal(X12),X4))))
| hAPP(X10,X3) = X4 )
| ~ spl0_542 ),
inference(avatar_component_clause,[],[f12937]) ).
fof(f36984,plain,
( spl0_1014
| ~ spl0_203
| ~ spl0_500 ),
inference(avatar_split_clause,[],[f11688,f11612,f2831,f36982]) ).
fof(f36982,plain,
( spl0_1014
<=> ! [X0,X3,X2,X1] :
( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(X0,X1),X0,X2,X3) = X1
| ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f11612,plain,
( spl0_500
<=> ! [X11,X0,X10,X2] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11,X0)
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(X10,X2),X10,X0,X11) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X2)),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f11688,plain,
( ! [X2,X3,X0,X1] :
( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(X0,X1),X0,X2,X3) = X1
| ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X2) )
| ~ spl0_203
| ~ spl0_500 ),
inference(resolution,[],[f11613,f2832]) ).
fof(f11613,plain,
( ! [X2,X10,X0,X11] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X2)),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11,X0)))
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(X10,X2),X10,X0,X11) = X2
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11,X0) )
| ~ spl0_500 ),
inference(avatar_component_clause,[],[f11612]) ).
fof(f36969,plain,
( spl0_1013
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1012 ),
inference(avatar_split_clause,[],[f36965,f36962,f18286,f2678,f36967]) ).
fof(f36967,plain,
( spl0_1013
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omkbot(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f36962,plain,
( spl0_1012
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omkbot(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f36965,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omkbot(X0,X1))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1012 ),
inference(forward_demodulation,[],[f36963,f19417]) ).
fof(f36963,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omkbot(X0,X1))) )
| ~ spl0_1012 ),
inference(avatar_component_clause,[],[f36962]) ).
fof(f36964,plain,
( spl0_1012
| ~ spl0_113
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f6929,f6710,f1546,f36962]) ).
fof(f6710,plain,
( spl0_360
<=> ! [X37,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1)),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f6929,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omkbot(X0,X1))) )
| ~ spl0_113
| ~ spl0_360 ),
inference(resolution,[],[f6711,f1547]) ).
fof(f6711,plain,
( ! [X1,X37] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_360 ),
inference(avatar_component_clause,[],[f6710]) ).
fof(f36949,plain,
( spl0_1011
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1010 ),
inference(avatar_split_clause,[],[f36945,f36942,f18286,f2678,f36947]) ).
fof(f36947,plain,
( spl0_1011
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omktop(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f36942,plain,
( spl0_1010
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omktop(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f36945,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omktop(X0,X1))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1010 ),
inference(forward_demodulation,[],[f36943,f19417]) ).
fof(f36943,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omktop(X0,X1))) )
| ~ spl0_1010 ),
inference(avatar_component_clause,[],[f36942]) ).
fof(f36944,plain,
( spl0_1010
| ~ spl0_113
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f6905,f6706,f1546,f36942]) ).
fof(f6706,plain,
( spl0_359
<=> ! [X37,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X37,X1)),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f6905,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omktop(X0,X1))) )
| ~ spl0_113
| ~ spl0_359 ),
inference(resolution,[],[f6707,f1547]) ).
fof(f6707,plain,
( ! [X1,X37] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X37,X1)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f6706]) ).
fof(f36940,plain,
( spl0_1009
| ~ spl0_112
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f6754,f6749,f1542,f36938]) ).
fof(f36938,plain,
( spl0_1009
<=> ! [X4,X0,X3,X2,X1] :
( c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1) = hAPP(c_fequal(X1),X0)
| ~ hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f6749,plain,
( spl0_368
<=> ! [X0,X14,X12,X6,X1] :
( c_Set_Oimage(c_COMBK(X14,X12,X0),X6,X0,X12) = hAPP(c_fequal(X12),X14)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f6754,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1) = hAPP(c_fequal(X1),X0)
| ~ hBOOL(hAPP(X3,X4)) )
| ~ spl0_112
| ~ spl0_368 ),
inference(resolution,[],[f6750,f1543]) ).
fof(f6750,plain,
( ! [X0,X1,X6,X14,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Set_Oimage(c_COMBK(X14,X12,X0),X6,X0,X12) = hAPP(c_fequal(X12),X14) )
| ~ spl0_368 ),
inference(avatar_component_clause,[],[f6749]) ).
fof(f36936,plain,
( spl0_1008
| ~ spl0_89
| ~ spl0_213
| ~ spl0_317
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5973,f5631,f4702,f2882,f1445,f36934]) ).
fof(f36934,plain,
( spl0_1008
<=> ! [X2,X0,X1,X3] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f5973,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X1))
| ~ spl0_89
| ~ spl0_213
| ~ spl0_317
| ~ spl0_336 ),
inference(forward_demodulation,[],[f5901,f5265]) ).
fof(f5901,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X1))
| ~ spl0_213
| ~ spl0_336 ),
inference(superposition,[],[f2883,f5632]) ).
fof(f36446,plain,
( spl0_1007
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1006 ),
inference(avatar_split_clause,[],[f36442,f36439,f18286,f2678,f36444]) ).
fof(f36444,plain,
( spl0_1007
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X2))
| hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f36439,plain,
( spl0_1006
<=> ! [X2,X0,X1] :
( hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f36442,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X2))
| hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2) = X2 )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_1006 ),
inference(forward_demodulation,[],[f36440,f19417]) ).
fof(f36440,plain,
( ! [X2,X0,X1] :
( hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X1)) )
| ~ spl0_1006 ),
inference(avatar_component_clause,[],[f36439]) ).
fof(f36441,plain,
( spl0_1006
| ~ spl0_29
| ~ spl0_48
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f5431,f5334,f1231,f1155,f36439]) ).
fof(f5431,plain,
( ! [X2,X0,X1] :
( hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X1)) )
| ~ spl0_29
| ~ spl0_48
| ~ spl0_319 ),
inference(forward_demodulation,[],[f5428,f1156]) ).
fof(f5428,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X1))
| hAPP(c_COMBI(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2)) = X2 )
| ~ spl0_48
| ~ spl0_319 ),
inference(superposition,[],[f5335,f1232]) ).
fof(f36437,plain,
( spl0_1005
| ~ spl0_137
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4954,f4666,f1838,f36435]) ).
fof(f36435,plain,
( spl0_1005
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0),X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f1838,plain,
( spl0_137
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f4954,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0),X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_137
| ~ spl0_308 ),
inference(resolution,[],[f4667,f1839]) ).
fof(f1839,plain,
( ! [X2,X0,X1,X5] :
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0)
| c_lessequals(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1838]) ).
fof(f36433,plain,
( spl0_1004
| ~ spl0_130
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4945,f4666,f1809,f36431]) ).
fof(f36431,plain,
( spl0_1004
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X0),X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f4945,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X0),X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_130
| ~ spl0_308 ),
inference(resolution,[],[f4667,f1810]) ).
fof(f36429,plain,
( spl0_1003
| ~ spl0_131
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4944,f4666,f1813,f36427]) ).
fof(f36427,plain,
( spl0_1003
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f1813,plain,
( spl0_131
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f4944,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_131
| ~ spl0_308 ),
inference(resolution,[],[f4667,f1814]) ).
fof(f1814,plain,
( ! [X3,X0,X1,X4] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X1,X0)
| c_lessequals(X3,X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1813]) ).
fof(f36425,plain,
( spl0_1002
| ~ spl0_137
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4715,f4658,f1838,f36423]) ).
fof(f36423,plain,
( spl0_1002
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f4715,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_137
| ~ spl0_306 ),
inference(resolution,[],[f4659,f1839]) ).
fof(f36421,plain,
( spl0_1001
| ~ spl0_138
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4714,f4658,f1842,f36419]) ).
fof(f36419,plain,
( spl0_1001
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f4714,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_138
| ~ spl0_306 ),
inference(resolution,[],[f4659,f1843]) ).
fof(f36417,plain,
( spl0_1000
| ~ spl0_131
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4705,f4658,f1813,f36415]) ).
fof(f36415,plain,
( spl0_1000
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f4705,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_131
| ~ spl0_306 ),
inference(resolution,[],[f4659,f1814]) ).
fof(f36332,plain,
( spl0_999
| ~ spl0_192
| ~ spl0_699
| ~ spl0_998 ),
inference(avatar_split_clause,[],[f36328,f36325,f18286,f2678,f36330]) ).
fof(f36330,plain,
( spl0_999
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(c_Set_Oimage(X3,X2,X0,X4),hAPP(X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f36325,plain,
( spl0_998
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Set_Oimage(X3,X2,X0,X4),hAPP(X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f36328,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(c_Set_Oimage(X3,X2,X0,X4),hAPP(X3,X1))) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_998 ),
inference(forward_demodulation,[],[f36326,f19417]) ).
fof(f36326,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Set_Oimage(X3,X2,X0,X4),hAPP(X3,X1))) )
| ~ spl0_998 ),
inference(avatar_component_clause,[],[f36325]) ).
fof(f36327,plain,
( spl0_998
| ~ spl0_113
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4625,f4514,f1546,f36325]) ).
fof(f4625,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Set_Oimage(X3,X2,X0,X4),hAPP(X3,X1))) )
| ~ spl0_113
| ~ spl0_303 ),
inference(resolution,[],[f4515,f1547]) ).
fof(f36322,plain,
( spl0_997
| ~ spl0_112
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4593,f4502,f1542,f36320]) ).
fof(f36320,plain,
( spl0_997
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f4593,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(X0,X3)) )
| ~ spl0_112
| ~ spl0_300 ),
inference(resolution,[],[f4503,f1543]) ).
fof(f36318,plain,
( spl0_996
| ~ spl0_107
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f4333,f4130,f1521,f36316]) ).
fof(f36316,plain,
( spl0_996
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| c_HOL_Ominus__class_Ominus(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f4333,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| c_HOL_Ominus__class_Ominus(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0 )
| ~ spl0_107
| ~ spl0_283 ),
inference(superposition,[],[f4131,f1522]) ).
fof(f36314,plain,
( spl0_995
| ~ spl0_230
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3749,f3584,f3116,f36312]) ).
fof(f36312,plain,
( spl0_995
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f3749,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) )
| ~ spl0_230
| ~ spl0_250 ),
inference(superposition,[],[f3117,f3585]) ).
fof(f36310,plain,
( spl0_994
| ~ spl0_229
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3748,f3584,f3112,f36308]) ).
fof(f36308,plain,
( spl0_994
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f3748,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) )
| ~ spl0_229
| ~ spl0_250 ),
inference(superposition,[],[f3113,f3585]) ).
fof(f36306,plain,
( spl0_993
| ~ spl0_219
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3747,f3584,f3063,f36304]) ).
fof(f36304,plain,
( spl0_993
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f3747,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) )
| ~ spl0_219
| ~ spl0_250 ),
inference(superposition,[],[f3064,f3585]) ).
fof(f36302,plain,
( spl0_992
| ~ spl0_218
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3746,f3584,f3059,f36300]) ).
fof(f36300,plain,
( spl0_992
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f3746,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) )
| ~ spl0_218
| ~ spl0_250 ),
inference(superposition,[],[f3060,f3585]) ).
fof(f36298,plain,
( spl0_991
| ~ spl0_95
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3724,f3580,f1473,f36296]) ).
fof(f36296,plain,
( spl0_991
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X0,X1,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f3724,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X0,X1,tc_fun(X3,tc_bool)) )
| ~ spl0_95
| ~ spl0_249 ),
inference(resolution,[],[f3581,f1474]) ).
fof(f36294,plain,
( spl0_990
| ~ spl0_94
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3704,f3580,f1469,f36292]) ).
fof(f36292,plain,
( spl0_990
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f3704,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) )
| ~ spl0_94
| ~ spl0_249 ),
inference(resolution,[],[f3581,f1470]) ).
fof(f36260,plain,
( spl0_989
| ~ spl0_93
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3703,f3580,f1465,f36258]) ).
fof(f36258,plain,
( spl0_989
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f3703,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) )
| ~ spl0_93
| ~ spl0_249 ),
inference(resolution,[],[f3581,f1466]) ).
fof(f36256,plain,
( spl0_988
| ~ spl0_185
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f3023,f2870,f2650,f36254]) ).
fof(f36254,plain,
( spl0_988
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_SetInterval_Oord_OlessThan(X0,X2,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f3023,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_SetInterval_Oord_OlessThan(X0,X2,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_185
| ~ spl0_210 ),
inference(resolution,[],[f2871,f2651]) ).
fof(f36252,plain,
( spl0_987
| ~ spl0_187
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f3022,f2870,f2658,f36250]) ).
fof(f36250,plain,
( spl0_987
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_SetInterval_Oord_OlessThan(X0,X2,X3),X3),X1,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f3022,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_SetInterval_Oord_OlessThan(X0,X2,X3),X3),X1,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_187
| ~ spl0_210 ),
inference(resolution,[],[f2871,f2659]) ).
fof(f36248,plain,
( spl0_986
| ~ spl0_185
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f3018,f2862,f2650,f36246]) ).
fof(f36246,plain,
( spl0_986
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(c_SetInterval_Oord_OgreaterThan(X0,X1,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f3018,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(c_SetInterval_Oord_OgreaterThan(X0,X1,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_185
| ~ spl0_208 ),
inference(resolution,[],[f2863,f2651]) ).
fof(f36244,plain,
( spl0_985
| ~ spl0_187
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f3017,f2862,f2658,f36242]) ).
fof(f36242,plain,
( spl0_985
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_SetInterval_Oord_OgreaterThan(X0,X1,X3),X3),X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f3017,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_SetInterval_Oord_OgreaterThan(X0,X1,X3),X3),X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_187
| ~ spl0_208 ),
inference(resolution,[],[f2863,f2659]) ).
fof(f36240,plain,
( spl0_984
| ~ spl0_185
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f3002,f2854,f2650,f36238]) ).
fof(f36238,plain,
( spl0_984
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_SetInterval_Oord_OatMost(X0,X2,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f3002,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_SetInterval_Oord_OatMost(X0,X2,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_185
| ~ spl0_206 ),
inference(resolution,[],[f2855,f2651]) ).
fof(f36236,plain,
( spl0_983
| ~ spl0_187
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f3001,f2854,f2658,f36234]) ).
fof(f36234,plain,
( spl0_983
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_SetInterval_Oord_OatMost(X0,X2,X3),X3),X1,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f3001,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_SetInterval_Oord_OatMost(X0,X2,X3),X3),X1,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_187
| ~ spl0_206 ),
inference(resolution,[],[f2855,f2659]) ).
fof(f36231,plain,
( spl0_982
| ~ spl0_52
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2973,f2831,f1247,f36229]) ).
fof(f36229,plain,
( spl0_982
<=> ! [X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(c_in(X4),X0),c_Set_Oimage(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f2973,plain,
( ! [X2,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_in(X4),X0),c_Set_Oimage(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4)))
| ~ spl0_52
| ~ spl0_203 ),
inference(superposition,[],[f2832,f1248]) ).
fof(f36227,plain,
( spl0_981
| ~ spl0_185
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2967,f2831,f2650,f36225]) ).
fof(f36225,plain,
( spl0_981
<=> ! [X0,X3,X2,X1] :
( c_lessequals(hAPP(X0,X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f2967,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(hAPP(X0,X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_185
| ~ spl0_203 ),
inference(resolution,[],[f2832,f2651]) ).
fof(f36223,plain,
( spl0_980
| ~ spl0_187
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2966,f2831,f2658,f36221]) ).
fof(f36221,plain,
( spl0_980
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),X2),hAPP(X0,X3),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f2966,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),X2),hAPP(X0,X3),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_187
| ~ spl0_203 ),
inference(resolution,[],[f2832,f2659]) ).
fof(f36189,plain,
( spl0_979
| ~ spl0_42
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2955,f2815,f1207,f36187]) ).
fof(f1207,plain,
( spl0_42
<=> ! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f2955,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2),hAPP(X3,X2),X0)
| ~ class_Orderings_Obot(tc_fun(X1,X0)) )
| ~ spl0_42
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1208]) ).
fof(f1208,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f36185,plain,
( spl0_978
| ~ spl0_41
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2945,f2815,f1203,f36183]) ).
fof(f36183,plain,
( spl0_978
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,X0)),X2),X0)
| ~ class_Orderings_Otop(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f1203,plain,
( spl0_41
<=> ! [X0,X1] :
( ~ class_Orderings_Otop(X0)
| c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f2945,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,X0)),X2),X0)
| ~ class_Orderings_Otop(tc_fun(X3,X0)) )
| ~ spl0_41
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1204]) ).
fof(f1204,plain,
( ! [X0,X1] :
( c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f36181,plain,
( spl0_977
| ~ spl0_148
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2928,f2811,f1883,f36179]) ).
fof(f36179,plain,
( spl0_977
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X0,X3,X4),X2,X4,X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f1883,plain,
( spl0_148
<=> ! [X10,X0,X12,X6,X7] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Set_Oimage(X10,X6,X0,X12) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2811,plain,
( spl0_198
<=> ! [X10,X0,X12,X6,X7] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Fun_Obij__betw(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X7,X6,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2928,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X0,X3,X4),X2,X4,X3) = X1 )
| ~ spl0_148
| ~ spl0_198 ),
inference(resolution,[],[f2812,f1884]) ).
fof(f1884,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Set_Oimage(X10,X6,X0,X12) = X7 )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1883]) ).
fof(f2812,plain,
( ! [X10,X0,X6,X7,X12] :
( c_Fun_Obij__betw(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X7,X6,X12,X0)
| ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2811]) ).
fof(f36177,plain,
( spl0_976
| ~ spl0_73
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2506,f2212,f1357,f36175]) ).
fof(f36175,plain,
( spl0_976
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_lessequals(X2,X1,X5)
| ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f2506,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(X2,X1,X5)
| ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5),X1,X5) )
| ~ spl0_73
| ~ spl0_158 ),
inference(superposition,[],[f2213,f1358]) ).
fof(f36173,plain,
( spl0_975
| ~ spl0_116
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f2020,f1834,f1622,f36171]) ).
fof(f36171,plain,
( spl0_975
<=> ! [X2,X0,X1,X3] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X1,X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f2020,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X1,X2) = X1 )
| ~ spl0_116
| ~ spl0_136 ),
inference(resolution,[],[f1835,f1623]) ).
fof(f36169,plain,
( spl0_974
| ~ spl0_119
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f2019,f1834,f1635,f36167]) ).
fof(f36167,plain,
( spl0_974
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f2019,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2) = X1 )
| ~ spl0_119
| ~ spl0_136 ),
inference(resolution,[],[f1835,f1636]) ).
fof(f36165,plain,
( spl0_973
| ~ spl0_116
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2008,f1830,f1622,f36163]) ).
fof(f36163,plain,
( spl0_973
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X1,X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f2008,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X1,X2) = X1 )
| ~ spl0_116
| ~ spl0_135 ),
inference(resolution,[],[f1831,f1623]) ).
fof(f36161,plain,
( spl0_972
| ~ spl0_119
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2007,f1830,f1635,f36159]) ).
fof(f36159,plain,
( spl0_972
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f2007,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2) = X1 )
| ~ spl0_119
| ~ spl0_135 ),
inference(resolution,[],[f1831,f1636]) ).
fof(f36157,plain,
( spl0_971
| ~ spl0_120
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1932,f1805,f1639,f36155]) ).
fof(f36155,plain,
( spl0_971
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f1932,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X2) = X0 )
| ~ spl0_120
| ~ spl0_129 ),
inference(resolution,[],[f1806,f1640]) ).
fof(f36153,plain,
( spl0_970
| ~ spl0_122
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1931,f1805,f1647,f36151]) ).
fof(f36151,plain,
( spl0_970
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f1931,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2) = X0 )
| ~ spl0_122
| ~ spl0_129 ),
inference(resolution,[],[f1806,f1648]) ).
fof(f36149,plain,
( spl0_969
| ~ spl0_26
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f32665,f30566,f1143,f36147]) ).
fof(f36147,plain,
( spl0_969
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f1143,plain,
( spl0_26
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f32665,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_26
| ~ spl0_883 ),
inference(resolution,[],[f30567,f1144]) ).
fof(f1144,plain,
( ! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f36145,plain,
( spl0_968
| ~ spl0_120
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1920,f1801,f1639,f36143]) ).
fof(f36143,plain,
( spl0_968
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f1920,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X2) = X0 )
| ~ spl0_120
| ~ spl0_128 ),
inference(resolution,[],[f1802,f1640]) ).
fof(f36141,plain,
( spl0_967
| ~ spl0_122
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1919,f1801,f1647,f36139]) ).
fof(f36139,plain,
( spl0_967
<=> ! [X2,X0,X1,X3] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f1919,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2) = X0 )
| ~ spl0_122
| ~ spl0_128 ),
inference(resolution,[],[f1802,f1648]) ).
fof(f36137,plain,
( spl0_966
| ~ spl0_55
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1904,f1781,f1265,f36135]) ).
fof(f36135,plain,
( spl0_966
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2) = X0
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olower__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f1904,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2) = X0
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_55
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1266]) ).
fof(f36133,plain,
( spl0_965
| ~ spl0_56
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1903,f1781,f1269,f36131]) ).
fof(f36131,plain,
( spl0_965
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2) = X0
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f1903,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2) = X0
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_56
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1270]) ).
fof(f36129,plain,
( spl0_964
| ~ spl0_54
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1902,f1781,f1261,f36127]) ).
fof(f36127,plain,
( spl0_964
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2) = X0
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olower__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f1902,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2) = X0
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_54
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1262]) ).
fof(f36125,plain,
( spl0_963
| ~ spl0_57
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1901,f1781,f1273,f36123]) ).
fof(f36123,plain,
( spl0_963
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2) = X0
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f1901,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2) = X0
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_57
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1274]) ).
fof(f36121,plain,
( spl0_962
| ~ spl0_64
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1896,f1781,f1301,f36119]) ).
fof(f36119,plain,
( spl0_962
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) = X1
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f1896,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) = X1
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_64
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1302]) ).
fof(f36117,plain,
( spl0_961
| ~ spl0_65
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1895,f1781,f1305,f36115]) ).
fof(f36115,plain,
( spl0_961
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) = X1
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f1895,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) = X1
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_65
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1306]) ).
fof(f36113,plain,
( spl0_960
| ~ spl0_63
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1894,f1781,f1297,f36111]) ).
fof(f36111,plain,
( spl0_960
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) = X0
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f1894,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) = X0
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_63
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1298]) ).
fof(f36109,plain,
( spl0_959
| ~ spl0_66
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1893,f1781,f1309,f36107]) ).
fof(f36107,plain,
( spl0_959
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) = X0
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f1893,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) = X0
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_66
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1310]) ).
fof(f36105,plain,
( spl0_958
| ~ spl0_27
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f32664,f30566,f1147,f36103]) ).
fof(f36103,plain,
( spl0_958
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f1147,plain,
( spl0_27
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f32664,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_27
| ~ spl0_883 ),
inference(resolution,[],[f30567,f1148]) ).
fof(f1148,plain,
( ! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f36101,plain,
( spl0_957
| ~ spl0_30
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1613,f1529,f1159,f36099]) ).
fof(f36099,plain,
( spl0_957
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,X1),tc_bool)),tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f1529,plain,
( spl0_109
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1613,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,X1),tc_bool)),tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_30
| ~ spl0_109 ),
inference(resolution,[],[f1530,f1160]) ).
fof(f1530,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f36097,plain,
( spl0_956
| ~ spl0_30
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1611,f1525,f1159,f36095]) ).
fof(f36095,plain,
( spl0_956
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)),tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f1525,plain,
( spl0_108
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1611,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)),tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_30
| ~ spl0_108 ),
inference(resolution,[],[f1526,f1160]) ).
fof(f1526,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1525]) ).
fof(f36093,plain,
( spl0_955
| ~ spl0_30
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1597,f1509,f1159,f36091]) ).
fof(f36091,plain,
( spl0_955
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)),tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f1509,plain,
( spl0_104
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1597,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)),tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_30
| ~ spl0_104 ),
inference(resolution,[],[f1510,f1160]) ).
fof(f1510,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1509]) ).
fof(f36089,plain,
( spl0_954
| ~ spl0_30
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1587,f1485,f1159,f36087]) ).
fof(f36087,plain,
( spl0_954
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,X1),tc_bool)),tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f1485,plain,
( spl0_98
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1587,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,X1),tc_bool)),tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_30
| ~ spl0_98 ),
inference(resolution,[],[f1486,f1160]) ).
fof(f1486,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f35626,plain,
( spl0_953
| ~ spl0_103
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f32663,f30566,f1505,f35624]) ).
fof(f35624,plain,
( spl0_953
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1505,plain,
( spl0_103
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f32663,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_103
| ~ spl0_883 ),
inference(resolution,[],[f30567,f1506]) ).
fof(f1506,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1505]) ).
fof(f33292,plain,
( spl0_951
| ~ spl0_952
| ~ spl0_115
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f32668,f30566,f1577,f33289,f33286]) ).
fof(f33286,plain,
( spl0_951
<=> ! [X2,X0,X1] : c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_nat),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f33289,plain,
( spl0_952
<=> class_Complete__Lattice_Ocomplete__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1577,plain,
( spl0_115
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f32668,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(tc_nat)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_nat),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),tc_nat) )
| ~ spl0_115
| ~ spl0_883 ),
inference(resolution,[],[f30567,f1578]) ).
fof(f1578,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1577]) ).
fof(f32925,plain,
( spl0_950
| ~ spl0_358
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f9667,f8277,f6702,f32923]) ).
fof(f32923,plain,
( spl0_950
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(c_Set_Oimage(X0,X1,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_Fun_Obij__betw(X0,X1,X4,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f9667,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Set_Oimage(X0,X1,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_Fun_Obij__betw(X0,X1,X4,X2,X3) )
| ~ spl0_358
| ~ spl0_422 ),
inference(resolution,[],[f8278,f6703]) ).
fof(f32921,plain,
( spl0_949
| ~ spl0_100
| ~ spl0_165
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f9127,f8249,f2240,f1493,f32919]) ).
fof(f32919,plain,
( spl0_949
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f2240,plain,
( spl0_165
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f9127,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_165
| ~ spl0_415 ),
inference(forward_demodulation,[],[f9062,f2241]) ).
fof(f2241,plain,
( ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f2240]) ).
fof(f9062,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_415 ),
inference(superposition,[],[f8250,f1494]) ).
fof(f32906,plain,
( spl0_948
| ~ spl0_100
| ~ spl0_164
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f9119,f8249,f2236,f1493,f32904]) ).
fof(f32904,plain,
( spl0_948
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f2236,plain,
( spl0_164
<=> ! [X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f9119,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_164
| ~ spl0_415 ),
inference(forward_demodulation,[],[f9056,f2237]) ).
fof(f2237,plain,
( ! [X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f2236]) ).
fof(f9056,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_415 ),
inference(superposition,[],[f8250,f1494]) ).
fof(f32884,plain,
( spl0_947
| ~ spl0_192
| ~ spl0_699
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f32880,f32877,f18286,f2678,f32882]) ).
fof(f32877,plain,
( spl0_946
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X3)),X2),c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f32880,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X3),X2))
| ~ spl0_192
| ~ spl0_699
| ~ spl0_946 ),
inference(forward_demodulation,[],[f32878,f19417]) ).
fof(f32878,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X3)),X2),c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X3)))
| ~ spl0_946 ),
inference(avatar_component_clause,[],[f32877]) ).
fof(f32879,plain,
( spl0_946
| ~ spl0_82
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f7340,f7052,f1393,f32877]) ).
fof(f1393,plain,
( spl0_82
<=> ! [X0,X3] : ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f7340,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X3)),X2),c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X3)))
| ~ spl0_82
| ~ spl0_376 ),
inference(resolution,[],[f7053,f1394]) ).
fof(f1394,plain,
( ! [X3,X0] : ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1393]) ).
fof(f32835,plain,
( spl0_945
| ~ spl0_192
| ~ spl0_699
| ~ spl0_944 ),
inference(avatar_split_clause,[],[f32831,f32828,f18286,f2678,f32833]) ).
fof(f32833,plain,
( spl0_945
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,X1))
| ~ c_lessequals(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f32828,plain,
( spl0_944
<=> ! [X2,X0,X1] :
( ~ c_lessequals(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f32831,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X2,X1))
| ~ c_lessequals(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_944 ),
inference(forward_demodulation,[],[f32829,f19417]) ).
fof(f32829,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) )
| ~ spl0_944 ),
inference(avatar_component_clause,[],[f32828]) ).
fof(f32830,plain,
( spl0_944
| ~ spl0_46
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f7110,f7085,f1223,f32828]) ).
fof(f7110,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) )
| ~ spl0_46
| ~ spl0_384 ),
inference(superposition,[],[f7086,f1224]) ).
fof(f32826,plain,
( spl0_943
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f6785,f6749,f4702,f2288,f1445,f32824]) ).
fof(f32824,plain,
( spl0_943
<=> ! [X0,X3,X2,X1] : hAPP(c_fequal(X1),X0) = c_Set_Oimage(c_COMBK(X0,X1,X2),hAPP(c_fequal(X2),X3),X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f6785,plain,
( ! [X2,X3,X0,X1] : hAPP(c_fequal(X1),X0) = c_Set_Oimage(c_COMBK(X0,X1,X2),hAPP(c_fequal(X2),X3),X2,X1)
| ~ spl0_89
| ~ spl0_177
| ~ spl0_317
| ~ spl0_368 ),
inference(forward_demodulation,[],[f6761,f5265]) ).
fof(f6761,plain,
( ! [X2,X3,X0,X1] : hAPP(c_fequal(X1),X0) = c_Set_Oimage(c_COMBK(X0,X1,X2),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),X2,X1)
| ~ spl0_177
| ~ spl0_368 ),
inference(resolution,[],[f6750,f2289]) ).
fof(f32822,plain,
( spl0_942
| ~ spl0_83
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f6765,f6749,f1397,f32820]) ).
fof(f32820,plain,
( spl0_942
<=> ! [X2,X0,X1] : hAPP(c_fequal(X1),X0) = c_Set_Oimage(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f6765,plain,
( ! [X2,X0,X1] : hAPP(c_fequal(X1),X0) = c_Set_Oimage(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X1)
| ~ spl0_83
| ~ spl0_368 ),
inference(resolution,[],[f6750,f1398]) ).
fof(f32814,plain,
( spl0_941
| ~ spl0_12
| ~ spl0_172
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f32666,f30566,f2268,f1075,f32812]) ).
fof(f32812,plain,
( spl0_941
<=> ! [X2,X0,X1] : c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_bool),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f2268,plain,
( spl0_172
<=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f32666,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_bool),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),tc_bool) )
| ~ spl0_172
| ~ spl0_883 ),
inference(resolution,[],[f30567,f2269]) ).
fof(f2269,plain,
( ! [X0] : c_lessequals(X0,X0,tc_bool)
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f2268]) ).
fof(f32810,plain,
( spl0_940
| ~ spl0_192
| ~ spl0_699
| ~ spl0_939 ),
inference(avatar_split_clause,[],[f32806,f32803,f18286,f2678,f32808]) ).
fof(f32808,plain,
( spl0_940
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f32803,plain,
( spl0_939
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f32806,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool)),X1))
| ~ spl0_192
| ~ spl0_699
| ~ spl0_939 ),
inference(forward_demodulation,[],[f32804,f19417]) ).
fof(f32804,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool))))
| ~ spl0_939 ),
inference(avatar_component_clause,[],[f32803]) ).
fof(f32805,plain,
( spl0_939
| ~ spl0_82
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f6614,f5675,f1393,f32803]) ).
fof(f6614,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool))))
| ~ spl0_82
| ~ spl0_347 ),
inference(resolution,[],[f5676,f1394]) ).
fof(f32783,plain,
( spl0_938
| ~ spl0_192
| ~ spl0_699
| ~ spl0_937 ),
inference(avatar_split_clause,[],[f32779,f32776,f18286,f2678,f32781]) ).
fof(f32781,plain,
( spl0_938
<=> ! [X0,X1] : hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f32776,plain,
( spl0_937
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f32779,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool)),X1))
| ~ spl0_192
| ~ spl0_699
| ~ spl0_937 ),
inference(forward_demodulation,[],[f32777,f19417]) ).
fof(f32777,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool))))
| ~ spl0_937 ),
inference(avatar_component_clause,[],[f32776]) ).
fof(f32778,plain,
( spl0_937
| ~ spl0_82
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f6570,f5671,f1393,f32776]) ).
fof(f6570,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X0,tc_bool),tc_bool)),tc_fun(X0,tc_bool))))
| ~ spl0_82
| ~ spl0_346 ),
inference(resolution,[],[f5672,f1394]) ).
fof(f32774,plain,
( spl0_936
| ~ spl0_100
| ~ spl0_165
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f6490,f5663,f2240,f1493,f32772]) ).
fof(f32772,plain,
( spl0_936
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f6490,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_165
| ~ spl0_344 ),
inference(forward_demodulation,[],[f6439,f2241]) ).
fof(f6439,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))
| ~ spl0_100
| ~ spl0_344 ),
inference(superposition,[],[f5664,f1494]) ).
fof(f32770,plain,
( spl0_935
| ~ spl0_204
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f6444,f5663,f2835,f32768]) ).
fof(f32768,plain,
( spl0_935
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f6444,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ spl0_204
| ~ spl0_344 ),
inference(superposition,[],[f5664,f2836]) ).
fof(f32765,plain,
( spl0_934
| ~ spl0_25
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f5476,f5342,f1139,f32763]) ).
fof(f32763,plain,
( spl0_934
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f5476,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| ~ spl0_25
| ~ spl0_321 ),
inference(resolution,[],[f5343,f1140]) ).
fof(f32712,plain,
( spl0_933
| ~ spl0_192
| ~ spl0_699
| ~ spl0_932 ),
inference(avatar_split_clause,[],[f32659,f32656,f18286,f2678,f32710]) ).
fof(f32710,plain,
( spl0_933
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,X2))
| ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f32656,plain,
( spl0_932
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f32659,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X1,X2))
| ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_932 ),
inference(forward_demodulation,[],[f32657,f19417]) ).
fof(f32657,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X2),X1)) )
| ~ spl0_932 ),
inference(avatar_component_clause,[],[f32656]) ).
fof(f32658,plain,
( spl0_932
| ~ spl0_83
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4600,f4502,f1397,f32656]) ).
fof(f4600,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X2),X1)) )
| ~ spl0_83
| ~ spl0_300 ),
inference(resolution,[],[f4503,f1398]) ).
fof(f32654,plain,
( spl0_931
| ~ spl0_114
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4416,f4158,f1550,f32652]) ).
fof(f32652,plain,
( spl0_931
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Arrow__Order__Mirabelle_OLin,X1,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f4416,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Arrow__Order__Mirabelle_OLin,X1,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_114
| ~ spl0_290 ),
inference(resolution,[],[f4159,f1552]) ).
fof(f32650,plain,
( spl0_930
| ~ spl0_111
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4415,f4158,f1537,f32648]) ).
fof(f32648,plain,
( spl0_930
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Arrow__Order__Mirabelle_OLin,X1,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f4415,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Arrow__Order__Mirabelle_OLin,X1,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_111
| ~ spl0_290 ),
inference(resolution,[],[f4159,f1539]) ).
fof(f32646,plain,
( spl0_929
| ~ spl0_110
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4408,f4158,f1533,f32644]) ).
fof(f32644,plain,
( spl0_929
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_OPow(X1,X2),X3,X0,tc_fun(X2,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f4408,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_OPow(X1,X2),X3,X0,tc_fun(X2,tc_bool)))) )
| ~ spl0_110
| ~ spl0_290 ),
inference(resolution,[],[f4159,f1534]) ).
fof(f32642,plain,
( spl0_928
| ~ spl0_112
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4401,f4158,f1542,f32640]) ).
fof(f32640,plain,
( spl0_928
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,X3,X0,X4)))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f4401,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,X3,X0,X4)))
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_112
| ~ spl0_290 ),
inference(resolution,[],[f4159,f1543]) ).
fof(f32638,plain,
( spl0_927
| ~ spl0_114
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4395,f4150,f1550,f32636]) ).
fof(f32636,plain,
( spl0_927
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X1,c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f4395,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X1,c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_114
| ~ spl0_288 ),
inference(resolution,[],[f4151,f1552]) ).
fof(f32634,plain,
( spl0_926
| ~ spl0_111
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4394,f4150,f1537,f32632]) ).
fof(f32632,plain,
( spl0_926
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X1,c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f4394,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X1,c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_111
| ~ spl0_288 ),
inference(resolution,[],[f4151,f1539]) ).
fof(f32630,plain,
( spl0_925
| ~ spl0_110
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4387,f4150,f1533,f32628]) ).
fof(f32628,plain,
( spl0_925
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,c_Set_OPow(X1,X3),X0,tc_fun(X3,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f4387,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,c_Set_OPow(X1,X3),X0,tc_fun(X3,tc_bool)))) )
| ~ spl0_110
| ~ spl0_288 ),
inference(resolution,[],[f4151,f1534]) ).
fof(f32626,plain,
( spl0_924
| ~ spl0_112
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4380,f4150,f1542,f32624]) ).
fof(f32624,plain,
( spl0_924
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,X3,X0,X4)))
| ~ hBOOL(hAPP(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f4380,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,X3,X0,X4)))
| ~ hBOOL(hAPP(X3,X1)) )
| ~ spl0_112
| ~ spl0_288 ),
inference(resolution,[],[f4151,f1543]) ).
fof(f32621,plain,
( spl0_923
| ~ spl0_112
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4369,f4146,f1542,f32619]) ).
fof(f32619,plain,
( spl0_923
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f4146,plain,
( spl0_287
<=> ! [X0,X14,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f4369,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_112
| ~ spl0_287 ),
inference(resolution,[],[f4147,f1543]) ).
fof(f4147,plain,
( ! [X0,X6,X7,X14] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X0),X14),X6)) )
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f4146]) ).
fof(f32611,plain,
( spl0_922
| ~ spl0_112
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4358,f4142,f1542,f32609]) ).
fof(f32609,plain,
( spl0_922
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f4142,plain,
( spl0_286
<=> ! [X0,X14,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f4358,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_112
| ~ spl0_286 ),
inference(resolution,[],[f4143,f1543]) ).
fof(f4143,plain,
( ! [X0,X6,X7,X14] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X0),X14),X7)) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f4142]) ).
fof(f32606,plain,
( spl0_921
| ~ spl0_112
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f4350,f4138,f1542,f32604]) ).
fof(f32604,plain,
( spl0_921
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f4138,plain,
( spl0_285
<=> ! [X0,X14,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f4350,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_112
| ~ spl0_285 ),
inference(resolution,[],[f4139,f1543]) ).
fof(f4139,plain,
( ! [X0,X6,X7,X14] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X0),X14),X6)) )
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f4138]) ).
fof(f32580,plain,
( spl0_920
| ~ spl0_192
| ~ spl0_699
| ~ spl0_919 ),
inference(avatar_split_clause,[],[f32576,f32573,f18286,f2678,f32578]) ).
fof(f32578,plain,
( spl0_920
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f32573,plain,
( spl0_919
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f32576,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_192
| ~ spl0_699
| ~ spl0_919 ),
inference(forward_demodulation,[],[f32574,f19417]) ).
fof(f32574,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_919 ),
inference(avatar_component_clause,[],[f32573]) ).
fof(f32575,plain,
( spl0_919
| ~ spl0_112
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f4341,f4134,f1542,f32573]) ).
fof(f4134,plain,
( spl0_284
<=> ! [X0,X14,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f4341,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_112
| ~ spl0_284 ),
inference(resolution,[],[f4135,f1543]) ).
fof(f4135,plain,
( ! [X0,X6,X7,X14] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X7)) )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f4134]) ).
fof(f32570,plain,
( spl0_918
| ~ spl0_113
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f4286,f4126,f1546,f32568]) ).
fof(f32568,plain,
( spl0_918
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f4286,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_113
| ~ spl0_282 ),
inference(resolution,[],[f4127,f1547]) ).
fof(f32565,plain,
( spl0_917
| ~ spl0_113
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f4263,f4122,f1546,f32563]) ).
fof(f32563,plain,
( spl0_917
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f4263,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_113
| ~ spl0_281 ),
inference(resolution,[],[f4123,f1547]) ).
fof(f32561,plain,
( spl0_916
| ~ spl0_48
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4191,f4102,f1231,f32559]) ).
fof(f32559,plain,
( spl0_916
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,tc_fun(X0,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f4191,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,tc_fun(X0,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,c_COMBI(X0),X0,X0),X2,X0,X0) )
| ~ spl0_48
| ~ spl0_276 ),
inference(superposition,[],[f4103,f1232]) ).
fof(f32557,plain,
( spl0_915
| ~ spl0_12
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3906,f3615,f1075,f32555]) ).
fof(f32555,plain,
( spl0_915
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = 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_915])]) ).
fof(f3906,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X2,tc_bool,X0),X0,tc_bool) = X2 )
| ~ spl0_12
| ~ spl0_257 ),
inference(resolution,[],[f3616,f1077]) ).
fof(f32553,plain,
( spl0_914
| ~ spl0_93
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3814,f3595,f1465,f32551]) ).
fof(f32551,plain,
( spl0_914
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f3814,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_93
| ~ spl0_252 ),
inference(superposition,[],[f1466,f3596]) ).
fof(f32549,plain,
( spl0_913
| ~ spl0_192
| ~ spl0_284
| ~ spl0_699
| ~ spl0_893 ),
inference(avatar_split_clause,[],[f32477,f32398,f18286,f4134,f2678,f32547]) ).
fof(f32547,plain,
( spl0_913
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X0),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X1))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f32398,plain,
( spl0_893
<=> ! [X0] : c_Arrow__Order__Mirabelle_OLin = c_HOL_Ominus__class_Ominus(c_Arrow__Order__Mirabelle_OLin,hAPP(c_fequal(X0),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f32477,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X0),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X1))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1)) )
| ~ spl0_192
| ~ spl0_284
| ~ spl0_699
| ~ spl0_893 ),
inference(forward_demodulation,[],[f32476,f19417]) ).
fof(f32476,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(c_fequal(X0),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))))) )
| ~ spl0_192
| ~ spl0_284
| ~ spl0_699
| ~ spl0_893 ),
inference(forward_demodulation,[],[f32450,f19417]) ).
fof(f32450,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(c_fequal(X0),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))))) )
| ~ spl0_284
| ~ spl0_893 ),
inference(superposition,[],[f4135,f32399]) ).
fof(f32399,plain,
( ! [X0] : c_Arrow__Order__Mirabelle_OLin = c_HOL_Ominus__class_Ominus(c_Arrow__Order__Mirabelle_OLin,hAPP(c_fequal(X0),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(X0,tc_bool))
| ~ spl0_893 ),
inference(avatar_component_clause,[],[f32398]) ).
fof(f32545,plain,
( spl0_912
| ~ spl0_94
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3775,f3588,f1469,f32543]) ).
fof(f32543,plain,
( spl0_912
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f3775,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_94
| ~ spl0_251 ),
inference(superposition,[],[f1470,f3589]) ).
fof(f32541,plain,
( spl0_911
| ~ spl0_95
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f3507,f3124,f1473,f32539]) ).
fof(f32539,plain,
( spl0_911
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f3507,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool))
| ~ spl0_95
| ~ spl0_232 ),
inference(resolution,[],[f3125,f1474]) ).
fof(f32537,plain,
( spl0_910
| ~ spl0_91
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f3487,f3120,f1453,f32535]) ).
fof(f32535,plain,
( spl0_910
<=> ! [X2,X0,X1,X3] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f3487,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| ~ spl0_91
| ~ spl0_231 ),
inference(forward_demodulation,[],[f3467,f461]) ).
fof(f461,axiom,
! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
fof(f3467,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| ~ spl0_91
| ~ spl0_231 ),
inference(resolution,[],[f3121,f1454]) ).
fof(f32533,plain,
( spl0_909
| ~ spl0_95
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f3478,f3120,f1473,f32531]) ).
fof(f32531,plain,
( spl0_909
<=> ! [X2,X0,X1,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f3478,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| ~ spl0_95
| ~ spl0_231 ),
inference(resolution,[],[f3121,f1474]) ).
fof(f32529,plain,
( spl0_908
| ~ spl0_92
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f3468,f3120,f1457,f32527]) ).
fof(f32527,plain,
( spl0_908
<=> ! [X2,X0,X1,X3] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f3468,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ spl0_92
| ~ spl0_231 ),
inference(resolution,[],[f3121,f1458]) ).
fof(f32525,plain,
( spl0_907
| ~ spl0_93
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f3273,f3063,f1465,f32523]) ).
fof(f32523,plain,
( spl0_907
<=> ! [X0,X3,X2,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f3273,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ spl0_93
| ~ spl0_219 ),
inference(resolution,[],[f3064,f1466]) ).
fof(f32521,plain,
( spl0_906
| ~ spl0_93
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f3237,f3059,f1465,f32519]) ).
fof(f32519,plain,
( spl0_906
<=> ! [X0,X3,X2,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f3237,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ spl0_93
| ~ spl0_218 ),
inference(resolution,[],[f3060,f1466]) ).
fof(f32516,plain,
( spl0_905
| ~ spl0_141
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f3039,f2886,f1854,f32514]) ).
fof(f32514,plain,
( spl0_905
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool))))
| hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f3039,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool))))
| hBOOL(hAPP(X1,X3)) )
| ~ spl0_141
| ~ spl0_214 ),
inference(superposition,[],[f2887,f1855]) ).
fof(f32491,plain,
( spl0_904
| ~ spl0_764
| ~ spl0_903 ),
inference(avatar_split_clause,[],[f32441,f32438,f20188,f32489]) ).
fof(f32438,plain,
( spl0_903
<=> ! [X2,X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f32441,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X1))
| ~ spl0_764
| ~ spl0_903 ),
inference(forward_demodulation,[],[f32439,f20189]) ).
fof(f32439,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)),X1))
| ~ spl0_903 ),
inference(avatar_component_clause,[],[f32438]) ).
fof(f32440,plain,
( spl0_903
| ~ spl0_139
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f3031,f2882,f1846,f32438]) ).
fof(f3031,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)),X1))
| ~ spl0_139
| ~ spl0_213 ),
inference(superposition,[],[f2883,f1847]) ).
fof(f32436,plain,
( spl0_902
| ~ spl0_110
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2756,f2658,f1533,f32434]) ).
fof(f32434,plain,
( spl0_902
<=> ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(X0,X1),tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f2756,plain,
( ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_OPow(X0,X1),tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) )
| ~ spl0_110
| ~ spl0_187 ),
inference(resolution,[],[f2659,f1534]) ).
fof(f32432,plain,
( spl0_901
| ~ spl0_78
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2498,f2212,f1377,f32430]) ).
fof(f32430,plain,
( spl0_901
<=> ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0),X2,X0)
| c_lessequals(X2,hAPP(X1,X2),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f2498,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0),X2,X0)
| c_lessequals(X2,hAPP(X1,X2),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_78
| ~ spl0_158 ),
inference(resolution,[],[f2213,f1378]) ).
fof(f32428,plain,
( spl0_900
| ~ spl0_78
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2447,f2204,f1377,f32426]) ).
fof(f32426,plain,
( spl0_900
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,X3,X2)
| c_lessequals(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f2447,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,X3,X2)
| c_lessequals(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_78
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1378]) ).
fof(f32424,plain,
( spl0_899
| ~ spl0_78
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2417,f2200,f1377,f32422]) ).
fof(f32422,plain,
( spl0_899
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X3,X1,X2)
| c_lessequals(X0,X3,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2417,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X3,X1,X2)
| c_lessequals(X0,X3,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_78
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1378]) ).
fof(f32420,plain,
( spl0_898
| ~ spl0_136
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f2079,f1842,f1834,f32418]) ).
fof(f32418,plain,
( spl0_898
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f2079,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X2),X2) )
| ~ spl0_136
| ~ spl0_138 ),
inference(duplicate_literal_removal,[],[f2066]) ).
fof(f2066,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_136
| ~ spl0_138 ),
inference(resolution,[],[f1843,f1835]) ).
fof(f32416,plain,
( spl0_897
| ~ spl0_135
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f2078,f1842,f1830,f32414]) ).
fof(f32414,plain,
( spl0_897
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f2078,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X2),X2) )
| ~ spl0_135
| ~ spl0_138 ),
inference(duplicate_literal_removal,[],[f2067]) ).
fof(f2067,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_135
| ~ spl0_138 ),
inference(resolution,[],[f1843,f1831]) ).
fof(f32412,plain,
( spl0_896
| ~ spl0_136
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f2052,f1838,f1834,f32410]) ).
fof(f2052,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X2) )
| ~ spl0_136
| ~ spl0_137 ),
inference(duplicate_literal_removal,[],[f2039]) ).
fof(f2039,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_136
| ~ spl0_137 ),
inference(resolution,[],[f1839,f1835]) ).
fof(f32408,plain,
( spl0_895
| ~ spl0_135
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f2051,f1838,f1830,f32406]) ).
fof(f2051,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X2) )
| ~ spl0_135
| ~ spl0_137 ),
inference(duplicate_literal_removal,[],[f2040]) ).
fof(f2040,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_135
| ~ spl0_137 ),
inference(resolution,[],[f1839,f1831]) ).
fof(f32404,plain,
( spl0_894
| ~ spl0_129
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1991,f1813,f1805,f32402]) ).
fof(f32402,plain,
( spl0_894
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X3),X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f1991,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X3),X1,X3) )
| ~ spl0_129
| ~ spl0_131 ),
inference(duplicate_literal_removal,[],[f1981]) ).
fof(f1981,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X3),X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_129
| ~ spl0_131 ),
inference(resolution,[],[f1814,f1806]) ).
fof(f32400,plain,
( spl0_893
| spl0_118
| ~ spl0_879 ),
inference(avatar_split_clause,[],[f32126,f26977,f1630,f32398]) ).
fof(f32126,plain,
( ! [X0] : c_Arrow__Order__Mirabelle_OLin = c_HOL_Ominus__class_Ominus(c_Arrow__Order__Mirabelle_OLin,hAPP(c_fequal(X0),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(X0,tc_bool))
| spl0_118
| ~ spl0_879 ),
inference(resolution,[],[f26978,f1632]) ).
fof(f26978,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X2))
| c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0 )
| ~ spl0_879 ),
inference(avatar_component_clause,[],[f26977]) ).
fof(f32396,plain,
( spl0_892
| ~ spl0_128
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1990,f1813,f1801,f32394]) ).
fof(f32394,plain,
( spl0_892
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f1990,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X3),X2,X3) )
| ~ spl0_128
| ~ spl0_131 ),
inference(duplicate_literal_removal,[],[f1982]) ).
fof(f1982,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_128
| ~ spl0_131 ),
inference(resolution,[],[f1814,f1802]) ).
fof(f32392,plain,
( spl0_891
| ~ spl0_129
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1965,f1809,f1805,f32390]) ).
fof(f32390,plain,
( spl0_891
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X0,X3),X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f1965,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X0,X3),X1,X3) )
| ~ spl0_129
| ~ spl0_130 ),
inference(duplicate_literal_removal,[],[f1955]) ).
fof(f1955,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X0,X3),X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_129
| ~ spl0_130 ),
inference(resolution,[],[f1810,f1806]) ).
fof(f32388,plain,
( spl0_890
| ~ spl0_128
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1964,f1809,f1801,f32386]) ).
fof(f32386,plain,
( spl0_890
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X0,X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f1964,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X0,X3),X2,X3) )
| ~ spl0_128
| ~ spl0_130 ),
inference(duplicate_literal_removal,[],[f1956]) ).
fof(f1956,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X0,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_128
| ~ spl0_130 ),
inference(resolution,[],[f1810,f1802]) ).
fof(f32384,plain,
( spl0_889
| ~ spl0_30
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f1433,f1401,f1159,f32382]) ).
fof(f32382,plain,
( spl0_889
<=> ! [X2,X0,X1] :
( c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,tc_fun(X1,X2),tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f1401,plain,
( spl0_84
<=> ! [X29,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X29,X0,X0),X0) = X29 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1433,plain,
( ! [X2,X0,X1] :
( c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,tc_fun(X1,X2),tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_30
| ~ spl0_84 ),
inference(resolution,[],[f1402,f1160]) ).
fof(f1402,plain,
( ! [X0,X29] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X29,X0,X0),X0) = X29 )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1401]) ).
fof(f32380,plain,
( spl0_888
| ~ spl0_34
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f1427,f1389,f1175,f32378]) ).
fof(f32378,plain,
( spl0_888
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,X1)),X2,tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f1175,plain,
( spl0_34
<=> ! [X59,X58] :
( ~ class_Lattices_Obounded__lattice(X59)
| class_Lattices_Obounded__lattice(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1389,plain,
( spl0_81
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1427,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,X1)),X2,tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_34
| ~ spl0_81 ),
inference(resolution,[],[f1390,f1176]) ).
fof(f1176,plain,
( ! [X58,X59] :
( class_Lattices_Obounded__lattice(tc_fun(X58,X59))
| ~ class_Lattices_Obounded__lattice(X59) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1175]) ).
fof(f1390,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1389]) ).
fof(f32376,plain,
( spl0_887
| ~ spl0_34
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f1425,f1385,f1175,f32374]) ).
fof(f32374,plain,
( spl0_887
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,X1)),tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f1385,plain,
( spl0_80
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1425,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,X1)),tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_34
| ~ spl0_80 ),
inference(resolution,[],[f1386,f1176]) ).
fof(f1386,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1385]) ).
fof(f32372,plain,
( spl0_886
| ~ spl0_34
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f1422,f1373,f1175,f32370]) ).
fof(f32370,plain,
( spl0_886
<=> ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(tc_fun(X0,X1)),tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f1373,plain,
( spl0_77
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1422,plain,
( ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(tc_fun(X0,X1)),tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_34
| ~ spl0_77 ),
inference(resolution,[],[f1374,f1176]) ).
fof(f1374,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(X0),X0) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f32368,plain,
( spl0_885
| ~ spl0_34
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1420,f1369,f1175,f32366]) ).
fof(f32366,plain,
( spl0_885
<=> ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,X1)),X2,tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f1369,plain,
( spl0_76
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1420,plain,
( ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,X1)),X2,tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_34
| ~ spl0_76 ),
inference(resolution,[],[f1370,f1176]) ).
fof(f1370,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X1,X0) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1369]) ).
fof(f31981,plain,
( spl0_884
| ~ spl0_192
| ~ spl0_303
| ~ spl0_699
| ~ spl0_805 ),
inference(avatar_split_clause,[],[f26068,f25505,f18286,f4514,f2678,f31979]) ).
fof(f25505,plain,
( spl0_805
<=> ! [X2,X0,X1,X3] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f26068,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,X6,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))) )
| ~ spl0_192
| ~ spl0_303
| ~ spl0_699
| ~ spl0_805 ),
inference(forward_demodulation,[],[f26067,f19417]) ).
fof(f26067,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,X6,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X6),X1),X5)) )
| ~ spl0_192
| ~ spl0_303
| ~ spl0_699
| ~ spl0_805 ),
inference(forward_demodulation,[],[f25909,f19417]) ).
fof(f25909,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,X6,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X6),X1),X5)) )
| ~ spl0_303
| ~ spl0_805 ),
inference(superposition,[],[f4515,f25506]) ).
fof(f25506,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)
| ~ spl0_805 ),
inference(avatar_component_clause,[],[f25505]) ).
fof(f30568,plain,
( spl0_883
| ~ spl0_158
| ~ spl0_805 ),
inference(avatar_split_clause,[],[f25904,f25505,f2212,f30566]) ).
fof(f25904,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X1,X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X4),X1,X4) )
| ~ spl0_158
| ~ spl0_805 ),
inference(superposition,[],[f2213,f25506]) ).
fof(f27359,plain,
( spl0_882
| ~ spl0_192
| ~ spl0_203
| ~ spl0_699
| ~ spl0_805 ),
inference(avatar_split_clause,[],[f26065,f25505,f18286,f2831,f2678,f27357]) ).
fof(f27357,plain,
( spl0_882
<=> ! [X3,X4,X0,X5,X2] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f26065,plain,
( ! [X2,X3,X0,X4,X5] : hBOOL(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)))
| ~ spl0_192
| ~ spl0_203
| ~ spl0_699
| ~ spl0_805 ),
inference(forward_demodulation,[],[f25905,f19417]) ).
fof(f25905,plain,
( ! [X2,X3,X0,X4,X5] : hBOOL(hAPP(hAPP(c_in(X4),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4)))
| ~ spl0_203
| ~ spl0_805 ),
inference(superposition,[],[f2832,f25506]) ).
fof(f26987,plain,
( spl0_881
| ~ spl0_74
| ~ spl0_805 ),
inference(avatar_split_clause,[],[f25903,f25505,f1361,f26985]) ).
fof(f26985,plain,
( spl0_881
<=> ! [X3,X4,X0,X5,X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f25903,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X4,X5)
| ~ spl0_74
| ~ spl0_805 ),
inference(superposition,[],[f1362,f25506]) ).
fof(f26983,plain,
( spl0_880
| ~ spl0_89
| ~ spl0_142
| ~ spl0_539 ),
inference(avatar_split_clause,[],[f12905,f12785,f1858,f1445,f26981]) ).
fof(f26981,plain,
( spl0_880
<=> ! [X0,X3,X2,X1] : hAPP(c_fequal(X3),hAPP(X2,X1)) = c_Set_Oimage(X2,hAPP(c_fequal(X0),X1),X0,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f12785,plain,
( spl0_539
<=> ! [X10,X0,X12,X3,X7] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X12),X3),X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),hAPP(X10,X3)),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f12905,plain,
( ! [X2,X3,X0,X1] : hAPP(c_fequal(X3),hAPP(X2,X1)) = c_Set_Oimage(X2,hAPP(c_fequal(X0),X1),X0,X3)
| ~ spl0_89
| ~ spl0_142
| ~ spl0_539 ),
inference(forward_demodulation,[],[f12904,f1446]) ).
fof(f12904,plain,
( ! [X2,X3,X0,X1] : c_Set_Oimage(X2,hAPP(c_fequal(X0),X1),X0,X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X3),hAPP(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ spl0_89
| ~ spl0_142
| ~ spl0_539 ),
inference(forward_demodulation,[],[f12796,f1859]) ).
fof(f12796,plain,
( ! [X2,X3,X0,X1] : c_Set_Oimage(X2,hAPP(c_fequal(X0),X1),X0,X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X3),hAPP(X2,X1)),c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X3),tc_fun(X3,tc_bool))
| ~ spl0_89
| ~ spl0_539 ),
inference(superposition,[],[f12786,f1446]) ).
fof(f12786,plain,
( ! [X3,X10,X0,X7,X12] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X12),X3),X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),hAPP(X10,X3)),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool))
| ~ spl0_539 ),
inference(avatar_component_clause,[],[f12785]) ).
fof(f26979,plain,
( spl0_879
| ~ spl0_113
| ~ spl0_526 ),
inference(avatar_split_clause,[],[f12004,f12001,f1546,f26977]) ).
fof(f12004,plain,
( ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,hAPP(c_fequal(X1),X2),tc_fun(X1,tc_bool)) = X0
| hBOOL(hAPP(X0,X2)) )
| ~ spl0_113
| ~ spl0_526 ),
inference(resolution,[],[f12002,f1547]) ).
fof(f26975,plain,
( spl0_878
| ~ spl0_28
| ~ spl0_48
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f7783,f7568,f1231,f1151,f26973]) ).
fof(f26973,plain,
( spl0_878
<=> ! [X0,X1] : c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_COMBI(X0),X0,X0),X1,X0,X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f7568,plain,
( spl0_392
<=> ! [X31,X10,X0,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X10,X0,X12),c_Set_Oimage(X10,X31,X0,X12),X12,X0) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f7783,plain,
( ! [X0,X1] : c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_COMBI(X0),X0,X0),X1,X0,X0) = X1
| ~ spl0_28
| ~ spl0_48
| ~ spl0_392 ),
inference(forward_demodulation,[],[f7782,f1232]) ).
fof(f7782,plain,
( ! [X0,X1] : c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_COMBI(X0),X0,X0),c_Set_Oimage(c_COMBI(X0),X1,X0,X0),X0,X0) = X1
| ~ spl0_28
| ~ spl0_392 ),
inference(resolution,[],[f7569,f1152]) ).
fof(f7569,plain,
( ! [X31,X10,X0,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X10,X0,X12),c_Set_Oimage(X10,X31,X0,X12),X12,X0) = X31 )
| ~ spl0_392 ),
inference(avatar_component_clause,[],[f7568]) ).
fof(f26970,plain,
( spl0_877
| ~ spl0_25
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f7091,f7085,f1139,f26968]) ).
fof(f26968,plain,
( spl0_877
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f7091,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool))))
| ~ spl0_25
| ~ spl0_384 ),
inference(resolution,[],[f7086,f1140]) ).
fof(f26966,plain,
( spl0_876
| ~ spl0_112
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f5375,f5371,f1542,f26964]) ).
fof(f26964,plain,
( spl0_876
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool)) = X2
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f5371,plain,
( spl0_328
<=> ! [X6,X0,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f5375,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X2,tc_fun(X0,tc_bool)) = X2
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_112
| ~ spl0_328 ),
inference(resolution,[],[f5372,f1543]) ).
fof(f5372,plain,
( ! [X3,X0,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_328 ),
inference(avatar_component_clause,[],[f5371]) ).
fof(f26962,plain,
( spl0_875
| ~ spl0_83
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4407,f4158,f1397,f26960]) ).
fof(f26960,plain,
( spl0_875
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f4407,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X0,X2))) )
| ~ spl0_83
| ~ spl0_290 ),
inference(resolution,[],[f4159,f1398]) ).
fof(f26958,plain,
( spl0_874
| ~ spl0_83
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4386,f4150,f1397,f26956]) ).
fof(f26956,plain,
( spl0_874
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f4386,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X0,X3))) )
| ~ spl0_83
| ~ spl0_288 ),
inference(resolution,[],[f4151,f1398]) ).
fof(f26954,plain,
( spl0_873
| ~ spl0_114
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f4068,f3671,f1550,f26952]) ).
fof(f26952,plain,
( spl0_873
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f4068,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_114
| ~ spl0_271 ),
inference(resolution,[],[f3672,f1552]) ).
fof(f26950,plain,
( spl0_872
| ~ spl0_111
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f4067,f3671,f1537,f26948]) ).
fof(f26948,plain,
( spl0_872
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f4067,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_111
| ~ spl0_271 ),
inference(resolution,[],[f3672,f1539]) ).
fof(f26946,plain,
( spl0_871
| ~ spl0_110
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f4062,f3671,f1533,f26944]) ).
fof(f26944,plain,
( spl0_871
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f4062,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) )
| ~ spl0_110
| ~ spl0_271 ),
inference(resolution,[],[f3672,f1534]) ).
fof(f26938,plain,
( spl0_870
| ~ spl0_112
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f4057,f3671,f1542,f26936]) ).
fof(f26936,plain,
( spl0_870
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f4057,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_112
| ~ spl0_271 ),
inference(resolution,[],[f3672,f1543]) ).
fof(f26934,plain,
( spl0_869
| ~ spl0_112
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f4055,f3667,f1542,f26932]) ).
fof(f26932,plain,
( spl0_869
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatLeastLessThan(X0,X3,X1,X4,X5),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f3667,plain,
( spl0_270
<=> ! [X41,X47,X0,X42,X25,X46] :
( hBOOL(hAPP(hAPP(X41,X46),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastLessThan(X41,X42,X46,X47,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f4055,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatLeastLessThan(X0,X3,X1,X4,X5),X2)) )
| ~ spl0_112
| ~ spl0_270 ),
inference(resolution,[],[f3668,f1543]) ).
fof(f3668,plain,
( ! [X41,X0,X46,X47,X25,X42] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastLessThan(X41,X42,X46,X47,X0)))
| hBOOL(hAPP(hAPP(X41,X46),X25)) )
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f3667]) ).
fof(f26930,plain,
( spl0_868
| ~ spl0_112
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f4053,f3663,f1542,f26928]) ).
fof(f26928,plain,
( spl0_868
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatLeastLessThan(X3,X0,X4,X2,X5),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f3663,plain,
( spl0_269
<=> ! [X42,X41,X47,X0,X25,X46] :
( hBOOL(hAPP(hAPP(X42,X25),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastLessThan(X41,X42,X46,X47,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f4053,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatLeastLessThan(X3,X0,X4,X2,X5),X1)) )
| ~ spl0_112
| ~ spl0_269 ),
inference(resolution,[],[f3664,f1543]) ).
fof(f3664,plain,
( ! [X41,X0,X46,X47,X25,X42] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastLessThan(X41,X42,X46,X47,X0)))
| hBOOL(hAPP(hAPP(X42,X25),X47)) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f3663]) ).
fof(f26926,plain,
( spl0_867
| ~ spl0_114
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4047,f3659,f1550,f26924]) ).
fof(f26924,plain,
( spl0_867
<=> ! [X0] :
( hBOOL(hAPP(X0,v_Lba____))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f4047,plain,
( ! [X0] :
( hBOOL(hAPP(X0,v_Lba____))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_114
| ~ spl0_268 ),
inference(resolution,[],[f3660,f1552]) ).
fof(f26922,plain,
( spl0_866
| ~ spl0_111
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4046,f3659,f1537,f26920]) ).
fof(f26920,plain,
( spl0_866
<=> ! [X0] :
( hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f4046,plain,
( ! [X0] :
( hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_111
| ~ spl0_268 ),
inference(resolution,[],[f3660,f1539]) ).
fof(f26918,plain,
( spl0_865
| ~ spl0_110
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4041,f3659,f1533,f26916]) ).
fof(f26916,plain,
( spl0_865
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f4041,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) )
| ~ spl0_110
| ~ spl0_268 ),
inference(resolution,[],[f3660,f1534]) ).
fof(f26914,plain,
( spl0_864
| ~ spl0_112
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4036,f3659,f1542,f26912]) ).
fof(f26912,plain,
( spl0_864
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f4036,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_112
| ~ spl0_268 ),
inference(resolution,[],[f3660,f1543]) ).
fof(f26910,plain,
( spl0_863
| ~ spl0_114
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f4030,f3655,f1550,f26908]) ).
fof(f26908,plain,
( spl0_863
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f4030,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_114
| ~ spl0_267 ),
inference(resolution,[],[f3656,f1552]) ).
fof(f26906,plain,
( spl0_862
| ~ spl0_111
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f4029,f3655,f1537,f26904]) ).
fof(f26904,plain,
( spl0_862
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f4029,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_111
| ~ spl0_267 ),
inference(resolution,[],[f3656,f1539]) ).
fof(f26902,plain,
( spl0_861
| ~ spl0_110
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f4024,f3655,f1533,f26900]) ).
fof(f26900,plain,
( spl0_861
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f4024,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) )
| ~ spl0_110
| ~ spl0_267 ),
inference(resolution,[],[f3656,f1534]) ).
fof(f26898,plain,
( spl0_860
| ~ spl0_192
| ~ spl0_203
| ~ spl0_699
| ~ spl0_839 ),
inference(avatar_split_clause,[],[f26815,f26742,f18286,f2831,f2678,f26896]) ).
fof(f26896,plain,
( spl0_860
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3),c_HOL_Oundefined(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f26742,plain,
( spl0_839
<=> ! [X2,X0,X1] : c_HOL_Oundefined(X2) = hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,X1,X2),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f26815,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3),c_HOL_Oundefined(X2)))
| ~ spl0_192
| ~ spl0_203
| ~ spl0_699
| ~ spl0_839 ),
inference(forward_demodulation,[],[f26787,f19417]) ).
fof(f26787,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_in(X3),c_HOL_Oundefined(X2)),c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3)))
| ~ spl0_203
| ~ spl0_839 ),
inference(superposition,[],[f2832,f26743]) ).
fof(f26743,plain,
( ! [X2,X0,X1] : c_HOL_Oundefined(X2) = hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,X1,X2),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))
| ~ spl0_839 ),
inference(avatar_component_clause,[],[f26742]) ).
fof(f26894,plain,
( spl0_859
| ~ spl0_112
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f4019,f3655,f1542,f26892]) ).
fof(f26892,plain,
( spl0_859
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f4019,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_112
| ~ spl0_267 ),
inference(resolution,[],[f3656,f1543]) ).
fof(f26890,plain,
( spl0_858
| ~ spl0_114
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3957,f3631,f1550,f26888]) ).
fof(f26888,plain,
( spl0_858
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f3957,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_114
| ~ spl0_261 ),
inference(resolution,[],[f3632,f1552]) ).
fof(f26886,plain,
( spl0_857
| ~ spl0_111
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3956,f3631,f1537,f26884]) ).
fof(f26884,plain,
( spl0_857
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f3956,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_111
| ~ spl0_261 ),
inference(resolution,[],[f3632,f1539]) ).
fof(f26882,plain,
( spl0_856
| ~ spl0_110
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3951,f3631,f1533,f26880]) ).
fof(f26880,plain,
( spl0_856
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f3951,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) )
| ~ spl0_110
| ~ spl0_261 ),
inference(resolution,[],[f3632,f1534]) ).
fof(f26878,plain,
( spl0_855
| ~ spl0_112
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3946,f3631,f1542,f26876]) ).
fof(f26876,plain,
( spl0_855
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f3946,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_112
| ~ spl0_261 ),
inference(resolution,[],[f3632,f1543]) ).
fof(f26874,plain,
( spl0_854
| ~ spl0_114
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3940,f3627,f1550,f26872]) ).
fof(f26872,plain,
( spl0_854
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f3940,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_Lba____))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_114
| ~ spl0_260 ),
inference(resolution,[],[f3628,f1552]) ).
fof(f26870,plain,
( spl0_853
| ~ spl0_111
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3939,f3627,f1537,f26868]) ).
fof(f26868,plain,
( spl0_853
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f3939,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
| ~ spl0_111
| ~ spl0_260 ),
inference(resolution,[],[f3628,f1539]) ).
fof(f26866,plain,
( spl0_852
| ~ spl0_110
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3934,f3627,f1533,f26864]) ).
fof(f26864,plain,
( spl0_852
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f3934,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_OPow(X1,X2),X0,tc_fun(X2,tc_bool)))) )
| ~ spl0_110
| ~ spl0_260 ),
inference(resolution,[],[f3628,f1534]) ).
fof(f26862,plain,
( spl0_851
| ~ spl0_112
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3929,f3627,f1542,f26860]) ).
fof(f26860,plain,
( spl0_851
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f3929,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X0,X3)))
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_112
| ~ spl0_260 ),
inference(resolution,[],[f3628,f1543]) ).
fof(f26858,plain,
( spl0_850
| ~ spl0_114
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3923,f3623,f1550,f26856]) ).
fof(f26856,plain,
( spl0_850
<=> ! [X0,X1] : hAPP(X0,v_Lba____) = hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),v_Lba____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f3923,plain,
( ! [X0,X1] : hAPP(X0,v_Lba____) = hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),v_Lba____)
| ~ spl0_114
| ~ spl0_259 ),
inference(resolution,[],[f3624,f1552]) ).
fof(f26784,plain,
( spl0_849
| ~ spl0_111
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3922,f3623,f1537,f26782]) ).
fof(f26782,plain,
( spl0_849
<=> ! [X0,X1] : hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1) = hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f3922,plain,
( ! [X0,X1] : hAPP(X0,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1) = hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1)
| ~ spl0_111
| ~ spl0_259 ),
inference(resolution,[],[f3624,f1539]) ).
fof(f26780,plain,
( spl0_848
| ~ spl0_110
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3917,f3623,f1533,f26778]) ).
fof(f26778,plain,
( spl0_848
<=> ! [X0,X3,X2,X1] : hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,c_Set_OPow(X1,X2),tc_fun(X2,tc_bool),X3),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f3917,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,c_Set_OPow(X1,X2),tc_fun(X2,tc_bool),X3),X1)
| ~ spl0_110
| ~ spl0_259 ),
inference(resolution,[],[f3624,f1534]) ).
fof(f26776,plain,
( spl0_847
| ~ spl0_112
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3912,f3623,f1542,f26774]) ).
fof(f26774,plain,
( spl0_847
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,X2,X3,X4),X1)
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f3912,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,X2,X3,X4),X1)
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_112
| ~ spl0_259 ),
inference(resolution,[],[f3624,f1543]) ).
fof(f26772,plain,
( spl0_846
| ~ spl0_18
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f3528,f3136,f1105,f26770]) ).
fof(f3136,plain,
( spl0_235
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f3528,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool)
| ~ spl0_18
| ~ spl0_235 ),
inference(resolution,[],[f3137,f1107]) ).
fof(f1107,plain,
( class_Lattices_Olattice(tc_bool)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f1105]) ).
fof(f3137,plain,
( ! [X2,X0,X1,X5] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0) )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f3136]) ).
fof(f26768,plain,
( spl0_845
| ~ spl0_8
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f3527,f3136,f1055,f26766]) ).
fof(f26766,plain,
( spl0_845
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1055,plain,
( spl0_8
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f3527,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),tc_nat)
| ~ spl0_8
| ~ spl0_235 ),
inference(resolution,[],[f3137,f1057]) ).
fof(f1057,plain,
( class_Lattices_Olattice(tc_nat)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f26764,plain,
( spl0_844
| ~ spl0_18
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f3525,f3132,f1105,f26762]) ).
fof(f3132,plain,
( spl0_234
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X5,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f3525,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool)
| ~ spl0_18
| ~ spl0_234 ),
inference(resolution,[],[f3133,f1107]) ).
fof(f3133,plain,
( ! [X2,X0,X1,X5] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X5,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f3132]) ).
fof(f26760,plain,
( spl0_843
| ~ spl0_8
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f3524,f3132,f1055,f26758]) ).
fof(f26758,plain,
( spl0_843
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f3524,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat)
| ~ spl0_8
| ~ spl0_234 ),
inference(resolution,[],[f3133,f1057]) ).
fof(f26756,plain,
( spl0_842
| ~ spl0_164
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f3486,f3120,f2236,f26754]) ).
fof(f26754,plain,
( spl0_842
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X2,X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f3486,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X2,X1,tc_fun(X0,tc_bool)) )
| ~ spl0_164
| ~ spl0_231 ),
inference(superposition,[],[f3121,f2237]) ).
fof(f26752,plain,
( spl0_841
| ~ spl0_13
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f3388,f3087,f1080,f26750]) ).
fof(f3087,plain,
( spl0_225
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f3388,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool)
| ~ spl0_13
| ~ spl0_225 ),
inference(resolution,[],[f3088,f1082]) ).
fof(f1082,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f1080]) ).
fof(f3088,plain,
( ! [X2,X0,X1,X5] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f3087]) ).
fof(f26748,plain,
( spl0_840
| ~ spl0_3
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f3387,f3087,f1030,f26746]) ).
fof(f26746,plain,
( spl0_840
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f1030,plain,
( spl0_3
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f3387,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),tc_nat)
| ~ spl0_3
| ~ spl0_225 ),
inference(resolution,[],[f3088,f1032]) ).
fof(f1032,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f26744,plain,
( spl0_839
| spl0_118
| ~ spl0_785 ),
inference(avatar_split_clause,[],[f24235,f23202,f1630,f26742]) ).
fof(f24235,plain,
( ! [X2,X0,X1] : c_HOL_Oundefined(X2) = hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,X1,X2),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))
| spl0_118
| ~ spl0_785 ),
inference(resolution,[],[f23203,f1632]) ).
fof(f23203,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,X4))
| hAPP(c_FuncSet_Orestrict(X0,X1,X2,X3),X4) = c_HOL_Oundefined(X3) )
| ~ spl0_785 ),
inference(avatar_component_clause,[],[f23202]) ).
fof(f26740,plain,
( spl0_838
| ~ spl0_13
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f3385,f3083,f1080,f26738]) ).
fof(f3083,plain,
( spl0_224
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X5,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f3385,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool)
| ~ spl0_13
| ~ spl0_224 ),
inference(resolution,[],[f3084,f1082]) ).
fof(f3084,plain,
( ! [X2,X0,X1,X5] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X5,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f3083]) ).
fof(f26736,plain,
( spl0_837
| ~ spl0_3
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f3384,f3083,f1030,f26734]) ).
fof(f26734,plain,
( spl0_837
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f3384,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat)
| ~ spl0_3
| ~ spl0_224 ),
inference(resolution,[],[f3084,f1032]) ).
fof(f26732,plain,
( spl0_836
| ~ spl0_89
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f3294,f3067,f1445,f26730]) ).
fof(f26730,plain,
( spl0_836
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f3067,plain,
( spl0_220
<=> ! [X0,X12,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X6,X12,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f3294,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,tc_fun(X2,tc_bool))
| ~ spl0_89
| ~ spl0_220 ),
inference(superposition,[],[f3068,f1446]) ).
fof(f3068,plain,
( ! [X0,X6,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X6,X12,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f3067]) ).
fof(f26728,plain,
( spl0_835
| ~ spl0_153
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f3251,f3059,f2192,f26726]) ).
fof(f26726,plain,
( spl0_835
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool))
| c_lessequals(X0,X2,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f2192,plain,
( spl0_153
<=> ! [X6,X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f3251,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool))
| c_lessequals(X0,X2,tc_fun(X1,tc_bool)) )
| ~ spl0_153
| ~ spl0_218 ),
inference(superposition,[],[f3060,f2193]) ).
fof(f2193,plain,
( ! [X0,X6] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f2192]) ).
fof(f26723,plain,
( spl0_834
| ~ spl0_29
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2974,f2831,f1155,f26721]) ).
fof(f26721,plain,
( spl0_834
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_in(X2),X1),c_Set_Oimage(c_COMBI(X0),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f2974,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_in(X2),X1),c_Set_Oimage(c_COMBI(X0),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X2)))
| ~ spl0_29
| ~ spl0_203 ),
inference(superposition,[],[f2832,f1156]) ).
fof(f26719,plain,
( spl0_833
| ~ spl0_105
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2961,f2823,f1513,f26717]) ).
fof(f26717,plain,
( spl0_833
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4)
| c_Fun_Oinj__on(c_FuncSet_Orestrict(X0,X1,X3,X4),X1,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f1513,plain,
( spl0_105
<=> ! [X10,X0,X12,X6,X7] :
( c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f2823,plain,
( spl0_201
<=> ! [X10,X0,X12,X6,X7] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Fun_Obij__betw(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X7,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2961,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4)
| c_Fun_Oinj__on(c_FuncSet_Orestrict(X0,X1,X3,X4),X1,X3,X4) )
| ~ spl0_105
| ~ spl0_201 ),
inference(resolution,[],[f2824,f1514]) ).
fof(f1514,plain,
( ! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Fun_Oinj__on(X10,X6,X0,X12) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1513]) ).
fof(f2824,plain,
( ! [X10,X0,X6,X7,X12] :
( c_Fun_Obij__betw(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X7,X0,X12)
| ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2823]) ).
fof(f26648,plain,
( spl0_832
| ~ spl0_22
| ~ spl0_93
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2936,f2815,f1465,f1125,f26646]) ).
fof(f26646,plain,
( spl0_832
<=> ! [X0,X3,X2,X1] : c_lessequals(hAPP(X0,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X3,tc_bool)),X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f2936,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(X0,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X3,tc_bool)),X1),tc_bool) )
| ~ spl0_93
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1466]) ).
fof(f26644,plain,
( spl0_831
| ~ spl0_105
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2929,f2811,f1513,f26642]) ).
fof(f26642,plain,
( spl0_831
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4)
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,X0,X3,X4),X2,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f2929,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4)
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,X0,X3,X4),X2,X4,X3) )
| ~ spl0_105
| ~ spl0_198 ),
inference(resolution,[],[f2812,f1514]) ).
fof(f26640,plain,
( spl0_830
| ~ spl0_92
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2918,f2807,f1457,f26638]) ).
fof(f26638,plain,
( spl0_830
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X0,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f2918,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X0,X2,X3,X4) )
| ~ spl0_92
| ~ spl0_197 ),
inference(resolution,[],[f2808,f1458]) ).
fof(f26622,plain,
( spl0_829
| ~ spl0_91
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2917,f2807,f1453,f26620]) ).
fof(f26620,plain,
( spl0_829
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X0,X1,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f2917,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X0,X1,X3,X4) )
| ~ spl0_91
| ~ spl0_197 ),
inference(resolution,[],[f2808,f1454]) ).
fof(f26617,plain,
( spl0_828
| ~ spl0_177
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2754,f2658,f2288,f26615]) ).
fof(f26615,plain,
( spl0_828
<=> ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2754,plain,
( ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_177
| ~ spl0_187 ),
inference(resolution,[],[f2659,f2289]) ).
fof(f26612,plain,
( spl0_827
| ~ spl0_177
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2746,f2650,f2288,f26610]) ).
fof(f26610,plain,
( spl0_827
<=> ! [X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X0),X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f2746,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X0),X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_177
| ~ spl0_185 ),
inference(resolution,[],[f2651,f2289]) ).
fof(f26608,plain,
( spl0_826
| ~ spl0_61
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2728,f2642,f1289,f26606]) ).
fof(f26606,plain,
( spl0_826
<=> ! [X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f2728,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_61
| ~ spl0_183 ),
inference(resolution,[],[f2643,f1290]) ).
fof(f26604,plain,
( spl0_825
| ~ spl0_52
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2505,f2212,f1247,f26602]) ).
fof(f26602,plain,
( spl0_825
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X3,X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,X1,X2),X4),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f2505,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X3,X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,X1,X2),X4),X3,X4) )
| ~ spl0_52
| ~ spl0_158 ),
inference(superposition,[],[f2213,f1248]) ).
fof(f26600,plain,
( spl0_824
| ~ spl0_56
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2461,f2204,f1269,f26598]) ).
fof(f26598,plain,
( spl0_824
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X2,X3)
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f2461,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X2,X3)
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_56
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1270]) ).
fof(f26596,plain,
( spl0_823
| ~ spl0_57
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2459,f2204,f1273,f26594]) ).
fof(f26594,plain,
( spl0_823
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X1,X3)
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f2459,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X1,X3)
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_57
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1274]) ).
fof(f26592,plain,
( spl0_822
| ~ spl0_65
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2451,f2204,f1305,f26590]) ).
fof(f26590,plain,
( spl0_822
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f2451,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_65
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1306]) ).
fof(f26588,plain,
( spl0_821
| ~ spl0_66
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2449,f2204,f1309,f26586]) ).
fof(f26586,plain,
( spl0_821
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f2449,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_66
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1310]) ).
fof(f26584,plain,
( spl0_820
| ~ spl0_56
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2431,f2200,f1269,f26582]) ).
fof(f2431,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X1,X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_56
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1270]) ).
fof(f26580,plain,
( spl0_819
| ~ spl0_159
| ~ spl0_192
| ~ spl0_519
| ~ spl0_699
| ~ spl0_805 ),
inference(avatar_split_clause,[],[f26085,f25505,f18286,f11814,f2678,f2216,f26578]) ).
fof(f26578,plain,
( spl0_819
<=> ! [X5,X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_fequal(X5),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f11814,plain,
( spl0_519
<=> ! [X10,X11,X0,X3] : hBOOL(hAPP(hAPP(c_in(X11),X3),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X11),X11,tc_fun(X0,tc_bool),tc_bool),hAPP(c_fequal(X0),hAPP(X10,X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f26085,plain,
( ! [X2,X3,X0,X1,X5] : hBOOL(hAPP(hAPP(c_fequal(X5),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)))
| ~ spl0_159
| ~ spl0_192
| ~ spl0_519
| ~ spl0_699
| ~ spl0_805 ),
inference(forward_demodulation,[],[f26084,f19417]) ).
fof(f26084,plain,
( ! [X2,X3,X0,X1,X5] : hBOOL(hAPP(hAPP(c_in(X5),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),hAPP(c_fequal(X5),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))))
| ~ spl0_159
| ~ spl0_192
| ~ spl0_519
| ~ spl0_699
| ~ spl0_805 ),
inference(forward_demodulation,[],[f26083,f2217]) ).
fof(f26083,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_COMBB(c_in(X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,tc_fun(tc_fun(X5,tc_bool),tc_bool),X4),X1),hAPP(c_fequal(X5),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))))
| ~ spl0_192
| ~ spl0_519
| ~ spl0_699
| ~ spl0_805 ),
inference(forward_demodulation,[],[f26082,f2679]) ).
fof(f26082,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_COMBC(c_COMBB(c_in(X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,tc_fun(tc_fun(X5,tc_bool),tc_bool),X4),X4,tc_fun(X5,tc_bool),tc_bool),hAPP(c_fequal(X5),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))),X1))
| ~ spl0_192
| ~ spl0_519
| ~ spl0_699
| ~ spl0_805 ),
inference(forward_demodulation,[],[f25917,f19417]) ).
fof(f25917,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_in(X4),X1),hAPP(c_COMBC(c_COMBB(c_in(X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,tc_fun(tc_fun(X5,tc_bool),tc_bool),X4),X4,tc_fun(X5,tc_bool),tc_bool),hAPP(c_fequal(X5),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)))))
| ~ spl0_519
| ~ spl0_805 ),
inference(superposition,[],[f11815,f25506]) ).
fof(f11815,plain,
( ! [X3,X10,X0,X11] : hBOOL(hAPP(hAPP(c_in(X11),X3),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X11),X11,tc_fun(X0,tc_bool),tc_bool),hAPP(c_fequal(X0),hAPP(X10,X3)))))
| ~ spl0_519 ),
inference(avatar_component_clause,[],[f11814]) ).
fof(f26576,plain,
( spl0_818
| ~ spl0_57
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2429,f2200,f1273,f26574]) ).
fof(f26574,plain,
( spl0_818
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X1,X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f2429,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X1,X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_57
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1274]) ).
fof(f26572,plain,
( spl0_817
| ~ spl0_65
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2421,f2200,f1305,f26570]) ).
fof(f26570,plain,
( spl0_817
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X3,X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2421,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X3,X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_65
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1306]) ).
fof(f26568,plain,
( spl0_816
| ~ spl0_66
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2419,f2200,f1309,f26566]) ).
fof(f26566,plain,
( spl0_816
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X0,X3,X2)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f2419,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X0,X3,X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_66
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1310]) ).
fof(f26564,plain,
( spl0_815
| ~ spl0_149
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2399,f2196,f2176,f26562]) ).
fof(f26562,plain,
( spl0_815
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != X1
| c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2196,plain,
( spl0_154
<=> ! [X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f2399,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != X1
| c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_149
| ~ spl0_154 ),
inference(superposition,[],[f2177,f2197]) ).
fof(f2197,plain,
( ! [X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f2196]) ).
fof(f26560,plain,
( spl0_814
| ~ spl0_89
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2300,f2176,f1445,f26558]) ).
fof(f26558,plain,
( spl0_814
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f2300,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) )
| ~ spl0_89
| ~ spl0_149 ),
inference(superposition,[],[f2177,f1446]) ).
fof(f26556,plain,
( spl0_813
| ~ spl0_78
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f2060,f1842,f1377,f26554]) ).
fof(f26554,plain,
( spl0_813
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f2060,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_78
| ~ spl0_138 ),
inference(resolution,[],[f1843,f1378]) ).
fof(f26552,plain,
( spl0_812
| ~ spl0_78
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f2033,f1838,f1377,f26550]) ).
fof(f26550,plain,
( spl0_812
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f2033,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_78
| ~ spl0_137 ),
inference(resolution,[],[f1839,f1378]) ).
fof(f26548,plain,
( spl0_811
| ~ spl0_78
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1973,f1813,f1377,f26546]) ).
fof(f26546,plain,
( spl0_811
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f1973,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_78
| ~ spl0_131 ),
inference(resolution,[],[f1814,f1378]) ).
fof(f26544,plain,
( spl0_810
| ~ spl0_78
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1947,f1809,f1377,f26542]) ).
fof(f26542,plain,
( spl0_810
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f1947,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_78
| ~ spl0_130 ),
inference(resolution,[],[f1810,f1378]) ).
fof(f26540,plain,
( spl0_809
| ~ spl0_32
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1592,f1497,f1167,f26538]) ).
fof(f26538,plain,
( spl0_809
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,X3))
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f1167,plain,
( spl0_32
<=> ! [X59,X58] :
( ~ class_Lattices_Olattice(X59)
| class_Lattices_Olower__semilattice(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1497,plain,
( spl0_101
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1592,plain,
( ! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,X3))
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_32
| ~ spl0_101 ),
inference(resolution,[],[f1498,f1168]) ).
fof(f1168,plain,
( ! [X58,X59] :
( class_Lattices_Olower__semilattice(tc_fun(X58,X59))
| ~ class_Lattices_Olattice(X59) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1167]) ).
fof(f1498,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1497]) ).
fof(f25894,plain,
( spl0_808
| ~ spl0_31
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1582,f1477,f1163,f25892]) ).
fof(f25892,plain,
( spl0_808
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,X3))
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f1477,plain,
( spl0_96
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1582,plain,
( ! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,X3))
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_31
| ~ spl0_96 ),
inference(resolution,[],[f1478,f1164]) ).
fof(f1478,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f25890,plain,
( spl0_807
| ~ spl0_36
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1559,f1441,f1183,f25888]) ).
fof(f25888,plain,
( spl0_807
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3)) = X0
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f1441,plain,
( spl0_88
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1559,plain,
( ! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3)) = X0
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_36
| ~ spl0_88 ),
inference(resolution,[],[f1442,f1184]) ).
fof(f1442,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1441]) ).
fof(f25886,plain,
( spl0_806
| ~ spl0_36
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1556,f1437,f1183,f25884]) ).
fof(f25884,plain,
( spl0_806
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3)) = X0
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f1437,plain,
( spl0_87
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1556,plain,
( ! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3)) = X0
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_36
| ~ spl0_87 ),
inference(resolution,[],[f1438,f1184]) ).
fof(f1438,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1437]) ).
fof(f25507,plain,
( spl0_805
| ~ spl0_804 ),
inference(avatar_split_clause,[],[f23611,f23362,f25505]) ).
fof(f23362,plain,
( spl0_804
<=> ! [X0,X1] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1) = hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f23611,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)
| ~ spl0_804 ),
inference(superposition,[],[f23363,f23363]) ).
fof(f23363,plain,
( ! [X0,X1] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1) = hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)
| ~ spl0_804 ),
inference(avatar_component_clause,[],[f23362]) ).
fof(f23364,plain,
( spl0_804
| ~ spl0_52
| ~ spl0_159
| ~ spl0_192
| ~ spl0_770 ),
inference(avatar_split_clause,[],[f23103,f23051,f2678,f2216,f1247,f23362]) ).
fof(f23051,plain,
( spl0_770
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBK(hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_bool),X0),X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_bool),c_Arrow__Order__Mirabelle_OLin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f23103,plain,
( ! [X0,X1] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1) = hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)
| ~ spl0_52
| ~ spl0_159
| ~ spl0_192
| ~ spl0_770 ),
inference(forward_demodulation,[],[f23102,f1248]) ).
fof(f23102,plain,
( ! [X0,X1] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1) = hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBK(hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),X1)),c_Arrow__Order__Mirabelle_OLin)
| ~ spl0_159
| ~ spl0_192
| ~ spl0_770 ),
inference(forward_demodulation,[],[f23066,f2217]) ).
fof(f23066,plain,
( ! [X0,X1] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1) = hAPP(hAPP(c_COMBB(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBK(hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_bool),X0),X1),c_Arrow__Order__Mirabelle_OLin)
| ~ spl0_192
| ~ spl0_770 ),
inference(superposition,[],[f2679,f23052]) ).
fof(f23052,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBK(hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_bool),X0),X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_bool),c_Arrow__Order__Mirabelle_OLin)
| ~ spl0_770 ),
inference(avatar_component_clause,[],[f23051]) ).
fof(f23289,plain,
( spl0_803
| ~ spl0_89
| ~ spl0_221
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f11965,f11865,f3071,f1445,f23287]) ).
fof(f23287,plain,
( spl0_803
<=> ! [X0,X3,X2,X1] : hAPP(X0,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X2),X1),X0,X2,tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f3071,plain,
( spl0_221
<=> ! [X0,X12,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f11965,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X2),X1),X0,X2,tc_fun(X3,tc_bool))
| ~ spl0_89
| ~ spl0_221
| ~ spl0_521 ),
inference(forward_demodulation,[],[f11881,f1446]) ).
fof(f11881,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X0,X2,tc_fun(X3,tc_bool))
| ~ spl0_221
| ~ spl0_521 ),
inference(superposition,[],[f11866,f3072]) ).
fof(f3072,plain,
( ! [X0,X6,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f3071]) ).
fof(f23285,plain,
( spl0_802
| ~ spl0_90
| ~ spl0_165
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f10262,f9955,f2240,f1449,f23283]) ).
fof(f23283,plain,
( spl0_802
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X1,tc_bool)) != X2
| c_lessequals(X2,X0,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f9955,plain,
( spl0_435
<=> ! [X0,X6,X8,X7] :
( c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f10262,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X1,tc_bool)) != X2
| c_lessequals(X2,X0,tc_fun(X1,tc_bool)) )
| ~ spl0_90
| ~ spl0_165
| ~ spl0_435 ),
inference(forward_demodulation,[],[f10237,f1450]) ).
fof(f10237,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| c_lessequals(X2,X0,tc_fun(X1,tc_bool)) )
| ~ spl0_165
| ~ spl0_435 ),
inference(superposition,[],[f9956,f2241]) ).
fof(f9956,plain,
( ! [X0,X8,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X8,X6,tc_fun(X0,tc_bool)) )
| ~ spl0_435 ),
inference(avatar_component_clause,[],[f9955]) ).
fof(f23281,plain,
( spl0_801
| ~ spl0_124
| ~ spl0_192
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f5307,f4702,f2678,f1785,f23279]) ).
fof(f23279,plain,
( spl0_801
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f5307,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2)) )
| ~ spl0_124
| ~ spl0_192
| ~ spl0_317 ),
inference(forward_demodulation,[],[f5274,f2679]) ).
fof(f5274,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X2)) )
| ~ spl0_124
| ~ spl0_317 ),
inference(superposition,[],[f1786,f4703]) ).
fof(f23277,plain,
( spl0_800
| ~ spl0_113
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4421,f4162,f1546,f23275]) ).
fof(f23275,plain,
( spl0_800
<=> ! [X0,X1] : hBOOL(hAPP(c_FuncSet_OPi(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),c_COMBI(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f4162,plain,
( spl0_291
<=> ! [X6,X0] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X0)),c_COMBI(X0)),c_FuncSet_OPi(X6,c_COMBK(X6,tc_fun(X0,tc_bool),X0),X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f4421,plain,
( ! [X0,X1] : hBOOL(hAPP(c_FuncSet_OPi(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),c_COMBI(X1)))
| ~ spl0_113
| ~ spl0_291 ),
inference(resolution,[],[f4163,f1547]) ).
fof(f4163,plain,
( ! [X0,X6] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X0)),c_COMBI(X0)),c_FuncSet_OPi(X6,c_COMBK(X6,tc_fun(X0,tc_bool),X0),X0,X0)))
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f4162]) ).
fof(f23273,plain,
( spl0_799
| ~ spl0_51
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f4327,f4130,f1243,f23271]) ).
fof(f23271,plain,
( spl0_799
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X1,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f1243,plain,
( spl0_51
<=> ! [X6,X0] : c_Lattices_Olower__semilattice__class_Oinf(X6,X6,tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f4327,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X1,tc_bool)) = X0 )
| ~ spl0_51
| ~ spl0_283 ),
inference(superposition,[],[f4131,f1244]) ).
fof(f1244,plain,
( ! [X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(X6,X6,tc_fun(X0,tc_bool)) = X6
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1243]) ).
fof(f23269,plain,
( spl0_798
| ~ spl0_83
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f4061,f3671,f1397,f23267]) ).
fof(f23267,plain,
( spl0_798
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f4061,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) )
| ~ spl0_83
| ~ spl0_271 ),
inference(resolution,[],[f3672,f1398]) ).
fof(f23265,plain,
( spl0_797
| ~ spl0_83
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4040,f3659,f1397,f23263]) ).
fof(f23263,plain,
( spl0_797
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f4040,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) )
| ~ spl0_83
| ~ spl0_268 ),
inference(resolution,[],[f3660,f1398]) ).
fof(f23247,plain,
( spl0_796
| ~ spl0_83
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f4023,f3655,f1397,f23245]) ).
fof(f23245,plain,
( spl0_796
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f4023,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) )
| ~ spl0_83
| ~ spl0_267 ),
inference(resolution,[],[f3656,f1398]) ).
fof(f23243,plain,
( spl0_794
| spl0_795
| ~ spl0_52
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3980,f3639,f1247,f23241,f23238]) ).
fof(f23238,plain,
( spl0_794
<=> ! [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_794])]) ).
fof(f23241,plain,
( spl0_795
<=> ! [X4,X3] : X3 = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f3639,plain,
( spl0_263
<=> ! [X10,X0,X12,X2,X1] :
( X1 = X2
| hAPP(X10,X1) != hAPP(X10,X2)
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f3980,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_52
| ~ spl0_263 ),
inference(trivial_inequality_removal,[],[f3979]) ).
fof(f3979,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_52
| ~ spl0_263 ),
inference(forward_demodulation,[],[f3967,f1248]) ).
fof(f3967,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_52
| ~ spl0_263 ),
inference(superposition,[],[f3640,f1248]) ).
fof(f3640,plain,
( ! [X2,X10,X0,X1,X12] :
( hAPP(X10,X1) != hAPP(X10,X2)
| X1 = X2
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12) )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f3639]) ).
fof(f23236,plain,
( spl0_793
| ~ spl0_83
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3950,f3631,f1397,f23234]) ).
fof(f23234,plain,
( spl0_793
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f3950,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) )
| ~ spl0_83
| ~ spl0_261 ),
inference(resolution,[],[f3632,f1398]) ).
fof(f23232,plain,
( spl0_792
| ~ spl0_83
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3933,f3627,f1397,f23230]) ).
fof(f23230,plain,
( spl0_792
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f3933,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X0,X2))) )
| ~ spl0_83
| ~ spl0_260 ),
inference(resolution,[],[f3628,f1398]) ).
fof(f23228,plain,
( spl0_791
| ~ spl0_83
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3916,f3623,f1397,f23226]) ).
fof(f23226,plain,
( spl0_791
<=> ! [X0,X3,X2,X1] : hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f3916,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1) = hAPP(c_FuncSet_Orestrict(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X1)
| ~ spl0_83
| ~ spl0_259 ),
inference(resolution,[],[f3624,f1398]) ).
fof(f23224,plain,
( spl0_790
| ~ spl0_112
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f3570,f3172,f1542,f23222]) ).
fof(f23222,plain,
( spl0_790
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatLeastAtMost(X0,X1,X3,X4),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f3172,plain,
( spl0_244
<=> ! [X41,X47,X0,X25,X46] :
( hBOOL(hAPP(hAPP(X41,X46),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastAtMost(X41,X46,X47,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f3570,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatLeastAtMost(X0,X1,X3,X4),X2)) )
| ~ spl0_112
| ~ spl0_244 ),
inference(resolution,[],[f3173,f1543]) ).
fof(f3173,plain,
( ! [X41,X0,X46,X47,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastAtMost(X41,X46,X47,X0)))
| hBOOL(hAPP(hAPP(X41,X46),X25)) )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f3172]) ).
fof(f23220,plain,
( spl0_789
| ~ spl0_112
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f3568,f3168,f1542,f23218]) ).
fof(f23218,plain,
( spl0_789
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatLeastAtMost(X0,X3,X2,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f3168,plain,
( spl0_243
<=> ! [X41,X47,X0,X25,X46] :
( hBOOL(hAPP(hAPP(X41,X25),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastAtMost(X41,X46,X47,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f3568,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatLeastAtMost(X0,X3,X2,X4),X1)) )
| ~ spl0_112
| ~ spl0_243 ),
inference(resolution,[],[f3169,f1543]) ).
fof(f3169,plain,
( ! [X41,X0,X46,X47,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastAtMost(X41,X46,X47,X0)))
| hBOOL(hAPP(hAPP(X41,X25),X47)) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f3168]) ).
fof(f23216,plain,
( spl0_788
| ~ spl0_112
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f3566,f3164,f1542,f23214]) ).
fof(f23214,plain,
( spl0_788
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OgreaterThanLessThan(X0,X3,X2,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f3164,plain,
( spl0_242
<=> ! [X42,X47,X0,X25,X46] :
( hBOOL(hAPP(hAPP(X42,X25),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThanLessThan(X42,X46,X47,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f3566,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OgreaterThanLessThan(X0,X3,X2,X4),X1)) )
| ~ spl0_112
| ~ spl0_242 ),
inference(resolution,[],[f3165,f1543]) ).
fof(f3165,plain,
( ! [X0,X46,X47,X25,X42] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThanLessThan(X42,X46,X47,X0)))
| hBOOL(hAPP(hAPP(X42,X25),X47)) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f3164]) ).
fof(f23212,plain,
( spl0_787
| ~ spl0_112
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f3564,f3160,f1542,f23210]) ).
fof(f23210,plain,
( spl0_787
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OgreaterThanLessThan(X0,X1,X3,X4),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f3160,plain,
( spl0_241
<=> ! [X42,X47,X0,X25,X46] :
( hBOOL(hAPP(hAPP(X42,X46),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThanLessThan(X42,X46,X47,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f3564,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OgreaterThanLessThan(X0,X1,X3,X4),X2)) )
| ~ spl0_112
| ~ spl0_241 ),
inference(resolution,[],[f3161,f1543]) ).
fof(f3161,plain,
( ! [X0,X46,X47,X25,X42] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThanLessThan(X42,X46,X47,X0)))
| hBOOL(hAPP(hAPP(X42,X46),X25)) )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f3160]) ).
fof(f23208,plain,
( spl0_786
| ~ spl0_652
| ~ spl0_769 ),
inference(avatar_split_clause,[],[f23157,f22298,f17409,f23206]) ).
fof(f23206,plain,
( spl0_786
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Oundefined(X1),c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f22298,plain,
( spl0_769
<=> ! [X0,X3,X2,X1] : c_lessequals(c_HOL_Oundefined(X0),c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f23157,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Oundefined(X1),c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool),tc_bool)
| ~ spl0_652
| ~ spl0_769 ),
inference(superposition,[],[f22299,f17410]) ).
fof(f22299,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_HOL_Oundefined(X0),c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool),tc_bool)
| ~ spl0_769 ),
inference(avatar_component_clause,[],[f22298]) ).
fof(f23204,plain,
( spl0_785
| ~ spl0_113
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3538,f3152,f1546,f23202]) ).
fof(f3538,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(c_FuncSet_Orestrict(X0,X1,X2,X3),X4) = c_HOL_Oundefined(X3)
| hBOOL(hAPP(X1,X4)) )
| ~ spl0_113
| ~ spl0_239 ),
inference(resolution,[],[f3153,f1547]) ).
fof(f23200,plain,
( spl0_784
| ~ spl0_26
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2933,f2815,f1143,f23198]) ).
fof(f23198,plain,
( spl0_784
<=> ! [X2,X0,X1,X3] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
| ~ class_Orderings_Oorder(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f2933,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
| ~ class_Orderings_Oorder(tc_fun(X3,X0)) )
| ~ spl0_26
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1144]) ).
fof(f23196,plain,
( spl0_783
| ~ spl0_27
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2932,f2815,f1147,f23194]) ).
fof(f23194,plain,
( spl0_783
<=> ! [X2,X0,X1,X3] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
| ~ class_Orderings_Opreorder(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f2932,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
| ~ class_Orderings_Opreorder(tc_fun(X3,X0)) )
| ~ spl0_27
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1148]) ).
fof(f23192,plain,
( spl0_782
| ~ spl0_139
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2301,f2176,f1846,f23190]) ).
fof(f23190,plain,
( spl0_782
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)) != X1
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f2301,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)) != X1
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) )
| ~ spl0_139
| ~ spl0_149 ),
inference(superposition,[],[f2177,f1847]) ).
fof(f23188,plain,
( spl0_781
| ~ spl0_55
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1775,f1647,f1265,f23186]) ).
fof(f23186,plain,
( spl0_781
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f1775,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X0) )
| ~ spl0_55
| ~ spl0_122 ),
inference(duplicate_literal_removal,[],[f1769]) ).
fof(f1769,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_55
| ~ spl0_122 ),
inference(resolution,[],[f1648,f1266]) ).
fof(f23184,plain,
( spl0_780
| ~ spl0_78
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1756,f1647,f1377,f23182]) ).
fof(f23182,plain,
( spl0_780
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X2
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f1756,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X2
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_78
| ~ spl0_122 ),
inference(resolution,[],[f1648,f1378]) ).
fof(f23180,plain,
( spl0_779
| ~ spl0_54
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1739,f1639,f1261,f23178]) ).
fof(f23178,plain,
( spl0_779
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f1739,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) )
| ~ spl0_54
| ~ spl0_120 ),
inference(duplicate_literal_removal,[],[f1730]) ).
fof(f1730,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_54
| ~ spl0_120 ),
inference(resolution,[],[f1640,f1262]) ).
fof(f23176,plain,
( spl0_778
| ~ spl0_55
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1738,f1639,f1265,f23174]) ).
fof(f23174,plain,
( spl0_778
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f1738,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) )
| ~ spl0_55
| ~ spl0_120 ),
inference(duplicate_literal_removal,[],[f1732]) ).
fof(f1732,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_55
| ~ spl0_120 ),
inference(resolution,[],[f1640,f1266]) ).
fof(f23172,plain,
( spl0_777
| ~ spl0_78
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1719,f1639,f1377,f23170]) ).
fof(f23170,plain,
( spl0_777
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X1
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f1719,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X1
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_78
| ~ spl0_120 ),
inference(resolution,[],[f1640,f1378]) ).
fof(f23168,plain,
( spl0_776
| ~ spl0_63
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1713,f1635,f1297,f23166]) ).
fof(f23166,plain,
( spl0_776
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f1713,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X1,X0) )
| ~ spl0_63
| ~ spl0_119 ),
inference(duplicate_literal_removal,[],[f1696]) ).
fof(f1696,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_63
| ~ spl0_119 ),
inference(resolution,[],[f1636,f1298]) ).
fof(f23148,plain,
( spl0_775
| ~ spl0_64
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1712,f1635,f1301,f23146]) ).
fof(f23146,plain,
( spl0_775
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f1712,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X2,X0) )
| ~ spl0_64
| ~ spl0_119 ),
inference(duplicate_literal_removal,[],[f1698]) ).
fof(f1698,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_64
| ~ spl0_119 ),
inference(resolution,[],[f1636,f1302]) ).
fof(f23144,plain,
( spl0_774
| ~ spl0_78
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1693,f1635,f1377,f23142]) ).
fof(f23142,plain,
( spl0_774
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f1693,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_78
| ~ spl0_119 ),
inference(resolution,[],[f1636,f1378]) ).
fof(f23140,plain,
( spl0_773
| ~ spl0_64
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1674,f1622,f1301,f23138]) ).
fof(f23138,plain,
( spl0_773
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f1674,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) )
| ~ spl0_64
| ~ spl0_116 ),
inference(duplicate_literal_removal,[],[f1660]) ).
fof(f1660,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_64
| ~ spl0_116 ),
inference(resolution,[],[f1623,f1302]) ).
fof(f23136,plain,
( spl0_772
| ~ spl0_78
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1655,f1622,f1377,f23134]) ).
fof(f23134,plain,
( spl0_772
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f1655,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_78
| ~ spl0_116 ),
inference(resolution,[],[f1623,f1378]) ).
fof(f23132,plain,
( spl0_771
| ~ spl0_52
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1417,f1361,f1247,f23130]) ).
fof(f23130,plain,
( spl0_771
<=> ! [X2,X4,X0,X5,X3,X1] : c_COMBK(X0,X1,X2) = c_Fun_Ofun__upd(c_COMBK(X0,X1,X2),X3,X0,X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f1417,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_COMBK(X0,X1,X2) = c_Fun_Ofun__upd(c_COMBK(X0,X1,X2),X3,X0,X4,X5)
| ~ spl0_52
| ~ spl0_74 ),
inference(superposition,[],[f1362,f1248]) ).
fof(f23053,plain,
( spl0_770
| spl0_23
| ~ spl0_523 ),
inference(avatar_split_clause,[],[f12507,f11987,f1130,f23051]) ).
fof(f12507,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBK(hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_bool),X0),X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_bool),c_Arrow__Order__Mirabelle_OLin)
| spl0_23
| ~ spl0_523 ),
inference(resolution,[],[f11988,f1132]) ).
fof(f22300,plain,
( ~ spl0_18
| spl0_769
| ~ spl0_66
| ~ spl0_768 ),
inference(avatar_split_clause,[],[f21915,f21229,f1309,f22298,f1105]) ).
fof(f21229,plain,
( spl0_768
<=> ! [X2,X0,X1,X3] :
( c_lessequals(c_HOL_Oundefined(X0),X3,tc_bool)
| ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f21915,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Oundefined(X0),c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool),tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_66
| ~ spl0_768 ),
inference(resolution,[],[f21230,f1310]) ).
fof(f21230,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool)
| c_lessequals(c_HOL_Oundefined(X0),X3,tc_bool) )
| ~ spl0_768 ),
inference(avatar_component_clause,[],[f21229]) ).
fof(f21231,plain,
( ~ spl0_14
| spl0_768
| ~ spl0_136
| ~ spl0_696 ),
inference(avatar_split_clause,[],[f18318,f18274,f1834,f21229,f1085]) ).
fof(f18274,plain,
( spl0_696
<=> ! [X2,X0,X1] : c_HOL_Oundefined(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oundefined(X0),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f18318,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Oundefined(X0),X3,tc_bool)
| ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool)
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_136
| ~ spl0_696 ),
inference(superposition,[],[f1835,f18275]) ).
fof(f18275,plain,
( ! [X2,X0,X1] : c_HOL_Oundefined(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oundefined(X0),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool)
| ~ spl0_696 ),
inference(avatar_component_clause,[],[f18274]) ).
fof(f20247,plain,
( spl0_767
| ~ spl0_655
| ~ spl0_755 ),
inference(avatar_split_clause,[],[f20203,f20152,f17432,f20245]) ).
fof(f20245,plain,
( spl0_767
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oundefined(X1),X0,tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,tc_bool),tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f20152,plain,
( spl0_755
<=> ! [X2,X0,X1,X3] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,c_HOL_Oundefined(X0),tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f20203,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oundefined(X1),X0,tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,tc_bool),tc_bool),tc_bool)
| ~ spl0_655
| ~ spl0_755 ),
inference(superposition,[],[f20153,f17433]) ).
fof(f20153,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,c_HOL_Oundefined(X0),tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool)
| ~ spl0_755 ),
inference(avatar_component_clause,[],[f20152]) ).
fof(f20211,plain,
( spl0_766
| ~ spl0_51
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f7297,f7040,f1243,f20209]) ).
fof(f20209,plain,
( spl0_766
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f7040,plain,
( spl0_373
<=> ! [X0,X6,X1,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f7297,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X0)) )
| ~ spl0_51
| ~ spl0_373 ),
inference(duplicate_literal_removal,[],[f7281]) ).
fof(f7281,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X0)) )
| ~ spl0_51
| ~ spl0_373 ),
inference(superposition,[],[f7041,f1244]) ).
fof(f7041,plain,
( ! [X0,X1,X6,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f7040]) ).
fof(f20194,plain,
( spl0_765
| ~ spl0_28
| ~ spl0_29
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f5434,f5338,f1155,f1151,f20192]) ).
fof(f20192,plain,
( spl0_765
<=> ! [X0,X1] : hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_COMBI(X0),X0,X0),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f5338,plain,
( spl0_320
<=> ! [X11,X0,X10,X1] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11,X0)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X10,X11,X0),hAPP(X10,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f5434,plain,
( ! [X0,X1] : hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_COMBI(X0),X0,X0),X1) = X1
| ~ spl0_28
| ~ spl0_29
| ~ spl0_320 ),
inference(forward_demodulation,[],[f5432,f1156]) ).
fof(f5432,plain,
( ! [X0,X1] : hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_COMBI(X0),X0,X0),hAPP(c_COMBI(X0),X1)) = X1
| ~ spl0_28
| ~ spl0_320 ),
inference(resolution,[],[f5339,f1152]) ).
fof(f5339,plain,
( ! [X10,X0,X11,X1] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11,X0)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X10,X11,X0),hAPP(X10,X1)) = X1 )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f5338]) ).
fof(f20190,plain,
( spl0_764
| ~ spl0_89
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f5265,f4702,f1445,f20188]) ).
fof(f20186,plain,
( spl0_763
| ~ spl0_204
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f4337,f4130,f2835,f20184]) ).
fof(f20184,plain,
( spl0_763
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f4337,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0
| ~ spl0_204
| ~ spl0_283 ),
inference(trivial_inequality_removal,[],[f4332]) ).
fof(f4332,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 )
| ~ spl0_204
| ~ spl0_283 ),
inference(superposition,[],[f4131,f2836]) ).
fof(f20182,plain,
( spl0_762
| ~ spl0_25
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4173,f4102,f1139,f20180]) ).
fof(f20180,plain,
( spl0_762
<=> ! [X0,X3,X2,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f4173,plain,
( ! [X2,X3,X0,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2)
| ~ spl0_25
| ~ spl0_276 ),
inference(resolution,[],[f4103,f1140]) ).
fof(f20178,plain,
( spl0_761
| ~ spl0_46
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f4093,f3686,f1223,f20176]) ).
fof(f20176,plain,
( spl0_761
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f4093,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1)
| ~ spl0_46
| ~ spl0_274 ),
inference(superposition,[],[f3687,f1224]) ).
fof(f20174,plain,
( spl0_760
| ~ spl0_113
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f4084,f3682,f1546,f20172]) ).
fof(f20172,plain,
( spl0_760
<=> ! [X2,X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omktop(X2,X0),c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f4084,plain,
( ! [X2,X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omktop(X2,X0),c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_113
| ~ spl0_273 ),
inference(resolution,[],[f3683,f1547]) ).
fof(f20170,plain,
( spl0_759
| ~ spl0_113
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f4074,f3675,f1546,f20168]) ).
fof(f20168,plain,
( spl0_759
<=> ! [X2,X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omkbot(X2,X0),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f4074,plain,
( ! [X2,X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omkbot(X2,X0),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_113
| ~ spl0_272 ),
inference(resolution,[],[f3676,f1547]) ).
fof(f20166,plain,
( spl0_758
| ~ spl0_113
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3910,f3619,f1546,f20164]) ).
fof(f20164,plain,
( spl0_758
<=> ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f3910,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_113
| ~ spl0_258 ),
inference(resolution,[],[f3620,f1547]) ).
fof(f20162,plain,
( spl0_757
| ~ spl0_82
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3540,f3152,f1393,f20160]) ).
fof(f20160,plain,
( spl0_757
<=> ! [X0,X3,X2,X1] : c_HOL_Oundefined(X2) = hAPP(c_FuncSet_Orestrict(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f3540,plain,
( ! [X2,X3,X0,X1] : c_HOL_Oundefined(X2) = hAPP(c_FuncSet_Orestrict(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2),X3)
| ~ spl0_82
| ~ spl0_239 ),
inference(resolution,[],[f3153,f1394]) ).
fof(f20158,plain,
( spl0_756
| ~ spl0_112
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f3026,f2874,f1542,f20156]) ).
fof(f20156,plain,
( spl0_756
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OlessThan(X0,X2,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f2874,plain,
( spl0_211
<=> ! [X42,X0,X27,X25] :
( hBOOL(hAPP(hAPP(X42,X25),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OlessThan(X42,X27,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f3026,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OlessThan(X0,X2,X3),X1)) )
| ~ spl0_112
| ~ spl0_211 ),
inference(resolution,[],[f2875,f1543]) ).
fof(f2875,plain,
( ! [X0,X27,X25,X42] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OlessThan(X42,X27,X0)))
| hBOOL(hAPP(hAPP(X42,X25),X27)) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2874]) ).
fof(f20154,plain,
( ~ spl0_14
| spl0_755
| ~ spl0_692
| ~ spl0_696 ),
inference(avatar_split_clause,[],[f19107,f18274,f18258,f20152,f1085]) ).
fof(f18258,plain,
( spl0_692
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f19107,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,c_HOL_Oundefined(X0),tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool)
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_692
| ~ spl0_696 ),
inference(superposition,[],[f18259,f18275]) ).
fof(f18259,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_692 ),
inference(avatar_component_clause,[],[f18258]) ).
fof(f20150,plain,
( spl0_754
| ~ spl0_113
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f3024,f2870,f1546,f20148]) ).
fof(f20148,plain,
( spl0_754
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_SetInterval_Oord_OlessThan(X0,X2,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f3024,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_SetInterval_Oord_OlessThan(X0,X2,X3),X1)) )
| ~ spl0_113
| ~ spl0_210 ),
inference(resolution,[],[f2871,f1547]) ).
fof(f20146,plain,
( spl0_753
| ~ spl0_112
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f3021,f2866,f1542,f20144]) ).
fof(f20144,plain,
( spl0_753
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OgreaterThan(X0,X1,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f2866,plain,
( spl0_209
<=> ! [X42,X0,X27,X25] :
( hBOOL(hAPP(hAPP(X42,X27),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThan(X42,X27,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f3021,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OgreaterThan(X0,X1,X3),X2)) )
| ~ spl0_112
| ~ spl0_209 ),
inference(resolution,[],[f2867,f1543]) ).
fof(f2867,plain,
( ! [X0,X27,X25,X42] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThan(X42,X27,X0)))
| hBOOL(hAPP(hAPP(X42,X27),X25)) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f2866]) ).
fof(f20142,plain,
( spl0_752
| ~ spl0_113
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f3019,f2862,f1546,f20140]) ).
fof(f20140,plain,
( spl0_752
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_SetInterval_Oord_OgreaterThan(X0,X1,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f3019,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_SetInterval_Oord_OgreaterThan(X0,X1,X3),X2)) )
| ~ spl0_113
| ~ spl0_208 ),
inference(resolution,[],[f2863,f1547]) ).
fof(f20138,plain,
( spl0_751
| ~ spl0_112
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f3016,f2858,f1542,f20136]) ).
fof(f20136,plain,
( spl0_751
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatMost(X0,X2,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f2858,plain,
( spl0_207
<=> ! [X41,X0,X27,X25] :
( hBOOL(hAPP(hAPP(X41,X25),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatMost(X41,X27,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f3016,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord_OatMost(X0,X2,X3),X1)) )
| ~ spl0_112
| ~ spl0_207 ),
inference(resolution,[],[f2859,f1543]) ).
fof(f2859,plain,
( ! [X41,X0,X27,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatMost(X41,X27,X0)))
| hBOOL(hAPP(hAPP(X41,X25),X27)) )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2858]) ).
fof(f20134,plain,
( spl0_750
| ~ spl0_113
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f3003,f2854,f1546,f20132]) ).
fof(f20132,plain,
( spl0_750
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_SetInterval_Oord_OatMost(X0,X2,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f3003,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
| hBOOL(hAPP(c_SetInterval_Oord_OatMost(X0,X2,X3),X1)) )
| ~ spl0_113
| ~ spl0_206 ),
inference(resolution,[],[f2855,f1547]) ).
fof(f20130,plain,
( spl0_749
| ~ spl0_113
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2968,f2831,f1546,f20128]) ).
fof(f20128,plain,
( spl0_749
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),hAPP(X0,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f2968,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),hAPP(X0,X3)))
| ~ spl0_113
| ~ spl0_203 ),
inference(resolution,[],[f2832,f1547]) ).
fof(f20110,plain,
( spl0_748
| ~ spl0_22
| ~ spl0_62
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2954,f2815,f1293,f1125,f20108]) ).
fof(f20108,plain,
( spl0_748
<=> ! [X2,X0,X1] : c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),hAPP(X2,X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f1293,plain,
( spl0_62
<=> ! [X6,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f2954,plain,
( ! [X2,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),hAPP(X2,X1),tc_bool) )
| ~ spl0_62
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1294]) ).
fof(f1294,plain,
( ! [X0,X6] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1293]) ).
fof(f20090,plain,
( spl0_747
| ~ spl0_22
| ~ spl0_61
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2944,f2815,f1289,f1125,f20088]) ).
fof(f20088,plain,
( spl0_747
<=> ! [X2,X0,X1] : c_lessequals(hAPP(X0,X1),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f2944,plain,
( ! [X2,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(X0,X1),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1),tc_bool) )
| ~ spl0_61
| ~ spl0_199 ),
inference(resolution,[],[f2816,f1290]) ).
fof(f20069,plain,
( spl0_746
| ~ spl0_48
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2788,f2682,f1231,f20067]) ).
fof(f20067,plain,
( spl0_746
<=> ! [X0,X1] :
( c_Fun_Obij__betw(c_COMBI(X0),X1,X1,X0,X0)
| ~ c_Fun_Oinj__on(c_COMBI(X0),X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f2788,plain,
( ! [X0,X1] :
( c_Fun_Obij__betw(c_COMBI(X0),X1,X1,X0,X0)
| ~ c_Fun_Oinj__on(c_COMBI(X0),X1,X0,X0) )
| ~ spl0_48
| ~ spl0_193 ),
inference(superposition,[],[f2683,f1232]) ).
fof(f20065,plain,
( spl0_745
| ~ spl0_154
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2768,f2662,f2196,f20063]) ).
fof(f20063,plain,
( spl0_745
<=> ! [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_745])]) ).
fof(f2768,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_154
| ~ spl0_188 ),
inference(superposition,[],[f2663,f2197]) ).
fof(f20061,plain,
( spl0_744
| ~ spl0_94
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2543,f2224,f1469,f20059]) ).
fof(f20059,plain,
( spl0_744
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f2543,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = X0
| ~ spl0_94
| ~ spl0_161 ),
inference(resolution,[],[f2225,f1470]) ).
fof(f20057,plain,
( spl0_743
| ~ spl0_93
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2542,f2224,f1465,f20055]) ).
fof(f20055,plain,
( spl0_743
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f2542,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1
| ~ spl0_93
| ~ spl0_161 ),
inference(resolution,[],[f2225,f1466]) ).
fof(f20053,plain,
( spl0_742
| ~ spl0_94
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2516,f2220,f1469,f20051]) ).
fof(f20051,plain,
( spl0_742
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f2516,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0
| ~ spl0_94
| ~ spl0_160 ),
inference(resolution,[],[f2221,f1470]) ).
fof(f20049,plain,
( spl0_741
| ~ spl0_93
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2515,f2220,f1465,f20047]) ).
fof(f20047,plain,
( spl0_741
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f2515,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0
| ~ spl0_93
| ~ spl0_160 ),
inference(resolution,[],[f2221,f1466]) ).
fof(f20045,plain,
( spl0_740
| ~ spl0_29
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2504,f2212,f1155,f20043]) ).
fof(f20043,plain,
( spl0_740
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X1,X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBI(X0),X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f2504,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBI(X0),X2),X1,X2) )
| ~ spl0_29
| ~ spl0_158 ),
inference(superposition,[],[f2213,f1156]) ).
fof(f20041,plain,
( spl0_739
| ~ spl0_95
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2497,f2208,f1473,f20039]) ).
fof(f20039,plain,
( spl0_739
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f2497,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),X1)) )
| ~ spl0_95
| ~ spl0_157 ),
inference(resolution,[],[f2209,f1474]) ).
fof(f20037,plain,
( spl0_738
| ~ spl0_42
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2467,f2204,f1207,f20035]) ).
fof(f20035,plain,
( spl0_738
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,X2,X1)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f2467,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,X2,X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_42
| ~ spl0_156 ),
inference(resolution,[],[f2205,f1208]) ).
fof(f20033,plain,
( spl0_737
| ~ spl0_41
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2427,f2200,f1203,f20031]) ).
fof(f20031,plain,
( spl0_737
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f2427,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_41
| ~ spl0_155 ),
inference(resolution,[],[f2201,f1204]) ).
fof(f20029,plain,
( spl0_736
| ~ spl0_652
| ~ spl0_715 ),
inference(avatar_split_clause,[],[f19981,f19930,f17409,f20027]) ).
fof(f20027,plain,
( spl0_736
<=> ! [X2,X0,X1,X3] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oundefined(X1),X0,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f19930,plain,
( spl0_715
<=> ! [X2,X0,X1,X3] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X3,c_HOL_Oundefined(X0),tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f19981,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oundefined(X1),X0,tc_bool),tc_bool)
| ~ spl0_652
| ~ spl0_715 ),
inference(superposition,[],[f19931,f17410]) ).
fof(f19931,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X3,c_HOL_Oundefined(X0),tc_bool),tc_bool)
| ~ spl0_715 ),
inference(avatar_component_clause,[],[f19930]) ).
fof(f20025,plain,
( spl0_735
| ~ spl0_95
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2359,f2188,f1473,f20023]) ).
fof(f20023,plain,
( spl0_735
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f2359,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = X0
| ~ spl0_95
| ~ spl0_152 ),
inference(resolution,[],[f2189,f1474]) ).
fof(f20021,plain,
( spl0_734
| ~ spl0_92
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2350,f2188,f1457,f20019]) ).
fof(f20019,plain,
( spl0_734
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f2350,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1
| ~ spl0_92
| ~ spl0_152 ),
inference(resolution,[],[f2189,f1458]) ).
fof(f20017,plain,
( spl0_733
| ~ spl0_91
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2349,f2188,f1453,f20015]) ).
fof(f20015,plain,
( spl0_733
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f2349,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = X0
| ~ spl0_91
| ~ spl0_152 ),
inference(resolution,[],[f2189,f1454]) ).
fof(f20013,plain,
( spl0_732
| ~ spl0_95
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f2332,f2180,f1473,f20011]) ).
fof(f20011,plain,
( spl0_732
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f2332,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0
| ~ spl0_95
| ~ spl0_150 ),
inference(resolution,[],[f2181,f1474]) ).
fof(f20009,plain,
( spl0_731
| ~ spl0_92
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f2323,f2180,f1457,f20007]) ).
fof(f20007,plain,
( spl0_731
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2323,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0
| ~ spl0_92
| ~ spl0_150 ),
inference(resolution,[],[f2181,f1458]) ).
fof(f20005,plain,
( spl0_730
| ~ spl0_91
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f2322,f2180,f1453,f20003]) ).
fof(f20003,plain,
( spl0_730
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2322,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0
| ~ spl0_91
| ~ spl0_150 ),
inference(resolution,[],[f2181,f1454]) ).
fof(f20001,plain,
( spl0_729
| ~ spl0_42
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1907,f1781,f1207,f19999]) ).
fof(f1907,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_42
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1208]) ).
fof(f19997,plain,
( spl0_728
| ~ spl0_41
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1899,f1781,f1203,f19995]) ).
fof(f19995,plain,
( spl0_728
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f1899,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_41
| ~ spl0_123 ),
inference(resolution,[],[f1782,f1204]) ).
fof(f19993,plain,
( spl0_727
| ~ spl0_64
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1761,f1647,f1301,f19991]) ).
fof(f19991,plain,
( spl0_727
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X2,X0) = X2
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f1761,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X2,X0) = X2
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_64
| ~ spl0_122 ),
inference(resolution,[],[f1648,f1302]) ).
fof(f19989,plain,
( spl0_726
| ~ spl0_65
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1760,f1647,f1305,f19987]) ).
fof(f19987,plain,
( spl0_726
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X2,X0) = X2
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f1760,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X2,X0) = X2
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_65
| ~ spl0_122 ),
inference(resolution,[],[f1648,f1306]) ).
fof(f19972,plain,
( spl0_725
| ~ spl0_63
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1759,f1647,f1297,f19970]) ).
fof(f19970,plain,
( spl0_725
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X1,X0) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f1759,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X1,X0) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_63
| ~ spl0_122 ),
inference(resolution,[],[f1648,f1298]) ).
fof(f19968,plain,
( spl0_724
| ~ spl0_66
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1758,f1647,f1309,f19966]) ).
fof(f19966,plain,
( spl0_724
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X1,X0) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1758,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X1,X0) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_66
| ~ spl0_122 ),
inference(resolution,[],[f1648,f1310]) ).
fof(f19964,plain,
( spl0_723
| ~ spl0_64
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1724,f1639,f1301,f19962]) ).
fof(f19962,plain,
( spl0_723
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f1724,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_64
| ~ spl0_120 ),
inference(resolution,[],[f1640,f1302]) ).
fof(f19960,plain,
( spl0_722
| ~ spl0_65
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1723,f1639,f1305,f19958]) ).
fof(f19958,plain,
( spl0_722
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f1723,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_65
| ~ spl0_120 ),
inference(resolution,[],[f1640,f1306]) ).
fof(f19956,plain,
( spl0_721
| ~ spl0_63
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1722,f1639,f1297,f19954]) ).
fof(f19954,plain,
( spl0_721
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f1722,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_63
| ~ spl0_120 ),
inference(resolution,[],[f1640,f1298]) ).
fof(f19952,plain,
( spl0_720
| ~ spl0_55
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1706,f1635,f1265,f19950]) ).
fof(f19950,plain,
( spl0_720
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X0) = X1
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f1706,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X0) = X1
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_55
| ~ spl0_119 ),
inference(resolution,[],[f1636,f1266]) ).
fof(f19948,plain,
( spl0_719
| ~ spl0_56
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1705,f1635,f1269,f19946]) ).
fof(f19946,plain,
( spl0_719
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X0) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f1705,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X0) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_56
| ~ spl0_119 ),
inference(resolution,[],[f1636,f1270]) ).
fof(f19944,plain,
( spl0_718
| ~ spl0_54
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1704,f1635,f1261,f19942]) ).
fof(f19942,plain,
( spl0_718
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1704,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_54
| ~ spl0_119 ),
inference(resolution,[],[f1636,f1262]) ).
fof(f19940,plain,
( spl0_717
| ~ spl0_55
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1668,f1622,f1265,f19938]) ).
fof(f19938,plain,
( spl0_717
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) = X2
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1668,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) = X2
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_55
| ~ spl0_116 ),
inference(resolution,[],[f1623,f1266]) ).
fof(f19936,plain,
( spl0_716
| ~ spl0_56
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1667,f1622,f1269,f19934]) ).
fof(f19934,plain,
( spl0_716
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) = X2
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1667,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) = X2
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_56
| ~ spl0_116 ),
inference(resolution,[],[f1623,f1270]) ).
fof(f19932,plain,
( ~ spl0_13
| spl0_715
| ~ spl0_590
| ~ spl0_686 ),
inference(avatar_split_clause,[],[f18427,f18234,f14539,f19930,f1080]) ).
fof(f14539,plain,
( spl0_590
<=> ! [X2,X0,X1] : c_HOL_Oundefined(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oundefined(X0),c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f18234,plain,
( spl0_686
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,X3),X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f18427,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X3,c_HOL_Oundefined(X0),tc_bool),tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_590
| ~ spl0_686 ),
inference(superposition,[],[f18235,f14540]) ).
fof(f14540,plain,
( ! [X2,X0,X1] : c_HOL_Oundefined(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oundefined(X0),c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool)
| ~ spl0_590 ),
inference(avatar_component_clause,[],[f14539]) ).
fof(f18235,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,X3),X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_686 ),
inference(avatar_component_clause,[],[f18234]) ).
fof(f19928,plain,
( spl0_714
| ~ spl0_54
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1666,f1622,f1261,f19926]) ).
fof(f19926,plain,
( spl0_714
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) = X1
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f1666,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) = X1
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_54
| ~ spl0_116 ),
inference(resolution,[],[f1623,f1262]) ).
fof(f19924,plain,
( spl0_713
| ~ spl0_57
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1665,f1622,f1273,f19922]) ).
fof(f19922,plain,
( spl0_713
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1665,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_57
| ~ spl0_116 ),
inference(resolution,[],[f1623,f1274]) ).
fof(f19920,plain,
( spl0_712
| ~ spl0_34
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1355,f1325,f1175,f19918]) ).
fof(f19918,plain,
( spl0_712
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X0,X1)),X2,tc_fun(X0,X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f1325,plain,
( spl0_70
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1355,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X0,X1)),X2,tc_fun(X0,X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_34
| ~ spl0_70 ),
inference(resolution,[],[f1326,f1176]) ).
fof(f1326,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X1,X0) = X1 )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1325]) ).
fof(f19916,plain,
( spl0_711
| ~ spl0_34
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f1353,f1321,f1175,f19914]) ).
fof(f19914,plain,
( spl0_711
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Lattices_Obounded__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f1321,plain,
( spl0_69
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1353,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Lattices_Obounded__lattice(X2) )
| ~ spl0_34
| ~ spl0_69 ),
inference(resolution,[],[f1322,f1176]) ).
fof(f1322,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(X0),X0) = X1 )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f19912,plain,
( spl0_710
| ~ spl0_34
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f1339,f1281,f1175,f19910]) ).
fof(f19910,plain,
( spl0_710
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Lattices_Obounded__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f1281,plain,
( spl0_59
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1339,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Lattices_Obounded__lattice(X2) )
| ~ spl0_34
| ~ spl0_59 ),
inference(resolution,[],[f1282,f1176]) ).
fof(f1282,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1281]) ).
fof(f19908,plain,
( spl0_709
| ~ spl0_34
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f1337,f1277,f1175,f19906]) ).
fof(f19906,plain,
( spl0_709
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,X1)),X2,tc_fun(X0,X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f1277,plain,
( spl0_58
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1337,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,X1)),X2,tc_fun(X0,X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_34
| ~ spl0_58 ),
inference(resolution,[],[f1278,f1176]) ).
fof(f1278,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f18695,plain,
( ~ spl0_14
| spl0_708
| ~ spl0_55
| ~ spl0_696 ),
inference(avatar_split_clause,[],[f18313,f18274,f1265,f18693,f1085]) ).
fof(f18693,plain,
( spl0_708
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Oundefined(X0),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f18313,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_HOL_Oundefined(X0),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool)
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_55
| ~ spl0_696 ),
inference(superposition,[],[f1266,f18275]) ).
fof(f18344,plain,
( spl0_707
| ~ spl0_113
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f3382,f3079,f1546,f18342]) ).
fof(f18342,plain,
( spl0_707
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Set_OPow(X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f3382,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Set_OPow(X1,X2),X0)) )
| ~ spl0_113
| ~ spl0_223 ),
inference(resolution,[],[f3080,f1547]) ).
fof(f18340,plain,
( spl0_706
| ~ spl0_112
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f3378,f3075,f1542,f18338]) ).
fof(f18338,plain,
( spl0_706
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(c_Set_OPow(X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f3378,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(c_Set_OPow(X1,X2),X0)) )
| ~ spl0_112
| ~ spl0_222 ),
inference(resolution,[],[f3076,f1543]) ).
fof(f18336,plain,
( spl0_705
| ~ spl0_112
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2753,f2658,f1542,f18334]) ).
fof(f2753,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,X1),X2,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(X0,X2)) )
| ~ spl0_112
| ~ spl0_187 ),
inference(resolution,[],[f2659,f1543]) ).
fof(f18310,plain,
( spl0_704
| ~ spl0_112
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2745,f2650,f1542,f18308]) ).
fof(f18308,plain,
( spl0_704
<=> ! [X2,X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(X1,X2),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f2745,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(X1,X2),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(X1,X0)) )
| ~ spl0_112
| ~ spl0_185 ),
inference(resolution,[],[f2651,f1543]) ).
fof(f18306,plain,
( spl0_703
| ~ spl0_89
| ~ spl0_317
| ~ spl0_702 ),
inference(avatar_split_clause,[],[f18302,f18299,f4702,f1445,f18304]) ).
fof(f18304,plain,
( spl0_703
<=> ! [X0] : c_Complete__Lattice_OSup__class_OSup(hAPP(c_fequal(tc_bool),X0),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f18299,plain,
( spl0_702
<=> ! [X0] : c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(tc_bool),tc_bool,tc_bool,tc_bool),X0),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f18302,plain,
( ! [X0] : c_Complete__Lattice_OSup__class_OSup(hAPP(c_fequal(tc_bool),X0),tc_bool) = X0
| ~ spl0_89
| ~ spl0_317
| ~ spl0_702 ),
inference(forward_demodulation,[],[f18300,f5265]) ).
fof(f18300,plain,
( ! [X0] : c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(tc_bool),tc_bool,tc_bool,tc_bool),X0),tc_bool) = X0
| ~ spl0_702 ),
inference(avatar_component_clause,[],[f18299]) ).
fof(f18301,plain,
( spl0_702
| ~ spl0_12
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2635,f2296,f1075,f18299]) ).
fof(f2635,plain,
( ! [X0] : c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(tc_bool),tc_bool,tc_bool,tc_bool),X0),tc_bool) = X0
| ~ spl0_12
| ~ spl0_179 ),
inference(resolution,[],[f2297,f1077]) ).
fof(f18297,plain,
( spl0_701
| ~ spl0_89
| ~ spl0_317
| ~ spl0_700 ),
inference(avatar_split_clause,[],[f18293,f18290,f4702,f1445,f18295]) ).
fof(f18290,plain,
( spl0_700
<=> ! [X0] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(tc_bool),tc_bool,tc_bool,tc_bool),X0),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f18293,plain,
( ! [X0] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_fequal(tc_bool),X0),tc_bool) = X0
| ~ spl0_89
| ~ spl0_317
| ~ spl0_700 ),
inference(forward_demodulation,[],[f18291,f5265]) ).
fof(f18291,plain,
( ! [X0] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(tc_bool),tc_bool,tc_bool,tc_bool),X0),tc_bool) = X0
| ~ spl0_700 ),
inference(avatar_component_clause,[],[f18290]) ).
fof(f18292,plain,
( spl0_700
| ~ spl0_12
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2633,f2292,f1075,f18290]) ).
fof(f2633,plain,
( ! [X0] : c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(tc_bool),tc_bool,tc_bool,tc_bool),X0),tc_bool) = X0
| ~ spl0_12
| ~ spl0_178 ),
inference(resolution,[],[f2293,f1077]) ).
fof(f18288,plain,
( spl0_699
| ~ spl0_24
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2629,f2284,f1135,f18286]) ).
fof(f2629,plain,
( ! [X0,X1] : hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X1) = X1
| ~ spl0_24
| ~ spl0_176 ),
inference(superposition,[],[f2285,f1136]) ).
fof(f18284,plain,
( spl0_698
| ~ spl0_18
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2618,f2264,f1105,f18282]) ).
fof(f18282,plain,
( spl0_698
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f2618,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool)
| ~ spl0_18
| ~ spl0_171 ),
inference(resolution,[],[f2265,f1107]) ).
fof(f18280,plain,
( spl0_697
| ~ spl0_8
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2617,f2264,f1055,f18278]) ).
fof(f18278,plain,
( spl0_697
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f2617,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat)
| ~ spl0_8
| ~ spl0_171 ),
inference(resolution,[],[f2265,f1057]) ).
fof(f18276,plain,
( spl0_696
| ~ spl0_14
| ~ spl0_12
| ~ spl0_563 ),
inference(avatar_split_clause,[],[f18231,f13698,f1075,f1085,f18274]) ).
fof(f13698,plain,
( spl0_563
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_HOL_Oundefined(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oundefined(X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f18231,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_bool)
| c_HOL_Oundefined(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oundefined(X0),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool) )
| ~ spl0_12
| ~ spl0_563 ),
inference(resolution,[],[f13699,f1077]) ).
fof(f13699,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_HOL_Oundefined(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oundefined(X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),X0) )
| ~ spl0_563 ),
inference(avatar_component_clause,[],[f13698]) ).
fof(f18272,plain,
( spl0_695
| ~ spl0_13
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2564,f2228,f1080,f18270]) ).
fof(f18270,plain,
( spl0_695
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f2564,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool)
| ~ spl0_13
| ~ spl0_162 ),
inference(resolution,[],[f2229,f1082]) ).
fof(f18268,plain,
( spl0_694
| ~ spl0_3
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2563,f2228,f1030,f18266]) ).
fof(f18266,plain,
( spl0_694
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f2563,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat)
| ~ spl0_3
| ~ spl0_162 ),
inference(resolution,[],[f2229,f1032]) ).
fof(f18264,plain,
( spl0_693
| ~ spl0_54
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f2081,f1842,f1261,f18262]) ).
fof(f18262,plain,
( spl0_693
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2),X1,X2)
| ~ class_Lattices_Olower__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f2081,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2),X1,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_54
| ~ spl0_138 ),
inference(duplicate_literal_removal,[],[f2063]) ).
fof(f2063,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2),X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_54
| ~ spl0_138 ),
inference(resolution,[],[f1843,f1262]) ).
fof(f18260,plain,
( spl0_692
| ~ spl0_55
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f2080,f1842,f1265,f18258]) ).
fof(f2080,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_55
| ~ spl0_138 ),
inference(duplicate_literal_removal,[],[f2065]) ).
fof(f2065,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_55
| ~ spl0_138 ),
inference(resolution,[],[f1843,f1266]) ).
fof(f18256,plain,
( spl0_691
| ~ spl0_54
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f2054,f1838,f1261,f18254]) ).
fof(f18254,plain,
( spl0_691
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2),X0,X2)
| ~ class_Lattices_Olower__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f2054,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2),X0,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_54
| ~ spl0_137 ),
inference(duplicate_literal_removal,[],[f2036]) ).
fof(f2036,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X3,X2),X0,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_54
| ~ spl0_137 ),
inference(resolution,[],[f1839,f1262]) ).
fof(f18252,plain,
( spl0_690
| ~ spl0_55
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f2053,f1838,f1265,f18250]) ).
fof(f18250,plain,
( spl0_690
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f2053,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_55
| ~ spl0_137 ),
inference(duplicate_literal_removal,[],[f2038]) ).
fof(f2038,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_55
| ~ spl0_137 ),
inference(resolution,[],[f1839,f1266]) ).
fof(f18248,plain,
( spl0_689
| ~ spl0_63
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1993,f1813,f1297,f18246]) ).
fof(f18246,plain,
( spl0_689
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1993,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_63
| ~ spl0_131 ),
inference(duplicate_literal_removal,[],[f1976]) ).
fof(f1976,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_63
| ~ spl0_131 ),
inference(resolution,[],[f1814,f1298]) ).
fof(f18244,plain,
( spl0_688
| ~ spl0_64
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1992,f1813,f1301,f18242]) ).
fof(f18242,plain,
( spl0_688
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,X3),X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f1992,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,X3),X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_64
| ~ spl0_131 ),
inference(duplicate_literal_removal,[],[f1978]) ).
fof(f1978,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,X3),X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_64
| ~ spl0_131 ),
inference(resolution,[],[f1814,f1302]) ).
fof(f18240,plain,
( spl0_687
| ~ spl0_63
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1967,f1809,f1297,f18238]) ).
fof(f18238,plain,
( spl0_687
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,X2),X3,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1967,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,X2),X3,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_63
| ~ spl0_130 ),
inference(duplicate_literal_removal,[],[f1950]) ).
fof(f1950,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,X2),X3,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_63
| ~ spl0_130 ),
inference(resolution,[],[f1810,f1298]) ).
fof(f18236,plain,
( spl0_686
| ~ spl0_64
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1966,f1809,f1301,f18234]) ).
fof(f1966,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,X3),X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_64
| ~ spl0_130 ),
inference(duplicate_literal_removal,[],[f1952]) ).
fof(f1952,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,X3),X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_64
| ~ spl0_130 ),
inference(resolution,[],[f1810,f1302]) ).
fof(f18230,plain,
( spl0_685
| ~ spl0_42
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1772,f1647,f1207,f18228]) ).
fof(f18228,plain,
( spl0_685
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f1772,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_42
| ~ spl0_122 ),
inference(resolution,[],[f1648,f1208]) ).
fof(f18226,plain,
( spl0_684
| ~ spl0_42
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1735,f1639,f1207,f18224]) ).
fof(f18224,plain,
( spl0_684
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f1735,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_42
| ~ spl0_120 ),
inference(resolution,[],[f1640,f1208]) ).
fof(f18222,plain,
( spl0_683
| ~ spl0_41
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1701,f1635,f1203,f18220]) ).
fof(f18220,plain,
( spl0_683
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f1701,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_41
| ~ spl0_119 ),
inference(resolution,[],[f1636,f1204]) ).
fof(f18218,plain,
( spl0_682
| ~ spl0_41
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1663,f1622,f1203,f18216]) ).
fof(f18216,plain,
( spl0_682
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(X0),X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1663,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(X0),X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_41
| ~ spl0_116 ),
inference(resolution,[],[f1623,f1204]) ).
fof(f18037,plain,
( spl0_681
| spl0_23
| ~ spl0_499 ),
inference(avatar_split_clause,[],[f11554,f11489,f1130,f18035]) ).
fof(f18035,plain,
( spl0_681
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f11489,plain,
( spl0_499
<=> ! [X0,X3,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f11554,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| spl0_23
| ~ spl0_499 ),
inference(resolution,[],[f11490,f1132]) ).
fof(f11490,plain,
( ! [X3,X0,X8,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X8))
| c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) )
| ~ spl0_499 ),
inference(avatar_component_clause,[],[f11489]) ).
fof(f18033,plain,
( spl0_680
| spl0_23
| ~ spl0_497 ),
inference(avatar_split_clause,[],[f11454,f11389,f1130,f18031]) ).
fof(f18031,plain,
( spl0_680
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Arrow__Order__Mirabelle_OLin,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f11389,plain,
( spl0_497
<=> ! [X0,X6,X3,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f11454,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Arrow__Order__Mirabelle_OLin,X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Arrow__Order__Mirabelle_OLin,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),X0,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| spl0_23
| ~ spl0_497 ),
inference(resolution,[],[f11390,f1132]) ).
fof(f11390,plain,
( ! [X3,X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) )
| ~ spl0_497 ),
inference(avatar_component_clause,[],[f11389]) ).
fof(f17951,plain,
( spl0_679
| ~ spl0_113
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f3000,f2850,f1546,f17949]) ).
fof(f3000,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_FuncSet_Oextensional(X0,X1,X2),c_FuncSet_Orestrict(X3,X0,X1,X2)))
| ~ spl0_113
| ~ spl0_205 ),
inference(resolution,[],[f2851,f1547]) ).
fof(f17947,plain,
( spl0_678
| ~ spl0_83
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2755,f2658,f1397,f17945]) ).
fof(f17945,plain,
( spl0_678
<=> ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f2755,plain,
( ! [X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0),X1,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_83
| ~ spl0_187 ),
inference(resolution,[],[f2659,f1398]) ).
fof(f17943,plain,
( spl0_677
| ~ spl0_83
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2747,f2650,f1397,f17941]) ).
fof(f17941,plain,
( spl0_677
<=> ! [X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f2747,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_83
| ~ spl0_185 ),
inference(resolution,[],[f2651,f1398]) ).
fof(f17939,plain,
( spl0_676
| ~ spl0_41
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1764,f1647,f1203,f17937]) ).
fof(f17937,plain,
( spl0_676
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X1,X0) = X1
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1764,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X1,X0) = X1
| ~ class_Orderings_Otop(X0) )
| ~ spl0_41
| ~ spl0_122 ),
inference(resolution,[],[f1648,f1204]) ).
fof(f17935,plain,
( spl0_675
| ~ spl0_41
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1727,f1639,f1203,f17933]) ).
fof(f17933,plain,
( spl0_675
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(X0),X0) = X1
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1727,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(X0),X0) = X1
| ~ class_Orderings_Otop(X0) )
| ~ spl0_41
| ~ spl0_120 ),
inference(resolution,[],[f1640,f1204]) ).
fof(f17931,plain,
( spl0_674
| ~ spl0_42
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1709,f1635,f1207,f17929]) ).
fof(f17929,plain,
( spl0_674
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f1709,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_42
| ~ spl0_119 ),
inference(resolution,[],[f1636,f1208]) ).
fof(f17927,plain,
( spl0_673
| ~ spl0_42
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1671,f1622,f1207,f17925]) ).
fof(f17925,plain,
( spl0_673
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f1671,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_42
| ~ spl0_116 ),
inference(resolution,[],[f1623,f1208]) ).
fof(f17923,plain,
( spl0_672
| spl0_23
| ~ spl0_469 ),
inference(avatar_split_clause,[],[f10687,f10631,f1130,f17921]) ).
fof(f17921,plain,
( spl0_672
<=> ! [X0] : c_Finite__Set_Osetsum(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_nat) = c_Finite__Set_Osetsum(X0,c_HOL_Ominus__class_Ominus(c_Arrow__Order__Mirabelle_OLin,hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f10687,plain,
( ! [X0] : c_Finite__Set_Osetsum(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_nat) = c_Finite__Set_Osetsum(X0,c_HOL_Ominus__class_Ominus(c_Arrow__Order__Mirabelle_OLin,hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_nat)
| spl0_23
| ~ spl0_469 ),
inference(resolution,[],[f10632,f1132]) ).
fof(f17862,plain,
( spl0_671
| ~ spl0_292
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f5268,f4702,f4166,f17860]) ).
fof(f17860,plain,
( spl0_671
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(c_fequal(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f5268,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(c_fequal(X0),X1)))
| ~ spl0_292
| ~ spl0_317 ),
inference(superposition,[],[f4167,f4703]) ).
fof(f17858,plain,
( ~ spl0_669
| spl0_670
| ~ spl0_78
| ~ spl0_613 ),
inference(avatar_split_clause,[],[f15989,f15663,f1377,f17856,f17852]) ).
fof(f17852,plain,
( spl0_669
<=> class_Orderings_Olinorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f17856,plain,
( spl0_670
<=> ! [X2,X0,X1,X3] :
( c_lessequals(X0,c_HOL_Oundefined(X1),tc_bool)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,tc_bool),tc_bool),X0,tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f15663,plain,
( spl0_613
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X3,c_HOL_Oundefined(X0),tc_bool)
| ~ c_lessequals(X3,c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f15989,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_HOL_Oundefined(X1),tc_bool)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,tc_bool),tc_bool),X0,tc_bool)
| ~ class_Orderings_Olinorder(tc_bool) )
| ~ spl0_78
| ~ spl0_613 ),
inference(resolution,[],[f15664,f1378]) ).
fof(f15664,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool)
| c_lessequals(X3,c_HOL_Oundefined(X0),tc_bool) )
| ~ spl0_613 ),
inference(avatar_component_clause,[],[f15663]) ).
fof(f17850,plain,
( spl0_668
| ~ spl0_112
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2805,f2690,f1542,f17848]) ).
fof(f17848,plain,
( spl0_668
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omktop(X0,X1),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f2690,plain,
( spl0_195
<=> ! [X2,X37,X1] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2805,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omktop(X0,X1),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_112
| ~ spl0_195 ),
inference(resolution,[],[f2691,f1543]) ).
fof(f2691,plain,
( ! [X2,X1,X37] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X1)))
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2690]) ).
fof(f17846,plain,
( spl0_667
| ~ spl0_112
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2778,f2670,f1542,f17844]) ).
fof(f17844,plain,
( spl0_667
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f2670,plain,
( spl0_190
<=> ! [X37,X1,X30] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f2778,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_112
| ~ spl0_190 ),
inference(resolution,[],[f2671,f1543]) ).
fof(f2671,plain,
( ! [X1,X37,X30] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1)))
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f2670]) ).
fof(f17842,plain,
( spl0_666
| ~ spl0_29
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1416,f1361,f1155,f17840]) ).
fof(f17840,plain,
( spl0_666
<=> ! [X0,X3,X2,X1] : c_COMBI(X0) = c_Fun_Ofun__upd(c_COMBI(X0),X1,X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f1416,plain,
( ! [X2,X3,X0,X1] : c_COMBI(X0) = c_Fun_Ofun__upd(c_COMBI(X0),X1,X1,X2,X3)
| ~ spl0_29
| ~ spl0_74 ),
inference(superposition,[],[f1362,f1156]) ).
fof(f17838,plain,
( spl0_665
| ~ spl0_32
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1259,f1239,f1167,f17836]) ).
fof(f17836,plain,
( spl0_665
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f1239,plain,
( spl0_50
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1259,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_32
| ~ spl0_50 ),
inference(resolution,[],[f1240,f1168]) ).
fof(f1240,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f17834,plain,
( spl0_664
| ~ spl0_31
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f1252,f1227,f1163,f17832]) ).
fof(f17832,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f1227,plain,
( spl0_47
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1252,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_31
| ~ spl0_47 ),
inference(resolution,[],[f1228,f1164]) ).
fof(f1228,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f17795,plain,
( spl0_663
| spl0_23
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5776,f5623,f1130,f17793]) ).
fof(f17793,plain,
( spl0_663
<=> ! [X2,X0,X1] : c_Set_Oimage(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1) = c_Set_Oimage(c_Fun_Ofun__upd(X0,hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),X2,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f5776,plain,
( ! [X2,X0,X1] : c_Set_Oimage(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1) = c_Set_Oimage(c_Fun_Ofun__upd(X0,hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),X2,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1)
| spl0_23
| ~ spl0_334 ),
inference(resolution,[],[f5624,f1132]) ).
fof(f17525,plain,
( ~ spl0_16
| spl0_662
| ~ spl0_134
| ~ spl0_590 ),
inference(avatar_split_clause,[],[f14740,f14539,f1826,f17523,f1095]) ).
fof(f1095,plain,
( spl0_16
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f17523,plain,
( spl0_662
<=> ! [X2,X0,X1] :
( c_HOL_Oundefined(X0) != c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f1826,plain,
( spl0_134
<=> ! [X6,X0,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X7
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f14740,plain,
( ! [X2,X0,X1] :
( c_HOL_Oundefined(X0) != c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool)
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_134
| ~ spl0_590 ),
inference(superposition,[],[f1827,f14540]) ).
fof(f1827,plain,
( ! [X0,X6,X7] :
( c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X0)
| c_Orderings_Obot__class_Obot(X0) = X7
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1826]) ).
fof(f17461,plain,
( spl0_661
| ~ spl0_274
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f5269,f4702,f3686,f17459]) ).
fof(f17459,plain,
( spl0_661
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_fequal(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f5269,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_fequal(X0),X1)
| ~ spl0_274
| ~ spl0_317 ),
inference(superposition,[],[f3687,f4703]) ).
fof(f17457,plain,
( spl0_660
| ~ spl0_113
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f3029,f2878,f1546,f17455]) ).
fof(f17455,plain,
( spl0_660
<=> ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f3029,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1))) )
| ~ spl0_113
| ~ spl0_212 ),
inference(resolution,[],[f2879,f1547]) ).
fof(f17453,plain,
( spl0_659
| ~ spl0_113
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2613,f2248,f1546,f17451]) ).
fof(f17451,plain,
( spl0_659
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_OPow(X0,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f2613,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_OPow(X0,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ spl0_113
| ~ spl0_167 ),
inference(resolution,[],[f2249,f1547]) ).
fof(f17449,plain,
( spl0_658
| ~ spl0_12
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1612,f1529,f1075,f17446]) ).
fof(f17446,plain,
( spl0_658
<=> c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f1612,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_12
| ~ spl0_109 ),
inference(resolution,[],[f1530,f1077]) ).
fof(f17444,plain,
( spl0_657
| ~ spl0_12
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1610,f1525,f1075,f17441]) ).
fof(f17441,plain,
( spl0_657
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f1610,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_12
| ~ spl0_108 ),
inference(resolution,[],[f1526,f1077]) ).
fof(f17439,plain,
( spl0_656
| ~ spl0_12
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1596,f1509,f1075,f17436]) ).
fof(f17436,plain,
( spl0_656
<=> c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f1596,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_12
| ~ spl0_104 ),
inference(resolution,[],[f1510,f1077]) ).
fof(f17434,plain,
( spl0_655
| ~ spl0_14
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1591,f1497,f1085,f17432]) ).
fof(f1591,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool)
| ~ spl0_14
| ~ spl0_101 ),
inference(resolution,[],[f1498,f1087]) ).
fof(f1087,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f17430,plain,
( spl0_654
| ~ spl0_4
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1590,f1497,f1035,f17428]) ).
fof(f17428,plain,
( spl0_654
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f1035,plain,
( spl0_4
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1590,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)
| ~ spl0_4
| ~ spl0_101 ),
inference(resolution,[],[f1498,f1037]) ).
fof(f1037,plain,
( class_Lattices_Olower__semilattice(tc_nat)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f1035]) ).
fof(f17416,plain,
( spl0_653
| ~ spl0_12
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1586,f1485,f1075,f17413]) ).
fof(f17413,plain,
( spl0_653
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f1586,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_12
| ~ spl0_98 ),
inference(resolution,[],[f1486,f1077]) ).
fof(f17411,plain,
( spl0_652
| ~ spl0_13
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1581,f1477,f1080,f17409]) ).
fof(f1581,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool)
| ~ spl0_13
| ~ spl0_96 ),
inference(resolution,[],[f1478,f1082]) ).
fof(f17407,plain,
( spl0_651
| ~ spl0_3
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1580,f1477,f1030,f17405]) ).
fof(f17405,plain,
( spl0_651
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1580,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat)
| ~ spl0_3
| ~ spl0_96 ),
inference(resolution,[],[f1478,f1032]) ).
fof(f17403,plain,
( spl0_650
| ~ spl0_18
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1558,f1441,f1105,f17401]) ).
fof(f17401,plain,
( spl0_650
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f1558,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = X0
| ~ spl0_18
| ~ spl0_88 ),
inference(resolution,[],[f1442,f1107]) ).
fof(f17399,plain,
( spl0_649
| ~ spl0_8
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1557,f1441,f1055,f17397]) ).
fof(f17397,plain,
( spl0_649
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f1557,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_8
| ~ spl0_88 ),
inference(resolution,[],[f1442,f1057]) ).
fof(f17395,plain,
( spl0_648
| ~ spl0_18
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1555,f1437,f1105,f17393]) ).
fof(f1555,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0
| ~ spl0_18
| ~ spl0_87 ),
inference(resolution,[],[f1438,f1107]) ).
fof(f17391,plain,
( spl0_647
| ~ spl0_8
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1554,f1437,f1055,f17389]) ).
fof(f17389,plain,
( spl0_647
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f1554,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_8
| ~ spl0_87 ),
inference(resolution,[],[f1438,f1057]) ).
fof(f17340,plain,
( ~ spl0_13
| spl0_646
| ~ spl0_130
| ~ spl0_590 ),
inference(avatar_split_clause,[],[f14737,f14539,f1809,f17338,f1080]) ).
fof(f17338,plain,
( spl0_646
<=> ! [X2,X0,X1,X3] :
( ~ c_lessequals(c_HOL_Oundefined(X0),X3,tc_bool)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f14737,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Oundefined(X0),X3,tc_bool)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_130
| ~ spl0_590 ),
inference(superposition,[],[f1810,f14540]) ).
fof(f17289,plain,
( spl0_645
| ~ spl0_12
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f1432,f1401,f1075,f17287]) ).
fof(f17287,plain,
( spl0_645
<=> ! [X0] : c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,tc_bool,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1432,plain,
( ! [X0] : c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,tc_bool,tc_bool),tc_bool) = X0
| ~ spl0_12
| ~ spl0_84 ),
inference(resolution,[],[f1402,f1077]) ).
fof(f17285,plain,
( spl0_644
| ~ spl0_16
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f1426,f1389,f1095,f17283]) ).
fof(f17283,plain,
( spl0_644
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f1426,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
| ~ spl0_16
| ~ spl0_81 ),
inference(resolution,[],[f1390,f1097]) ).
fof(f1097,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f17281,plain,
( spl0_643
| ~ spl0_16
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f1424,f1385,f1095,f17279]) ).
fof(f17279,plain,
( spl0_643
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f1424,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| ~ spl0_16
| ~ spl0_80 ),
inference(resolution,[],[f1386,f1097]) ).
fof(f17277,plain,
( spl0_642
| ~ spl0_16
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f1421,f1373,f1095,f17275]) ).
fof(f17275,plain,
( spl0_642
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f1421,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ spl0_16
| ~ spl0_77 ),
inference(resolution,[],[f1374,f1097]) ).
fof(f16908,plain,
spl0_641,
inference(avatar_split_clause,[],[f281,f16906]) ).
fof(f16906,plain,
( spl0_641
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f281,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_3) ).
fof(f16904,plain,
spl0_640,
inference(avatar_split_clause,[],[f280,f16902]) ).
fof(f16902,plain,
( spl0_640
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f280,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_2) ).
fof(f16900,plain,
spl0_639,
inference(avatar_split_clause,[],[f279,f16898]) ).
fof(f16898,plain,
( spl0_639
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f279,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_1) ).
fof(f16896,plain,
spl0_638,
inference(avatar_split_clause,[],[f278,f16894]) ).
fof(f16894,plain,
( spl0_638
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f278,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X2__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_0) ).
fof(f16892,plain,
spl0_637,
inference(avatar_split_clause,[],[f277,f16890]) ).
fof(f16890,plain,
( spl0_637
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X1__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X1__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f277,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X1__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X1__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_1_1) ).
fof(f16888,plain,
spl0_636,
inference(avatar_split_clause,[],[f276,f16886]) ).
fof(f16886,plain,
( spl0_636
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X1__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X1__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f276,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| X3 = X34
| X4 = X33
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X1__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X1__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_1_0) ).
fof(f16834,plain,
( ~ spl0_18
| spl0_635
| ~ spl0_56
| ~ spl0_613 ),
inference(avatar_split_clause,[],[f15993,f15663,f1269,f16832,f1105]) ).
fof(f16832,plain,
( spl0_635
<=> ! [X2,X0,X1,X3] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,tc_bool),tc_bool),tc_bool),c_HOL_Oundefined(X2),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f15993,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,tc_bool),tc_bool),tc_bool),c_HOL_Oundefined(X2),tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_56
| ~ spl0_613 ),
inference(resolution,[],[f15664,f1270]) ).
fof(f16642,plain,
spl0_634,
inference(avatar_split_clause,[],[f293,f16640]) ).
fof(f16640,plain,
( spl0_634
<=> ! [X35,X4,X20,X14,X3] :
( X3 = X4
| X4 = X14
| X3 = X14
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X4__1(X20,X35,X3,X4,X14))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X4__1(X20,X35,X3,X4,X14)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f293,axiom,
! [X3,X14,X4,X35,X20] :
( X3 = X4
| X4 = X14
| X3 = X14
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X4__1(X20,X35,X3,X4,X14))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X4__1(X20,X35,X3,X4,X14)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_4_3) ).
fof(f16638,plain,
spl0_633,
inference(avatar_split_clause,[],[f292,f16636]) ).
fof(f16636,plain,
( spl0_633
<=> ! [X35,X4,X20,X14,X3] :
( X3 = X4
| X4 = X14
| X3 = X14
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X4__1(X20,X35,X3,X4,X14))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X4__1(X20,X35,X3,X4,X14)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f292,axiom,
! [X3,X14,X4,X35,X20] :
( X3 = X4
| X4 = X14
| X3 = X14
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X4__1(X20,X35,X3,X4,X14))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X4__1(X20,X35,X3,X4,X14)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_4_2) ).
fof(f16634,plain,
spl0_632,
inference(avatar_split_clause,[],[f291,f16632]) ).
fof(f16632,plain,
( spl0_632
<=> ! [X35,X4,X20,X14,X3] :
( X3 = X4
| X4 = X14
| X3 = X14
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X4__1(X20,X35,X3,X4,X14))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X4__1(X20,X35,X3,X4,X14)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f291,axiom,
! [X3,X14,X4,X35,X20] :
( X3 = X4
| X4 = X14
| X3 = X14
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X4__1(X20,X35,X3,X4,X14))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X4__1(X20,X35,X3,X4,X14)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_4_1) ).
fof(f16630,plain,
spl0_631,
inference(avatar_split_clause,[],[f290,f16628]) ).
fof(f16628,plain,
( spl0_631
<=> ! [X35,X4,X20,X14,X3] :
( X3 = X4
| X4 = X14
| X3 = X14
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X4__1(X20,X35,X3,X4,X14))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X4__1(X20,X35,X3,X4,X14)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f290,axiom,
! [X3,X14,X4,X35,X20] :
( X3 = X4
| X4 = X14
| X3 = X14
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X4__1(X20,X35,X3,X4,X14))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X4__1(X20,X35,X3,X4,X14)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_4_0) ).
fof(f16377,plain,
spl0_630,
inference(avatar_split_clause,[],[f285,f16375]) ).
fof(f16375,plain,
( spl0_630
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f285,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pairwise__neutrality_3) ).
fof(f16373,plain,
spl0_629,
inference(avatar_split_clause,[],[f284,f16371]) ).
fof(f16371,plain,
( spl0_629
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f284,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pairwise__neutrality_2) ).
fof(f16369,plain,
spl0_628,
inference(avatar_split_clause,[],[f283,f16367]) ).
fof(f16367,plain,
( spl0_628
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f283,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pairwise__neutrality_1) ).
fof(f16365,plain,
spl0_627,
inference(avatar_split_clause,[],[f282,f16363]) ).
fof(f16363,plain,
( spl0_627
<=> ! [X35,X4,X34,X20,X3,X33] :
( X3 = X4
| X33 = X34
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f282,axiom,
! [X3,X4,X34,X35,X33,X20] :
( X3 = X4
| X33 = X34
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X34,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__Xpairwise__neutrality__1(X20,X35,X3,X33,X4,X34)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pairwise__neutrality_0) ).
fof(f16123,plain,
spl0_626,
inference(avatar_split_clause,[],[f289,f16121]) ).
fof(f16121,plain,
( spl0_626
<=> ! [X35,X4,X20,X3] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X3__1(X20,X35,X3,X4))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X3__1(X20,X35,X3,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f289,axiom,
! [X3,X4,X35,X20] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X3__1(X20,X35,X3,X4))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X3__1(X20,X35,X3,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_3) ).
fof(f16119,plain,
spl0_625,
inference(avatar_split_clause,[],[f288,f16117]) ).
fof(f16117,plain,
( spl0_625
<=> ! [X35,X4,X20,X3] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X3__1(X20,X35,X3,X4))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X3__1(X20,X35,X3,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f288,axiom,
! [X3,X4,X35,X20] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X3__1(X20,X35,X3,X4))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X3__1(X20,X35,X3,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_2) ).
fof(f16115,plain,
( ~ spl0_18
| spl0_624
| ~ spl0_57
| ~ spl0_613 ),
inference(avatar_split_clause,[],[f15991,f15663,f1273,f16113,f1105]) ).
fof(f16113,plain,
( spl0_624
<=> ! [X2,X0,X1,X3] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool),c_HOL_Oundefined(X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f15991,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),X3,tc_bool),c_HOL_Oundefined(X1),tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_57
| ~ spl0_613 ),
inference(resolution,[],[f15664,f1274]) ).
fof(f16111,plain,
spl0_623,
inference(avatar_split_clause,[],[f287,f16109]) ).
fof(f16109,plain,
( spl0_623
<=> ! [X35,X4,X20,X3] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X3__1(X20,X35,X3,X4))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X3__1(X20,X35,X3,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f287,axiom,
! [X3,X4,X35,X20] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X3__1(X20,X35,X3,X4))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X3__1(X20,X35,X3,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_1) ).
fof(f16107,plain,
spl0_622,
inference(avatar_split_clause,[],[f286,f16105]) ).
fof(f16105,plain,
( spl0_622
<=> ! [X35,X4,X20,X3] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X3__1(X20,X35,X3,X4))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X3__1(X20,X35,X3,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f286,axiom,
! [X3,X4,X35,X20] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X20),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X35),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X20)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,X35)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X20,v_sko__local__X3__1(X20,X35,X3,X4))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X35,v_sko__local__X3__1(X20,X35,X3,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_0) ).
fof(f16015,plain,
spl0_621,
inference(avatar_split_clause,[],[f297,f16013]) ).
fof(f16013,plain,
( spl0_621
<=> ! [X3,X4,X36,X1,X30] :
( ~ c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X30),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X30)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X30,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f297,axiom,
! [X3,X36,X1,X4,X30] :
( ~ c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X30),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X30)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X30,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_3) ).
fof(f16011,plain,
spl0_620,
inference(avatar_split_clause,[],[f296,f16009]) ).
fof(f16009,plain,
( spl0_620
<=> ! [X3,X4,X36,X1,X30] :
( ~ c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X30),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X30)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X30,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f296,axiom,
! [X3,X36,X1,X4,X30] :
( ~ c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X30),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X30)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X30,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_2) ).
fof(f16007,plain,
spl0_619,
inference(avatar_split_clause,[],[f295,f16005]) ).
fof(f16005,plain,
( spl0_619
<=> ! [X3,X4,X36,X1,X30] :
( ~ c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X30),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X30)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X30,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f295,axiom,
! [X3,X36,X1,X4,X30] :
( ~ c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X30),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X30)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X30,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_1) ).
fof(f16003,plain,
spl0_618,
inference(avatar_split_clause,[],[f294,f16001]) ).
fof(f16001,plain,
( spl0_618
<=> ! [X3,X4,X36,X1,X30] :
( ~ c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X30),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X30)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X30,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f294,axiom,
! [X3,X36,X1,X4,X30] :
( ~ c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X30),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X30)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X30,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X3,X4,X1,X30)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_0) ).
fof(f15960,plain,
spl0_617,
inference(avatar_split_clause,[],[f807,f15958]) ).
fof(f807,plain,
! [X10,X0,X18,X8,X6,X56,X7,X55,X9,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X12,X18)),X17),c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X18,X56)),X55),c_FuncSet_OPi(X8,c_COMBK(X9,tc_fun(X56,tc_bool),X18),X18,X56)))
| c_FuncSet_Orestrict(c_COMBB(X55,c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X18,X56,X0),X6,X0,X56) = c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBB(X55,X17,X18,X56,X12),X7,X12,X56),X10,X12,X56,X0),X6,X0,X56) ),
inference(definition_unfolding,[],[f620,f231,f231,f231,f231]) ).
fof(f231,axiom,
! [X10,X0,X18,X6,X17,X12] : c_FuncSet_Ocompose(X6,X17,X10,X0,X18,X12) = c_FuncSet_Orestrict(c_COMBB(X17,X10,X18,X12,X0),X6,X0,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compose__def_0) ).
fof(f620,axiom,
! [X10,X0,X18,X8,X6,X56,X7,X55,X9,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X12,X18)),X17),c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X18,X56)),X55),c_FuncSet_OPi(X8,c_COMBK(X9,tc_fun(X56,tc_bool),X18),X18,X56)))
| c_FuncSet_Ocompose(X6,X55,c_FuncSet_Ocompose(X6,X17,X10,X0,X12,X18),X0,X18,X56) = c_FuncSet_Ocompose(X6,c_FuncSet_Ocompose(X7,X55,X17,X12,X18,X56),X10,X0,X12,X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compose__assoc_0) ).
fof(f15872,plain,
spl0_616,
inference(avatar_split_clause,[],[f420,f15870]) ).
fof(f15870,plain,
( spl0_616
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f420,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_14) ).
fof(f15868,plain,
spl0_615,
inference(avatar_split_clause,[],[f405,f15866]) ).
fof(f15866,plain,
( spl0_615
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f405,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_14) ).
fof(f15669,plain,
spl0_614,
inference(avatar_split_clause,[],[f859,f15667]) ).
fof(f15667,plain,
( spl0_614
<=> ! [X6,X10,X0,X12,X7] : hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f859,plain,
! [X10,X0,X6,X7,X12] : hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f858,f330]) ).
fof(f330,axiom,
! [X0,X20] : c_Collect(X20,X0) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f858,plain,
! [X10,X0,X6,X7,X12] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool))),X0) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f857,f330]) ).
fof(f857,plain,
! [X10,X0,X6,X7,X12] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool))),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),X0),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f720,f330]) ).
fof(f720,plain,
! [X10,X0,X6,X7,X12] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool))),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),X0),c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),X0),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f392,f259,f259,f259]) ).
fof(f259,axiom,
! [X10,X0,X7,X12] : c_Set_Ovimage(X10,X7,X0,X12) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__def_0) ).
fof(f392,axiom,
! [X10,X0,X6,X7,X12] : c_Set_Ovimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool)),X0,X12) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X10,X6,X0,X12),c_Set_Ovimage(X10,X7,X0,X12),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
fof(f15665,plain,
( ~ spl0_13
| spl0_613
| ~ spl0_128
| ~ spl0_590 ),
inference(avatar_split_clause,[],[f14735,f14539,f1801,f15663,f1080]) ).
fof(f14735,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X3,c_HOL_Oundefined(X0),tc_bool)
| ~ c_lessequals(X3,c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_128
| ~ spl0_590 ),
inference(superposition,[],[f1802,f14540]) ).
fof(f15661,plain,
spl0_612,
inference(avatar_split_clause,[],[f856,f15659]) ).
fof(f15659,plain,
( spl0_612
<=> ! [X6,X10,X0,X12,X7] : hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f856,plain,
! [X10,X0,X6,X7,X12] : hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f855,f330]) ).
fof(f855,plain,
! [X10,X0,X6,X7,X12] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool))),X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f854,f330]) ).
fof(f854,plain,
! [X10,X0,X6,X7,X12] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool))),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),X0),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f719,f330]) ).
fof(f719,plain,
! [X10,X0,X6,X7,X12] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool))),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),X0),c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),X0),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f217,f259,f259,f259]) ).
fof(f217,axiom,
! [X10,X0,X6,X7,X12] : c_Set_Ovimage(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool)),X0,X12) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X10,X6,X0,X12),c_Set_Ovimage(X10,X7,X0,X12),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
fof(f15657,plain,
spl0_611,
inference(avatar_split_clause,[],[f853,f15655]) ).
fof(f15655,plain,
( spl0_611
<=> ! [X6,X10,X0,X12,X7] : hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X12,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f853,plain,
! [X10,X0,X6,X7,X12] : hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X12,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f852,f330]) ).
fof(f852,plain,
! [X10,X0,X6,X7,X12] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X12,tc_bool))),X0) = c_HOL_Ominus__class_Ominus(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f851,f330]) ).
fof(f851,plain,
! [X10,X0,X6,X7,X12] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X12,tc_bool))),X0) = c_HOL_Ominus__class_Ominus(c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),X0),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f718,f330]) ).
fof(f718,plain,
! [X10,X0,X6,X7,X12] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X12,tc_bool))),X0) = c_HOL_Ominus__class_Ominus(c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),X0),c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),X0),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f328,f259,f259,f259]) ).
fof(f328,axiom,
! [X10,X0,X6,X7,X12] : c_Set_Ovimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X12,tc_bool)),X0,X12) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X10,X6,X0,X12),c_Set_Ovimage(X10,X7,X0,X12),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
fof(f15629,plain,
spl0_610,
inference(avatar_split_clause,[],[f805,f15627]) ).
fof(f15627,plain,
( spl0_610
<=> ! [X18,X10,X0,X12,X6,X17,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X12,X18)),X17),c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18)))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X18)),c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18)),c_FuncSet_OPi(X6,c_COMBK(X8,tc_fun(X18,tc_bool),X0),X0,X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f805,plain,
! [X10,X0,X18,X8,X6,X7,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X12,X18)),X17),c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18)))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X18)),c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18)),c_FuncSet_OPi(X6,c_COMBK(X8,tc_fun(X18,tc_bool),X0),X0,X18))) ),
inference(definition_unfolding,[],[f621,f231]) ).
fof(f621,axiom,
! [X10,X0,X18,X8,X6,X7,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X12,X18)),X17),c_FuncSet_OPi(X7,c_COMBK(X8,tc_fun(X18,tc_bool),X12),X12,X18)))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X18)),c_FuncSet_Ocompose(X6,X17,X10,X0,X12,X18)),c_FuncSet_OPi(X6,c_COMBK(X8,tc_fun(X18,tc_bool),X0),X0,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__compose_0) ).
fof(f15457,plain,
spl0_609,
inference(avatar_split_clause,[],[f418,f15455]) ).
fof(f15455,plain,
( spl0_609
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f418,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_8) ).
fof(f15453,plain,
spl0_608,
inference(avatar_split_clause,[],[f417,f15451]) ).
fof(f15451,plain,
( spl0_608
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X2 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f417,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X2 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_10) ).
fof(f15440,plain,
spl0_607,
inference(avatar_split_clause,[],[f403,f15438]) ).
fof(f15438,plain,
( spl0_607
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X1 = X2
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f403,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X1 = X2
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_8) ).
fof(f15436,plain,
spl0_606,
inference(avatar_split_clause,[],[f402,f15434]) ).
fof(f15434,plain,
( spl0_606
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X1 = X3
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f402,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X1 = X3
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_10) ).
fof(f15102,plain,
( spl0_605
| ~ spl0_139
| ~ spl0_141
| ~ spl0_410
| ~ spl0_417
| ~ spl0_604 ),
inference(avatar_split_clause,[],[f15098,f15094,f8257,f8229,f1854,f1846,f15100]) ).
fof(f15100,plain,
( spl0_605
<=> ! [X0,X6,X8,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f15094,plain,
( spl0_604
<=> ! [X0,X6,X8,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f15098,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_139
| ~ spl0_141
| ~ spl0_410
| ~ spl0_417
| ~ spl0_604 ),
inference(forward_demodulation,[],[f15097,f9289]) ).
fof(f9289,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_141
| ~ spl0_417 ),
inference(superposition,[],[f8258,f1855]) ).
fof(f15097,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_139
| ~ spl0_410
| ~ spl0_604 ),
inference(forward_demodulation,[],[f15095,f8586]) ).
fof(f8586,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_139
| ~ spl0_410 ),
inference(superposition,[],[f8230,f1847]) ).
fof(f15095,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_604 ),
inference(avatar_component_clause,[],[f15094]) ).
fof(f15096,plain,
spl0_604,
inference(avatar_split_clause,[],[f869,f15094]) ).
fof(f869,plain,
! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f192,f361]) ).
fof(f361,axiom,
! [X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f192,axiom,
! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
fof(f15008,plain,
spl0_603,
inference(avatar_split_clause,[],[f423,f15006]) ).
fof(f15006,plain,
( spl0_603
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X1 = X3
| X1 = X2
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f423,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X1 = X3
| X1 = X2
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_4) ).
fof(f15004,plain,
spl0_602,
inference(avatar_split_clause,[],[f408,f15002]) ).
fof(f15002,plain,
( spl0_602
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X2 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f408,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X2 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_4) ).
fof(f14979,plain,
( ~ spl0_13
| spl0_601
| ~ spl0_64
| ~ spl0_590 ),
inference(avatar_split_clause,[],[f14731,f14539,f1301,f14977,f1080]) ).
fof(f14977,plain,
( spl0_601
<=> ! [X2,X0,X1] : c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),c_HOL_Oundefined(X0),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f14731,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),c_HOL_Oundefined(X0),tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_64
| ~ spl0_590 ),
inference(superposition,[],[f1302,f14540]) ).
fof(f14808,plain,
spl0_600,
inference(avatar_split_clause,[],[f413,f14806]) ).
fof(f14806,plain,
( spl0_600
<=> ! [X37,X4,X2,X1] :
( X2 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f413,axiom,
! [X2,X1,X37,X4] :
( X2 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_2) ).
fof(f14804,plain,
spl0_599,
inference(avatar_split_clause,[],[f412,f14802]) ).
fof(f14802,plain,
( spl0_599
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X2 = X3
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f412,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X2 = X3
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_3) ).
fof(f14800,plain,
spl0_598,
inference(avatar_split_clause,[],[f398,f14798]) ).
fof(f14798,plain,
( spl0_598
<=> ! [X37,X3,X1,X30] :
( X3 = X30
| X1 = X30
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f398,axiom,
! [X3,X1,X37,X30] :
( X3 = X30
| X1 = X30
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_2) ).
fof(f14796,plain,
spl0_597,
inference(avatar_split_clause,[],[f397,f14794]) ).
fof(f14794,plain,
( spl0_597
<=> ! [X37,X4,X3,X2,X1] :
( X3 = X4
| X1 = X4
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f397,axiom,
! [X2,X3,X1,X37,X4] :
( X3 = X4
| X1 = X4
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_3) ).
fof(f14792,plain,
spl0_596,
inference(avatar_split_clause,[],[f274,f14790]) ).
fof(f14790,plain,
( spl0_596
<=> ! [X6,X10,X0,X12,X7] :
( ~ c_Fun_Oinj__on(X10,X7,X0,X12)
| ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12)
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),X0,X12),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f274,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,X7,X0,X12)
| ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12)
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),X0,X12),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
fof(f14673,plain,
spl0_595,
inference(avatar_split_clause,[],[f903,f14671]) ).
fof(f14671,plain,
( spl0_595
<=> ! [X6,X10,X0,X12,X7] :
( c_lessequals(hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X7),tc_fun(X12,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f903,plain,
! [X10,X0,X6,X7,X12] :
( c_lessequals(hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X7),tc_fun(X12,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f902,f330]) ).
fof(f902,plain,
! [X10,X0,X6,X7,X12] :
( c_lessequals(c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),X12),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X7),tc_fun(X12,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f739,f330]) ).
fof(f739,plain,
! [X10,X0,X6,X7,X12] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),X12),c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X7),X12),tc_fun(X12,tc_bool)) ),
inference(definition_unfolding,[],[f194,f259,f259]) ).
fof(f194,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Ovimage(X10,X6,X12,X0),c_Set_Ovimage(X10,X7,X12,X0),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
fof(f14669,plain,
spl0_594,
inference(avatar_split_clause,[],[f652,f14666]) ).
fof(f652,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f14664,plain,
spl0_593,
inference(avatar_split_clause,[],[f298,f14662]) ).
fof(f14662,plain,
( spl0_593
<=> ! [X3,X4,X36,X1] :
( ~ c_Arrow__Order__Mirabelle_Ounanimity(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X3,X4,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f298,axiom,
! [X3,X36,X1,X4] :
( ~ c_Arrow__Order__Mirabelle_Ounanimity(X36)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),X1),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X36,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X3,X4,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unanimity__def_0) ).
fof(f14551,plain,
( spl0_592
| ~ spl0_89
| ~ spl0_317
| ~ spl0_591 ),
inference(avatar_split_clause,[],[f14547,f14543,f4702,f1445,f14549]) ).
fof(f14549,plain,
( spl0_592
<=> ! [X10,X0,X12,X6,X3] :
( c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,X12)))
| ~ c_Fun_Oinj__on(X10,X6,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f14543,plain,
( spl0_591
<=> ! [X10,X0,X12,X6,X3] :
( hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),tc_fun(X0,tc_bool)),X0,X12)))
| c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ c_Fun_Oinj__on(X10,X6,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f14547,plain,
( ! [X3,X10,X0,X6,X12] :
( c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,X12)))
| ~ c_Fun_Oinj__on(X10,X6,X0,X12) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_591 ),
inference(forward_demodulation,[],[f14546,f5265]) ).
fof(f14546,plain,
( ! [X3,X10,X0,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,X12)))
| c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ c_Fun_Oinj__on(X10,X6,X0,X12) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_591 ),
inference(forward_demodulation,[],[f14544,f5265]) ).
fof(f14544,plain,
( ! [X3,X10,X0,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),tc_fun(X0,tc_bool)),X0,X12)))
| c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ c_Fun_Oinj__on(X10,X6,X0,X12) )
| ~ spl0_591 ),
inference(avatar_component_clause,[],[f14543]) ).
fof(f14545,plain,
spl0_591,
inference(avatar_split_clause,[],[f994,f14543]) ).
fof(f994,plain,
! [X3,X10,X0,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),tc_fun(X0,tc_bool)),X0,X12)))
| c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ c_Fun_Oinj__on(X10,X6,X0,X12) ),
inference(forward_demodulation,[],[f993,f330]) ).
fof(f993,plain,
! [X3,X10,X0,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),tc_fun(X0,tc_bool)),X0,X12)))
| c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ c_Fun_Oinj__on(X10,X6,X0,X12) ),
inference(forward_demodulation,[],[f992,f33]) ).
fof(f33,axiom,
! [X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f992,plain,
! [X3,X10,X0,X6,X12] :
( c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0,X12))) ),
inference(forward_demodulation,[],[f788,f330]) ).
fof(f788,plain,
! [X3,X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X6,tc_fun(X0,tc_bool)),X0,X12)
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0,X12))) ),
inference(definition_unfolding,[],[f310,f240,f240]) ).
fof(f240,axiom,
! [X3,X0,X7] : c_Set_Oinsert(X3,X7,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
fof(f310,axiom,
! [X3,X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(X10,c_Set_Oinsert(X3,X6,X0),X0,X12)
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
fof(f14541,plain,
( ~ spl0_13
| spl0_590
| ~ spl0_12
| ~ spl0_13
| ~ spl0_96
| ~ spl0_551 ),
inference(avatar_split_clause,[],[f14362,f13181,f1477,f1080,f1075,f14539,f1080]) ).
fof(f13181,plain,
( spl0_551
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_HOL_Oundefined(X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),c_HOL_Oundefined(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f14362,plain,
( ! [X2,X0,X1] :
( c_HOL_Oundefined(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oundefined(X0),c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_12
| ~ spl0_13
| ~ spl0_96
| ~ spl0_551 ),
inference(forward_demodulation,[],[f14360,f1581]) ).
fof(f14360,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_bool)
| c_HOL_Oundefined(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,tc_bool),tc_bool),c_HOL_Oundefined(X0),tc_bool) )
| ~ spl0_12
| ~ spl0_551 ),
inference(resolution,[],[f13182,f1077]) ).
fof(f13182,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_HOL_Oundefined(X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),c_HOL_Oundefined(X2),X0) )
| ~ spl0_551 ),
inference(avatar_component_clause,[],[f13181]) ).
fof(f14533,plain,
spl0_589,
inference(avatar_split_clause,[],[f976,f14531]) ).
fof(f14531,plain,
( spl0_589
<=> ! [X4,X0,X14,X3,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X3 = X14
| X3 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f976,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X3 = X14
| X3 = X15 ),
inference(forward_demodulation,[],[f975,f330]) ).
fof(f975,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X3 = X14
| X3 = X15 ),
inference(forward_demodulation,[],[f974,f330]) ).
fof(f974,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X3 = X14
| X3 = X15 ),
inference(forward_demodulation,[],[f973,f33]) ).
fof(f973,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X3 = X14
| X3 = X15 ),
inference(forward_demodulation,[],[f972,f330]) ).
fof(f972,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X3 = X14
| X3 = X15 ),
inference(forward_demodulation,[],[f971,f330]) ).
fof(f971,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),X0),tc_fun(X0,tc_bool))
| X3 = X14
| X3 = X15 ),
inference(forward_demodulation,[],[f782,f33]) ).
fof(f782,plain,
! [X3,X0,X14,X4,X15] :
( X3 = X14
| X3 = X15
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f491,f240,f240,f240,f240]) ).
fof(f491,axiom,
! [X3,X0,X14,X4,X15] :
( X3 = X14
| X3 = X15
| c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X14,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
fof(f14521,plain,
( spl0_588
| ~ spl0_89
| ~ spl0_317
| ~ spl0_587 ),
inference(avatar_split_clause,[],[f14517,f14511,f4702,f1445,f14519]) ).
fof(f14511,plain,
( spl0_587
<=> ! [X4,X0,X14,X3,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f14517,plain,
( ! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X14),hAPP(c_fequal(X0),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_587 ),
inference(forward_demodulation,[],[f14516,f5265]) ).
fof(f14516,plain,
( ! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X14),hAPP(c_fequal(X0),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_587 ),
inference(forward_demodulation,[],[f14515,f5265]) ).
fof(f14515,plain,
( ! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X14),hAPP(c_fequal(X0),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_587 ),
inference(forward_demodulation,[],[f14514,f5265]) ).
fof(f14514,plain,
( ! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_fequal(X0),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_587 ),
inference(forward_demodulation,[],[f14512,f5265]) ).
fof(f14512,plain,
( ! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 )
| ~ spl0_587 ),
inference(avatar_component_clause,[],[f14511]) ).
fof(f14513,plain,
spl0_587,
inference(avatar_split_clause,[],[f970,f14511]) ).
fof(f970,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 ),
inference(forward_demodulation,[],[f969,f330]) ).
fof(f969,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 ),
inference(forward_demodulation,[],[f968,f330]) ).
fof(f968,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 ),
inference(forward_demodulation,[],[f967,f33]) ).
fof(f967,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 ),
inference(forward_demodulation,[],[f966,f330]) ).
fof(f966,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 ),
inference(forward_demodulation,[],[f965,f330]) ).
fof(f965,plain,
! [X3,X0,X14,X4,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),X0),tc_fun(X0,tc_bool))
| X4 = X15
| X3 = X15 ),
inference(forward_demodulation,[],[f781,f33]) ).
fof(f781,plain,
! [X3,X0,X14,X4,X15] :
( X4 = X15
| X3 = X15
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X15),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f493,f240,f240,f240,f240]) ).
fof(f493,axiom,
! [X3,X0,X14,X4,X15] :
( X4 = X15
| X3 = X15
| c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X14,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
fof(f14417,plain,
( spl0_586
| ~ spl0_89
| ~ spl0_317
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f14413,f14409,f4702,f1445,f14415]) ).
fof(f14409,plain,
( spl0_585
<=> ! [X2,X10,X0,X12,X6,X1] :
( c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f14413,plain,
( ! [X2,X10,X0,X1,X6,X12] :
( c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X12),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_585 ),
inference(forward_demodulation,[],[f14412,f5265]) ).
fof(f14412,plain,
( ! [X2,X10,X0,X1,X6,X12] :
( c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X12),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_585 ),
inference(forward_demodulation,[],[f14410,f5265]) ).
fof(f14410,plain,
( ! [X2,X10,X0,X1,X6,X12] :
( c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) )
| ~ spl0_585 ),
inference(avatar_component_clause,[],[f14409]) ).
fof(f14411,plain,
spl0_585,
inference(avatar_split_clause,[],[f927,f14409]) ).
fof(f927,plain,
! [X2,X10,X0,X1,X6,X12] :
( c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) ),
inference(forward_demodulation,[],[f926,f330]) ).
fof(f926,plain,
! [X2,X10,X0,X1,X6,X12] :
( c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X0),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X1),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) ),
inference(forward_demodulation,[],[f925,f330]) ).
fof(f925,plain,
! [X2,X10,X0,X1,X6,X12] :
( c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X0),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X1),X12),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6)) ),
inference(forward_demodulation,[],[f756,f33]) ).
fof(f756,plain,
! [X2,X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X0),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X1),X12),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f269,f240,f240]) ).
fof(f269,axiom,
! [X2,X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) = c_Set_Oinsert(X2,c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)),X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
fof(f14407,plain,
spl0_584,
inference(avatar_split_clause,[],[f804,f14405]) ).
fof(f804,plain,
! [X10,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12)))
| c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_COMBI(X12),X7,X12,X12),X10,X12,X12,X0),X6,X0,X12) = X10
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
inference(definition_unfolding,[],[f311,f231]) ).
fof(f311,axiom,
! [X10,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12)))
| c_FuncSet_Ocompose(X6,c_FuncSet_Orestrict(c_COMBI(X12),X7,X12,X12),X10,X0,X12,X12) = X10
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__compose_0) ).
fof(f14403,plain,
spl0_583,
inference(avatar_split_clause,[],[f803,f14401]) ).
fof(f803,plain,
! [X0,X6,X7,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_Oextensional(X6,X0,X12)))
| c_FuncSet_Orestrict(c_COMBB(X17,c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0),X0,X12,X0),X6,X0,X12) = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
inference(definition_unfolding,[],[f312,f231]) ).
fof(f312,axiom,
! [X0,X6,X7,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_Oextensional(X6,X0,X12)))
| c_FuncSet_Ocompose(X6,X17,c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0),X0,X0,X12) = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compose__Id_0) ).
fof(f14174,plain,
spl0_582,
inference(avatar_split_clause,[],[f813,f14172]) ).
fof(f14172,plain,
( spl0_582
<=> ! [X37,X3,X30,X1] :
( X1 = X3
| X1 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f813,plain,
! [X3,X1,X37,X30] :
( X1 = X3
| X1 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X1))) ),
inference(duplicate_literal_removal,[],[f411]) ).
fof(f411,axiom,
! [X3,X1,X37,X30] :
( X1 = X3
| X1 = X30
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_6) ).
fof(f14170,plain,
spl0_581,
inference(avatar_split_clause,[],[f812,f14168]) ).
fof(f14168,plain,
( spl0_581
<=> ! [X37,X3,X1,X30] :
( X1 = X30
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f812,plain,
! [X3,X1,X37,X30] :
( X1 = X30
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X1))) ),
inference(duplicate_literal_removal,[],[f395]) ).
fof(f395,axiom,
! [X3,X1,X37,X30] :
( X1 = X30
| X1 = X3
| X1 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_7) ).
fof(f14166,plain,
spl0_580,
inference(avatar_split_clause,[],[f811,f14164]) ).
fof(f14164,plain,
( spl0_580
<=> ! [X37,X4,X2,X1] :
( X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f811,plain,
! [X2,X1,X37,X4] :
( X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X4))) ),
inference(duplicate_literal_removal,[],[f410]) ).
fof(f410,axiom,
! [X2,X1,X37,X4] :
( X1 = X2
| X1 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_7) ).
fof(f14162,plain,
spl0_579,
inference(avatar_split_clause,[],[f810,f14160]) ).
fof(f14160,plain,
( spl0_579
<=> ! [X2,X37,X4,X1] :
( X1 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X1,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f810,plain,
! [X2,X1,X37,X4] :
( X1 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X1,X4))) ),
inference(duplicate_literal_removal,[],[f396]) ).
fof(f396,axiom,
! [X2,X1,X37,X4] :
( X1 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X1,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_6) ).
fof(f14158,plain,
spl0_578,
inference(avatar_split_clause,[],[f422,f14156]) ).
fof(f14156,plain,
( spl0_578
<=> ! [X37,X4,X30,X1] :
( X1 = X30
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f422,axiom,
! [X1,X37,X4,X30] :
( X1 = X30
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_9) ).
fof(f14154,plain,
( spl0_577
| ~ spl0_297
| ~ spl0_475 ),
inference(avatar_split_clause,[],[f10966,f10897,f4490,f14152]) ).
fof(f14152,plain,
( spl0_577
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),c_HOL_Oundefined(X1)),c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),X3,X4,X0)))
| ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f10897,plain,
( spl0_475
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X4,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),c_HOL_Oundefined(X1)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f10966,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),c_HOL_Oundefined(X1)),c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),X3,X4,X0)))
| ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) )
| ~ spl0_297
| ~ spl0_475 ),
inference(resolution,[],[f10898,f4491]) ).
fof(f10898,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X4,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),c_HOL_Oundefined(X1)),X4)) )
| ~ spl0_475 ),
inference(avatar_component_clause,[],[f10897]) ).
fof(f14150,plain,
spl0_576,
inference(avatar_split_clause,[],[f407,f14148]) ).
fof(f14148,plain,
( spl0_576
<=> ! [X37,X3,X2,X1] :
( X1 = X2
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f407,axiom,
! [X2,X3,X1,X37] :
( X1 = X2
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_9) ).
fof(f14104,plain,
( spl0_575
| ~ spl0_89
| ~ spl0_317
| ~ spl0_574 ),
inference(avatar_split_clause,[],[f14100,f14097,f4702,f1445,f14102]) ).
fof(f14102,plain,
( spl0_575
<=> ! [X0,X6,X1,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X7,tc_fun(X0,tc_bool))
| X6 = X7
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f14097,plain,
( spl0_574
<=> ! [X0,X6,X1,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X7,tc_fun(X0,tc_bool))
| X6 = X7
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f14100,plain,
( ! [X0,X1,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X7,tc_fun(X0,tc_bool))
| X6 = X7
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_574 ),
inference(forward_demodulation,[],[f14098,f5265]) ).
fof(f14098,plain,
( ! [X0,X1,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X7,tc_fun(X0,tc_bool))
| X6 = X7
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_574 ),
inference(avatar_component_clause,[],[f14097]) ).
fof(f14099,plain,
spl0_574,
inference(avatar_split_clause,[],[f1018,f14097]) ).
fof(f1018,plain,
! [X0,X1,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X7,tc_fun(X0,tc_bool))
| X6 = X7
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ),
inference(forward_demodulation,[],[f806,f330]) ).
fof(f806,plain,
! [X0,X1,X6,X7] :
( X6 = X7
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X6,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X7,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f572,f240,f240]) ).
fof(f572,axiom,
! [X0,X1,X6,X7] :
( X6 = X7
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_Set_Oinsert(X1,X6,X0) != c_Set_Oinsert(X1,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f13997,plain,
( spl0_573
| ~ spl0_89
| ~ spl0_317
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f13993,f13990,f4702,f1445,f13995]) ).
fof(f13990,plain,
( spl0_572
<=> ! [X0,X6,X1,X7] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f13993,plain,
( ! [X0,X1,X6,X7] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_572 ),
inference(forward_demodulation,[],[f13991,f5265]) ).
fof(f13991,plain,
( ! [X0,X1,X6,X7] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_572 ),
inference(avatar_component_clause,[],[f13990]) ).
fof(f13992,plain,
spl0_572,
inference(avatar_split_clause,[],[f935,f13990]) ).
fof(f935,plain,
! [X0,X1,X6,X7] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ),
inference(forward_demodulation,[],[f763,f330]) ).
fof(f763,plain,
! [X0,X1,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f386,f240,f240]) ).
fof(f386,axiom,
! [X0,X1,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X7,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
fof(f13884,plain,
( spl0_571
| ~ spl0_89
| ~ spl0_317
| ~ spl0_569 ),
inference(avatar_split_clause,[],[f13876,f13873,f4702,f1445,f13882]) ).
fof(f13882,plain,
( spl0_571
<=> ! [X0,X3,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f13873,plain,
( spl0_569
<=> ! [X0,X3,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f13876,plain,
( ! [X3,X0,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_569 ),
inference(forward_demodulation,[],[f13874,f5265]) ).
fof(f13874,plain,
( ! [X3,X0,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) )
| ~ spl0_569 ),
inference(avatar_component_clause,[],[f13873]) ).
fof(f13880,plain,
( spl0_570
| ~ spl0_122
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4462,f4154,f1647,f13878]) ).
fof(f13878,plain,
( spl0_570
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_HOL_Oundefined(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),c_HOL_Oundefined(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f4154,plain,
( spl0_289
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_HOL_Oundefined(X0),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f4462,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_HOL_Oundefined(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),c_HOL_Oundefined(X2),X0) )
| ~ spl0_122
| ~ spl0_289 ),
inference(resolution,[],[f4155,f1648]) ).
fof(f4155,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Oundefined(X0),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f4154]) ).
fof(f13875,plain,
spl0_569,
inference(avatar_split_clause,[],[f922,f13873]) ).
fof(f922,plain,
! [X3,X0,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) ),
inference(forward_demodulation,[],[f754,f330]) ).
fof(f754,plain,
! [X3,X0,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X8))
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f506,f240,f240]) ).
fof(f506,axiom,
! [X3,X0,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X8))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X7,X0),X8,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
fof(f13782,plain,
( spl0_568
| ~ spl0_89
| ~ spl0_317
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f13778,f13775,f4702,f1445,f13780]) ).
fof(f13780,plain,
( spl0_568
<=> ! [X0,X6,X3,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f13775,plain,
( spl0_567
<=> ! [X0,X6,X3,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f13778,plain,
( ! [X3,X0,X6,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_567 ),
inference(forward_demodulation,[],[f13776,f5265]) ).
fof(f13776,plain,
( ! [X3,X0,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_567 ),
inference(avatar_component_clause,[],[f13775]) ).
fof(f13777,plain,
spl0_567,
inference(avatar_split_clause,[],[f921,f13775]) ).
fof(f921,plain,
! [X3,X0,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ),
inference(forward_demodulation,[],[f753,f330]) ).
fof(f753,plain,
! [X3,X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f507,f240,f240]) ).
fof(f507,axiom,
! [X3,X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oinsert(X3,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
fof(f13773,plain,
spl0_566,
inference(avatar_split_clause,[],[f487,f13771]) ).
fof(f13771,plain,
( spl0_566
<=> ! [X17,X10,X0,X6,X12] :
( X10 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_Oextensional(X6,X0,X12)))
| hAPP(X10,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X6,X10,X17,X0,X12)) != hAPP(X17,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X6,X10,X17,X0,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f487,axiom,
! [X10,X0,X6,X17,X12] :
( X10 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_Oextensional(X6,X0,X12)))
| hAPP(X10,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X6,X10,X17,X0,X12)) != hAPP(X17,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X6,X10,X17,X0,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extensionalityI_1) ).
fof(f13745,plain,
spl0_565,
inference(avatar_split_clause,[],[f414,f13743]) ).
fof(f13743,plain,
( spl0_565
<=> ! [X37,X4,X30,X1] :
( X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f414,axiom,
! [X1,X37,X4,X30] :
( X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_1) ).
fof(f13741,plain,
spl0_564,
inference(avatar_split_clause,[],[f399,f13739]) ).
fof(f13739,plain,
( spl0_564
<=> ! [X37,X3,X2,X1] :
( X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f399,axiom,
! [X2,X3,X1,X37] :
( X1 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_1) ).
fof(f13700,plain,
( spl0_563
| ~ spl0_120
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4461,f4154,f1639,f13698]) ).
fof(f4461,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_HOL_Oundefined(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oundefined(X1),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),X0) )
| ~ spl0_120
| ~ spl0_289 ),
inference(resolution,[],[f4155,f1640]) ).
fof(f13579,plain,
spl0_562,
inference(avatar_split_clause,[],[f1017,f13577]) ).
fof(f13577,plain,
( spl0_562
<=> ! [X10,X0,X12,X6,X7] :
( c_lessequals(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),X6,tc_fun(X0,tc_bool))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ c_lessequals(X7,c_Set_Oimage(X10,X6,X0,X12),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f1017,plain,
! [X10,X0,X6,X7,X12] :
( c_lessequals(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),X6,tc_fun(X0,tc_bool))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ c_lessequals(X7,c_Set_Oimage(X10,X6,X0,X12),tc_fun(X12,tc_bool)) ),
inference(forward_demodulation,[],[f802,f330]) ).
fof(f802,plain,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ c_lessequals(X7,c_Set_Oimage(X10,X6,X0,X12),tc_fun(X12,tc_bool))
| c_lessequals(c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),X0),X6,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f261,f259]) ).
fof(f261,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ c_lessequals(X7,c_Set_Oimage(X10,X6,X0,X12),tc_fun(X12,tc_bool))
| c_lessequals(c_Set_Ovimage(X10,X7,X0,X12),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
fof(f13541,plain,
( spl0_561
| ~ spl0_89
| ~ spl0_317
| ~ spl0_560 ),
inference(avatar_split_clause,[],[f13537,f13533,f4702,f1445,f13539]) ).
fof(f13539,plain,
( spl0_561
<=> ! [X10,X0,X12,X6,X3] :
( ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f13533,plain,
( spl0_560
<=> ! [X10,X0,X12,X6,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),tc_fun(X0,tc_bool)),X0,X12)))
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f13537,plain,
( ! [X3,X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,X12))) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_560 ),
inference(forward_demodulation,[],[f13536,f5265]) ).
fof(f13536,plain,
( ! [X3,X10,X0,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,X12)))
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_560 ),
inference(forward_demodulation,[],[f13534,f5265]) ).
fof(f13534,plain,
( ! [X3,X10,X0,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),tc_fun(X0,tc_bool)),X0,X12)))
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12) )
| ~ spl0_560 ),
inference(avatar_component_clause,[],[f13533]) ).
fof(f13535,plain,
spl0_560,
inference(avatar_split_clause,[],[f941,f13533]) ).
fof(f941,plain,
! [X3,X10,X0,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),tc_fun(X0,tc_bool)),X0,X12)))
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12) ),
inference(forward_demodulation,[],[f940,f330]) ).
fof(f940,plain,
! [X3,X10,X0,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),tc_fun(X0,tc_bool)),X0,X12)))
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12) ),
inference(forward_demodulation,[],[f939,f33]) ).
fof(f939,plain,
! [X3,X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0,X12))) ),
inference(forward_demodulation,[],[f766,f330]) ).
fof(f766,plain,
! [X3,X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X6,tc_fun(X0,tc_bool)),X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0,X12))) ),
inference(definition_unfolding,[],[f384,f240,f240]) ).
fof(f384,axiom,
! [X3,X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,c_Set_Oinsert(X3,X6,X0),X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
fof(f13531,plain,
spl0_559,
inference(avatar_split_clause,[],[f249,f13529]) ).
fof(f13529,plain,
( spl0_559
<=> ! [X6,X10,X0,X12,X8,X7] :
( ~ c_Fun_Oinj__on(X10,X8,X0,X12)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f249,axiom,
! [X10,X0,X8,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,X8,X0,X12)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
fof(f13527,plain,
spl0_558,
inference(avatar_split_clause,[],[f244,f13525]) ).
fof(f13525,plain,
( spl0_558
<=> ! [X6,X10,X0,X12,X8,X7] :
( ~ c_Fun_Oinj__on(X10,X8,X0,X12)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_Set_Oimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0,X12) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f244,axiom,
! [X10,X0,X8,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,X8,X0,X12)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_Set_Oimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0,X12) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
fof(f13366,plain,
( spl0_557
| ~ spl0_119
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f4310,f4110,f1635,f13364]) ).
fof(f13364,plain,
( spl0_557
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_HOL_Oundefined(X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oundefined(X1),c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f4110,plain,
( spl0_278
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3),c_HOL_Oundefined(X1),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f4310,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_HOL_Oundefined(X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oundefined(X1),c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),X0) )
| ~ spl0_119
| ~ spl0_278 ),
inference(resolution,[],[f4111,f1636]) ).
fof(f4111,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3),c_HOL_Oundefined(X1),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f4110]) ).
fof(f13362,plain,
spl0_556,
inference(avatar_split_clause,[],[f629,f13360]) ).
fof(f13360,plain,
( spl0_556
<=> ! [X2,X37,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f629,axiom,
! [X2,X1,X37] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
fof(f13358,plain,
spl0_555,
inference(avatar_split_clause,[],[f105,f13356]) ).
fof(f13356,plain,
( spl0_555
<=> ! [X6,X10,X0,X12,X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),c_Set_Oimage(X10,X6,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X2),c_Set_Oimage(X10,X6,X0,X12)))
| hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f105,axiom,
! [X2,X10,X0,X1,X6,X12] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),c_Set_Oimage(X10,X6,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X2),c_Set_Oimage(X10,X6,X0,X12)))
| hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).
fof(f13242,plain,
spl0_554,
inference(avatar_split_clause,[],[f610,f13240]) ).
fof(f13240,plain,
( spl0_554
<=> ! [X17,X10,X0,X6,X12] :
( X10 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_Oextensional(X6,X0,X12)))
| hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X6,X10,X17,X0,X12)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f610,axiom,
! [X10,X0,X6,X17,X12] :
( X10 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X17),c_FuncSet_Oextensional(X6,X0,X12)))
| hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X6,X10,X17,X0,X12)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extensionalityI_0) ).
fof(f13238,plain,
spl0_553,
inference(avatar_split_clause,[],[f273,f13236]) ).
fof(f273,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12)
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),X0,X12),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
fof(f13188,plain,
spl0_552,
inference(avatar_split_clause,[],[f958,f13186]) ).
fof(f13186,plain,
( spl0_552
<=> ! [X40,X38,X3,X39,X0,X44,X45,X4,X41,X42,X43] :
( hAPP(hAPP(X44,X3),X4) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f958,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X4,X42,X43] :
( hAPP(hAPP(X44,X3),X4) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f957,f330]) ).
fof(f957,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X4,X42,X43] :
( hAPP(hAPP(X44,X3),X4) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f956,f330]) ).
fof(f956,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X4,X42,X43] :
( hAPP(hAPP(X44,X3),X4) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f777,f33]) ).
fof(f777,plain,
! [X40,X38,X41,X39,X0,X3,X44,X45,X4,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(hAPP(X44,X3),X4) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))) ),
inference(definition_unfolding,[],[f346,f240,f240]) ).
fof(f346,axiom,
! [X40,X38,X41,X39,X0,X3,X44,X45,X4,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(X38,c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)) = hAPP(hAPP(X44,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
fof(f13183,plain,
( spl0_551
| ~ spl0_116
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f4309,f4110,f1622,f13181]) ).
fof(f4309,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_HOL_Oundefined(X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X0),c_HOL_Oundefined(X2),X0) )
| ~ spl0_116
| ~ spl0_278 ),
inference(resolution,[],[f4111,f1623]) ).
fof(f13179,plain,
( spl0_550
| ~ spl0_89
| ~ spl0_317
| ~ spl0_549 ),
inference(avatar_split_clause,[],[f13175,f13171,f4702,f1445,f13177]) ).
fof(f13177,plain,
( spl0_550
<=> ! [X40,X38,X3,X39,X0,X44,X45,X4,X41,X42,X43] :
( hAPP(hAPP(X43,X3),X4) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f13171,plain,
( spl0_549
<=> ! [X40,X38,X3,X39,X0,X44,X45,X4,X41,X42,X43] :
( hAPP(hAPP(X43,X3),X4) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f13175,plain,
( ! [X40,X38,X3,X41,X0,X39,X44,X45,X4,X42,X43] :
( hAPP(hAPP(X43,X3),X4) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_549 ),
inference(forward_demodulation,[],[f13174,f5265]) ).
fof(f13174,plain,
( ! [X40,X38,X3,X41,X0,X39,X44,X45,X4,X42,X43] :
( hAPP(hAPP(X43,X3),X4) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_549 ),
inference(forward_demodulation,[],[f13172,f5265]) ).
fof(f13172,plain,
( ! [X40,X38,X3,X41,X0,X39,X44,X45,X4,X42,X43] :
( hAPP(hAPP(X43,X3),X4) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) )
| ~ spl0_549 ),
inference(avatar_component_clause,[],[f13171]) ).
fof(f13173,plain,
spl0_549,
inference(avatar_split_clause,[],[f955,f13171]) ).
fof(f955,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X4,X42,X43] :
( hAPP(hAPP(X43,X3),X4) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f954,f330]) ).
fof(f954,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X4,X42,X43] :
( hAPP(hAPP(X43,X3),X4) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f953,f330]) ).
fof(f953,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X4,X42,X43] :
( hAPP(hAPP(X43,X3),X4) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f776,f33]) ).
fof(f776,plain,
! [X40,X38,X41,X39,X0,X3,X44,X45,X4,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(hAPP(X43,X3),X4) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))) ),
inference(definition_unfolding,[],[f347,f240,f240]) ).
fof(f347,axiom,
! [X40,X38,X41,X39,X0,X3,X44,X45,X4,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(X40,c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)) = hAPP(hAPP(X43,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
fof(f13169,plain,
spl0_548,
inference(avatar_split_clause,[],[f498,f13167]) ).
fof(f13167,plain,
( spl0_548
<=> ! [X20,X7,X12,X6,X0,X1,X30] :
( ~ hBOOL(hAPP(X20,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X30),hAPP(X7,X1)))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X6,X7,X20,X12,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f498,axiom,
! [X0,X1,X6,X7,X12,X30,X20] :
( ~ hBOOL(hAPP(X20,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X30),hAPP(X7,X1)))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X6,X7,X20,X12,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UN_3) ).
fof(f13165,plain,
spl0_547,
inference(avatar_split_clause,[],[f263,f13163]) ).
fof(f13163,plain,
( spl0_547
<=> ! [X10,X0,X12,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_OPi(X6,X7,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__XrestrictI__1__1(X6,X7,X10,X0,X12))),hAPP(X7,c_FuncSet_Osko__FuncSet__XrestrictI__1__1(X6,X7,X10,X0,X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f263,axiom,
! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_OPi(X6,X7,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__XrestrictI__1__1(X6,X7,X10,X0,X12))),hAPP(X7,c_FuncSet_Osko__FuncSet__XrestrictI__1__1(X6,X7,X10,X0,X12)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrictI_1) ).
fof(f13023,plain,
( spl0_546
| ~ spl0_89
| ~ spl0_317
| ~ spl0_545 ),
inference(avatar_split_clause,[],[f13019,f13016,f4702,f1445,f13021]) ).
fof(f13021,plain,
( spl0_546
<=> ! [X5,X6,X10,X0,X12,X2,X1] :
( c_Finite__Set_Ofold__graph(X10,X5,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),hAPP(hAPP(X10,X1),X2),X0,X12)
| ~ c_Finite__Set_Ofold__graph(X10,X5,X6,X2,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f13016,plain,
( spl0_545
<=> ! [X5,X6,X10,X0,X12,X2,X1] :
( c_Finite__Set_Ofold__graph(X10,X5,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),hAPP(hAPP(X10,X1),X2),X0,X12)
| ~ c_Finite__Set_Ofold__graph(X10,X5,X6,X2,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f13019,plain,
( ! [X2,X10,X0,X1,X6,X5,X12] :
( c_Finite__Set_Ofold__graph(X10,X5,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),hAPP(hAPP(X10,X1),X2),X0,X12)
| ~ c_Finite__Set_Ofold__graph(X10,X5,X6,X2,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_545 ),
inference(forward_demodulation,[],[f13017,f5265]) ).
fof(f13017,plain,
( ! [X2,X10,X0,X1,X6,X5,X12] :
( c_Finite__Set_Ofold__graph(X10,X5,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),hAPP(hAPP(X10,X1),X2),X0,X12)
| ~ c_Finite__Set_Ofold__graph(X10,X5,X6,X2,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_545 ),
inference(avatar_component_clause,[],[f13016]) ).
fof(f13018,plain,
spl0_545,
inference(avatar_split_clause,[],[f1016,f13016]) ).
fof(f1016,plain,
! [X2,X10,X0,X1,X6,X5,X12] :
( c_Finite__Set_Ofold__graph(X10,X5,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),hAPP(hAPP(X10,X1),X2),X0,X12)
| ~ c_Finite__Set_Ofold__graph(X10,X5,X6,X2,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f801,f330]) ).
fof(f801,plain,
! [X2,X10,X0,X1,X6,X5,X12] :
( ~ c_Finite__Set_Ofold__graph(X10,X5,X6,X2,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X6,tc_fun(X0,tc_bool)),hAPP(hAPP(X10,X1),X2),X0,X12) ),
inference(definition_unfolding,[],[f97,f240]) ).
fof(f97,axiom,
! [X2,X10,X0,X1,X6,X5,X12] :
( ~ c_Finite__Set_Ofold__graph(X10,X5,X6,X2,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,c_Set_Oinsert(X1,X6,X0),hAPP(hAPP(X10,X1),X2),X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
fof(f12966,plain,
( spl0_544
| ~ spl0_89
| ~ spl0_317
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f12962,f12959,f4702,f1445,f12964]) ).
fof(f12964,plain,
( spl0_544
<=> ! [X5,X6,X10,X0,X12,X2,X1] :
( ~ c_Finite__Set_Ofold__graph(X10,X5,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X2,X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,X6,hAPP(hAPP(X10,X1),X2),X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f12959,plain,
( spl0_543
<=> ! [X5,X6,X10,X0,X12,X2,X1] :
( ~ c_Finite__Set_Ofold__graph(X10,X5,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)),X2,X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,X6,hAPP(hAPP(X10,X1),X2),X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f12962,plain,
( ! [X2,X10,X0,X1,X6,X5,X12] :
( ~ c_Finite__Set_Ofold__graph(X10,X5,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),X2,X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,X6,hAPP(hAPP(X10,X1),X2),X0,X12) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_543 ),
inference(forward_demodulation,[],[f12960,f5265]) ).
fof(f12960,plain,
( ! [X2,X10,X0,X1,X6,X5,X12] :
( ~ c_Finite__Set_Ofold__graph(X10,X5,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)),X2,X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,X6,hAPP(hAPP(X10,X1),X2),X0,X12) )
| ~ spl0_543 ),
inference(avatar_component_clause,[],[f12959]) ).
fof(f12961,plain,
spl0_543,
inference(avatar_split_clause,[],[f1015,f12959]) ).
fof(f1015,plain,
! [X2,X10,X0,X1,X6,X5,X12] :
( ~ c_Finite__Set_Ofold__graph(X10,X5,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)),X2,X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,X6,hAPP(hAPP(X10,X1),X2),X0,X12) ),
inference(forward_demodulation,[],[f1014,f330]) ).
fof(f1014,plain,
! [X2,X10,X0,X1,X6,X5,X12] :
( ~ c_Finite__Set_Ofold__graph(X10,X5,c_HOL_Ominus__class_Ominus(X6,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),tc_fun(X0,tc_bool)),X2,X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,X6,hAPP(hAPP(X10,X1),X2),X0,X12) ),
inference(forward_demodulation,[],[f800,f33]) ).
fof(f800,plain,
! [X2,X10,X0,X1,X6,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,X6,hAPP(hAPP(X10,X1),X2),X0,X12)
| ~ c_Finite__Set_Ofold__graph(X10,X5,c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X2,X0,X12) ),
inference(definition_unfolding,[],[f252,f240]) ).
fof(f252,axiom,
! [X2,X10,X0,X1,X6,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Finite__Set_Ofold__graph(X10,X5,X6,hAPP(hAPP(X10,X1),X2),X0,X12)
| ~ c_Finite__Set_Ofold__graph(X10,X5,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X2,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
fof(f12939,plain,
( spl0_542
| ~ spl0_89
| ~ spl0_317
| ~ spl0_541 ),
inference(avatar_split_clause,[],[f12935,f12932,f4702,f1445,f12937]) ).
fof(f12932,plain,
( spl0_541
<=> ! [X4,X0,X12,X3,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X4))))
| hAPP(X10,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f12935,plain,
( ! [X3,X10,X0,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),hAPP(c_fequal(X12),X4))))
| hAPP(X10,X3) = X4 )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_541 ),
inference(forward_demodulation,[],[f12933,f5265]) ).
fof(f12933,plain,
( ! [X3,X10,X0,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X4))))
| hAPP(X10,X3) = X4 )
| ~ spl0_541 ),
inference(avatar_component_clause,[],[f12932]) ).
fof(f12934,plain,
spl0_541,
inference(avatar_split_clause,[],[f894,f12932]) ).
fof(f894,plain,
! [X3,X10,X0,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X4))))
| hAPP(X10,X3) = X4 ),
inference(forward_demodulation,[],[f893,f330]) ).
fof(f893,plain,
! [X3,X10,X0,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X4),X12))))
| hAPP(X10,X3) = X4 ),
inference(forward_demodulation,[],[f892,f33]) ).
fof(f892,plain,
! [X3,X10,X0,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X4),X12),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)))))
| hAPP(X10,X3) = X4 ),
inference(forward_demodulation,[],[f734,f330]) ).
fof(f734,plain,
! [X3,X10,X0,X4,X12] :
( hAPP(X10,X3) = X4
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X4),X12),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool))),X0))) ),
inference(definition_unfolding,[],[f510,f259,f240]) ).
fof(f510,axiom,
! [X3,X10,X0,X4,X12] :
( hAPP(X10,X3) = X4
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Set_Ovimage(X10,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
fof(f12930,plain,
spl0_540,
inference(avatar_split_clause,[],[f849,f12928]) ).
fof(f12928,plain,
( spl0_540
<=> ! [X10,X0,X12,X6] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f849,plain,
! [X10,X0,X6,X12] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),X12,X0),
inference(forward_demodulation,[],[f716,f330]) ).
fof(f716,plain,
! [X10,X0,X6,X12] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),X12),X12,X0),
inference(definition_unfolding,[],[f480,f259]) ).
fof(f480,axiom,
! [X10,X0,X6,X12] : c_Set_Oimage(X10,c_Set_Ovimage(X10,X6,X12,X0),X12,X0) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
fof(f12787,plain,
( spl0_539
| ~ spl0_89
| ~ spl0_317
| ~ spl0_538 ),
inference(avatar_split_clause,[],[f12783,f12779,f4702,f1445,f12785]) ).
fof(f12779,plain,
( spl0_538
<=> ! [X10,X0,X12,X3,X7] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X7,tc_fun(X12,tc_bool)),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f12783,plain,
( ! [X3,X10,X0,X7,X12] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X12),X3),X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),hAPP(X10,X3)),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool))
| ~ spl0_89
| ~ spl0_317
| ~ spl0_538 ),
inference(forward_demodulation,[],[f12782,f5265]) ).
fof(f12782,plain,
( ! [X3,X10,X0,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X12),X3),X7,tc_fun(X12,tc_bool)),X12,X0)
| ~ spl0_89
| ~ spl0_317
| ~ spl0_538 ),
inference(forward_demodulation,[],[f12780,f5265]) ).
fof(f12780,plain,
( ! [X3,X10,X0,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X7,tc_fun(X12,tc_bool)),X12,X0)
| ~ spl0_538 ),
inference(avatar_component_clause,[],[f12779]) ).
fof(f12781,plain,
spl0_538,
inference(avatar_split_clause,[],[f836,f12779]) ).
fof(f836,plain,
! [X3,X10,X0,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X7,tc_fun(X12,tc_bool)),X12,X0),
inference(forward_demodulation,[],[f835,f330]) ).
fof(f835,plain,
! [X3,X10,X0,X7,X12] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12),X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f707,f330]) ).
fof(f707,plain,
! [X3,X10,X0,X7,X12] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12),X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)),X0),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f508,f240,f240]) ).
fof(f508,axiom,
! [X3,X10,X0,X7,X12] : c_Set_Oimage(X10,c_Set_Oinsert(X3,X7,X12),X12,X0) = c_Set_Oinsert(hAPP(X10,X3),c_Set_Oimage(X10,X7,X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f12749,plain,
spl0_537,
inference(avatar_split_clause,[],[f724,f12747]) ).
fof(f12747,plain,
( spl0_537
<=> ! [X10,X0,X12,X6] : c_FuncSet_Orestrict(c_COMBI(X0),c_Set_Oimage(X10,X6,X12,X0),X0,X0) = c_FuncSet_Orestrict(c_COMBB(X10,c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),c_Set_Oimage(X10,X6,X12,X0),X0,X12),X12,X0,X0),c_Set_Oimage(X10,X6,X12,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f724,plain,
! [X10,X0,X6,X12] : c_FuncSet_Orestrict(c_COMBI(X0),c_Set_Oimage(X10,X6,X12,X0),X0,X0) = c_FuncSet_Orestrict(c_COMBB(X10,c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),c_Set_Oimage(X10,X6,X12,X0),X0,X12),X12,X0,X0),c_Set_Oimage(X10,X6,X12,X0),X0,X0),
inference(definition_unfolding,[],[f265,f231]) ).
fof(f265,axiom,
! [X10,X0,X6,X12] : c_FuncSet_Ocompose(c_Set_Oimage(X10,X6,X12,X0),X10,c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),c_Set_Oimage(X10,X6,X12,X0),X0,X12),X0,X12,X0) = c_FuncSet_Orestrict(c_COMBI(X0),c_Set_Oimage(X10,X6,X12,X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compose__id__inv__into_0) ).
fof(f12745,plain,
spl0_536,
inference(avatar_split_clause,[],[f630,f12743]) ).
fof(f12743,plain,
( spl0_536
<=> ! [X4,X37,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f630,axiom,
! [X3,X37,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
fof(f12637,plain,
( spl0_535
| ~ spl0_89
| ~ spl0_317
| ~ spl0_534 ),
inference(avatar_split_clause,[],[f12633,f12630,f4702,f1445,f12635]) ).
fof(f12635,plain,
( spl0_535
<=> ! [X3,X0,X9,X8] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X8,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f12630,plain,
( spl0_534
<=> ! [X3,X0,X9,X8] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X8,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f12633,plain,
( ! [X3,X0,X8,X9] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X8,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_534 ),
inference(forward_demodulation,[],[f12631,f5265]) ).
fof(f12631,plain,
( ! [X3,X0,X8,X9] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X8,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) )
| ~ spl0_534 ),
inference(avatar_component_clause,[],[f12630]) ).
fof(f12632,plain,
spl0_534,
inference(avatar_split_clause,[],[f900,f12630]) ).
fof(f900,plain,
! [X3,X0,X8,X9] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X8,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f738,f330]) ).
fof(f738,plain,
! [X3,X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X8,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f91,f240,f240]) ).
fof(f91,axiom,
! [X3,X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X3,X8,X0),c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f12621,plain,
( spl0_533
| ~ spl0_89
| ~ spl0_317
| ~ spl0_532 ),
inference(avatar_split_clause,[],[f12617,f12613,f4702,f1445,f12619]) ).
fof(f12613,plain,
( spl0_532
<=> ! [X4,X0,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f12617,plain,
( ! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X3 = X4 )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_532 ),
inference(forward_demodulation,[],[f12616,f5265]) ).
fof(f12616,plain,
( ! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X3 = X4 )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_532 ),
inference(forward_demodulation,[],[f12614,f5265]) ).
fof(f12614,plain,
( ! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X3 = X4 )
| ~ spl0_532 ),
inference(avatar_component_clause,[],[f12613]) ).
fof(f12615,plain,
spl0_532,
inference(avatar_split_clause,[],[f885,f12613]) ).
fof(f885,plain,
! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X3 = X4 ),
inference(forward_demodulation,[],[f884,f330]) ).
fof(f884,plain,
! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X3 = X4 ),
inference(forward_demodulation,[],[f732,f330]) ).
fof(f732,plain,
! [X3,X0,X4] :
( X3 = X4
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f366,f240,f240]) ).
fof(f366,axiom,
! [X3,X0,X4] :
( X3 = X4
| c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f12611,plain,
spl0_531,
inference(avatar_split_clause,[],[f619,f12609]) ).
fof(f12609,plain,
( spl0_531
<=> ! [X6,X10,X0,X12,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X6,X7,X10,X0,X12))),X7))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f619,axiom,
! [X10,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X6,X7,X10,X0,X12))),X7))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__in__funcset_1) ).
fof(f12607,plain,
( spl0_530
| spl0_23
| ~ spl0_526 ),
inference(avatar_split_clause,[],[f12067,f12001,f1130,f12604]) ).
fof(f12604,plain,
( spl0_530
<=> c_Arrow__Order__Mirabelle_OLin = c_HOL_Ominus__class_Ominus(c_Arrow__Order__Mirabelle_OLin,hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f12067,plain,
( c_Arrow__Order__Mirabelle_OLin = c_HOL_Ominus__class_Ominus(c_Arrow__Order__Mirabelle_OLin,hAPP(c_fequal(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| spl0_23
| ~ spl0_526 ),
inference(resolution,[],[f12002,f1132]) ).
fof(f12584,plain,
spl0_529,
inference(avatar_split_clause,[],[f385,f12582]) ).
fof(f385,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X1),X8))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X6,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__disjoint_0) ).
fof(f12094,plain,
spl0_528,
inference(avatar_split_clause,[],[f945,f12092]) ).
fof(f12092,plain,
( spl0_528
<=> ! [X10,X0,X12,X6,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6)))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f945,plain,
! [X3,X10,X0,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6)))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),X6)) ),
inference(forward_demodulation,[],[f770,f330]) ).
fof(f770,plain,
! [X3,X10,X0,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),X0))) ),
inference(definition_unfolding,[],[f583,f259]) ).
fof(f583,axiom,
! [X3,X10,X0,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Set_Ovimage(X10,X6,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
fof(f12090,plain,
spl0_527,
inference(avatar_split_clause,[],[f942,f12088]) ).
fof(f942,plain,
! [X3,X10,X0,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),X7)) ),
inference(forward_demodulation,[],[f767,f330]) ).
fof(f767,plain,
! [X3,X10,X0,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X3),c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X7),X0))) ),
inference(definition_unfolding,[],[f579,f259]) ).
fof(f579,axiom,
! [X3,X10,X0,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X3),c_Set_Ovimage(X10,X7,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
fof(f12003,plain,
( spl0_526
| ~ spl0_89
| ~ spl0_90
| ~ spl0_100
| ~ spl0_317
| ~ spl0_420
| ~ spl0_525 ),
inference(avatar_split_clause,[],[f11999,f11995,f8269,f4702,f1493,f1449,f1445,f12001]) ).
fof(f11995,plain,
( spl0_525
<=> ! [X6,X0,X1] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f11999,plain,
( ! [X0,X1,X6] :
( c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_89
| ~ spl0_90
| ~ spl0_100
| ~ spl0_317
| ~ spl0_420
| ~ spl0_525 ),
inference(forward_demodulation,[],[f11998,f5265]) ).
fof(f11998,plain,
( ! [X0,X1,X6] :
( c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_90
| ~ spl0_100
| ~ spl0_420
| ~ spl0_525 ),
inference(forward_demodulation,[],[f11996,f9606]) ).
fof(f11996,plain,
( ! [X0,X1,X6] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_525 ),
inference(avatar_component_clause,[],[f11995]) ).
fof(f11997,plain,
spl0_525,
inference(avatar_split_clause,[],[f934,f11995]) ).
fof(f934,plain,
! [X0,X1,X6] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f933,f330]) ).
fof(f933,plain,
! [X0,X1,X6] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X6,tc_fun(X0,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f762,f33]) ).
fof(f762,plain,
! [X0,X1,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
inference(definition_unfolding,[],[f390,f240,f240]) ).
fof(f390,axiom,
! [X0,X1,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
fof(f11993,plain,
( spl0_524
| ~ spl0_139
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f11791,f11717,f1846,f11991]) ).
fof(f11991,plain,
( spl0_524
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,tc_fun(X4,tc_bool)),c_HOL_Oundefined(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f11717,plain,
( spl0_508
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),c_HOL_Oundefined(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f11791,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,tc_fun(X4,tc_bool)),c_HOL_Oundefined(X2)))
| ~ spl0_139
| ~ spl0_508 ),
inference(superposition,[],[f11718,f1847]) ).
fof(f11718,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),c_HOL_Oundefined(X2)))
| ~ spl0_508 ),
inference(avatar_component_clause,[],[f11717]) ).
fof(f11989,plain,
spl0_523,
inference(avatar_split_clause,[],[f930,f11987]) ).
fof(f930,plain,
! [X0,X6,X14,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6)
| hBOOL(hAPP(hAPP(c_in(X12),X14),X6)) ),
inference(forward_demodulation,[],[f759,f330]) ).
fof(f759,plain,
! [X0,X6,X14,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),X14),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),X0) ),
inference(definition_unfolding,[],[f616,f259]) ).
fof(f616,axiom,
! [X0,X6,X14,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),X14),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X14,X12,X0),X6,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
fof(f11985,plain,
spl0_522,
inference(avatar_split_clause,[],[f913,f11983]) ).
fof(f913,plain,
! [X0,X6,X14,X12] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6)
| ~ hBOOL(hAPP(hAPP(c_in(X12),X14),X6)) ),
inference(forward_demodulation,[],[f747,f330]) ).
fof(f747,plain,
! [X0,X6,X14,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X14),X6))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),c_COMBK(X14,X12,X0),X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),X6),X0) ),
inference(definition_unfolding,[],[f615,f259]) ).
fof(f615,axiom,
! [X0,X6,X14,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X14),X6))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X14,X12,X0),X6,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).
fof(f11867,plain,
( spl0_521
| ~ spl0_89
| ~ spl0_317
| ~ spl0_520 ),
inference(avatar_split_clause,[],[f11863,f11860,f4702,f1445,f11865]) ).
fof(f11860,plain,
( spl0_520
<=> ! [X0,X12,X6,X3,X7] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X6,tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f11863,plain,
( ! [X3,X0,X6,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X12),X3),X6,tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool))
| ~ spl0_89
| ~ spl0_317
| ~ spl0_520 ),
inference(forward_demodulation,[],[f11861,f5265]) ).
fof(f11861,plain,
( ! [X3,X0,X6,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X6,tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool))
| ~ spl0_520 ),
inference(avatar_component_clause,[],[f11860]) ).
fof(f11862,plain,
spl0_520,
inference(avatar_split_clause,[],[f850,f11860]) ).
fof(f850,plain,
! [X3,X0,X6,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X6,tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f717,f330]) ).
fof(f717,plain,
! [X3,X0,X6,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12),X6,tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f124,f240]) ).
fof(f124,axiom,
! [X3,X0,X6,X7,X12] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X3,X6,X12),X7,X12,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
fof(f11816,plain,
( spl0_519
| ~ spl0_89
| ~ spl0_317
| ~ spl0_518 ),
inference(avatar_split_clause,[],[f11812,f11809,f4702,f1445,f11814]) ).
fof(f11809,plain,
( spl0_518
<=> ! [X10,X11,X0,X3] : hBOOL(hAPP(hAPP(c_in(X11),X3),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X11),X11,tc_fun(X0,tc_bool),tc_bool),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f11812,plain,
( ! [X3,X10,X0,X11] : hBOOL(hAPP(hAPP(c_in(X11),X3),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X11),X11,tc_fun(X0,tc_bool),tc_bool),hAPP(c_fequal(X0),hAPP(X10,X3)))))
| ~ spl0_89
| ~ spl0_317
| ~ spl0_518 ),
inference(forward_demodulation,[],[f11810,f5265]) ).
fof(f11810,plain,
( ! [X3,X10,X0,X11] : hBOOL(hAPP(hAPP(c_in(X11),X3),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X11),X11,tc_fun(X0,tc_bool),tc_bool),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)))))
| ~ spl0_518 ),
inference(avatar_component_clause,[],[f11809]) ).
fof(f11811,plain,
spl0_518,
inference(avatar_split_clause,[],[f841,f11809]) ).
fof(f841,plain,
! [X3,X10,X0,X11] : hBOOL(hAPP(hAPP(c_in(X11),X3),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X11),X11,tc_fun(X0,tc_bool),tc_bool),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3))))),
inference(forward_demodulation,[],[f840,f330]) ).
fof(f840,plain,
! [X3,X10,X0,X11] : hBOOL(hAPP(hAPP(c_in(X11),X3),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X11),X11,tc_fun(X0,tc_bool),tc_bool),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)),X0)))),
inference(forward_demodulation,[],[f839,f33]) ).
fof(f839,plain,
! [X3,X10,X0,X11] : hBOOL(hAPP(hAPP(c_in(X11),X3),hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X11),X11,tc_fun(X0,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))))),
inference(forward_demodulation,[],[f710,f330]) ).
fof(f710,plain,
! [X3,X10,X0,X11] : hBOOL(hAPP(hAPP(c_in(X11),X3),c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X11),X11,tc_fun(X0,tc_bool),tc_bool),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X10,X3)),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),X11))),
inference(definition_unfolding,[],[f336,f259,f240]) ).
fof(f336,axiom,
! [X3,X10,X0,X11] : hBOOL(hAPP(hAPP(c_in(X11),X3),c_Set_Ovimage(X10,c_Set_Oinsert(hAPP(X10,X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X11,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
fof(f11807,plain,
spl0_517,
inference(avatar_split_clause,[],[f647,f11805]) ).
fof(f11805,plain,
( spl0_517
<=> ! [X10,X0,X12,X6,X1,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X1)),X7))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f647,axiom,
! [X10,X0,X1,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X1)),X7))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__mem_0) ).
fof(f11803,plain,
spl0_516,
inference(avatar_split_clause,[],[f618,f11801]) ).
fof(f618,axiom,
! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__in__funcset_0) ).
fof(f11787,plain,
spl0_515,
inference(avatar_split_clause,[],[f611,f11785]) ).
fof(f11785,plain,
( spl0_515
<=> ! [X10,X0,X12,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X6,X7,X10,X0,X12))),hAPP(X7,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X6,X7,X10,X0,X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f611,axiom,
! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X6,X7,X10,X0,X12))),hAPP(X7,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X6,X7,X10,X0,X12)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_1) ).
fof(f11783,plain,
spl0_514,
inference(avatar_split_clause,[],[f609,f11781]) ).
fof(f11781,plain,
( spl0_514
<=> ! [X10,X0,X12,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X6,X7,X10,X0,X12))),hAPP(X7,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X6,X7,X10,X0,X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f609,axiom,
! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X6,X7,X10,X0,X12))),hAPP(X7,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X6,X7,X10,X0,X12)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_1) ).
fof(f11779,plain,
spl0_513,
inference(avatar_split_clause,[],[f550,f11777]) ).
fof(f11777,plain,
( spl0_513
<=> ! [X37,X5,X2,X1] :
( X1 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f550,axiom,
! [X2,X1,X37,X5] :
( X1 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
fof(f11775,plain,
spl0_512,
inference(avatar_split_clause,[],[f549,f11773]) ).
fof(f11773,plain,
( spl0_512
<=> ! [X37,X5,X2,X1] :
( X1 = X5
| X2 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f549,axiom,
! [X2,X1,X37,X5] :
( X1 = X5
| X2 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
fof(f11771,plain,
spl0_511,
inference(avatar_split_clause,[],[f304,f11769]) ).
fof(f11769,plain,
( spl0_511
<=> ! [X37,X5,X2,X1] :
( X2 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f304,axiom,
! [X2,X1,X37,X5] :
( X2 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
fof(f11767,plain,
spl0_510,
inference(avatar_split_clause,[],[f303,f11765]) ).
fof(f11765,plain,
( spl0_510
<=> ! [X37,X5,X2,X1] :
( X2 = X5
| X1 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f303,axiom,
! [X2,X1,X37,X5] :
( X2 = X5
| X1 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
fof(f11763,plain,
spl0_509,
inference(avatar_split_clause,[],[f275,f11761]) ).
fof(f275,axiom,
! [X10,X0,X6,X12] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),c_Set_Oimage(X10,X6,X12,X0),X0,X12)),c_FuncSet_OPi(c_Set_Oimage(X10,X6,X12,X0),c_COMBK(X6,tc_fun(X12,tc_bool),X0),X0,X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__funcset_0) ).
fof(f11719,plain,
( spl0_508
| ~ spl0_113
| ~ spl0_490 ),
inference(avatar_split_clause,[],[f11617,f11207,f1546,f11717]) ).
fof(f11207,plain,
( spl0_490
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(hAPP(c_in(X0),c_HOL_Oundefined(X1)),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Set_Oimage(c_FuncSet_Orestrict(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X0),tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f11617,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),c_HOL_Oundefined(X2)))
| ~ spl0_113
| ~ spl0_490 ),
inference(resolution,[],[f11208,f1547]) ).
fof(f11208,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_in(X0),c_HOL_Oundefined(X1)),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Set_Oimage(c_FuncSet_Orestrict(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X0),tc_fun(X0,tc_bool))))
| ~ spl0_490 ),
inference(avatar_component_clause,[],[f11207]) ).
fof(f11686,plain,
spl0_507,
inference(avatar_split_clause,[],[f952,f11684]) ).
fof(f11684,plain,
( spl0_507
<=> ! [X40,X38,X3,X39,X0,X44,X45,X6,X41,X42,X43] :
( hAPP(hAPP(X43,X3),hAPP(X40,X6)) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f952,plain,
! [X40,X38,X3,X41,X0,X39,X6,X44,X45,X42,X43] :
( hAPP(hAPP(X43,X3),hAPP(X40,X6)) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f775,f330]) ).
fof(f775,plain,
! [X40,X38,X41,X39,X0,X3,X44,X6,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(hAPP(X43,X3),hAPP(X40,X6)) = hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X6,tc_fun(X0,tc_bool))) ),
inference(definition_unfolding,[],[f497,f240]) ).
fof(f497,axiom,
! [X40,X38,X41,X39,X0,X3,X44,X6,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(X40,c_Set_Oinsert(X3,X6,X0)) = hAPP(hAPP(X43,X3),hAPP(X40,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
fof(f11681,plain,
( spl0_506
| ~ spl0_89
| ~ spl0_317
| ~ spl0_505 ),
inference(avatar_split_clause,[],[f11677,f11674,f4702,f1445,f11679]) ).
fof(f11679,plain,
( spl0_506
<=> ! [X40,X38,X3,X39,X0,X44,X45,X6,X41,X42,X43] :
( hAPP(hAPP(X44,X3),hAPP(X38,X6)) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f11674,plain,
( spl0_505
<=> ! [X40,X38,X3,X39,X0,X44,X45,X6,X41,X42,X43] :
( hAPP(hAPP(X44,X3),hAPP(X38,X6)) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f11677,plain,
( ! [X40,X38,X3,X41,X0,X39,X44,X6,X45,X42,X43] :
( hAPP(hAPP(X44,X3),hAPP(X38,X6)) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_505 ),
inference(forward_demodulation,[],[f11675,f5265]) ).
fof(f11675,plain,
( ! [X40,X38,X3,X41,X0,X39,X44,X6,X45,X42,X43] :
( hAPP(hAPP(X44,X3),hAPP(X38,X6)) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) )
| ~ spl0_505 ),
inference(avatar_component_clause,[],[f11674]) ).
fof(f11676,plain,
spl0_505,
inference(avatar_split_clause,[],[f951,f11674]) ).
fof(f951,plain,
! [X40,X38,X3,X41,X0,X39,X44,X6,X45,X42,X43] :
( hAPP(hAPP(X44,X3),hAPP(X38,X6)) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f774,f330]) ).
fof(f774,plain,
! [X40,X38,X41,X39,X0,X3,X44,X6,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(hAPP(X44,X3),hAPP(X38,X6)) = hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X6,tc_fun(X0,tc_bool))) ),
inference(definition_unfolding,[],[f496,f240]) ).
fof(f496,axiom,
! [X40,X38,X41,X39,X0,X3,X44,X6,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(X38,c_Set_Oinsert(X3,X6,X0)) = hAPP(hAPP(X44,X3),hAPP(X38,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
fof(f11672,plain,
spl0_504,
inference(avatar_split_clause,[],[f938,f11670]) ).
fof(f11670,plain,
( spl0_504
<=> ! [X10,X0,X12,X6] :
( hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Set_Oimage(X10,X6,X0,X12)) = X6
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f938,plain,
! [X10,X0,X6,X12] :
( hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Set_Oimage(X10,X6,X0,X12)) = X6
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12) ),
inference(forward_demodulation,[],[f765,f330]) ).
fof(f765,plain,
! [X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Set_Oimage(X10,X6,X0,X12)),X0) = X6 ),
inference(definition_unfolding,[],[f329,f259]) ).
fof(f329,axiom,
! [X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Ovimage(X10,c_Set_Oimage(X10,X6,X0,X12),X0,X12) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
fof(f11668,plain,
spl0_503,
inference(avatar_split_clause,[],[f531,f11666]) ).
fof(f11666,plain,
( spl0_503
<=> ! [X4,X0,X12,X6,X3,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X4),hAPP(X7,X3)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Product__Type_OSigma(X6,X7,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f531,axiom,
! [X3,X0,X6,X7,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X4),hAPP(X7,X3)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Product__Type_OSigma(X6,X7,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
fof(f11664,plain,
spl0_502,
inference(avatar_split_clause,[],[f370,f11662]) ).
fof(f11662,plain,
( spl0_502
<=> ! [X6,X10,X0,X12,X7] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f370,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
fof(f11660,plain,
spl0_501,
inference(avatar_split_clause,[],[f345,f11658]) ).
fof(f11658,plain,
( spl0_501
<=> ! [X6,X10,X0,X12,X7] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0,X12) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f345,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0,X12) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
fof(f11614,plain,
spl0_500,
inference(avatar_split_clause,[],[f257,f11612]) ).
fof(f257,axiom,
! [X2,X10,X0,X11] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11,X0)
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(X10,X2),X10,X0,X11) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X2)),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_1) ).
fof(f11491,plain,
( spl0_499
| ~ spl0_89
| ~ spl0_317
| ~ spl0_498 ),
inference(avatar_split_clause,[],[f11487,f11484,f4702,f1445,f11489]) ).
fof(f11484,plain,
( spl0_498
<=> ! [X0,X3,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f11487,plain,
( ! [X3,X0,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_498 ),
inference(forward_demodulation,[],[f11485,f5265]) ).
fof(f11485,plain,
( ! [X3,X0,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) )
| ~ spl0_498 ),
inference(avatar_component_clause,[],[f11484]) ).
fof(f11486,plain,
spl0_498,
inference(avatar_split_clause,[],[f932,f11484]) ).
fof(f932,plain,
! [X3,X0,X8,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X8)) ),
inference(forward_demodulation,[],[f761,f330]) ).
fof(f761,plain,
! [X3,X0,X8,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X8))
| c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f376,f240]) ).
fof(f376,axiom,
! [X3,X0,X8,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X8))
| c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X7,X0),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
fof(f11391,plain,
( spl0_497
| ~ spl0_89
| ~ spl0_317
| ~ spl0_496 ),
inference(avatar_split_clause,[],[f11387,f11384,f4702,f1445,f11389]) ).
fof(f11384,plain,
( spl0_496
<=> ! [X0,X6,X3,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f11387,plain,
( ! [X3,X0,X6,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_496 ),
inference(forward_demodulation,[],[f11385,f5265]) ).
fof(f11385,plain,
( ! [X3,X0,X6,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_496 ),
inference(avatar_component_clause,[],[f11384]) ).
fof(f11386,plain,
spl0_496,
inference(avatar_split_clause,[],[f931,f11384]) ).
fof(f931,plain,
! [X3,X0,X6,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ),
inference(forward_demodulation,[],[f760,f330]) ).
fof(f760,plain,
! [X3,X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f375,f240]) ).
fof(f375,axiom,
! [X3,X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oinsert(X3,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
fof(f11318,plain,
( spl0_495
| ~ spl0_89
| ~ spl0_317
| ~ spl0_493 ),
inference(avatar_split_clause,[],[f11310,f11307,f4702,f1445,f11316]) ).
fof(f11307,plain,
( spl0_493
<=> ! [X0,X6,X1,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f11310,plain,
( ! [X0,X1,X6,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_493 ),
inference(forward_demodulation,[],[f11308,f5265]) ).
fof(f11308,plain,
( ! [X0,X1,X6,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_493 ),
inference(avatar_component_clause,[],[f11307]) ).
fof(f11314,plain,
( spl0_494
| ~ spl0_94
| ~ spl0_475 ),
inference(avatar_split_clause,[],[f10976,f10897,f1469,f11312]) ).
fof(f11312,plain,
( spl0_494
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(hAPP(c_in(X0),c_HOL_Oundefined(X1)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X4,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f10976,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_in(X0),c_HOL_Oundefined(X1)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X0),X4,tc_fun(X0,tc_bool))))
| ~ spl0_94
| ~ spl0_475 ),
inference(resolution,[],[f10898,f1470]) ).
fof(f11309,plain,
spl0_493,
inference(avatar_split_clause,[],[f915,f11307]) ).
fof(f915,plain,
! [X0,X1,X6,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ),
inference(forward_demodulation,[],[f750,f330]) ).
fof(f750,plain,
! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f319,f240]) ).
fof(f319,axiom,
! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
fof(f11304,plain,
spl0_492,
inference(avatar_split_clause,[],[f914,f11302]) ).
fof(f11302,plain,
( spl0_492
<=> ! [X10,X0,X12,X6,X1] :
( c_Set_Oimage(X10,X6,X0,X12) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),hAPP(X10,X1)),c_Set_Oimage(X10,X6,X0,X12),tc_fun(X12,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f914,plain,
! [X10,X0,X1,X6,X12] :
( c_Set_Oimage(X10,X6,X0,X12) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),hAPP(X10,X1)),c_Set_Oimage(X10,X6,X0,X12),tc_fun(X12,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f749,f330]) ).
fof(f749,plain,
! [X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Set_Oimage(X10,X6,X0,X12) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),hAPP(X10,X1)),X12),c_Set_Oimage(X10,X6,X0,X12),tc_fun(X12,tc_bool)) ),
inference(definition_unfolding,[],[f374,f240]) ).
fof(f374,axiom,
! [X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Set_Oimage(X10,X6,X0,X12) = c_Set_Oinsert(hAPP(X10,X1),c_Set_Oimage(X10,X6,X0,X12),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
fof(f11300,plain,
spl0_491,
inference(avatar_split_clause,[],[f631,f11298]) ).
fof(f631,axiom,
! [X10,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X6,X7,X10,X0,X12))),X7))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcsetI_1) ).
fof(f11209,plain,
( spl0_490
| ~ spl0_93
| ~ spl0_475 ),
inference(avatar_split_clause,[],[f10975,f10897,f1465,f11207]) ).
fof(f10975,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_in(X0),c_HOL_Oundefined(X1)),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Set_Oimage(c_FuncSet_Orestrict(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X0),tc_fun(X0,tc_bool))))
| ~ spl0_93
| ~ spl0_475 ),
inference(resolution,[],[f10898,f1466]) ).
fof(f11062,plain,
( spl0_489
| ~ spl0_89
| ~ spl0_317
| ~ spl0_488 ),
inference(avatar_split_clause,[],[f11058,f11055,f4702,f1445,f11060]) ).
fof(f11060,plain,
( spl0_489
<=> ! [X0,X6,X1,X7] :
( ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f11055,plain,
( spl0_488
<=> ! [X0,X6,X1,X7] :
( ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f11058,plain,
( ! [X0,X1,X6,X7] :
( ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_488 ),
inference(forward_demodulation,[],[f11056,f5265]) ).
fof(f11056,plain,
( ! [X0,X1,X6,X7] :
( ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_488 ),
inference(avatar_component_clause,[],[f11055]) ).
fof(f11057,plain,
spl0_488,
inference(avatar_split_clause,[],[f1003,f11055]) ).
fof(f1003,plain,
! [X0,X1,X6,X7] :
( ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f795,f330]) ).
fof(f795,plain,
! [X0,X1,X6,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f100,f240]) ).
fof(f100,axiom,
! [X0,X1,X6,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ c_lessequals(X6,c_Set_Oinsert(X1,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
fof(f11009,plain,
( spl0_487
| ~ spl0_89
| ~ spl0_317
| ~ spl0_486 ),
inference(avatar_split_clause,[],[f11005,f11002,f4702,f1445,f11007]) ).
fof(f11002,plain,
( spl0_486
<=> ! [X0,X6,X1,X7] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f11005,plain,
( ! [X0,X1,X6,X7] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_486 ),
inference(forward_demodulation,[],[f11003,f5265]) ).
fof(f11003,plain,
( ! [X0,X1,X6,X7] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_486 ),
inference(avatar_component_clause,[],[f11002]) ).
fof(f11004,plain,
spl0_486,
inference(avatar_split_clause,[],[f995,f11002]) ).
fof(f995,plain,
! [X0,X1,X6,X7] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ),
inference(forward_demodulation,[],[f789,f330]) ).
fof(f789,plain,
! [X0,X1,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f103,f240]) ).
fof(f103,axiom,
! [X0,X1,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| c_lessequals(c_Set_Oinsert(X1,X6,X0),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f10989,plain,
( spl0_485
| ~ spl0_89
| ~ spl0_317
| ~ spl0_484 ),
inference(avatar_split_clause,[],[f10965,f10962,f4702,f1445,f10987]) ).
fof(f10987,plain,
( spl0_485
<=> ! [X24,X4,X0,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_fequal(X12),X3),X12,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f10962,plain,
( spl0_484
<=> ! [X24,X4,X0,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f10965,plain,
( ! [X3,X0,X4,X24,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_fequal(X12),X3),X12,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_484 ),
inference(forward_demodulation,[],[f10963,f5265]) ).
fof(f10963,plain,
( ! [X3,X0,X4,X24,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) )
| ~ spl0_484 ),
inference(avatar_component_clause,[],[f10962]) ).
fof(f10964,plain,
spl0_484,
inference(avatar_split_clause,[],[f964,f10962]) ).
fof(f964,plain,
! [X3,X0,X4,X24,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) ),
inference(forward_demodulation,[],[f963,f330]) ).
fof(f963,plain,
! [X3,X0,X4,X24,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12),X12,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) ),
inference(forward_demodulation,[],[f780,f33]) ).
fof(f780,plain,
! [X3,X0,X4,X24,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)),X12,X0))) ),
inference(definition_unfolding,[],[f267,f240]) ).
fof(f267,axiom,
! [X3,X0,X4,X24,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),X12,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
fof(f10932,plain,
( spl0_483
| ~ spl0_89
| ~ spl0_317
| ~ spl0_482 ),
inference(avatar_split_clause,[],[f10928,f10925,f4702,f1445,f10930]) ).
fof(f10930,plain,
( spl0_483
<=> ! [X24,X4,X0,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_fequal(X12),X3),X12,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f10925,plain,
( spl0_482
<=> ! [X24,X4,X0,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f10928,plain,
( ! [X3,X0,X4,X24,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_fequal(X12),X3),X12,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_482 ),
inference(forward_demodulation,[],[f10926,f5265]) ).
fof(f10926,plain,
( ! [X3,X0,X4,X24,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) )
| ~ spl0_482 ),
inference(avatar_component_clause,[],[f10925]) ).
fof(f10927,plain,
spl0_482,
inference(avatar_split_clause,[],[f962,f10925]) ).
fof(f962,plain,
! [X3,X0,X4,X24,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) ),
inference(forward_demodulation,[],[f961,f330]) ).
fof(f961,plain,
! [X3,X0,X4,X24,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12),X12,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24)) ),
inference(forward_demodulation,[],[f779,f33]) ).
fof(f779,plain,
! [X3,X0,X4,X24,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24))
| hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)),X12,X0))) ),
inference(definition_unfolding,[],[f268,f240]) ).
fof(f268,axiom,
! [X3,X0,X4,X24,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X3,X4,X12,X0)),X24))
| hBOOL(hAPP(hAPP(c_in(X0),X4),c_Relation_OImage(X24,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),X12,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
fof(f10923,plain,
spl0_481,
inference(avatar_split_clause,[],[f740,f10921]) ).
fof(f10921,plain,
( spl0_481
<=> ! [X10,X0,X12,X6,X7] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0) = c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X7,X12,X0),X10,X12,X0,X0),X6,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f740,plain,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0) = c_FuncSet_Orestrict(c_COMBB(c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X7,X12,X0),X10,X12,X0,X0),X6,X0,X0) ),
inference(definition_unfolding,[],[f266,f231]) ).
fof(f266,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_FuncSet_Ocompose(X6,c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X7,X12,X0),X10,X0,X12,X0) = c_FuncSet_Orestrict(c_COMBI(X0),X6,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compose__inv__into__id_0) ).
fof(f10919,plain,
spl0_480,
inference(avatar_split_clause,[],[f646,f10917]) ).
fof(f646,axiom,
! [X37] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(X37,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_const__Lin__Prof_0) ).
fof(f10915,plain,
spl0_479,
inference(avatar_split_clause,[],[f637,f10913]) ).
fof(f10913,plain,
( spl0_479
<=> ! [X12,X7,X8,X0,X6,X1] :
( X6 = X7
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X8))
| c_Product__Type_OSigma(X6,c_COMBK(X8,tc_fun(X0,tc_bool),X12),X12,X0) != c_Product__Type_OSigma(X7,c_COMBK(X8,tc_fun(X0,tc_bool),X12),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f637,axiom,
! [X0,X1,X8,X6,X7,X12] :
( X6 = X7
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X8))
| c_Product__Type_OSigma(X6,c_COMBK(X8,tc_fun(X0,tc_bool),X12),X12,X0) != c_Product__Type_OSigma(X7,c_COMBK(X8,tc_fun(X0,tc_bool),X12),X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
fof(f10911,plain,
spl0_478,
inference(avatar_split_clause,[],[f633,f10909]) ).
fof(f633,axiom,
! [X10,X0,X1,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X1)),hAPP(X7,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__mem_0) ).
fof(f10907,plain,
spl0_477,
inference(avatar_split_clause,[],[f489,f10905]) ).
fof(f10905,plain,
( spl0_477
<=> ! [X37,X5,X2,X1] :
( X2 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f489,axiom,
! [X2,X1,X37,X5] :
( X2 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
fof(f10903,plain,
spl0_476,
inference(avatar_split_clause,[],[f378,f10901]) ).
fof(f10901,plain,
( spl0_476
<=> ! [X37,X5,X2,X1] :
( X1 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f378,axiom,
! [X2,X1,X37,X5] :
( X1 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
fof(f10899,plain,
( spl0_475
| ~ spl0_262
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4599,f4502,f3635,f10897]) ).
fof(f3635,plain,
( spl0_262
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_in(X2),c_HOL_Oundefined(X1)),c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f4599,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X4,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),c_HOL_Oundefined(X1)),X4)) )
| ~ spl0_262
| ~ spl0_300 ),
inference(resolution,[],[f4503,f3636]) ).
fof(f3636,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_in(X2),c_HOL_Oundefined(X1)),c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X2)))
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f3635]) ).
fof(f10895,plain,
spl0_474,
inference(avatar_split_clause,[],[f256,f10893]) ).
fof(f256,axiom,
! [X10,X0,X4,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| hAPP(X10,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X4,X10,X12,X0)) = X4
| ~ hBOOL(hAPP(hAPP(c_in(X12),X4),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_0) ).
fof(f10891,plain,
spl0_473,
inference(avatar_split_clause,[],[f234,f10889]) ).
fof(f234,axiom,
! [X3,X0,X6,X4,X24,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(hAPP(c_in(X12),X4),c_Relation_OImage(X24,X6,X0,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
fof(f10887,plain,
spl0_472,
inference(avatar_split_clause,[],[f82,f10885]) ).
fof(f10885,plain,
( spl0_472
<=> ! [X6,X0,X12,X21,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool)),X21,X12,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X21,X12,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X21,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f82,axiom,
! [X21,X0,X6,X7,X12] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool)),X21,X12,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X21,X12,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X21,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
fof(f10714,plain,
( spl0_471
| ~ spl0_89
| ~ spl0_317
| ~ spl0_470 ),
inference(avatar_split_clause,[],[f10710,f10707,f4702,f1445,f10712]) ).
fof(f10707,plain,
( spl0_470
<=> ! [X24,X0,X31,X6] :
( c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0,X0) = X31
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f10710,plain,
( ! [X31,X0,X6,X24] :
( c_Relation_OImage(X24,hAPP(c_fequal(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0,X0) = X31
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0))) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_470 ),
inference(forward_demodulation,[],[f10708,f5265]) ).
fof(f10708,plain,
( ! [X31,X0,X6,X24] :
( c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0,X0) = X31
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0))) )
| ~ spl0_470 ),
inference(avatar_component_clause,[],[f10707]) ).
fof(f10709,plain,
spl0_470,
inference(avatar_split_clause,[],[f960,f10707]) ).
fof(f960,plain,
! [X31,X0,X6,X24] :
( c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0,X0) = X31
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0))) ),
inference(forward_demodulation,[],[f959,f330]) ).
fof(f959,plain,
! [X31,X0,X6,X24] :
( c_Relation_OImage(X24,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0),X0,X0) = X31
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0))) ),
inference(forward_demodulation,[],[f778,f33]) ).
fof(f778,plain,
! [X31,X0,X6,X24] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| c_Relation_OImage(X24,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0,X0) = X31 ),
inference(definition_unfolding,[],[f301,f240]) ).
fof(f301,axiom,
! [X31,X0,X6,X24] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| c_Relation_OImage(X24,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientE_0) ).
fof(f10633,plain,
( spl0_469
| ~ spl0_89
| ~ spl0_317
| ~ spl0_468 ),
inference(avatar_split_clause,[],[f10629,f10626,f4702,f1445,f10631]) ).
fof(f10626,plain,
( spl0_468
<=> ! [X10,X0,X6,X3] :
( c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),tc_fun(X0,tc_bool)),X0,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f10629,plain,
( ! [X3,X10,X0,X6] :
( c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_fequal(X0),X3),tc_fun(X0,tc_bool)),X0,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_468 ),
inference(forward_demodulation,[],[f10627,f5265]) ).
fof(f10627,plain,
( ! [X3,X10,X0,X6] :
( c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),tc_fun(X0,tc_bool)),X0,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_468 ),
inference(avatar_component_clause,[],[f10626]) ).
fof(f10628,plain,
spl0_468,
inference(avatar_split_clause,[],[f937,f10626]) ).
fof(f937,plain,
! [X3,X10,X0,X6] :
( c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),tc_fun(X0,tc_bool)),X0,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ),
inference(forward_demodulation,[],[f936,f330]) ).
fof(f936,plain,
! [X3,X10,X0,X6] :
( c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),tc_fun(X0,tc_bool)),X0,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ),
inference(forward_demodulation,[],[f764,f33]) ).
fof(f764,plain,
! [X3,X10,X0,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) = c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0,tc_nat) ),
inference(definition_unfolding,[],[f251,f240]) ).
fof(f251,axiom,
! [X3,X10,X0,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,tc_nat) = c_Finite__Set_Osetsum(X10,X6,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
fof(f10595,plain,
( spl0_467
| ~ spl0_89
| ~ spl0_317
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f10591,f10588,f4702,f1445,f10593]) ).
fof(f10588,plain,
( spl0_466
<=> ! [X24,X0,X6,X1] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0,X0)),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f10591,plain,
( ! [X0,X1,X6,X24] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Relation_OImage(X24,hAPP(c_fequal(X0),X1),X0,X0)),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_466 ),
inference(forward_demodulation,[],[f10589,f5265]) ).
fof(f10589,plain,
( ! [X0,X1,X6,X24] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0,X0)),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_466 ),
inference(avatar_component_clause,[],[f10588]) ).
fof(f10590,plain,
spl0_466,
inference(avatar_split_clause,[],[f924,f10588]) ).
fof(f924,plain,
! [X0,X1,X6,X24] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Relation_OImage(X24,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0,X0)),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f923,f330]) ).
fof(f923,plain,
! [X0,X1,X6,X24] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Relation_OImage(X24,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X0,X0)),c_Equiv__Relations_Oquotient(X6,X24,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f755,f33]) ).
fof(f755,plain,
! [X0,X1,X6,X24] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Relation_OImage(X24,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0,X0)),c_Equiv__Relations_Oquotient(X6,X24,X0))) ),
inference(definition_unfolding,[],[f272,f240]) ).
fof(f272,axiom,
! [X0,X1,X6,X24] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Relation_OImage(X24,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0)),c_Equiv__Relations_Oquotient(X6,X24,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientI_0) ).
fof(f10586,plain,
spl0_465,
inference(avatar_split_clause,[],[f817,f10584]) ).
fof(f10584,plain,
( spl0_465
<=> ! [X37,X1,X30] :
( X1 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X30,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X30))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f817,plain,
! [X1,X37,X30] :
( X1 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X30,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X30))) ),
inference(duplicate_literal_removal,[],[f404]) ).
fof(f404,axiom,
! [X1,X37,X30] :
( X1 = X30
| X1 = X30
| X1 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X30,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X30))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_5) ).
fof(f10582,plain,
spl0_464,
inference(avatar_split_clause,[],[f816,f10580]) ).
fof(f10580,plain,
( spl0_464
<=> ! [X37,X1,X30] :
( X1 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X30,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f816,plain,
! [X1,X37,X30] :
( X1 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X30,X1))) ),
inference(duplicate_literal_removal,[],[f419]) ).
fof(f419,axiom,
! [X1,X37,X30] :
( X1 = X30
| X1 = X30
| X1 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X30,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_5) ).
fof(f10578,plain,
( spl0_463
| ~ spl0_29
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f10510,f8988,f1155,f10576]) ).
fof(f10576,plain,
( spl0_463
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X5,c_COMBI(X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f8988,plain,
( spl0_433
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X5,X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f10510,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X5,c_COMBI(X0),X4)) )
| ~ spl0_29
| ~ spl0_433 ),
inference(forward_demodulation,[],[f10506,f1156]) ).
fof(f10506,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X5,c_COMBI(X0),X4))
| ~ hBOOL(hAPP(c_COMBI(X0),c_HOL_Oundefined(X2))) )
| ~ spl0_29
| ~ spl0_433 ),
inference(superposition,[],[f8989,f1156]) ).
fof(f8989,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X5,X0,X4)))
| ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1))) )
| ~ spl0_433 ),
inference(avatar_component_clause,[],[f8988]) ).
fof(f10574,plain,
spl0_462,
inference(avatar_split_clause,[],[f632,f10572]) ).
fof(f632,axiom,
! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcsetI_0) ).
fof(f10570,plain,
spl0_461,
inference(avatar_split_clause,[],[f409,f10568]) ).
fof(f10568,plain,
( spl0_461
<=> ! [X37,X4,X3,X1] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f409,axiom,
! [X3,X1,X37,X4] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_0) ).
fof(f10566,plain,
spl0_460,
inference(avatar_split_clause,[],[f394,f10564]) ).
fof(f10564,plain,
( spl0_460
<=> ! [X37,X4,X3,X1] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f394,axiom,
! [X3,X1,X37,X4] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X37,X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_0) ).
fof(f10562,plain,
spl0_459,
inference(avatar_split_clause,[],[f254,f10560]) ).
fof(f10560,plain,
( spl0_459
<=> ! [X10,X20,X0,X12,X1] :
( hBOOL(hAPP(X20,X1))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| hBOOL(hAPP(hAPP(c_in(X12),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(X20,X10,X0,X12)),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f254,axiom,
! [X10,X0,X1,X12,X20] :
( hBOOL(hAPP(X20,X1))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| hBOOL(hAPP(hAPP(c_in(X12),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(X20,X10,X0,X12)),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__transfer_0) ).
fof(f10556,plain,
spl0_458,
inference(avatar_split_clause,[],[f116,f10554]) ).
fof(f10554,plain,
( spl0_458
<=> ! [X0,X28,X16] :
( ~ c_lessequals(X16,X28,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X16),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X28),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f116,axiom,
! [X28,X0,X16] :
( ~ c_lessequals(X16,X28,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X16),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X28),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
fof(f10550,plain,
spl0_457,
inference(avatar_split_clause,[],[f115,f10548]) ).
fof(f10548,plain,
( spl0_457
<=> ! [X0,X28,X16] :
( c_lessequals(X16,X28,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X16),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X28),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f115,axiom,
! [X28,X0,X16] :
( c_lessequals(X16,X28,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X16),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X28),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
fof(f10114,plain,
( spl0_456
| ~ spl0_89
| ~ spl0_317
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f10110,f10106,f4702,f1445,f10112]) ).
fof(f10112,plain,
( spl0_456
<=> ! [X6,X0,X1] :
( hAPP(c_fequal(X0),X1) = X6
| ~ c_lessequals(X6,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f10106,plain,
( spl0_455
<=> ! [X6,X0,X1] :
( ~ c_lessequals(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f10110,plain,
( ! [X0,X1,X6] :
( hAPP(c_fequal(X0),X1) = X6
| ~ c_lessequals(X6,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_455 ),
inference(forward_demodulation,[],[f10109,f5265]) ).
fof(f10109,plain,
( ! [X0,X1,X6] :
( ~ c_lessequals(X6,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_455 ),
inference(forward_demodulation,[],[f10107,f5265]) ).
fof(f10107,plain,
( ! [X0,X1,X6] :
( ~ c_lessequals(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_455 ),
inference(avatar_component_clause,[],[f10106]) ).
fof(f10108,plain,
spl0_455,
inference(avatar_split_clause,[],[f1002,f10106]) ).
fof(f1002,plain,
! [X0,X1,X6] :
( ~ c_lessequals(X6,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ),
inference(forward_demodulation,[],[f1001,f330]) ).
fof(f1001,plain,
! [X0,X1,X6] :
( ~ c_lessequals(X6,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ),
inference(forward_demodulation,[],[f1000,f33]) ).
fof(f1000,plain,
! [X0,X1,X6] :
( hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f999,f330]) ).
fof(f999,plain,
! [X0,X1,X6] :
( c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f794,f33]) ).
fof(f794,plain,
! [X0,X1,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f121,f240,f240]) ).
fof(f121,axiom,
! [X0,X1,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X6
| ~ c_lessequals(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f10084,plain,
( spl0_454
| ~ spl0_89
| ~ spl0_317
| ~ spl0_453 ),
inference(avatar_split_clause,[],[f10080,f10077,f4702,f1445,f10082]) ).
fof(f10077,plain,
( spl0_453
<=> ! [X4,X0,X6,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X6,tc_fun(X0,tc_bool))))
| X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f10080,plain,
( ! [X3,X0,X6,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X4),X6,tc_fun(X0,tc_bool))))
| X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_453 ),
inference(forward_demodulation,[],[f10078,f5265]) ).
fof(f10078,plain,
( ! [X3,X0,X6,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X6,tc_fun(X0,tc_bool))))
| X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f10077]) ).
fof(f10079,plain,
spl0_453,
inference(avatar_split_clause,[],[f990,f10077]) ).
fof(f990,plain,
! [X3,X0,X6,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X6,tc_fun(X0,tc_bool))))
| X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ),
inference(forward_demodulation,[],[f786,f330]) ).
fof(f786,plain,
! [X3,X0,X6,X4] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),X6,tc_fun(X0,tc_bool)))) ),
inference(definition_unfolding,[],[f438,f240]) ).
fof(f438,axiom,
! [X3,X0,X6,X4] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Set_Oinsert(X4,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f10073,plain,
( spl0_452
| ~ spl0_89
| ~ spl0_317
| ~ spl0_451 ),
inference(avatar_split_clause,[],[f10069,f10065,f4702,f1445,f10071]) ).
fof(f10065,plain,
( spl0_451
<=> ! [X4,X0,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f10069,plain,
( ! [X3,X0,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_451 ),
inference(forward_demodulation,[],[f10068,f5265]) ).
fof(f10068,plain,
( ! [X3,X0,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_451 ),
inference(forward_demodulation,[],[f10066,f5265]) ).
fof(f10066,plain,
( ! [X3,X0,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_451 ),
inference(avatar_component_clause,[],[f10065]) ).
fof(f10067,plain,
spl0_451,
inference(avatar_split_clause,[],[f881,f10065]) ).
fof(f881,plain,
! [X3,X0,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f880,f330]) ).
fof(f880,plain,
! [X3,X0,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f879,f330]) ).
fof(f879,plain,
! [X3,X0,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f730,f33]) ).
fof(f730,plain,
! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) ),
inference(definition_unfolding,[],[f393,f240,f240]) ).
fof(f393,axiom,
! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
fof(f10061,plain,
( spl0_450
| ~ spl0_29
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f10015,f8407,f1155,f10059]) ).
fof(f10059,plain,
( spl0_450
<=> ! [X2,X4,X0,X5,X3,X1] :
( ~ hBOOL(c_HOL_Oundefined(X3))
| hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X1,c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5),c_COMBI(X0),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f8407,plain,
( spl0_429
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,c_Set_Oimage(c_FuncSet_Orestrict(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5),X0,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f10015,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_HOL_Oundefined(X3))
| hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X1,c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5),c_COMBI(X0),X5)) )
| ~ spl0_29
| ~ spl0_429 ),
inference(forward_demodulation,[],[f10011,f1156]) ).
fof(f10011,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X1,c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5),c_COMBI(X0),X5))
| ~ hBOOL(hAPP(c_COMBI(X0),c_HOL_Oundefined(X3))) )
| ~ spl0_29
| ~ spl0_429 ),
inference(superposition,[],[f8408,f1156]) ).
fof(f8408,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,c_Set_Oimage(c_FuncSet_Orestrict(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5),X0,X5)))
| ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1))) )
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f8407]) ).
fof(f10057,plain,
( spl0_449
| ~ spl0_89
| ~ spl0_317
| ~ spl0_448 ),
inference(avatar_split_clause,[],[f10053,f10049,f4702,f1445,f10055]) ).
fof(f10049,plain,
( spl0_448
<=> ! [X4,X0,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f10053,plain,
( ! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_448 ),
inference(forward_demodulation,[],[f10052,f5265]) ).
fof(f10052,plain,
( ! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_fequal(X0),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_448 ),
inference(forward_demodulation,[],[f10050,f5265]) ).
fof(f10050,plain,
( ! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_448 ),
inference(avatar_component_clause,[],[f10049]) ).
fof(f10051,plain,
spl0_448,
inference(avatar_split_clause,[],[f878,f10049]) ).
fof(f878,plain,
! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f877,f330]) ).
fof(f877,plain,
! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f876,f330]) ).
fof(f876,plain,
! [X3,X0,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f729,f33]) ).
fof(f729,plain,
! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X4),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) ),
inference(definition_unfolding,[],[f241,f240,f240]) ).
fof(f241,axiom,
! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
fof(f10047,plain,
spl0_447,
inference(avatar_split_clause,[],[f699,f10045]) ).
fof(f10045,plain,
( spl0_447
<=> ! [X0,X12,X10] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f699,plain,
! [X10,X0,X12] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))),X0),
inference(definition_unfolding,[],[f547,f259]) ).
fof(f547,axiom,
! [X10,X0,X12] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X0,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
fof(f10043,plain,
spl0_446,
inference(avatar_split_clause,[],[f698,f10041]) ).
fof(f10041,plain,
( spl0_446
<=> ! [X0,X12,X10] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f698,plain,
! [X10,X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X12),X10,X12,tc_fun(tc_fun(X12,tc_bool),tc_bool),X0),X0,tc_fun(X12,tc_bool),tc_bool),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool))),X0),
inference(definition_unfolding,[],[f331,f259]) ).
fof(f331,axiom,
! [X10,X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool)),X0,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
fof(f10039,plain,
spl0_445,
inference(avatar_split_clause,[],[f596,f10037]) ).
fof(f10037,plain,
( spl0_445
<=> ! [X18,X4,X0,X14,X12,X6,X3,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(X7,X3),X4),X14))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_fun(X18,tc_bool))),X4),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f596,axiom,
! [X3,X0,X18,X6,X7,X14,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(X7,X3),X4),X14))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_fun(X18,tc_bool))),X4),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP2__I_0) ).
fof(f10035,plain,
spl0_444,
inference(avatar_split_clause,[],[f578,f10033]) ).
fof(f10033,plain,
( spl0_444
<=> ! [X20,X7,X12,X6,X0,X1,X30] :
( ~ hBOOL(hAPP(X20,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X30),hAPP(X7,X1)))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X6,X7,X20,X12,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f578,axiom,
! [X0,X1,X6,X7,X12,X30,X20] :
( ~ hBOOL(hAPP(X20,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X30),hAPP(X7,X1)))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X6,X7,X20,X12,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UN_4) ).
fof(f10031,plain,
spl0_443,
inference(avatar_split_clause,[],[f575,f10029]) ).
fof(f10029,plain,
( spl0_443
<=> ! [X4,X0,X12,X6,X3,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X4),hAPP(X7,X3)))
| hBOOL(hAPP(hAPP(c_in(X12),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f575,axiom,
! [X3,X0,X6,X7,X4,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X4),hAPP(X7,X3)))
| hBOOL(hAPP(hAPP(c_in(X12),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
fof(f10027,plain,
spl0_442,
inference(avatar_split_clause,[],[f557,f10025]) ).
fof(f10025,plain,
( spl0_442
<=> ! [X6,X10,X0,X12,X2,X1] :
( X1 = X2
| ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| hAPP(X10,X1) != hAPP(X10,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f557,axiom,
! [X2,X10,X0,X1,X6,X12] :
( X1 = X2
| ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| hAPP(X10,X1) != hAPP(X10,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
fof(f10023,plain,
spl0_441,
inference(avatar_split_clause,[],[f521,f10021]) ).
fof(f10021,plain,
( spl0_441
<=> ! [X24,X4,X0,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X4,X3,X12,X0)),X24))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Relation_Oconverse(X24,X12,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f521,axiom,
! [X3,X0,X4,X24,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X4,X3,X12,X0)),X24))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Relation_Oconverse(X24,X12,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
fof(f10019,plain,
spl0_440,
inference(avatar_split_clause,[],[f519,f10017]) ).
fof(f10017,plain,
( spl0_440
<=> ! [X24,X4,X0,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X4,X3,X12,X0)),X24))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Relation_Oconverse(X24,X12,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f519,axiom,
! [X3,X0,X4,X24,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X12,X0)),c_Pair(X4,X3,X12,X0)),X24))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Relation_Oconverse(X24,X12,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
fof(f9973,plain,
spl0_439,
inference(avatar_split_clause,[],[f264,f9971]) ).
fof(f9971,plain,
( spl0_439
<=> ! [X10,X0,X12,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XrestrictI__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_OPi(X6,X7,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f264,axiom,
! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XrestrictI__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_OPi(X6,X7,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrictI_0) ).
fof(f9969,plain,
spl0_438,
inference(avatar_split_clause,[],[f243,f9967]) ).
fof(f9967,plain,
( spl0_438
<=> ! [X6,X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X6,X8,X0),X6,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f243,axiom,
! [X0,X8,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X6,X8,X0),X6,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__disjoint_2) ).
fof(f9965,plain,
spl0_437,
inference(avatar_split_clause,[],[f114,f9963]) ).
fof(f114,axiom,
! [X0,X6,X26,X27,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X27),X26))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X6,X27),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X0,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
fof(f9961,plain,
spl0_436,
inference(avatar_split_clause,[],[f83,f9959]) ).
fof(f9959,plain,
( spl0_436
<=> ! [X10,X20,X0,X12,X1] :
( hBOOL(hAPP(X20,X1))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ hBOOL(hAPP(X20,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X10,X0,X12),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(X20,X10,X0,X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f83,axiom,
! [X10,X0,X1,X12,X20] :
( hBOOL(hAPP(X20,X1))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ hBOOL(hAPP(X20,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X10,X0,X12),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(X20,X10,X0,X12)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__transfer_1) ).
fof(f9957,plain,
spl0_435,
inference(avatar_split_clause,[],[f42,f9955]) ).
fof(f42,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
fof(f9953,plain,
spl0_434,
inference(avatar_split_clause,[],[f41,f9951]) ).
fof(f9951,plain,
( spl0_434
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f41,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
fof(f8990,plain,
( spl0_433
| ~ spl0_262
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4406,f4158,f3635,f8988]) ).
fof(f4406,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X5,X0,X4))) )
| ~ spl0_262
| ~ spl0_290 ),
inference(resolution,[],[f4159,f3636]) ).
fof(f8422,plain,
spl0_432,
inference(avatar_split_clause,[],[f864,f8420]) ).
fof(f8420,plain,
( spl0_432
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f864,plain,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f471,f534]) ).
fof(f534,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ominus__class_Ominus(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
fof(f471,axiom,
! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X8,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
fof(f8417,plain,
spl0_431,
inference(avatar_split_clause,[],[f832,f8415]) ).
fof(f8415,plain,
( spl0_431
<=> ! [X10,X0,X12,X6] : c_lessequals(c_Set_Oimage(X10,hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),X12,X0),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f832,plain,
! [X10,X0,X6,X12] : c_lessequals(c_Set_Oimage(X10,hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),X12,X0),X6,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f702,f330]) ).
fof(f702,plain,
! [X10,X0,X6,X12] : c_lessequals(c_Set_Oimage(X10,c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X0),X10,X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X12),X12,tc_fun(X0,tc_bool),tc_bool),X6),X12),X12,X0),X6,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f139,f259]) ).
fof(f139,axiom,
! [X10,X0,X6,X12] : c_lessequals(c_Set_Oimage(X10,c_Set_Ovimage(X10,X6,X12,X0),X12,X0),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
fof(f8413,plain,
spl0_430,
inference(avatar_split_clause,[],[f645,f8411]) ).
fof(f645,axiom,
! [X2,X1,X37] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X37,X1,X2)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_above__Lin_0) ).
fof(f8409,plain,
( spl0_429
| ~ spl0_262
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4385,f4150,f3635,f8407]) ).
fof(f4385,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X2,c_Set_Oimage(c_FuncSet_Orestrict(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5),X0,X5))) )
| ~ spl0_262
| ~ spl0_288 ),
inference(resolution,[],[f4151,f3636]) ).
fof(f8405,plain,
spl0_428,
inference(avatar_split_clause,[],[f641,f8403]) ).
fof(f641,axiom,
! [X2,X1,X37] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X37,X1,X2)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__Lin_0) ).
fof(f8401,plain,
spl0_427,
inference(avatar_split_clause,[],[f484,f8399]) ).
fof(f8399,plain,
( spl0_427
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f484,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
fof(f8296,plain,
( spl0_426
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f8292,f8289,f8294]) ).
fof(f8289,plain,
( spl0_425
<=> ! [X0,X6,X8,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f8292,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ spl0_425 ),
inference(forward_demodulation,[],[f8290,f484]) ).
fof(f8290,plain,
( ! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_425 ),
inference(avatar_component_clause,[],[f8289]) ).
fof(f8291,plain,
spl0_425,
inference(avatar_split_clause,[],[f472,f8289]) ).
fof(f472,axiom,
! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
fof(f8287,plain,
spl0_424,
inference(avatar_split_clause,[],[f451,f8285]) ).
fof(f8285,plain,
( spl0_424
<=> ! [X10,X0,X12,X6,X3] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,X6,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f451,axiom,
! [X3,X10,X0,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X12),hAPP(X10,X3)),c_Set_Oimage(X10,X6,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
fof(f8283,plain,
spl0_423,
inference(avatar_split_clause,[],[f364,f8281]) ).
fof(f8281,plain,
( spl0_423
<=> ! [X40,X38,X41,X39,X0,X44,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| c_Complete__Lattice_Ocomplete__lattice(X38,X40,c_COMBC(X41,X0,X0,tc_bool),c_COMBC(X42,X0,X0,tc_bool),X44,X43,X39,X45,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f364,axiom,
! [X40,X38,X41,X39,X0,X44,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| c_Complete__Lattice_Ocomplete__lattice(X38,X40,c_COMBC(X41,X0,X0,tc_bool),c_COMBC(X42,X0,X0,tc_bool),X44,X43,X39,X45,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
fof(f8279,plain,
spl0_422,
inference(avatar_split_clause,[],[f262,f8277]) ).
fof(f262,axiom,
! [X10,X0,X6,X7,X12] :
( c_lessequals(c_Set_Oimage(X10,X6,X0,X12),X7,tc_fun(X12,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__image_0) ).
fof(f8275,plain,
spl0_421,
inference(avatar_split_clause,[],[f246,f8273]) ).
fof(f8273,plain,
( spl0_421
<=> ! [X10,X0,X12,X6,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ c_lessequals(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f246,axiom,
! [X10,X0,X6,X7,X12] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| ~ c_lessequals(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
fof(f8271,plain,
spl0_420,
inference(avatar_split_clause,[],[f210,f8269]) ).
fof(f210,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
fof(f8267,plain,
( spl0_419
| ~ spl0_259
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3915,f3635,f3623,f8265]) ).
fof(f8265,plain,
( spl0_419
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(X0,c_HOL_Oundefined(X1)) = hAPP(c_FuncSet_Orestrict(X0,c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4,X5),c_HOL_Oundefined(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f3915,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(X0,c_HOL_Oundefined(X1)) = hAPP(c_FuncSet_Orestrict(X0,c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4,X5),c_HOL_Oundefined(X1))
| ~ spl0_259
| ~ spl0_262 ),
inference(resolution,[],[f3624,f3636]) ).
fof(f8263,plain,
spl0_418,
inference(avatar_split_clause,[],[f158,f8261]) ).
fof(f158,axiom,
! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
fof(f8259,plain,
spl0_417,
inference(avatar_split_clause,[],[f157,f8257]) ).
fof(f157,axiom,
! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
fof(f8255,plain,
spl0_416,
inference(avatar_split_clause,[],[f135,f8253]) ).
fof(f135,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
fof(f8251,plain,
spl0_415,
inference(avatar_split_clause,[],[f134,f8249]) ).
fof(f134,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
fof(f8247,plain,
spl0_414,
inference(avatar_split_clause,[],[f132,f8245]) ).
fof(f8245,plain,
( spl0_414
<=> ! [X10,X0,X12,X6,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X10,X6,X12,X0),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f132,axiom,
! [X10,X0,X6,X7,X12] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X10,X6,X12,X0),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X12,tc_bool)),X12,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
fof(f8243,plain,
spl0_413,
inference(avatar_split_clause,[],[f125,f8241]) ).
fof(f125,axiom,
! [X10,X0,X6,X7,X12] : c_lessequals(c_Set_Oimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool)),X12,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,X6,X12,X0),c_Set_Oimage(X10,X7,X12,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
fof(f8239,plain,
spl0_412,
inference(avatar_split_clause,[],[f80,f8237]) ).
fof(f8237,plain,
( spl0_412
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f80,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
fof(f8235,plain,
spl0_411,
inference(avatar_split_clause,[],[f60,f8233]) ).
fof(f60,axiom,
! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
fof(f8231,plain,
spl0_410,
inference(avatar_split_clause,[],[f59,f8229]) ).
fof(f59,axiom,
! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
fof(f8227,plain,
spl0_409,
inference(avatar_split_clause,[],[f43,f8225]) ).
fof(f43,axiom,
! [X0,X6,X16,X7,X12] : c_lessequals(c_Relation_OImage(X16,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X12,tc_bool)),X12,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X16,X6,X12,X0),c_Relation_OImage(X16,X7,X12,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
fof(f8223,plain,
spl0_408,
inference(avatar_split_clause,[],[f30,f8221]) ).
fof(f8221,plain,
( spl0_408
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f30,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
fof(f8219,plain,
spl0_407,
inference(avatar_split_clause,[],[f8,f8217]) ).
fof(f8217,plain,
( spl0_407
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f8,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
fof(f8017,plain,
( spl0_406
| ~ spl0_29
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f7906,f5367,f1155,f8015]) ).
fof(f8015,plain,
( spl0_406
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f5367,plain,
( spl0_327
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f7906,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) )
| ~ spl0_29
| ~ spl0_327 ),
inference(forward_demodulation,[],[f7902,f1156]) ).
fof(f7902,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4))
| ~ hBOOL(hAPP(c_COMBI(X0),c_HOL_Oundefined(X2))) )
| ~ spl0_29
| ~ spl0_327 ),
inference(superposition,[],[f5368,f1156]) ).
fof(f5368,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4)))
| ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1))) )
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f5367]) ).
fof(f7938,plain,
spl0_405,
inference(avatar_split_clause,[],[f793,f7936]) ).
fof(f7936,plain,
( spl0_405
<=> ! [X18,X10,X0,X12,X6,X17,X8,X7] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| ~ c_Fun_Obij__betw(X17,X7,X8,X12,X18)
| c_Fun_Obij__betw(c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X6,X8,X0,X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f793,plain,
! [X10,X0,X18,X8,X6,X7,X17,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| ~ c_Fun_Obij__betw(X17,X7,X8,X12,X18)
| c_Fun_Obij__betw(c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X6,X8,X0,X18) ),
inference(definition_unfolding,[],[f482,f231]) ).
fof(f482,axiom,
! [X10,X0,X18,X8,X6,X7,X17,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| ~ c_Fun_Obij__betw(X17,X7,X8,X12,X18)
| c_Fun_Obij__betw(c_FuncSet_Ocompose(X6,X17,X10,X0,X12,X18),X6,X8,X0,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__compose_0) ).
fof(f7934,plain,
spl0_404,
inference(avatar_split_clause,[],[f636,f7932]) ).
fof(f636,axiom,
! [X31,X0,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X6),X31))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),X8))
| hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionI_0) ).
fof(f7930,plain,
spl0_403,
inference(avatar_split_clause,[],[f635,f7928]) ).
fof(f7928,plain,
( spl0_403
<=> ! [X31,X0,X6,X8] :
( hBOOL(hAPP(hAPP(c_in(X0),X6),X31))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f635,axiom,
! [X31,X0,X8,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),X6),X31))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterD_0) ).
fof(f7926,plain,
spl0_402,
inference(avatar_split_clause,[],[f464,f7924]) ).
fof(f464,axiom,
! [X0,X1,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X7,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X12,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
fof(f7922,plain,
spl0_401,
inference(avatar_split_clause,[],[f450,f7920]) ).
fof(f450,axiom,
! [X0,X49,X6,X19,X20] :
( hBOOL(hAPP(X20,X49))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X49),X6))
| ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)))
| ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_2) ).
fof(f7918,plain,
spl0_400,
inference(avatar_split_clause,[],[f449,f7916]) ).
fof(f449,axiom,
! [X48,X0,X19,X6,X20] :
( hBOOL(hAPP(X19,X48))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X48),X6))
| ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)))
| ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_3) ).
fof(f7914,plain,
spl0_399,
inference(avatar_split_clause,[],[f258,f7912]) ).
fof(f258,axiom,
! [X0,X8,X6] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X6,X8,X0)),X8))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__disjoint_1) ).
fof(f7910,plain,
spl0_398,
inference(avatar_split_clause,[],[f233,f7908]) ).
fof(f7908,plain,
( spl0_398
<=> ! [X7,X20,X0,X6,X30] :
( ~ hBOOL(hAPP(X20,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X30),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0)),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f233,axiom,
! [X0,X6,X7,X30,X20] :
( ~ hBOOL(hAPP(X20,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X30),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0)),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_4) ).
fof(f7867,plain,
spl0_397,
inference(avatar_split_clause,[],[f232,f7865]) ).
fof(f7865,plain,
( spl0_397
<=> ! [X20,X0,X6,X1,X7] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0)),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f232,axiom,
! [X0,X1,X6,X7,X20] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0)),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_6) ).
fof(f7863,plain,
spl0_396,
inference(avatar_split_clause,[],[f113,f7861]) ).
fof(f7861,plain,
( spl0_396
<=> ! [X6,X0,X7,X12,X1,X26] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X26))
| c_lessequals(hAPP(X6,X1),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X12,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f113,axiom,
! [X0,X1,X6,X26,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X26))
| c_lessequals(hAPP(X6,X1),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26,X6,X12,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
fof(f7582,plain,
spl0_395,
inference(avatar_split_clause,[],[f567,f7580]) ).
fof(f7580,plain,
( spl0_395
<=> ! [X0,X14,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X14),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f567,axiom,
! [X0,X6,X7,X14] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X14),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
fof(f7578,plain,
spl0_394,
inference(avatar_split_clause,[],[f426,f7576]) ).
fof(f7576,plain,
( spl0_394
<=> ! [X0,X14,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f426,axiom,
! [X0,X6,X7,X14] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
fof(f7574,plain,
spl0_393,
inference(avatar_split_clause,[],[f306,f7572]) ).
fof(f306,axiom,
! [X3,X0,X6,X7,X4,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),X4),hAPP(X7,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Product__Type_OSigma(X6,X7,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
fof(f7570,plain,
spl0_392,
inference(avatar_split_clause,[],[f247,f7568]) ).
fof(f247,axiom,
! [X31,X10,X0,X12] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X10,X0,X12),c_Set_Oimage(X10,X31,X0,X12),X12,X0) = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).
fof(f7566,plain,
spl0_391,
inference(avatar_split_clause,[],[f239,f7564]) ).
fof(f7564,plain,
( spl0_391
<=> ! [X10,X0,X12,X6,X2,X1] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X10,X1,X2,X0,X12),X6,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X12),X2),c_Set_Oimage(X10,X6,X0,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f239,axiom,
! [X2,X10,X0,X1,X6,X12] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X10,X1,X2,X0,X12),X6,X0,X12)
| hBOOL(hAPP(hAPP(c_in(X12),X2),c_Set_Oimage(X10,X6,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
fof(f7562,plain,
spl0_390,
inference(avatar_split_clause,[],[f230,f7560]) ).
fof(f7560,plain,
( spl0_390
<=> ! [X0,X14,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f230,axiom,
! [X0,X6,X7,X14] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f7558,plain,
spl0_389,
inference(avatar_split_clause,[],[f161,f7556]) ).
fof(f161,axiom,
! [X28,X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_lessequals(X28,X6,tc_fun(X0,tc_bool))
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),c_Set_Oimage(X10,X28,X0,X12),X12,X0) = X28 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).
fof(f7554,plain,
spl0_388,
inference(avatar_split_clause,[],[f128,f7552]) ).
fof(f7552,plain,
( spl0_388
<=> ! [X18,X10,X0,X6,X12,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(X10,X6,X18,X12),X7,X12,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBB(X7,X10,X12,tc_fun(X0,tc_bool),X18),X18,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f128,axiom,
! [X10,X0,X18,X6,X7,X12] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(X10,X6,X18,X12),X7,X12,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBB(X7,X10,X12,tc_fun(X0,tc_bool),X18),X18,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).
fof(f7550,plain,
( spl0_387
| ~ spl0_29
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f7313,f5238,f1155,f7548]) ).
fof(f7548,plain,
( spl0_387
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_HOL_Oundefined(X2))
| ~ hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f5238,plain,
( spl0_318
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f7313,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_HOL_Oundefined(X2))
| ~ hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) )
| ~ spl0_29
| ~ spl0_318 ),
inference(forward_demodulation,[],[f7309,f1156]) ).
fof(f7309,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4))
| hBOOL(hAPP(c_COMBI(X0),c_HOL_Oundefined(X2))) )
| ~ spl0_29
| ~ spl0_318 ),
inference(superposition,[],[f5239,f1156]) ).
fof(f5239,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4)))
| hBOOL(hAPP(X0,c_HOL_Oundefined(X1))) )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f5238]) ).
fof(f7546,plain,
spl0_386,
inference(avatar_split_clause,[],[f106,f7544]) ).
fof(f7544,plain,
( spl0_386
<=> ! [X10,X7,X0,X12,X6,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X1)),X7))
| ~ c_lessequals(c_Set_Oimage(X10,X6,X12,X0),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f106,axiom,
! [X10,X0,X1,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X1)),X7))
| ~ c_lessequals(c_Set_Oimage(X10,X6,X12,X0),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f7542,plain,
spl0_385,
inference(avatar_split_clause,[],[f40,f7540]) ).
fof(f40,axiom,
! [X3,X0,X14,X4,X15,X12,X13] :
( X3 = X14
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X13,X3,X4,X0,X12),X14,X15,X0,X12) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X13,X14,X15,X0,X12),X3,X4,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
fof(f7087,plain,
( spl0_384
| ~ spl0_89
| ~ spl0_317
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f7083,f7080,f4702,f1445,f7085]) ).
fof(f7080,plain,
( spl0_383
<=> ! [X0,X6,X1,X7] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f7083,plain,
( ! [X0,X1,X6,X7] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_383 ),
inference(forward_demodulation,[],[f7081,f5265]) ).
fof(f7081,plain,
( ! [X0,X1,X6,X7] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f7080]) ).
fof(f7082,plain,
spl0_383,
inference(avatar_split_clause,[],[f929,f7080]) ).
fof(f929,plain,
! [X0,X1,X6,X7] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X7)) ),
inference(forward_demodulation,[],[f758,f330]) ).
fof(f758,plain,
! [X0,X1,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f102,f240]) ).
fof(f102,axiom,
! [X0,X1,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f7078,plain,
spl0_382,
inference(avatar_split_clause,[],[f787,f7076]) ).
fof(f7076,plain,
( spl0_382
<=> ! [X18,X10,X7,X0,X6,X12,X17] :
( ~ c_Fun_Oinj__on(X17,X7,X12,X18)
| ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Fun_Oinj__on(c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X6,X0,X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f787,plain,
! [X10,X0,X18,X6,X7,X17,X12] :
( ~ c_Fun_Oinj__on(X17,X7,X12,X18)
| ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Fun_Oinj__on(c_FuncSet_Orestrict(c_COMBB(X17,X10,X12,X18,X0),X6,X0,X18),X6,X0,X18) ),
inference(definition_unfolding,[],[f544,f231]) ).
fof(f544,axiom,
! [X10,X0,X18,X6,X7,X17,X12] :
( ~ c_Fun_Oinj__on(X17,X7,X12,X18)
| ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Fun_Oinj__on(c_FuncSet_Ocompose(X6,X17,X10,X0,X12,X18),X6,X0,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__compose_0) ).
fof(f7074,plain,
spl0_381,
inference(avatar_split_clause,[],[f748,f7072]) ).
fof(f748,plain,
! [X10,X0,X1,X18,X6,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hAPP(X17,hAPP(X10,X1)) = hAPP(c_FuncSet_Orestrict(c_COMBB(X17,X10,X18,X12,X0),X6,X0,X12),X1) ),
inference(definition_unfolding,[],[f439,f231]) ).
fof(f439,axiom,
! [X10,X0,X1,X18,X6,X17,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hAPP(c_FuncSet_Ocompose(X6,X17,X10,X0,X18,X12),X1) = hAPP(X17,hAPP(X10,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compose__eq_0) ).
fof(f7070,plain,
spl0_380,
inference(avatar_split_clause,[],[f644,f7068]) ).
fof(f644,axiom,
! [X37] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X37,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).
fof(f7066,plain,
spl0_379,
inference(avatar_split_clause,[],[f643,f7064]) ).
fof(f643,axiom,
! [X37] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X37,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_0) ).
fof(f7062,plain,
spl0_378,
inference(avatar_split_clause,[],[f608,f7060]) ).
fof(f608,axiom,
! [X10,X0,X1,X6,X12] :
( hAPP(X10,X1) = c_HOL_Oundefined(X12)
| hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_Oextensional(X6,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extensional__arb_0) ).
fof(f7058,plain,
spl0_377,
inference(avatar_split_clause,[],[f607,f7056]) ).
fof(f607,axiom,
! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).
fof(f7054,plain,
spl0_376,
inference(avatar_split_clause,[],[f606,f7052]) ).
fof(f606,axiom,
! [X10,X0,X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X6,X7,X10,X0,X12)),X6))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,X7,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_0) ).
fof(f7050,plain,
spl0_375,
inference(avatar_split_clause,[],[f585,f7048]) ).
fof(f7048,plain,
( spl0_375
<=> ! [X40,X38,X41,X39,X0,X1,X44,X45,X6,X42,X43] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(X41,X1),hAPP(X38,X6)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f585,axiom,
! [X40,X38,X41,X39,X0,X1,X6,X44,X45,X42,X43] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(X41,X1),hAPP(X38,X6)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
fof(f7046,plain,
spl0_374,
inference(avatar_split_clause,[],[f584,f7044]) ).
fof(f7044,plain,
( spl0_374
<=> ! [X40,X38,X41,X39,X0,X1,X44,X45,X6,X42,X43] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(X41,hAPP(X40,X6)),X1))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f584,axiom,
! [X40,X38,X41,X39,X0,X1,X6,X44,X45,X42,X43] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(X41,hAPP(X40,X6)),X1))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
fof(f7042,plain,
spl0_373,
inference(avatar_split_clause,[],[f475,f7040]) ).
fof(f475,axiom,
! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f7038,plain,
spl0_372,
inference(avatar_split_clause,[],[f164,f7036]) ).
fof(f164,axiom,
! [X0,X6,X16,X7,X12] : c_Relation_OImage(X16,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X12,tc_bool)),X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X16,X6,X12,X0),c_Relation_OImage(X16,X7,X12,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
fof(f7034,plain,
spl0_371,
inference(avatar_split_clause,[],[f93,f7032]) ).
fof(f7030,plain,
( spl0_370
| ~ spl0_29
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f6837,f4698,f1155,f7028]) ).
fof(f7028,plain,
( spl0_370
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f4698,plain,
( spl0_316
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f6837,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) )
| ~ spl0_29
| ~ spl0_316 ),
inference(forward_demodulation,[],[f6833,f1156]) ).
fof(f6833,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4))
| ~ hBOOL(hAPP(c_COMBI(X0),c_HOL_Oundefined(X2))) )
| ~ spl0_29
| ~ spl0_316 ),
inference(superposition,[],[f4699,f1156]) ).
fof(f4699,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4)))
| ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1))) )
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f4698]) ).
fof(f7026,plain,
spl0_369,
inference(avatar_split_clause,[],[f86,f7024]) ).
fof(f86,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X7,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
fof(f6751,plain,
( spl0_368
| ~ spl0_89
| ~ spl0_317
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f6747,f6744,f4702,f1445,f6749]) ).
fof(f6744,plain,
( spl0_367
<=> ! [X0,X14,X12,X6,X1] :
( c_Set_Oimage(c_COMBK(X14,X12,X0),X6,X0,X12) = hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X14)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f6747,plain,
( ! [X0,X1,X6,X14,X12] :
( c_Set_Oimage(c_COMBK(X14,X12,X0),X6,X0,X12) = hAPP(c_fequal(X12),X14)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_367 ),
inference(forward_demodulation,[],[f6745,f5265]) ).
fof(f6745,plain,
( ! [X0,X1,X6,X14,X12] :
( c_Set_Oimage(c_COMBK(X14,X12,X0),X6,X0,X12) = hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X14)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) )
| ~ spl0_367 ),
inference(avatar_component_clause,[],[f6744]) ).
fof(f6746,plain,
spl0_367,
inference(avatar_split_clause,[],[f917,f6744]) ).
fof(f917,plain,
! [X0,X1,X6,X14,X12] :
( c_Set_Oimage(c_COMBK(X14,X12,X0),X6,X0,X12) = hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X14)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f916,f330]) ).
fof(f916,plain,
! [X0,X1,X6,X14,X12] :
( c_Set_Oimage(c_COMBK(X14,X12,X0),X6,X0,X12) = c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X14),X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f751,f33]) ).
fof(f751,plain,
! [X0,X1,X6,X14,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Set_Oimage(c_COMBK(X14,X12,X0),X6,X0,X12) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X14),X12),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) ),
inference(definition_unfolding,[],[f317,f240]) ).
fof(f317,axiom,
! [X0,X1,X6,X14,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| c_Set_Oimage(c_COMBK(X14,X12,X0),X6,X0,X12) = c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
fof(f6740,plain,
( spl0_366
| ~ spl0_89
| ~ spl0_317
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f6736,f6733,f4702,f1445,f6738]) ).
fof(f6733,plain,
( spl0_365
<=> ! [X6,X0,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f6736,plain,
( ! [X3,X0,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_365 ),
inference(forward_demodulation,[],[f6734,f5265]) ).
fof(f6734,plain,
( ! [X3,X0,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_365 ),
inference(avatar_component_clause,[],[f6733]) ).
fof(f6735,plain,
spl0_365,
inference(avatar_split_clause,[],[f875,f6733]) ).
fof(f875,plain,
! [X3,X0,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f728,f330]) ).
fof(f728,plain,
! [X3,X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X6,tc_fun(X0,tc_bool)),X0) ),
inference(definition_unfolding,[],[f129,f240]) ).
fof(f129,axiom,
! [X3,X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X3,X6,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
fof(f6729,plain,
( spl0_364
| ~ spl0_89
| ~ spl0_317
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f6725,f6722,f4702,f1445,f6727]) ).
fof(f6722,plain,
( spl0_363
<=> ! [X6,X0,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Complete__Lattice_OInf__class_OInf(X6,X0),X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f6725,plain,
( ! [X3,X0,X6] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Complete__Lattice_OInf__class_OInf(X6,X0),X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_363 ),
inference(forward_demodulation,[],[f6723,f5265]) ).
fof(f6723,plain,
( ! [X3,X0,X6] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Complete__Lattice_OInf__class_OInf(X6,X0),X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f6722]) ).
fof(f6724,plain,
spl0_363,
inference(avatar_split_clause,[],[f874,f6722]) ).
fof(f874,plain,
! [X3,X0,X6] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Complete__Lattice_OInf__class_OInf(X6,X0),X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f727,f330]) ).
fof(f727,plain,
! [X3,X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Complete__Lattice_OInf__class_OInf(X6,X0),X0) = c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X6,tc_fun(X0,tc_bool)),X0) ),
inference(definition_unfolding,[],[f327,f240]) ).
fof(f327,axiom,
! [X3,X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X3,X6,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Complete__Lattice_OInf__class_OInf(X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
fof(f6720,plain,
spl0_362,
inference(avatar_split_clause,[],[f714,f6718]) ).
fof(f6718,plain,
( spl0_362
<=> ! [X18,X10,X0,X12,X6,X17] : c_Set_Oimage(X17,c_Set_Oimage(X10,X6,X12,X0),X0,X18) = c_Set_Oimage(c_FuncSet_Orestrict(c_COMBB(X17,X10,X0,X18,X12),X6,X12,X18),X6,X12,X18) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f714,plain,
! [X10,X0,X18,X6,X17,X12] : c_Set_Oimage(X17,c_Set_Oimage(X10,X6,X12,X0),X0,X18) = c_Set_Oimage(c_FuncSet_Orestrict(c_COMBB(X17,X10,X0,X18,X12),X6,X12,X18),X6,X12,X18),
inference(definition_unfolding,[],[f495,f231]) ).
fof(f495,axiom,
! [X10,X0,X18,X6,X17,X12] : c_Set_Oimage(c_FuncSet_Ocompose(X6,X17,X10,X12,X0,X18),X6,X12,X18) = c_Set_Oimage(X17,c_Set_Oimage(X10,X6,X12,X0),X0,X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__compose_0) ).
fof(f6716,plain,
spl0_361,
inference(avatar_split_clause,[],[f690,f6714]) ).
fof(f690,plain,
! [X0,X32] : c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X0),c_COMBI(X0),X0,tc_fun(tc_fun(X0,tc_bool),tc_bool),X0),X0,tc_fun(X0,tc_bool),tc_bool),X32),X0) = X32,
inference(definition_unfolding,[],[f455,f259]) ).
fof(f455,axiom,
! [X0,X32] : c_Set_Ovimage(c_COMBI(X0),X32,X0,X0) = X32,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__ident_0) ).
fof(f6712,plain,
spl0_360,
inference(avatar_split_clause,[],[f640,f6710]) ).
fof(f640,axiom,
! [X1,X37] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).
fof(f6708,plain,
spl0_359,
inference(avatar_split_clause,[],[f639,f6706]) ).
fof(f639,axiom,
! [X1,X37] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X37),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X37,X1)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).
fof(f6704,plain,
spl0_358,
inference(avatar_split_clause,[],[f623,f6702]) ).
fof(f623,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),X10),c_FuncSet_OPi(X6,c_COMBK(X7,tc_fun(X12,tc_bool),X0),X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__imp__funcset_0) ).
fof(f6700,plain,
spl0_357,
inference(avatar_split_clause,[],[f562,f6698]) ).
fof(f6698,plain,
( spl0_357
<=> ! [X16,X28,X0] :
( X16 = X28
| hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X16) != hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f562,axiom,
! [X28,X0,X16] :
( X16 = X28
| hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X16) != hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
fof(f6696,plain,
spl0_356,
inference(avatar_split_clause,[],[f427,f6694]) ).
fof(f427,axiom,
! [X41,X46,X0,X47,X25,X42] :
( ~ hBOOL(hAPP(hAPP(X41,X46),X25))
| ~ hBOOL(hAPP(hAPP(X42,X25),X47))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastLessThan(X41,X42,X46,X47,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_2) ).
fof(f6692,plain,
spl0_355,
inference(avatar_split_clause,[],[f305,f6690]) ).
fof(f305,axiom,
! [X3,X0,X6,X7,X4,X12] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X12)),c_Pair(X3,X4,X0,X12)),c_Product__Type_OSigma(X6,X7,X0,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
fof(f6688,plain,
spl0_354,
inference(avatar_split_clause,[],[f130,f6686]) ).
fof(f6686,plain,
( spl0_354
<=> ! [X10,X0,X12,X6,X7] :
( X6 = X7
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(X10,X6,X0,X12) != c_Set_Oimage(X10,X7,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f130,axiom,
! [X10,X0,X6,X7,X12] :
( X6 = X7
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(X10,X6,X0,X12) != c_Set_Oimage(X10,X7,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
fof(f6684,plain,
spl0_353,
inference(avatar_split_clause,[],[f104,f6682]) ).
fof(f104,axiom,
! [X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Set_Oimage(X10,X6,X12,X0)))
| hBOOL(hAPP(hAPP(c_in(X12),hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),X1)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).
fof(f6680,plain,
( spl0_352
| ~ spl0_29
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f6173,f4654,f1155,f6678]) ).
fof(f6678,plain,
( spl0_352
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f4654,plain,
( spl0_305
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f6173,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) )
| ~ spl0_29
| ~ spl0_305 ),
inference(forward_demodulation,[],[f6169,f1156]) ).
fof(f6169,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4))
| ~ hBOOL(hAPP(c_COMBI(X0),c_HOL_Oundefined(X2))) )
| ~ spl0_29
| ~ spl0_305 ),
inference(superposition,[],[f4655,f1156]) ).
fof(f4655,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4)))
| ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1))) )
| ~ spl0_305 ),
inference(avatar_component_clause,[],[f4654]) ).
fof(f5705,plain,
spl0_351,
inference(avatar_split_clause,[],[f991,f5703]) ).
fof(f991,plain,
! [X0,X1,X6,X20] :
( hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Olower__semilattice__class_Oinf(X6,X20,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
inference(forward_demodulation,[],[f540,f330]) ).
fof(f540,axiom,
! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Olower__semilattice__class_Oinf(X6,c_Collect(X20,X0),tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
fof(f5690,plain,
( spl0_350
| ~ spl0_89
| ~ spl0_317
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5686,f5683,f4702,f1445,f5688]) ).
fof(f5683,plain,
( spl0_349
<=> ! [X0,X6,X2,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X6,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X6,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f5686,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),X6,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X6,X1)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_349 ),
inference(forward_demodulation,[],[f5684,f5265]) ).
fof(f5684,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X6,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X6,X1)) )
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f5683]) ).
fof(f5685,plain,
spl0_349,
inference(avatar_split_clause,[],[f989,f5683]) ).
fof(f989,plain,
! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X6,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X6,X1)) ),
inference(forward_demodulation,[],[f785,f330]) ).
fof(f785,plain,
! [X2,X0,X1,X6] :
( X1 = X2
| hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X0),X6,tc_fun(X0,tc_bool)),X1)) ),
inference(definition_unfolding,[],[f339,f240]) ).
fof(f339,axiom,
! [X2,X0,X1,X6] :
( X1 = X2
| hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,X6,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f5681,plain,
spl0_348,
inference(avatar_split_clause,[],[f614,f5679]) ).
fof(f614,axiom,
! [X31,X0,X6,X24] :
( hBOOL(hAPP(hAPP(c_in(X0),c_List_Osko__Equiv__Relations__XquotientE__1__1(X6,X31,X24,X0)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X31),c_Equiv__Relations_Oquotient(X6,X24,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientE_1) ).
fof(f5677,plain,
spl0_347,
inference(avatar_split_clause,[],[f613,f5675]) ).
fof(f613,axiom,
! [X0,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X6,X8,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionE_1) ).
fof(f5673,plain,
spl0_346,
inference(avatar_split_clause,[],[f612,f5671]) ).
fof(f612,axiom,
! [X0,X8,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X6,X8,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_0) ).
fof(f5669,plain,
spl0_345,
inference(avatar_split_clause,[],[f595,f5667]) ).
fof(f595,axiom,
! [X0,X1,X6,X7,X4,X12] :
( ~ hBOOL(hAPP(hAPP(X7,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_bool)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
fof(f5665,plain,
spl0_344,
inference(avatar_split_clause,[],[f534,f5663]) ).
fof(f5661,plain,
spl0_343,
inference(avatar_split_clause,[],[f462,f5659]) ).
fof(f462,axiom,
! [X0,X8,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
fof(f5657,plain,
spl0_342,
inference(avatar_split_clause,[],[f461,f5655]) ).
fof(f5653,plain,
spl0_341,
inference(avatar_split_clause,[],[f437,f5651]) ).
fof(f437,axiom,
! [X46,X0,X47,X42,X25] :
( ~ hBOOL(hAPP(hAPP(X42,X46),X25))
| ~ hBOOL(hAPP(hAPP(X42,X25),X47))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThanLessThan(X42,X46,X47,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_2) ).
fof(f5649,plain,
spl0_340,
inference(avatar_split_clause,[],[f431,f5647]) ).
fof(f431,axiom,
! [X41,X46,X0,X47,X25] :
( ~ hBOOL(hAPP(hAPP(X41,X46),X25))
| ~ hBOOL(hAPP(hAPP(X41,X25),X47))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastAtMost(X41,X46,X47,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).
fof(f5645,plain,
spl0_339,
inference(avatar_split_clause,[],[f180,f5643]) ).
fof(f5643,plain,
( spl0_339
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f180,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
fof(f5641,plain,
( spl0_338
| ~ spl0_29
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f5467,f4518,f1155,f5639]) ).
fof(f5639,plain,
( spl0_338
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f4518,plain,
( spl0_304
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f5467,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_HOL_Oundefined(X2))
| hBOOL(c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4)) )
| ~ spl0_29
| ~ spl0_304 ),
inference(forward_demodulation,[],[f5463,f1156]) ).
fof(f5463,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),c_COMBI(X0),X4))
| ~ hBOOL(hAPP(c_COMBI(X0),c_HOL_Oundefined(X2))) )
| ~ spl0_29
| ~ spl0_304 ),
inference(superposition,[],[f4519,f1156]) ).
fof(f4519,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4)))
| ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1))) )
| ~ spl0_304 ),
inference(avatar_component_clause,[],[f4518]) ).
fof(f5637,plain,
spl0_337,
inference(avatar_split_clause,[],[f167,f5635]) ).
fof(f167,axiom,
! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
fof(f5633,plain,
spl0_336,
inference(avatar_split_clause,[],[f166,f5631]) ).
fof(f166,axiom,
! [X0,X8,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
fof(f5629,plain,
spl0_335,
inference(avatar_split_clause,[],[f117,f5627]) ).
fof(f117,axiom,
! [X10,X0,X1,X6,X12] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),hAPP(X10,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).
fof(f5625,plain,
spl0_334,
inference(avatar_split_clause,[],[f108,f5623]) ).
fof(f108,axiom,
! [X2,X10,X0,X1,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| c_Set_Oimage(X10,X6,X12,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X10,X1,X2,X12,X0),X6,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
fof(f5621,plain,
spl0_333,
inference(avatar_split_clause,[],[f53,f5619]) ).
fof(f5619,plain,
( spl0_333
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f53,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
fof(f5417,plain,
( spl0_332
| ~ spl0_89
| ~ spl0_317
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5413,f5410,f4702,f1445,f5415]) ).
fof(f5415,plain,
( spl0_332
<=> ! [X40,X38,X41,X39,X0,X3,X44,X45,X42,X43] :
( hAPP(X38,hAPP(c_fequal(X0),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f5410,plain,
( spl0_331
<=> ! [X40,X38,X41,X39,X0,X3,X44,X45,X42,X43] :
( hAPP(X38,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f5413,plain,
( ! [X40,X38,X3,X41,X0,X39,X44,X45,X42,X43] :
( hAPP(X38,hAPP(c_fequal(X0),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_331 ),
inference(forward_demodulation,[],[f5411,f5265]) ).
fof(f5411,plain,
( ! [X40,X38,X3,X41,X0,X39,X44,X45,X42,X43] :
( hAPP(X38,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f5410]) ).
fof(f5412,plain,
spl0_331,
inference(avatar_split_clause,[],[f950,f5410]) ).
fof(f950,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X42,X43] :
( hAPP(X38,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f949,f330]) ).
fof(f949,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X42,X43] :
( hAPP(X38,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f773,f33]) ).
fof(f773,plain,
! [X40,X38,X41,X39,X0,X3,X44,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(X38,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))) = X3 ),
inference(definition_unfolding,[],[f535,f240]) ).
fof(f535,axiom,
! [X40,X38,X41,X39,X0,X3,X44,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(X38,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
fof(f5408,plain,
( spl0_330
| ~ spl0_89
| ~ spl0_317
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f5404,f5401,f4702,f1445,f5406]) ).
fof(f5406,plain,
( spl0_330
<=> ! [X40,X38,X41,X39,X0,X3,X44,X45,X42,X43] :
( hAPP(X40,hAPP(c_fequal(X0),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f5401,plain,
( spl0_329
<=> ! [X40,X38,X41,X39,X0,X3,X44,X45,X42,X43] :
( hAPP(X40,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f5404,plain,
( ! [X40,X38,X3,X41,X0,X39,X44,X45,X42,X43] :
( hAPP(X40,hAPP(c_fequal(X0),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_329 ),
inference(forward_demodulation,[],[f5402,f5265]) ).
fof(f5402,plain,
( ! [X40,X38,X3,X41,X0,X39,X44,X45,X42,X43] :
( hAPP(X40,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) )
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f5401]) ).
fof(f5403,plain,
spl0_329,
inference(avatar_split_clause,[],[f948,f5401]) ).
fof(f948,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X42,X43] :
( hAPP(X40,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f947,f330]) ).
fof(f947,plain,
! [X40,X38,X3,X41,X0,X39,X44,X45,X42,X43] :
( hAPP(X40,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
inference(forward_demodulation,[],[f772,f33]) ).
fof(f772,plain,
! [X40,X38,X41,X39,X0,X3,X44,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(X40,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))) = X3 ),
inference(definition_unfolding,[],[f536,f240]) ).
fof(f536,axiom,
! [X40,X38,X41,X39,X0,X3,X44,X45,X42,X43] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0)
| hAPP(X40,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
fof(f5373,plain,
( spl0_328
| ~ spl0_89
| ~ spl0_317
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f5365,f5362,f4702,f1445,f5371]) ).
fof(f5362,plain,
( spl0_326
<=> ! [X6,X0,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f5365,plain,
( ! [X3,X0,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X3),X6,tc_fun(X0,tc_bool)) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_89
| ~ spl0_317
| ~ spl0_326 ),
inference(forward_demodulation,[],[f5363,f5265]) ).
fof(f5363,plain,
( ! [X3,X0,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) )
| ~ spl0_326 ),
inference(avatar_component_clause,[],[f5362]) ).
fof(f5369,plain,
( spl0_327
| ~ spl0_262
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f4060,f3671,f3635,f5367]) ).
fof(f4060,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) )
| ~ spl0_262
| ~ spl0_271 ),
inference(resolution,[],[f3672,f3636]) ).
fof(f5364,plain,
spl0_326,
inference(avatar_split_clause,[],[f906,f5362]) ).
fof(f906,plain,
! [X3,X0,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ),
inference(forward_demodulation,[],[f742,f330]) ).
fof(f742,plain,
! [X3,X0,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X6,tc_fun(X0,tc_bool)) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ),
inference(definition_unfolding,[],[f591,f240]) ).
fof(f591,axiom,
! [X3,X0,X6] :
( c_Set_Oinsert(X3,X6,X0) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f5360,plain,
spl0_325,
inference(avatar_split_clause,[],[f570,f5358]) ).
fof(f570,axiom,
! [X0,X54,X6,X19,X20] :
( hBOOL(hAPP(X20,X54))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X54),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_0) ).
fof(f5356,plain,
spl0_324,
inference(avatar_split_clause,[],[f569,f5354]) ).
fof(f569,axiom,
! [X0,X19,X6,X53,X20] :
( hBOOL(hAPP(X19,X53))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X53),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X6,X20,X19,X0)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_1) ).
fof(f5352,plain,
spl0_323,
inference(avatar_split_clause,[],[f467,f5350]) ).
fof(f5350,plain,
( spl0_323
<=> ! [X10,X0,X12,X6,X7] :
( X6 = X7
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(X10,X6,X0,X12) != c_Set_Oimage(X10,X7,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f467,axiom,
! [X10,X0,X6,X7,X12] :
( X6 = X7
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12)
| c_Set_Oimage(X10,X6,X0,X12) != c_Set_Oimage(X10,X7,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
fof(f5348,plain,
spl0_322,
inference(avatar_split_clause,[],[f222,f5346]) ).
fof(f222,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
fof(f5344,plain,
spl0_321,
inference(avatar_split_clause,[],[f221,f5342]) ).
fof(f221,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
fof(f5340,plain,
spl0_320,
inference(avatar_split_clause,[],[f137,f5338]) ).
fof(f137,axiom,
! [X10,X0,X11,X1] :
( ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11,X0)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X10,X11,X0),hAPP(X10,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).
fof(f5336,plain,
spl0_319,
inference(avatar_split_clause,[],[f107,f5334]) ).
fof(f107,axiom,
! [X2,X10,X0,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Oimage(X10,X6,X12,X0)))
| hAPP(X10,hAPP(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).
fof(f5240,plain,
( spl0_318
| ~ spl0_262
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f4039,f3659,f3635,f5238]) ).
fof(f4039,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XballE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) )
| ~ spl0_262
| ~ spl0_268 ),
inference(resolution,[],[f3660,f3636]) ).
fof(f4704,plain,
spl0_317,
inference(avatar_split_clause,[],[f831,f4702]) ).
fof(f831,plain,
! [X3,X0] : hAPP(c_fequal(X0),X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f830,f330]) ).
fof(f830,plain,
! [X3,X0] : c_Collect(hAPP(c_fequal(X0),X3),X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f701,f330]) ).
fof(f701,plain,
! [X3,X0] : c_Collect(hAPP(c_fequal(X0),X3),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f546,f240]) ).
fof(f546,axiom,
! [X3,X0] : c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Collect(hAPP(c_fequal(X0),X3),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
fof(f4700,plain,
( spl0_316
| ~ spl0_262
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f4022,f3655,f3635,f4698]) ).
fof(f4022,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) )
| ~ spl0_262
| ~ spl0_267 ),
inference(resolution,[],[f3656,f3636]) ).
fof(f4696,plain,
spl0_315,
inference(avatar_split_clause,[],[f600,f4694]) ).
fof(f600,axiom,
! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X6,X20,X0)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_0) ).
fof(f4692,plain,
spl0_314,
inference(avatar_split_clause,[],[f590,f4690]) ).
fof(f590,axiom,
! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XbexE__1__1(X6,X20,X0)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexE_0) ).
fof(f4688,plain,
spl0_313,
inference(avatar_split_clause,[],[f573,f4686]) ).
fof(f573,axiom,
! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XbexI__1__1(X6,X20,X0)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexI_0) ).
fof(f4684,plain,
spl0_312,
inference(avatar_split_clause,[],[f551,f4682]) ).
fof(f551,axiom,
! [X0,X1,X6,X20] :
( hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XballE__1__1(X6,X20,X0)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ballE_0) ).
fof(f4680,plain,
spl0_311,
inference(avatar_split_clause,[],[f432,f4678]) ).
fof(f432,axiom,
! [X3,X0,X6,X20] :
( ~ hBOOL(hAPP(X20,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X6,X20,X0)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexCI_2) ).
fof(f4676,plain,
spl0_310,
inference(avatar_split_clause,[],[f316,f4674]) ).
fof(f316,axiom,
! [X0,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X6,X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_1) ).
fof(f4672,plain,
spl0_309,
inference(avatar_split_clause,[],[f307,f4670]) ).
fof(f307,axiom,
! [X0,X8,X6] :
( hBOOL(hAPP(hAPP(c_in(X0),X6),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X6,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X6),c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionE_0) ).
fof(f4668,plain,
spl0_308,
inference(avatar_split_clause,[],[f190,f4666]) ).
fof(f190,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
fof(f4664,plain,
spl0_307,
inference(avatar_split_clause,[],[f112,f4662]) ).
fof(f112,axiom,
! [X3,X0,X6,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_lessequals(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X7,X0,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
fof(f4660,plain,
spl0_306,
inference(avatar_split_clause,[],[f29,f4658]) ).
fof(f29,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
fof(f4656,plain,
( spl0_305
| ~ spl0_261
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3949,f3635,f3631,f4654]) ).
fof(f3949,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) )
| ~ spl0_261
| ~ spl0_262 ),
inference(resolution,[],[f3632,f3636]) ).
fof(f4520,plain,
( spl0_304
| ~ spl0_260
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3932,f3635,f3627,f4518]) ).
fof(f3932,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,c_HOL_Oundefined(X1)))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Set_Oimage(c_FuncSet_Orestrict(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X0,X4))) )
| ~ spl0_260
| ~ spl0_262 ),
inference(resolution,[],[f3628,f3636]) ).
fof(f4516,plain,
spl0_303,
inference(avatar_split_clause,[],[f603,f4514]) ).
fof(f603,axiom,
! [X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X1)),c_Set_Oimage(X10,X6,X12,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
fof(f4512,plain,
spl0_302,
inference(avatar_split_clause,[],[f525,f4510]) ).
fof(f4510,plain,
( spl0_302
<=> ! [X6,X0,X12] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool),X12),X12,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f525,axiom,
! [X0,X6,X12] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool),X12),X12,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
fof(f4508,plain,
spl0_301,
inference(avatar_split_clause,[],[f371,f4506]) ).
fof(f4506,plain,
( spl0_301
<=> ! [X0,X14,X12,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X14,tc_fun(X0,tc_bool),X12),X12,tc_fun(X0,tc_bool)) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f371,axiom,
! [X0,X6,X14,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X14,tc_fun(X0,tc_bool),X12),X12,tc_fun(X0,tc_bool)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_1) ).
fof(f4504,plain,
spl0_300,
inference(avatar_split_clause,[],[f224,f4502]) ).
fof(f224,axiom,
! [X0,X29,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X29),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X29),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
fof(f4500,plain,
spl0_299,
inference(avatar_split_clause,[],[f160,f4498]) ).
fof(f160,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),c_Lattices_Olower__semilattice__class_Oinf(X5,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f4496,plain,
spl0_298,
inference(avatar_split_clause,[],[f159,f4494]) ).
fof(f159,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f4492,plain,
spl0_297,
inference(avatar_split_clause,[],[f89,f4490]) ).
fof(f89,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oimage(X10,X6,X0,X12),c_Set_Oimage(X10,X7,X0,X12),tc_fun(X12,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
fof(f4488,plain,
spl0_296,
inference(avatar_split_clause,[],[f61,f4486]) ).
fof(f61,axiom,
! [X10,X0,X18,X6,X17,X12] : c_Set_Oimage(X10,c_Set_Oimage(X17,X6,X18,X12),X12,X0) = c_Set_Oimage(c_COMBB(X10,X17,X12,X0,X18),X6,X18,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
fof(f4484,plain,
spl0_295,
inference(avatar_split_clause,[],[f58,f4482]) ).
fof(f58,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f4480,plain,
spl0_294,
inference(avatar_split_clause,[],[f57,f4478]) ).
fof(f57,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X5,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f4172,plain,
spl0_293,
inference(avatar_split_clause,[],[f905,f4170]) ).
fof(f905,plain,
! [X0,X6,X14,X12] :
( c_Set_Oimage(c_COMBK(X14,X0,X12),X6,X12,X0) = hAPP(c_fequal(X0),X14)
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6 ),
inference(forward_demodulation,[],[f904,f831]) ).
fof(f904,plain,
! [X0,X6,X14,X12] :
( c_Set_Oimage(c_COMBK(X14,X0,X12),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6 ),
inference(forward_demodulation,[],[f741,f330]) ).
fof(f741,plain,
! [X0,X6,X14,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6
| c_Set_Oimage(c_COMBK(X14,X0,X12),X6,X12,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X14),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f473,f240]) ).
fof(f473,axiom,
! [X0,X6,X14,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6
| c_Set_Oimage(c_COMBK(X14,X0,X12),X6,X12,X0) = c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
fof(f4168,plain,
spl0_292,
inference(avatar_split_clause,[],[f824,f4166]) ).
fof(f824,plain,
! [X0,X1,X7] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X7,tc_fun(X0,tc_bool)))),
inference(forward_demodulation,[],[f694,f330]) ).
fof(f694,plain,
! [X0,X1,X7] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X7,tc_fun(X0,tc_bool)))),
inference(definition_unfolding,[],[f448,f240]) ).
fof(f448,axiom,
! [X0,X1,X7] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Set_Oinsert(X1,X7,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f4164,plain,
spl0_291,
inference(avatar_split_clause,[],[f622,f4162]) ).
fof(f622,axiom,
! [X0,X6] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X0)),c_COMBI(X0)),c_FuncSet_OPi(X6,c_COMBK(X6,tc_fun(X0,tc_bool),X0),X0,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__id_0) ).
fof(f4160,plain,
spl0_290,
inference(avatar_split_clause,[],[f589,f4158]) ).
fof(f589,axiom,
! [X0,X6,X7,X30,X20] :
( ~ hBOOL(hAPP(X20,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X30),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_5) ).
fof(f4156,plain,
( spl0_289
| ~ spl0_185
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3679,f3635,f2650,f4154]) ).
fof(f3679,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Oundefined(X0),c_Complete__Lattice_OSup__class_OSup(c_Set_Oimage(c_FuncSet_Orestrict(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X0),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_185
| ~ spl0_262 ),
inference(resolution,[],[f3636,f2651]) ).
fof(f4152,plain,
spl0_288,
inference(avatar_split_clause,[],[f588,f4150]) ).
fof(f588,axiom,
! [X0,X1,X6,X7,X20] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X7))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X6,X7,X20,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_7) ).
fof(f4148,plain,
spl0_287,
inference(avatar_split_clause,[],[f556,f4146]) ).
fof(f556,axiom,
! [X0,X6,X7,X14] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f4144,plain,
spl0_286,
inference(avatar_split_clause,[],[f555,f4142]) ).
fof(f555,axiom,
! [X0,X6,X7,X14] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f4140,plain,
spl0_285,
inference(avatar_split_clause,[],[f442,f4138]) ).
fof(f442,axiom,
! [X0,X6,X7,X14] :
( hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f4136,plain,
spl0_284,
inference(avatar_split_clause,[],[f441,f4134]) ).
fof(f441,axiom,
! [X0,X6,X7,X14] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X14),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f4132,plain,
spl0_283,
inference(avatar_split_clause,[],[f314,f4130]) ).
fof(f314,axiom,
! [X0,X6,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
fof(f4128,plain,
spl0_282,
inference(avatar_split_clause,[],[f229,f4126]) ).
fof(f229,axiom,
! [X0,X6,X7,X14] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f4124,plain,
spl0_281,
inference(avatar_split_clause,[],[f228,f4122]) ).
fof(f228,axiom,
! [X0,X6,X7,X14] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X14),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X14),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f4120,plain,
spl0_280,
inference(avatar_split_clause,[],[f143,f4118]) ).
fof(f143,axiom,
! [X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X7),X6))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inter__lower_0) ).
fof(f4116,plain,
spl0_279,
inference(avatar_split_clause,[],[f131,f4114]) ).
fof(f131,axiom,
! [X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X7),X6))
| c_lessequals(X7,c_Complete__Lattice_OSup__class_OSup(X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__upper_0) ).
fof(f4112,plain,
( spl0_278
| ~ spl0_187
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3678,f3635,f2658,f4110]) ).
fof(f3678,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3),c_HOL_Oundefined(X1),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_187
| ~ spl0_262 ),
inference(resolution,[],[f3636,f2659]) ).
fof(f4108,plain,
spl0_277,
inference(avatar_split_clause,[],[f111,f4106]) ).
fof(f111,axiom,
! [X21,X0,X6,X12,X25] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X12)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),X6))
| c_lessequals(hAPP(X21,X25),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X21,X0,X12),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
fof(f4104,plain,
spl0_276,
inference(avatar_split_clause,[],[f32,f4102]) ).
fof(f32,axiom,
! [X10,X0,X6,X7,X12] :
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X6,X10,X12,X0),X7,X0,X12)
| ~ c_lessequals(X7,c_Set_Oimage(X10,X6,X12,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).
fof(f3893,plain,
( spl0_275
| ~ spl0_113
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3680,f3635,f1546,f3891]) ).
fof(f3891,plain,
( spl0_275
<=> ! [X2,X0,X1,X3] : hBOOL(hAPP(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),c_HOL_Oundefined(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f3680,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),c_HOL_Oundefined(X1)))
| ~ spl0_113
| ~ spl0_262 ),
inference(resolution,[],[f3636,f1547]) ).
fof(f3688,plain,
spl0_274,
inference(avatar_split_clause,[],[f821,f3686]) ).
fof(f821,plain,
! [X3,X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X6,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f691,f330]) ).
fof(f691,plain,
! [X3,X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X6,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f334,f240]) ).
fof(f334,axiom,
! [X3,X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X3,X6,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
fof(f3684,plain,
spl0_273,
inference(avatar_split_clause,[],[f819,f3682]) ).
fof(f819,plain,
! [X1,X37,X30] :
( X1 = X30
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X1))) ),
inference(duplicate_literal_removal,[],[f367]) ).
fof(f367,axiom,
! [X1,X37,X30] :
( X1 = X30
| X1 = X30
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).
fof(f3677,plain,
spl0_272,
inference(avatar_split_clause,[],[f818,f3675]) ).
fof(f818,plain,
! [X2,X1,X37] :
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1))) ),
inference(duplicate_literal_removal,[],[f454]) ).
fof(f454,axiom,
! [X2,X1,X37] :
( X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
fof(f3673,plain,
spl0_271,
inference(avatar_split_clause,[],[f601,f3671]) ).
fof(f601,axiom,
! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X6,X20,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
fof(f3669,plain,
spl0_270,
inference(avatar_split_clause,[],[f599,f3667]) ).
fof(f599,axiom,
! [X41,X46,X0,X47,X25,X42] :
( hBOOL(hAPP(hAPP(X41,X46),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastLessThan(X41,X42,X46,X47,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_0) ).
fof(f3665,plain,
spl0_269,
inference(avatar_split_clause,[],[f598,f3663]) ).
fof(f598,axiom,
! [X41,X0,X46,X47,X42,X25] :
( hBOOL(hAPP(hAPP(X42,X25),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastLessThan(X41,X42,X46,X47,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_1) ).
fof(f3661,plain,
spl0_268,
inference(avatar_split_clause,[],[f571,f3659]) ).
fof(f571,axiom,
! [X0,X1,X6,X20] :
( hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XballE__1__1(X6,X20,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ballE_1) ).
fof(f3657,plain,
spl0_267,
inference(avatar_split_clause,[],[f552,f3655]) ).
fof(f552,axiom,
! [X3,X0,X6,X20] :
( ~ hBOOL(hAPP(X20,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X6,X20,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexCI_3) ).
fof(f3653,plain,
spl0_266,
inference(avatar_split_clause,[],[f524,f3651]) ).
fof(f3651,plain,
( spl0_266
<=> ! [X40,X38,X41,X39,X0,X44,X45,X42,X43] :
( hAPP(X40,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X39
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f524,axiom,
! [X40,X38,X41,X39,X0,X44,X45,X42,X43] :
( hAPP(X40,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X39
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
fof(f3649,plain,
spl0_265,
inference(avatar_split_clause,[],[f523,f3647]) ).
fof(f3647,plain,
( spl0_265
<=> ! [X38,X43,X41,X42,X0,X44,X40,X45,X39] :
( hAPP(X38,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X45
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f523,axiom,
! [X40,X38,X41,X39,X0,X44,X45,X42,X43] :
( hAPP(X38,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X45
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
fof(f3645,plain,
spl0_264,
inference(avatar_split_clause,[],[f517,f3643]) ).
fof(f3643,plain,
( spl0_264
<=> ! [X6,X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f517,axiom,
! [X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f3641,plain,
spl0_263,
inference(avatar_split_clause,[],[f453,f3639]) ).
fof(f453,axiom,
! [X2,X10,X0,X1,X12] :
( X1 = X2
| hAPP(X10,X1) != hAPP(X10,X2)
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
fof(f3637,plain,
( spl0_262
| ~ spl0_203
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f3591,f3549,f2831,f3635]) ).
fof(f3549,plain,
( spl0_247
<=> ! [X0,X1] : hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) = c_HOL_Oundefined(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f3591,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_in(X2),c_HOL_Oundefined(X1)),c_Set_Oimage(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X2)))
| ~ spl0_203
| ~ spl0_247 ),
inference(superposition,[],[f2832,f3550]) ).
fof(f3550,plain,
( ! [X0,X1] : hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) = c_HOL_Oundefined(X1)
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f3549]) ).
fof(f3633,plain,
spl0_261,
inference(avatar_split_clause,[],[f445,f3631]) ).
fof(f445,axiom,
! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XbexE__1__1(X6,X20,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexE_1) ).
fof(f3629,plain,
spl0_260,
inference(avatar_split_clause,[],[f444,f3627]) ).
fof(f444,axiom,
! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Set__XbexI__1__1(X6,X20,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexI_1) ).
fof(f3625,plain,
spl0_259,
inference(avatar_split_clause,[],[f430,f3623]) ).
fof(f430,axiom,
! [X10,X0,X1,X6,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hAPP(X10,X1) = hAPP(c_FuncSet_Orestrict(X10,X6,X12,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__apply_0) ).
fof(f3621,plain,
spl0_258,
inference(avatar_split_clause,[],[f383,f3619]) ).
fof(f383,axiom,
! [X3,X4] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
fof(f3617,plain,
spl0_257,
inference(avatar_split_clause,[],[f372,f3615]) ).
fof(f372,axiom,
! [X21,X0,X6,X12] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X12)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X21,X12,X0),X0,X12) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).
fof(f3613,plain,
spl0_256,
inference(avatar_split_clause,[],[f354,f3611]) ).
fof(f3611,plain,
( spl0_256
<=> ! [X6,X0,X7] : c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f354,axiom,
! [X0,X6,X7] : c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f3609,plain,
spl0_255,
inference(avatar_split_clause,[],[f322,f3607]) ).
fof(f3607,plain,
( spl0_255
<=> ! [X40,X38,X41,X39,X0,X44,X45,X42,X43] :
( hAPP(X40,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X45
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f322,axiom,
! [X40,X38,X41,X39,X0,X44,X45,X42,X43] :
( hAPP(X40,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X45
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).
fof(f3605,plain,
spl0_254,
inference(avatar_split_clause,[],[f321,f3603]) ).
fof(f3603,plain,
( spl0_254
<=> ! [X38,X43,X41,X42,X0,X44,X40,X45,X39] :
( hAPP(X38,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X39
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f321,axiom,
! [X40,X38,X41,X39,X0,X44,X45,X42,X43] :
( hAPP(X38,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X39
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X38,X41,X42,X43,X44,X45,X39,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
fof(f3601,plain,
spl0_253,
inference(avatar_split_clause,[],[f214,f3599]) ).
fof(f3599,plain,
( spl0_253
<=> ! [X6,X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f214,axiom,
! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f3597,plain,
spl0_252,
inference(avatar_split_clause,[],[f200,f3595]) ).
fof(f200,axiom,
! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
fof(f3590,plain,
spl0_251,
inference(avatar_split_clause,[],[f199,f3588]) ).
fof(f199,axiom,
! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
fof(f3586,plain,
spl0_250,
inference(avatar_split_clause,[],[f133,f3584]) ).
fof(f133,axiom,
! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
fof(f3582,plain,
spl0_249,
inference(avatar_split_clause,[],[f74,f3580]) ).
fof(f74,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f3578,plain,
spl0_248,
inference(avatar_split_clause,[],[f31,f3576]) ).
fof(f31,axiom,
! [X2,X10,X0,X1,X5,X12] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X10,X1,X2,X0,X12),X1,X5,X0,X12) = c_Fun_Ofun__upd(X10,X1,X5,X0,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
fof(f3551,plain,
( spl0_247
| spl0_23
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3544,f3152,f1130,f3549]) ).
fof(f3544,plain,
( ! [X0,X1] : hAPP(c_FuncSet_Orestrict(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X1),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) = c_HOL_Oundefined(X1)
| spl0_23
| ~ spl0_239 ),
inference(resolution,[],[f3153,f1132]) ).
fof(f3441,plain,
( spl0_246
| ~ spl0_16
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1419,f1369,f1095,f3439]) ).
fof(f3439,plain,
( spl0_246
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1419,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool)
| ~ spl0_16
| ~ spl0_76 ),
inference(resolution,[],[f1370,f1097]) ).
fof(f3178,plain,
spl0_245,
inference(avatar_split_clause,[],[f883,f3176]) ).
fof(f883,plain,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)))
| X3 = X4 ),
inference(forward_demodulation,[],[f882,f330]) ).
fof(f882,plain,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0)))
| X3 = X4 ),
inference(forward_demodulation,[],[f731,f33]) ).
fof(f731,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)))) ),
inference(definition_unfolding,[],[f315,f240]) ).
fof(f315,axiom,
! [X3,X0,X4] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f3174,plain,
spl0_244,
inference(avatar_split_clause,[],[f587,f3172]) ).
fof(f587,axiom,
! [X41,X46,X0,X47,X25] :
( hBOOL(hAPP(hAPP(X41,X46),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastAtMost(X41,X46,X47,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).
fof(f3170,plain,
spl0_243,
inference(avatar_split_clause,[],[f586,f3168]) ).
fof(f586,axiom,
! [X41,X0,X46,X47,X25] :
( hBOOL(hAPP(hAPP(X41,X25),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatLeastAtMost(X41,X46,X47,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).
fof(f3166,plain,
spl0_242,
inference(avatar_split_clause,[],[f554,f3164]) ).
fof(f554,axiom,
! [X0,X46,X47,X42,X25] :
( hBOOL(hAPP(hAPP(X42,X25),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThanLessThan(X42,X46,X47,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_1) ).
fof(f3162,plain,
spl0_241,
inference(avatar_split_clause,[],[f553,f3160]) ).
fof(f553,axiom,
! [X46,X0,X47,X42,X25] :
( hBOOL(hAPP(hAPP(X42,X46),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThanLessThan(X42,X46,X47,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_0) ).
fof(f3158,plain,
spl0_240,
inference(avatar_split_clause,[],[f545,f3156]) ).
fof(f3156,plain,
( spl0_240
<=> ! [X0,X6,X1,X7] :
( ~ hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(X7,X1))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f545,axiom,
! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(X7,X1))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f3154,plain,
spl0_239,
inference(avatar_split_clause,[],[f463,f3152]) ).
fof(f463,axiom,
! [X10,X0,X1,X6,X12] :
( hBOOL(hAPP(hAPP(c_in(X12),X1),X6))
| hAPP(c_FuncSet_Orestrict(X10,X6,X12,X0),X1) = c_HOL_Oundefined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__apply_1) ).
fof(f3150,plain,
( ~ spl0_14
| spl0_238
| ~ spl0_55
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2890,f2654,f1265,f3148,f1085]) ).
fof(f3148,plain,
( spl0_238
<=> ! [X0] : c_lessequals(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2890,plain,
( ! [X0] :
( c_lessequals(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_55
| ~ spl0_186 ),
inference(superposition,[],[f1266,f2655]) ).
fof(f3146,plain,
spl0_237,
inference(avatar_split_clause,[],[f460,f3144]) ).
fof(f3144,plain,
( spl0_237
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X5,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f460,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X5,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f3142,plain,
spl0_236,
inference(avatar_split_clause,[],[f459,f3140]) ).
fof(f3140,plain,
( spl0_236
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f459,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f3138,plain,
spl0_235,
inference(avatar_split_clause,[],[f458,f3136]) ).
fof(f458,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f3134,plain,
spl0_234,
inference(avatar_split_clause,[],[f457,f3132]) ).
fof(f457,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X5,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f3130,plain,
spl0_233,
inference(avatar_split_clause,[],[f351,f3128]) ).
fof(f3128,plain,
( spl0_233
<=> ! [X0,X12,X6,X7] : c_HOL_Ominus__class_Ominus(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f351,axiom,
! [X0,X6,X7,X12] : c_HOL_Ominus__class_Ominus(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
fof(f3126,plain,
spl0_232,
inference(avatar_split_clause,[],[f203,f3124]) ).
fof(f203,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f3122,plain,
spl0_231,
inference(avatar_split_clause,[],[f202,f3120]) ).
fof(f202,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f3118,plain,
spl0_230,
inference(avatar_split_clause,[],[f196,f3116]) ).
fof(f196,axiom,
! [X0,X6,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f3114,plain,
spl0_229,
inference(avatar_split_clause,[],[f195,f3112]) ).
fof(f195,axiom,
! [X0,X6,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X7
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f3110,plain,
spl0_228,
inference(avatar_split_clause,[],[f184,f3108]) ).
fof(f184,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X1,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
fof(f3097,plain,
spl0_227,
inference(avatar_split_clause,[],[f171,f3095]) ).
fof(f3095,plain,
( spl0_227
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X5,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f171,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X5,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f3093,plain,
spl0_226,
inference(avatar_split_clause,[],[f170,f3091]) ).
fof(f3091,plain,
( spl0_226
<=> ! [X0,X5,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f170,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f3089,plain,
spl0_225,
inference(avatar_split_clause,[],[f169,f3087]) ).
fof(f169,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f3085,plain,
spl0_224,
inference(avatar_split_clause,[],[f168,f3083]) ).
fof(f168,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X5,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f3081,plain,
spl0_223,
inference(avatar_split_clause,[],[f141,f3079]) ).
fof(f141,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X6),c_Set_OPow(X7,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PowI_0) ).
fof(f3077,plain,
spl0_222,
inference(avatar_split_clause,[],[f140,f3075]) ).
fof(f140,axiom,
! [X0,X6,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X6),c_Set_OPow(X7,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PowD_0) ).
fof(f3073,plain,
spl0_221,
inference(avatar_split_clause,[],[f123,f3071]) ).
fof(f123,axiom,
! [X0,X6,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X7,X12,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
fof(f3069,plain,
spl0_220,
inference(avatar_split_clause,[],[f122,f3067]) ).
fof(f122,axiom,
! [X0,X6,X7,X12] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X6,X12,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
fof(f3065,plain,
spl0_219,
inference(avatar_split_clause,[],[f69,f3063]) ).
fof(f69,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f3061,plain,
spl0_218,
inference(avatar_split_clause,[],[f68,f3059]) ).
fof(f68,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f3057,plain,
( ~ spl0_13
| spl0_217
| ~ spl0_63
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2790,f2567,f1297,f3055,f1080]) ).
fof(f3055,plain,
( spl0_217
<=> ! [X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f2790,plain,
( ! [X0] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_63
| ~ spl0_180 ),
inference(superposition,[],[f1298,f2568]) ).
fof(f3053,plain,
spl0_216,
inference(avatar_split_clause,[],[f39,f3051]) ).
fof(f39,axiom,
! [X0,X1,X6,X7] :
( hBOOL(hAPP(X7,X1))
| hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f3049,plain,
spl0_215,
inference(avatar_split_clause,[],[f3,f3047]) ).
fof(f3,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X1,X4,X0)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
fof(f2888,plain,
spl0_214,
inference(avatar_split_clause,[],[f891,f2886]) ).
fof(f891,plain,
! [X0,X1,X6,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Olower__semilattice__class_Oinf(X6,X20,tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X20,X1)) ),
inference(forward_demodulation,[],[f313,f330]) ).
fof(f313,axiom,
! [X0,X1,X6,X20] :
( hBOOL(hAPP(X20,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Olower__semilattice__class_Oinf(X6,c_Collect(X20,X0),tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
fof(f2884,plain,
spl0_213,
inference(avatar_split_clause,[],[f820,f2882]) ).
fof(f820,plain,
! [X0,X1,X6] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X6,tc_fun(X0,tc_bool)),X1)),
inference(forward_demodulation,[],[f689,f330]) ).
fof(f689,plain,
! [X0,X1,X6] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X6,tc_fun(X0,tc_bool)),X1)),
inference(definition_unfolding,[],[f514,f240]) ).
fof(f514,axiom,
! [X0,X1,X6] : hBOOL(hAPP(c_Set_Oinsert(X1,X6,X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f2880,plain,
spl0_212,
inference(avatar_split_clause,[],[f638,f2878]) ).
fof(f638,axiom,
! [X3,X4] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X3,X4)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_0) ).
fof(f2876,plain,
spl0_211,
inference(avatar_split_clause,[],[f593,f2874]) ).
fof(f593,axiom,
! [X0,X27,X42,X25] :
( hBOOL(hAPP(hAPP(X42,X25),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OlessThan(X42,X27,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_0) ).
fof(f2872,plain,
spl0_210,
inference(avatar_split_clause,[],[f592,f2870]) ).
fof(f592,axiom,
! [X0,X27,X42,X25] :
( ~ hBOOL(hAPP(hAPP(X42,X25),X27))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OlessThan(X42,X27,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).
fof(f2868,plain,
spl0_209,
inference(avatar_split_clause,[],[f577,f2866]) ).
fof(f577,axiom,
! [X0,X27,X42,X25] :
( hBOOL(hAPP(hAPP(X42,X27),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThan(X42,X27,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_0) ).
fof(f2864,plain,
spl0_208,
inference(avatar_split_clause,[],[f576,f2862]) ).
fof(f576,axiom,
! [X0,X27,X42,X25] :
( ~ hBOOL(hAPP(hAPP(X42,X27),X25))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OgreaterThan(X42,X27,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_1) ).
fof(f2860,plain,
spl0_207,
inference(avatar_split_clause,[],[f566,f2858]) ).
fof(f566,axiom,
! [X41,X0,X27,X25] :
( hBOOL(hAPP(hAPP(X41,X25),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatMost(X41,X27,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatMost__iff_0) ).
fof(f2856,plain,
spl0_206,
inference(avatar_split_clause,[],[f565,f2854]) ).
fof(f565,axiom,
! [X41,X0,X27,X25] :
( ~ hBOOL(hAPP(hAPP(X41,X25),X27))
| hBOOL(hAPP(hAPP(c_in(X0),X25),c_SetInterval_Oord_OatMost(X41,X27,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatMost__iff_1) ).
fof(f2852,plain,
spl0_205,
inference(avatar_split_clause,[],[f486,f2850]) ).
fof(f486,axiom,
! [X10,X0,X6,X12] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X12)),c_FuncSet_Orestrict(X10,X6,X0,X12)),c_FuncSet_Oextensional(X6,X0,X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__extensional_0) ).
fof(f2837,plain,
spl0_204,
inference(avatar_split_clause,[],[f380,f2835]) ).
fof(f380,axiom,
! [X0,X6,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
fof(f2833,plain,
spl0_203,
inference(avatar_split_clause,[],[f355,f2831]) ).
fof(f355,axiom,
! [X10,X0,X1,X12] : hBOOL(hAPP(hAPP(c_in(X0),hAPP(X10,X1)),c_Set_Oimage(X10,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_bool)),X12,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
fof(f2829,plain,
spl0_202,
inference(avatar_split_clause,[],[f326,f2827]) ).
fof(f326,axiom,
! [X10,X0,X6,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X10,X6,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
fof(f2825,plain,
spl0_201,
inference(avatar_split_clause,[],[f309,f2823]) ).
fof(f309,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Fun_Obij__betw(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X7,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__restrict__eq_1) ).
fof(f2821,plain,
spl0_200,
inference(avatar_split_clause,[],[f308,f2819]) ).
fof(f308,axiom,
! [X10,X0,X6,X7,X12] :
( c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| ~ c_Fun_Obij__betw(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X7,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__restrict__eq_0) ).
fof(f2817,plain,
spl0_199,
inference(avatar_split_clause,[],[f223,f2815]) ).
fof(f223,axiom,
! [X10,X0,X1,X17,X12] :
( ~ class_HOL_Oord(X12)
| ~ c_lessequals(X10,X17,tc_fun(X0,X12))
| c_lessequals(hAPP(X10,X1),hAPP(X17,X1),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f2813,plain,
spl0_198,
inference(avatar_split_clause,[],[f201,f2811]) ).
fof(f201,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Fun_Obij__betw(c_Hilbert__Choice_Oinv__into(X6,X10,X0,X12),X7,X6,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__inv__into_0) ).
fof(f2809,plain,
spl0_197,
inference(avatar_split_clause,[],[f75,f2807]) ).
fof(f75,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,X7,X0,X12)
| c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
fof(f2713,plain,
( spl0_196
| ~ spl0_16
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1354,f1325,f1095,f2711]) ).
fof(f2711,plain,
( spl0_196
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1354,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) = X0
| ~ spl0_16
| ~ spl0_70 ),
inference(resolution,[],[f1326,f1097]) ).
fof(f2692,plain,
spl0_195,
inference(avatar_split_clause,[],[f502,f2690]) ).
fof(f502,axiom,
! [X2,X1,X37] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X37,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
fof(f2688,plain,
spl0_194,
inference(avatar_split_clause,[],[f481,f2686]) ).
fof(f481,axiom,
! [X10,X0,X6,X12] : c_Set_Oimage(X10,X6,X12,X0) = c_Set_Oimage(c_FuncSet_Orestrict(X10,X6,X12,X0),X6,X12,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__restrict__eq_0) ).
fof(f2684,plain,
spl0_193,
inference(avatar_split_clause,[],[f466,f2682]) ).
fof(f466,axiom,
! [X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Obij__betw(X10,X6,c_Set_Oimage(X10,X6,X0,X12),X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__def_2) ).
fof(f2680,plain,
spl0_192,
inference(avatar_split_clause,[],[f352,f2678]) ).
fof(f352,axiom,
! [X0,X18,X19,X16,X12,X20] : hAPP(hAPP(c_COMBC(X20,X12,X18,X0),X19),X16) = hAPP(hAPP(X20,X16),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
fof(f2676,plain,
spl0_191,
inference(avatar_split_clause,[],[f325,f2674]) ).
fof(f2674,plain,
( spl0_191
<=> ! [X10,X0,X12,X6,X7] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f325,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(X10,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
fof(f2672,plain,
spl0_190,
inference(avatar_split_clause,[],[f323,f2670]) ).
fof(f323,axiom,
! [X1,X37,X30] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X37,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
fof(f2668,plain,
spl0_189,
inference(avatar_split_clause,[],[f220,f2666]) ).
fof(f220,axiom,
! [X10,X0,X6,X7,X12] :
( c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
fof(f2664,plain,
spl0_188,
inference(avatar_split_clause,[],[f219,f2662]) ).
fof(f219,axiom,
! [X10,X0,X6,X7,X12] :
( c_Fun_Oinj__on(X10,X7,X0,X12)
| ~ c_Fun_Oinj__on(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
fof(f2660,plain,
spl0_187,
inference(avatar_split_clause,[],[f138,f2658]) ).
fof(f138,axiom,
! [X0,X1,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,X0),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
fof(f2656,plain,
( spl0_186
| ~ spl0_16
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f1352,f1321,f1095,f2654]) ).
fof(f1352,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0
| ~ spl0_16
| ~ spl0_69 ),
inference(resolution,[],[f1322,f1097]) ).
fof(f2652,plain,
spl0_185,
inference(avatar_split_clause,[],[f119,f2650]) ).
fof(f119,axiom,
! [X0,X1,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
fof(f2648,plain,
spl0_184,
inference(avatar_split_clause,[],[f85,f2646]) ).
fof(f85,axiom,
! [X2,X10,X0,X1,X5,X12] :
( X1 = X5
| hAPP(X10,X5) = hAPP(c_Fun_Ofun__upd(X10,X1,X2,X0,X12),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
fof(f2644,plain,
spl0_183,
inference(avatar_split_clause,[],[f26,f2642]) ).
fof(f26,axiom,
! [X0,X6,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
fof(f2640,plain,
spl0_182,
inference(avatar_split_clause,[],[f10,f2638]) ).
fof(f10,axiom,
! [X0,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f2626,plain,
( spl0_181
| ~ spl0_16
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f1338,f1281,f1095,f2624]) ).
fof(f1338,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_16
| ~ spl0_59 ),
inference(resolution,[],[f1282,f1097]) ).
fof(f2569,plain,
( spl0_180
| ~ spl0_16
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f1336,f1277,f1095,f2567]) ).
fof(f1336,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_16
| ~ spl0_58 ),
inference(resolution,[],[f1278,f1097]) ).
fof(f2298,plain,
spl0_179,
inference(avatar_split_clause,[],[f873,f2296]) ).
fof(f873,plain,
! [X3,X0] :
( c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f872,f330]) ).
fof(f872,plain,
! [X3,X0] :
( c_Complete__Lattice_OSup__class_OSup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f726,f33]) ).
fof(f726,plain,
! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X3 ),
inference(definition_unfolding,[],[f529,f240]) ).
fof(f529,axiom,
! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
fof(f2294,plain,
spl0_178,
inference(avatar_split_clause,[],[f871,f2292]) ).
fof(f871,plain,
! [X3,X0] :
( c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f870,f330]) ).
fof(f870,plain,
! [X3,X0] :
( c_Complete__Lattice_OInf__class_OInf(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),X0) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f725,f33]) ).
fof(f725,plain,
! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X3 ),
inference(definition_unfolding,[],[f381,f240]) ).
fof(f381,axiom,
! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
fof(f2290,plain,
spl0_177,
inference(avatar_split_clause,[],[f829,f2288]) ).
fof(f829,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1))),
inference(forward_demodulation,[],[f828,f330]) ).
fof(f828,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0))),
inference(forward_demodulation,[],[f700,f33]) ).
fof(f700,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)))),
inference(definition_unfolding,[],[f539,f240]) ).
fof(f539,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
fof(f2286,plain,
spl0_176,
inference(avatar_split_clause,[],[f548,f2284]) ).
fof(f548,axiom,
! [X0,X6] : c_Collect(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X6),X0) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
fof(f2282,plain,
spl0_175,
inference(avatar_split_clause,[],[f538,f2280]) ).
fof(f2280,plain,
( spl0_175
<=> ! [X4,X34,X0,X12,X33,X3] :
( X4 = X34
| c_Pair(X3,X4,X0,X12) != c_Pair(X33,X34,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f538,axiom,
! [X3,X0,X4,X34,X12,X33] :
( X4 = X34
| c_Pair(X3,X4,X0,X12) != c_Pair(X33,X34,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
fof(f2278,plain,
spl0_174,
inference(avatar_split_clause,[],[f537,f2276]) ).
fof(f2276,plain,
( spl0_174
<=> ! [X33,X34,X0,X4,X12,X3] :
( X3 = X33
| c_Pair(X3,X4,X0,X12) != c_Pair(X33,X34,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f537,axiom,
! [X3,X0,X4,X34,X12,X33] :
( X3 = X33
| c_Pair(X3,X4,X0,X12) != c_Pair(X33,X34,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
fof(f2274,plain,
spl0_173,
inference(avatar_split_clause,[],[f516,f2272]) ).
fof(f2272,plain,
( spl0_173
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f516,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f2270,plain,
( ~ spl0_18
| spl0_172
| ~ spl0_60
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1408,f1309,f1285,f2268,f1105]) ).
fof(f1285,plain,
( spl0_60
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1408,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_60
| ~ spl0_66 ),
inference(superposition,[],[f1310,f1286]) ).
fof(f1286,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f2266,plain,
spl0_171,
inference(avatar_split_clause,[],[f515,f2264]) ).
fof(f515,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f2262,plain,
spl0_170,
inference(avatar_split_clause,[],[f509,f2260]) ).
fof(f2260,plain,
( spl0_170
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f509,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
fof(f2258,plain,
spl0_169,
inference(avatar_split_clause,[],[f500,f2256]) ).
fof(f2256,plain,
( spl0_169
<=> ! [X10,X0,X12,X6] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f500,axiom,
! [X10,X0,X6,X12] :
( ~ c_Fun_Oinj__on(X10,X6,X0,X12)
| c_Fun_Oinj__on(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__restrict__eq_1) ).
fof(f2254,plain,
spl0_168,
inference(avatar_split_clause,[],[f499,f2252]) ).
fof(f2252,plain,
( spl0_168
<=> ! [X10,X0,X12,X6] :
( c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_Fun_Oinj__on(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f499,axiom,
! [X10,X0,X6,X12] :
( c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_Fun_Oinj__on(c_FuncSet_Orestrict(X10,X6,X0,X12),X6,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__restrict__eq_0) ).
fof(f2250,plain,
spl0_167,
inference(avatar_split_clause,[],[f483,f2248]) ).
fof(f483,axiom,
! [X0,X7] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),c_Set_OPow(X7,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pow__bottom_0) ).
fof(f2246,plain,
spl0_166,
inference(avatar_split_clause,[],[f465,f2244]) ).
fof(f2244,plain,
( spl0_166
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f465,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f2242,plain,
spl0_165,
inference(avatar_split_clause,[],[f344,f2240]) ).
fof(f344,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f2238,plain,
spl0_164,
inference(avatar_split_clause,[],[f343,f2236]) ).
fof(f343,axiom,
! [X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f2234,plain,
spl0_163,
inference(avatar_split_clause,[],[f216,f2232]) ).
fof(f2232,plain,
( spl0_163
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f216,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f2230,plain,
spl0_162,
inference(avatar_split_clause,[],[f215,f2228]) ).
fof(f215,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f2226,plain,
spl0_161,
inference(avatar_split_clause,[],[f173,f2224]) ).
fof(f173,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f2222,plain,
spl0_160,
inference(avatar_split_clause,[],[f172,f2220]) ).
fof(f172,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f2218,plain,
spl0_159,
inference(avatar_split_clause,[],[f165,f2216]) ).
fof(f165,axiom,
! [X0,X18,X19,X16,X12,X20] : hAPP(c_COMBB(X20,X19,X12,X0,X18),X16) = hAPP(X20,hAPP(X19,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
fof(f2214,plain,
spl0_158,
inference(avatar_split_clause,[],[f81,f2212]) ).
fof(f81,axiom,
! [X10,X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_lessequals(hAPP(X10,X6),X6,X0)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(X10,X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lfp__lowerbound_0) ).
fof(f2210,plain,
spl0_157,
inference(avatar_split_clause,[],[f76,f2208]) ).
fof(f76,axiom,
! [X0,X1,X19,X20] :
( ~ hBOOL(hAPP(X20,X1))
| hBOOL(hAPP(X19,X1))
| ~ c_lessequals(X20,X19,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
fof(f2206,plain,
spl0_156,
inference(avatar_split_clause,[],[f71,f2204]) ).
fof(f71,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X5,X0)
| c_lessequals(X1,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f2202,plain,
spl0_155,
inference(avatar_split_clause,[],[f70,f2200]) ).
fof(f70,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X2,X0)
| c_lessequals(X5,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f2198,plain,
spl0_154,
inference(avatar_split_clause,[],[f48,f2196]) ).
fof(f48,axiom,
! [X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
fof(f2194,plain,
spl0_153,
inference(avatar_split_clause,[],[f47,f2192]) ).
fof(f47,axiom,
! [X0,X6] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
fof(f2190,plain,
spl0_152,
inference(avatar_split_clause,[],[f18,f2188]) ).
fof(f18,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f2186,plain,
( spl0_151
| ~ spl0_110
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1618,f1546,f1533,f2184]) ).
fof(f1618,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_OPow(X0,X1),X0))
| ~ spl0_110
| ~ spl0_113 ),
inference(resolution,[],[f1547,f1534]) ).
fof(f2182,plain,
spl0_150,
inference(avatar_split_clause,[],[f17,f2180]) ).
fof(f17,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f2178,plain,
spl0_149,
inference(avatar_split_clause,[],[f16,f2176]) ).
fof(f16,axiom,
! [X0,X6,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f1885,plain,
spl0_148,
inference(avatar_split_clause,[],[f522,f1883]) ).
fof(f522,axiom,
! [X10,X0,X6,X7,X12] :
( ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12)
| c_Set_Oimage(X10,X6,X0,X12) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__def_1) ).
fof(f1881,plain,
spl0_147,
inference(avatar_split_clause,[],[f469,f1879]) ).
fof(f1879,plain,
( spl0_147
<=> ! [X6,X0,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X6
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f469,axiom,
! [X0,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X6
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
fof(f1877,plain,
spl0_146,
inference(avatar_split_clause,[],[f468,f1875]) ).
fof(f1875,plain,
( spl0_146
<=> ! [X6,X0,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X7
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f468,axiom,
! [X0,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X7
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
fof(f1873,plain,
spl0_145,
inference(avatar_split_clause,[],[f388,f1871]) ).
fof(f388,axiom,
! [X0,X1,X6,X7] :
( hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f1869,plain,
( spl0_144
| ~ spl0_113
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1620,f1550,f1546,f1866]) ).
fof(f1620,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____))
| ~ spl0_113
| ~ spl0_114 ),
inference(resolution,[],[f1552,f1547]) ).
fof(f1864,plain,
spl0_143,
inference(avatar_split_clause,[],[f387,f1862]) ).
fof(f387,axiom,
! [X0,X1,X6,X7] :
( hBOOL(hAPP(X7,X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f1860,plain,
spl0_142,
inference(avatar_split_clause,[],[f379,f1858]) ).
fof(f379,axiom,
! [X10,X0,X12] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
fof(f1856,plain,
spl0_141,
inference(avatar_split_clause,[],[f361,f1854]) ).
fof(f1852,plain,
spl0_140,
inference(avatar_split_clause,[],[f218,f1850]) ).
fof(f1850,plain,
( spl0_140
<=> ! [X10,X0,X12,X2,X1] :
( hAPP(X10,X1) = X2
| c_Fun_Ofun__upd(X10,X1,X2,X0,X12) != X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f218,axiom,
! [X2,X10,X0,X1,X12] :
( hAPP(X10,X1) = X2
| c_Fun_Ofun__upd(X10,X1,X2,X0,X12) != X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
fof(f1848,plain,
spl0_139,
inference(avatar_split_clause,[],[f211,f1846]) ).
fof(f211,axiom,
! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f1844,plain,
spl0_138,
inference(avatar_split_clause,[],[f209,f1842]) ).
fof(f209,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X5,X0)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
fof(f1840,plain,
spl0_137,
inference(avatar_split_clause,[],[f208,f1838]) ).
fof(f208,axiom,
! [X2,X0,X1,X5] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f1836,plain,
spl0_136,
inference(avatar_split_clause,[],[f207,f1834]) ).
fof(f207,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X1,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f1832,plain,
spl0_135,
inference(avatar_split_clause,[],[f206,f1830]) ).
fof(f206,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f1828,plain,
spl0_134,
inference(avatar_split_clause,[],[f198,f1826]) ).
fof(f198,axiom,
! [X0,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X7
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f1824,plain,
( spl0_133
| ~ spl0_111
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1619,f1546,f1537,f1821]) ).
fof(f1619,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| ~ spl0_111
| ~ spl0_113 ),
inference(resolution,[],[f1547,f1539]) ).
fof(f1819,plain,
spl0_132,
inference(avatar_split_clause,[],[f197,f1817]) ).
fof(f1817,plain,
( spl0_132
<=> ! [X6,X0,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X6
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f197,axiom,
! [X0,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X6
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f1815,plain,
spl0_131,
inference(avatar_split_clause,[],[f67,f1813]) ).
fof(f67,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
fof(f1811,plain,
spl0_130,
inference(avatar_split_clause,[],[f66,f1809]) ).
fof(f66,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X4,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
fof(f1807,plain,
spl0_129,
inference(avatar_split_clause,[],[f65,f1805]) ).
fof(f65,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f1803,plain,
spl0_128,
inference(avatar_split_clause,[],[f64,f1801]) ).
fof(f64,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X4,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f1799,plain,
spl0_127,
inference(avatar_split_clause,[],[f46,f1797]) ).
fof(f1797,plain,
( spl0_127
<=> ! [X0,X12,X16] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Relation_OImage(X16,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f46,axiom,
! [X0,X16,X12] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Relation_OImage(X16,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
fof(f1795,plain,
spl0_126,
inference(avatar_split_clause,[],[f44,f1793]) ).
fof(f1793,plain,
( spl0_126
<=> ! [X5,X10,X0,X12,X1] :
( X1 = X5
| ~ c_Finite__Set_Ofold__graph(X10,X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f44,axiom,
! [X10,X0,X1,X5,X12] :
( X1 = X5
| ~ c_Finite__Set_Ofold__graph(X10,X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
fof(f1791,plain,
spl0_125,
inference(avatar_split_clause,[],[f38,f1789]) ).
fof(f38,axiom,
! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(X7,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f1787,plain,
spl0_124,
inference(avatar_split_clause,[],[f37,f1785]) ).
fof(f37,axiom,
! [X0,X1,X6,X7] :
( ~ hBOOL(hAPP(X6,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f1783,plain,
spl0_123,
inference(avatar_split_clause,[],[f24,f1781]) ).
fof(f24,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
fof(f1649,plain,
spl0_122,
inference(avatar_split_clause,[],[f176,f1647]) ).
fof(f176,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f1645,plain,
spl0_121,
inference(avatar_split_clause,[],[f175,f1643]) ).
fof(f175,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f1641,plain,
spl0_120,
inference(avatar_split_clause,[],[f174,f1639]) ).
fof(f174,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f1637,plain,
spl0_119,
inference(avatar_split_clause,[],[f21,f1635]) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f1633,plain,
( ~ spl0_118
| spl0_23
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1614,f1542,f1130,f1630]) ).
fof(f1614,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))))
| spl0_23
| ~ spl0_112 ),
inference(resolution,[],[f1543,f1132]) ).
fof(f1628,plain,
spl0_117,
inference(avatar_split_clause,[],[f20,f1626]) ).
fof(f1626,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f20,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f1624,plain,
spl0_116,
inference(avatar_split_clause,[],[f19,f1622]) ).
fof(f19,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f1579,plain,
( ~ spl0_3
| spl0_115
| ~ spl0_53
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f1341,f1297,f1254,f1577,f1030]) ).
fof(f1254,plain,
( spl0_53
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1341,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_nat)
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_53
| ~ spl0_63 ),
inference(superposition,[],[f1298,f1255]) ).
fof(f1255,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1254]) ).
fof(f1553,plain,
spl0_114,
inference(avatar_split_clause,[],[f651,f1550]) ).
fof(f651,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f1548,plain,
spl0_113,
inference(avatar_split_clause,[],[f649,f1546]) ).
fof(f649,axiom,
! [X28,X0,X1] :
( hBOOL(hAPP(X28,X1))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1544,plain,
spl0_112,
inference(avatar_split_clause,[],[f648,f1542]) ).
fof(f648,axiom,
! [X28,X0,X1] :
( ~ hBOOL(hAPP(X28,X1))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1540,plain,
spl0_111,
inference(avatar_split_clause,[],[f642,f1537]) ).
fof(f642,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__alt_0) ).
fof(f1535,plain,
spl0_110,
inference(avatar_split_clause,[],[f617,f1533]) ).
fof(f617,axiom,
! [X0,X6] : hBOOL(hAPP(hAPP(c_in(tc_fun(X0,tc_bool)),X6),c_Set_OPow(X6,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pow__top_0) ).
fof(f1531,plain,
spl0_109,
inference(avatar_split_clause,[],[f518,f1529]) ).
fof(f518,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
fof(f1527,plain,
spl0_108,
inference(avatar_split_clause,[],[f485,f1525]) ).
fof(f485,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
fof(f1523,plain,
spl0_107,
inference(avatar_split_clause,[],[f479,f1521]) ).
fof(f479,axiom,
! [X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
fof(f1519,plain,
spl0_106,
inference(avatar_split_clause,[],[f478,f1517]) ).
fof(f478,axiom,
! [X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
fof(f1515,plain,
spl0_105,
inference(avatar_split_clause,[],[f391,f1513]) ).
fof(f391,axiom,
! [X10,X0,X6,X7,X12] :
( c_Fun_Oinj__on(X10,X6,X0,X12)
| ~ c_Fun_Obij__betw(X10,X6,X7,X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__def_0) ).
fof(f1511,plain,
spl0_104,
inference(avatar_split_clause,[],[f389,f1509]) ).
fof(f389,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
fof(f1507,plain,
( spl0_103
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f1423,f1377,f1505]) ).
fof(f1423,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_78 ),
inference(factoring,[],[f1378]) ).
fof(f1503,plain,
spl0_102,
inference(avatar_split_clause,[],[f363,f1501]) ).
fof(f1501,plain,
( spl0_102
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f363,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f1499,plain,
spl0_101,
inference(avatar_split_clause,[],[f362,f1497]) ).
fof(f362,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f1495,plain,
spl0_100,
inference(avatar_split_clause,[],[f350,f1493]) ).
fof(f350,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f1491,plain,
spl0_99,
inference(avatar_split_clause,[],[f349,f1489]) ).
fof(f1489,plain,
( spl0_99
<=> ! [X6,X0] : c_HOL_Ominus__class_Ominus(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f349,axiom,
! [X0,X6] : c_HOL_Ominus__class_Ominus(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f1487,plain,
spl0_98,
inference(avatar_split_clause,[],[f348,f1485]) ).
fof(f348,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
fof(f1483,plain,
spl0_97,
inference(avatar_split_clause,[],[f213,f1481]) ).
fof(f1481,plain,
( spl0_97
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f213,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f1479,plain,
spl0_96,
inference(avatar_split_clause,[],[f212,f1477]) ).
fof(f212,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f1475,plain,
spl0_95,
inference(avatar_split_clause,[],[f191,f1473]) ).
fof(f191,axiom,
! [X0,X6,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f1471,plain,
spl0_94,
inference(avatar_split_clause,[],[f179,f1469]) ).
fof(f179,axiom,
! [X0,X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f1467,plain,
spl0_93,
inference(avatar_split_clause,[],[f178,f1465]) ).
fof(f178,axiom,
! [X0,X6,X7] : c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f1459,plain,
spl0_92,
inference(avatar_split_clause,[],[f52,f1457]) ).
fof(f52,axiom,
! [X0,X6,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f1455,plain,
spl0_91,
inference(avatar_split_clause,[],[f51,f1453]) ).
fof(f51,axiom,
! [X0,X6,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f1451,plain,
spl0_90,
inference(avatar_split_clause,[],[f34,f1449]) ).
fof(f34,axiom,
! [X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f1447,plain,
spl0_89,
inference(avatar_split_clause,[],[f33,f1445]) ).
fof(f1443,plain,
spl0_88,
inference(avatar_split_clause,[],[f28,f1441]) ).
fof(f28,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f1439,plain,
spl0_87,
inference(avatar_split_clause,[],[f22,f1437]) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f1415,plain,
spl0_86,
inference(avatar_split_clause,[],[f887,f1413]) ).
fof(f1413,plain,
( spl0_86
<=> ! [X20,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X20
| ~ hBOOL(hAPP(X20,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f887,plain,
! [X0,X1,X20] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X20
| ~ hBOOL(hAPP(X20,X1)) ),
inference(forward_demodulation,[],[f490,f330]) ).
fof(f490,axiom,
! [X0,X1,X20] :
( ~ hBOOL(hAPP(X20,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Collect(X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
fof(f1407,plain,
spl0_85,
inference(avatar_split_clause,[],[f688,f1405]) ).
fof(f1405,plain,
( spl0_85
<=> ! [X32,X0,X31] :
( X31 = X32
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X31),X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f688,axiom,
! [X31,X0,X32] :
( X31 = X32
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X31),X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1403,plain,
spl0_84,
inference(avatar_split_clause,[],[f624,f1401]) ).
fof(f624,axiom,
! [X0,X29] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X29,X0,X0),X0) = X29 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lfp__const_0) ).
fof(f1399,plain,
spl0_83,
inference(avatar_split_clause,[],[f440,f1397]) ).
fof(f440,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP(c_in(X0),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f1395,plain,
spl0_82,
inference(avatar_split_clause,[],[f436,f1393]) ).
fof(f436,axiom,
! [X3,X0] : ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
fof(f1391,plain,
spl0_81,
inference(avatar_split_clause,[],[f342,f1389]) ).
fof(f342,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f1387,plain,
spl0_80,
inference(avatar_split_clause,[],[f341,f1385]) ).
fof(f341,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f1383,plain,
spl0_79,
inference(avatar_split_clause,[],[f193,f1381]) ).
fof(f1381,plain,
( spl0_79
<=> ! [X5,X0,X12,X10] : c_Finite__Set_Ofold__graph(X10,X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,X0,X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f193,axiom,
! [X10,X0,X5,X12] : c_Finite__Set_Ofold__graph(X10,X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,X0,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
fof(f1379,plain,
spl0_78,
inference(avatar_split_clause,[],[f94,f1377]) ).
fof(f94,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1375,plain,
spl0_77,
inference(avatar_split_clause,[],[f50,f1373]) ).
fof(f50,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
fof(f1371,plain,
spl0_76,
inference(avatar_split_clause,[],[f49,f1369]) ).
fof(f49,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
fof(f1367,plain,
( spl0_75
| ~ spl0_14
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1258,f1239,f1085,f1365]) ).
fof(f1365,plain,
( spl0_75
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1258,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
| ~ spl0_14
| ~ spl0_50 ),
inference(resolution,[],[f1240,f1087]) ).
fof(f1363,plain,
spl0_74,
inference(avatar_split_clause,[],[f13,f1361]) ).
fof(f13,axiom,
! [X10,X0,X1,X12] : c_Fun_Ofun__upd(X10,X1,hAPP(X10,X1),X0,X12) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
fof(f1359,plain,
spl0_73,
inference(avatar_split_clause,[],[f12,f1357]) ).
fof(f12,axiom,
! [X2,X10,X0,X11,X1] : hAPP(c_Fun_Ofun__upd(X10,X1,X2,X0,X11),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
fof(f1345,plain,
( spl0_72
| ~ spl0_4
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1257,f1239,f1035,f1343]) ).
fof(f1343,plain,
( spl0_72
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1257,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0
| ~ spl0_4
| ~ spl0_50 ),
inference(resolution,[],[f1240,f1037]) ).
fof(f1331,plain,
spl0_71,
inference(avatar_split_clause,[],[f541,f1329]) ).
fof(f541,axiom,
! [X0,X6] : c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X6,X0),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__Pow__eq_0) ).
fof(f1327,plain,
spl0_70,
inference(avatar_split_clause,[],[f477,f1325]) ).
fof(f477,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
fof(f1323,plain,
spl0_69,
inference(avatar_split_clause,[],[f476,f1321]) ).
fof(f476,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
fof(f1319,plain,
spl0_68,
inference(avatar_split_clause,[],[f474,f1317]) ).
fof(f1317,plain,
( spl0_68
<=> ! [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_68])]) ).
fof(f474,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(f1315,plain,
spl0_67,
inference(avatar_split_clause,[],[f456,f1313]) ).
fof(f1313,plain,
( spl0_67
<=> ! [X0,X12,X24] : c_Relation_Oconverse(c_Relation_Oconverse(X24,X0,X12),X12,X0) = X24 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f456,axiom,
! [X0,X24,X12] : c_Relation_Oconverse(c_Relation_Oconverse(X24,X0,X12),X12,X0) = X24,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
fof(f1311,plain,
spl0_66,
inference(avatar_split_clause,[],[f187,f1309]) ).
fof(f187,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f1307,plain,
spl0_65,
inference(avatar_split_clause,[],[f186,f1305]) ).
fof(f186,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f1303,plain,
spl0_64,
inference(avatar_split_clause,[],[f183,f1301]) ).
fof(f183,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1299,plain,
spl0_63,
inference(avatar_split_clause,[],[f182,f1297]) ).
fof(f182,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1295,plain,
spl0_62,
inference(avatar_split_clause,[],[f152,f1293]) ).
fof(f152,axiom,
! [X0,X6] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f1291,plain,
spl0_61,
inference(avatar_split_clause,[],[f55,f1289]) ).
fof(f55,axiom,
! [X0,X6] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
fof(f1287,plain,
( spl0_60
| ~ spl0_13
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f1251,f1227,f1080,f1285]) ).
fof(f1251,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_13
| ~ spl0_47 ),
inference(resolution,[],[f1228,f1082]) ).
fof(f1283,plain,
spl0_59,
inference(avatar_split_clause,[],[f36,f1281]) ).
fof(f36,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1279,plain,
spl0_58,
inference(avatar_split_clause,[],[f35,f1277]) ).
fof(f35,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1275,plain,
spl0_57,
inference(avatar_split_clause,[],[f7,f1273]) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f1271,plain,
spl0_56,
inference(avatar_split_clause,[],[f6,f1269]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f1267,plain,
spl0_55,
inference(avatar_split_clause,[],[f2,f1265]) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f1263,plain,
spl0_54,
inference(avatar_split_clause,[],[f1,f1261]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f1256,plain,
( spl0_53
| ~ spl0_3
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f1250,f1227,f1030,f1254]) ).
fof(f1250,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
| ~ spl0_3
| ~ spl0_47 ),
inference(resolution,[],[f1228,f1032]) ).
fof(f1249,plain,
spl0_52,
inference(avatar_split_clause,[],[f650,f1247]) ).
fof(f650,axiom,
! [X0,X19,X12,X20] : hAPP(c_COMBK(X20,X0,X12),X19) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f1245,plain,
spl0_51,
inference(avatar_split_clause,[],[f528,f1243]) ).
fof(f528,axiom,
! [X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(X6,X6,tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f1241,plain,
spl0_50,
inference(avatar_split_clause,[],[f527,f1239]) ).
fof(f527,axiom,
! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f1237,plain,
spl0_49,
inference(avatar_split_clause,[],[f360,f1235]) ).
fof(f1235,plain,
( spl0_49
<=> ! [X0,X12,X10] : c_Fun_Oinj__on(X10,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f360,axiom,
! [X10,X0,X12] : c_Fun_Oinj__on(X10,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
fof(f1233,plain,
spl0_48,
inference(avatar_split_clause,[],[f320,f1231]) ).
fof(f320,axiom,
! [X0,X32] : c_Set_Oimage(c_COMBI(X0),X32,X0,X0) = X32,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_0) ).
fof(f1229,plain,
spl0_47,
inference(avatar_split_clause,[],[f163,f1227]) ).
fof(f163,axiom,
! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f1225,plain,
spl0_46,
inference(avatar_split_clause,[],[f162,f1223]) ).
fof(f162,axiom,
! [X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(X6,X6,tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f1221,plain,
spl0_45,
inference(avatar_split_clause,[],[f687,f1219]) ).
fof(f687,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(f1217,plain,
spl0_44,
inference(avatar_split_clause,[],[f488,f1215]) ).
fof(f488,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(f1213,plain,
spl0_43,
inference(avatar_split_clause,[],[f470,f1211]) ).
fof(f470,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(f1209,plain,
spl0_42,
inference(avatar_split_clause,[],[f151,f1207]) ).
fof(f151,axiom,
! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1205,plain,
spl0_41,
inference(avatar_split_clause,[],[f56,f1203]) ).
fof(f56,axiom,
! [X0,X1] :
( ~ class_Orderings_Otop(X0)
| c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
fof(f1201,plain,
spl0_40,
inference(avatar_split_clause,[],[f664,f1199]) ).
fof(f1199,plain,
( spl0_40
<=> ! [X59,X58] :
( ~ class_HOL_Oord(X59)
| class_HOL_Oord(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f664,axiom,
! [X58,X59] :
( ~ class_HOL_Oord(X59)
| class_HOL_Oord(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f1197,plain,
spl0_39,
inference(avatar_split_clause,[],[f663,f1195]) ).
fof(f663,axiom,
! [X58,X59] :
( ~ class_Orderings_Obot(X59)
| class_Orderings_Obot(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1193,plain,
spl0_38,
inference(avatar_split_clause,[],[f662,f1191]) ).
fof(f1191,plain,
( spl0_38
<=> ! [X59,X58] :
( ~ class_Orderings_Otop(X59)
| class_Orderings_Otop(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f662,axiom,
! [X58,X59] :
( ~ class_Orderings_Otop(X59)
| class_Orderings_Otop(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
fof(f1189,plain,
spl0_37,
inference(avatar_split_clause,[],[f661,f1187]) ).
fof(f1187,plain,
( spl0_37
<=> ! [X59,X58] :
( ~ class_Orderings_Oorder(X59)
| class_Orderings_Oorder(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f661,axiom,
! [X58,X59] :
( ~ class_Orderings_Oorder(X59)
| class_Orderings_Oorder(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1185,plain,
spl0_36,
inference(avatar_split_clause,[],[f660,f1183]) ).
fof(f660,axiom,
! [X58,X59] :
( ~ class_Lattices_Olattice(X59)
| class_Lattices_Olattice(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f1181,plain,
spl0_35,
inference(avatar_split_clause,[],[f659,f1179]) ).
fof(f1179,plain,
( spl0_35
<=> ! [X59,X58] :
( ~ class_Orderings_Opreorder(X59)
| class_Orderings_Opreorder(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f659,axiom,
! [X58,X59] :
( ~ class_Orderings_Opreorder(X59)
| class_Orderings_Opreorder(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1177,plain,
spl0_34,
inference(avatar_split_clause,[],[f658,f1175]) ).
fof(f658,axiom,
! [X58,X59] :
( ~ class_Lattices_Obounded__lattice(X59)
| class_Lattices_Obounded__lattice(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f1173,plain,
spl0_33,
inference(avatar_split_clause,[],[f657,f1171]) ).
fof(f1171,plain,
( spl0_33
<=> ! [X59,X58] :
( ~ class_Lattices_Odistrib__lattice(X59)
| class_Lattices_Odistrib__lattice(tc_fun(X58,X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f657,axiom,
! [X58,X59] :
( ~ class_Lattices_Odistrib__lattice(X59)
| class_Lattices_Odistrib__lattice(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f1169,plain,
spl0_32,
inference(avatar_split_clause,[],[f656,f1167]) ).
fof(f656,axiom,
! [X58,X59] :
( ~ class_Lattices_Olattice(X59)
| class_Lattices_Olower__semilattice(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f1165,plain,
spl0_31,
inference(avatar_split_clause,[],[f655,f1163]) ).
fof(f655,axiom,
! [X58,X59] :
( ~ class_Lattices_Olattice(X59)
| class_Lattices_Oupper__semilattice(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f1161,plain,
spl0_30,
inference(avatar_split_clause,[],[f654,f1159]) ).
fof(f654,axiom,
! [X58,X59] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X59)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f1157,plain,
spl0_29,
inference(avatar_split_clause,[],[f353,f1155]) ).
fof(f353,axiom,
! [X0,X20] : hAPP(c_COMBI(X0),X20) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
fof(f1153,plain,
spl0_28,
inference(avatar_split_clause,[],[f335,f1151]) ).
fof(f335,axiom,
! [X0,X6] : c_Fun_Oinj__on(c_COMBI(X0),X6,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
fof(f1149,plain,
spl0_27,
inference(avatar_split_clause,[],[f78,f1147]) ).
fof(f78,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1145,plain,
spl0_26,
inference(avatar_split_clause,[],[f77,f1143]) ).
fof(f77,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1141,plain,
spl0_25,
inference(avatar_split_clause,[],[f72,f1139]) ).
fof(f72,axiom,
! [X0,X1] : c_lessequals(X1,X1,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
fof(f1137,plain,
spl0_24,
inference(avatar_split_clause,[],[f330,f1135]) ).
fof(f1133,plain,
~ spl0_23,
inference(avatar_split_clause,[],[f653,f1130]) ).
fof(f653,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1128,plain,
spl0_22,
inference(avatar_split_clause,[],[f684,f1125]) ).
fof(f684,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f1123,plain,
spl0_21,
inference(avatar_split_clause,[],[f683,f1120]) ).
fof(f683,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f1118,plain,
spl0_20,
inference(avatar_split_clause,[],[f682,f1115]) ).
fof(f1115,plain,
( spl0_20
<=> class_Orderings_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f682,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
fof(f1113,plain,
spl0_19,
inference(avatar_split_clause,[],[f681,f1110]) ).
fof(f681,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f1108,plain,
spl0_18,
inference(avatar_split_clause,[],[f680,f1105]) ).
fof(f680,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f1103,plain,
spl0_17,
inference(avatar_split_clause,[],[f679,f1100]) ).
fof(f679,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f1098,plain,
spl0_16,
inference(avatar_split_clause,[],[f678,f1095]) ).
fof(f678,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f1093,plain,
spl0_15,
inference(avatar_split_clause,[],[f677,f1090]) ).
fof(f677,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f1088,plain,
spl0_14,
inference(avatar_split_clause,[],[f676,f1085]) ).
fof(f676,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f1083,plain,
spl0_13,
inference(avatar_split_clause,[],[f675,f1080]) ).
fof(f675,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f1078,plain,
spl0_12,
inference(avatar_split_clause,[],[f674,f1075]) ).
fof(f674,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(f1073,plain,
spl0_11,
inference(avatar_split_clause,[],[f673,f1070]) ).
fof(f1070,plain,
( spl0_11
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f673,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
fof(f1068,plain,
spl0_10,
inference(avatar_split_clause,[],[f672,f1065]) ).
fof(f1065,plain,
( spl0_10
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f672,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f1063,plain,
spl0_9,
inference(avatar_split_clause,[],[f671,f1060]) ).
fof(f1060,plain,
( spl0_9
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f671,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1058,plain,
spl0_8,
inference(avatar_split_clause,[],[f670,f1055]) ).
fof(f670,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f1053,plain,
spl0_7,
inference(avatar_split_clause,[],[f669,f1050]) ).
fof(f1050,plain,
( spl0_7
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f669,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1048,plain,
spl0_6,
inference(avatar_split_clause,[],[f668,f1045]) ).
fof(f1045,plain,
( spl0_6
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f668,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1043,plain,
spl0_5,
inference(avatar_split_clause,[],[f667,f1040]) ).
fof(f667,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f1038,plain,
spl0_4,
inference(avatar_split_clause,[],[f666,f1035]) ).
fof(f666,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f1033,plain,
spl0_3,
inference(avatar_split_clause,[],[f665,f1030]) ).
fof(f665,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f1028,plain,
spl0_2,
inference(avatar_split_clause,[],[f627,f1025]) ).
fof(f1025,plain,
( spl0_2
<=> c_Arrow__Order__Mirabelle_Ounanimity(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f627,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_u_0) ).
fof(f1023,plain,
spl0_1,
inference(avatar_split_clause,[],[f626,f1020]) ).
fof(f1020,plain,
( spl0_1
<=> c_Arrow__Order__Mirabelle_OIIA(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f626,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I3_J_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SCT080-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 22:29:46 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (27326)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.42 % (27327)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.42 % (27331)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)
% 0.14/0.42 % (27329)WARNING: value z3 for option sas not known
% 0.14/0.42 % (27330)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.42 % (27333)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)
% 0.14/0.42 % (27328)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.42 % (27332)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)
% 0.14/0.42 % (27329)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)
% 3.22/0.85 TRYING [1]
% 3.57/0.91 TRYING [2]
% 9.60/1.77 TRYING [1]
% 9.68/1.80 TRYING [2]
% 10.09/1.87 TRYING [3]
% 10.09/1.88 TRYING [1]
% 11.17/2.04 TRYING [2]
% 14.90/2.54 TRYING [3]
% 33.93/5.30 TRYING [3]
% 55.74/8.44 TRYING [4]
% 59.95/9.04 TRYING [4]
% 120.27/17.61 % (27331)First to succeed.
% 121.14/17.74 % (27331)Refutation found. Thanks to Tanya!
% 121.14/17.74 % SZS status Unsatisfiable for theBenchmark
% 121.14/17.74 % SZS output start Proof for theBenchmark
% See solution above
% 121.42/17.79 % (27331)------------------------------
% 121.42/17.79 % (27331)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 121.42/17.79 % (27331)Termination reason: Refutation
% 121.42/17.79
% 121.42/17.79 % (27331)Memory used [KB]: 71026
% 121.42/17.79 % (27331)Time elapsed: 17.297 s
% 121.42/17.79 % (27331)Instructions burned: 42174 (million)
% 121.42/17.79 % (27331)------------------------------
% 121.42/17.79 % (27331)------------------------------
% 121.42/17.79 % (27326)Success in time 17.34 s
%------------------------------------------------------------------------------