TSTP Solution File: SCT074-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT074-1 : 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 : n020.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 14:55:37 EDT 2024
% Result : Unsatisfiable 20.22s 3.31s
% Output : Refutation 20.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1856
% Syntax : Number of formulae : 4362 ( 785 unt; 0 def)
% Number of atoms : 12250 (1444 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 14258 (6370 ~;6621 |; 0 &)
% (1267 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 1294 (1292 usr;1268 prp; 0-3 aty)
% Number of functors : 81 ( 81 usr; 7 con; 0-7 aty)
% Number of variables : 9973 (9973 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43338,plain,
$false,
inference(avatar_sat_refutation,[],[f854,f859,f864,f869,f874,f879,f884,f889,f894,f899,f903,f907,f911,f915,f919,f923,f927,f931,f935,f939,f943,f947,f951,f955,f959,f963,f967,f971,f975,f979,f983,f987,f991,f995,f999,f1003,f1007,f1011,f1015,f1019,f1023,f1027,f1031,f1035,f1039,f1044,f1048,f1052,f1056,f1061,f1066,f1070,f1074,f1078,f1082,f1086,f1090,f1094,f1098,f1102,f1106,f1110,f1115,f1121,f1125,f1140,f1144,f1148,f1152,f1156,f1161,f1165,f1169,f1173,f1177,f1181,f1185,f1189,f1193,f1197,f1201,f1206,f1210,f1214,f1218,f1222,f1226,f1230,f1234,f1238,f1242,f1246,f1250,f1254,f1283,f1313,f1318,f1322,f1326,f1330,f1334,f1338,f1343,f1353,f1373,f1377,f1381,f1385,f1389,f1396,f1400,f1404,f1408,f1412,f1416,f1420,f1424,f1428,f1432,f1436,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1492,f1496,f1500,f1511,f1559,f1579,f1583,f1587,f1591,f1599,f1603,f1607,f1611,f1616,f1620,f1683,f1742,f1746,f1750,f1754,f1758,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1846,f1855,f1859,f1863,f1867,f1871,f1875,f1879,f1883,f1887,f1891,f1895,f1899,f1903,f1983,f2161,f2264,f2269,f2273,f2277,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2313,f2317,f2321,f2325,f2329,f2333,f2337,f2341,f2345,f2349,f2363,f2367,f2371,f2375,f2379,f2383,f2387,f2391,f2395,f2399,f2403,f2407,f2411,f2415,f2419,f2423,f2427,f2431,f2435,f2439,f2611,f2690,f2879,f2883,f2887,f2891,f2895,f2899,f2903,f2907,f2911,f2915,f2919,f2923,f2927,f2931,f2935,f2939,f2943,f2947,f2951,f3125,f3129,f3133,f3137,f3141,f3145,f3149,f3153,f3157,f3161,f3165,f3169,f3173,f3177,f3181,f3185,f3189,f3193,f3206,f3366,f3370,f3374,f3378,f3382,f3387,f3391,f3395,f3399,f3403,f3407,f3411,f3415,f3419,f3423,f3427,f3431,f3435,f3439,f3443,f3447,f3451,f3455,f3459,f3463,f3467,f3471,f3475,f3479,f3483,f3487,f3491,f3495,f3499,f3503,f3507,f3511,f3515,f3519,f3881,f3964,f3968,f3972,f3976,f3980,f3984,f3988,f3992,f3996,f4000,f4004,f4009,f4013,f4017,f4021,f4025,f4029,f4033,f4037,f4041,f4045,f4049,f4303,f4475,f4479,f4483,f4487,f4491,f4495,f4499,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4531,f4535,f4539,f4543,f4547,f4892,f5024,f5028,f5032,f5036,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5068,f5072,f5076,f5080,f5084,f5088,f5092,f5096,f5100,f5104,f5108,f5388,f5524,f5528,f5533,f5537,f5541,f5545,f5549,f5553,f5557,f5561,f5565,f5600,f6169,f6173,f6177,f6181,f6185,f6189,f6193,f6197,f6201,f6205,f6209,f6213,f6217,f6383,f6561,f6565,f6569,f6573,f6584,f6588,f6592,f6596,f6600,f6604,f6608,f6612,f6616,f6620,f6625,f6629,f6633,f6637,f6641,f6645,f6649,f7628,f7864,f7868,f7872,f7876,f7889,f7893,f7897,f7901,f7905,f7909,f7913,f7917,f7921,f7925,f7929,f7933,f7937,f7941,f7945,f7949,f8150,f8575,f8579,f8583,f8587,f8591,f8595,f8600,f8604,f8821,f8825,f8829,f8833,f8837,f8841,f8845,f8849,f8853,f9276,f9280,f9284,f9288,f9292,f9296,f9300,f9304,f9308,f9312,f9316,f9320,f9324,f9328,f9332,f9336,f9343,f9955,f9959,f9963,f9967,f9971,f9975,f9979,f9984,f10095,f10099,f10103,f10107,f10111,f10117,f10121,f10125,f10129,f10133,f10137,f10141,f10145,f10149,f10153,f10157,f10161,f10165,f10169,f10173,f10177,f10181,f11561,f11890,f12033,f12037,f12041,f12045,f12049,f12235,f12306,f12375,f12379,f12421,f12425,f12429,f12440,f12445,f12495,f12768,f12772,f12776,f12787,f12791,f12795,f12799,f12803,f12807,f12811,f12815,f12819,f13349,f13413,f13417,f13425,f13429,f13614,f13618,f13623,f13627,f13631,f13785,f13789,f13793,f13797,f13801,f13805,f13809,f14160,f14164,f14168,f14172,f14176,f14180,f14184,f14188,f14192,f14196,f14200,f14204,f14208,f14212,f14216,f14220,f14224,f14228,f14232,f14299,f14921,f15249,f15253,f15257,f15261,f15275,f15279,f15283,f15287,f15291,f15295,f15807,f15811,f15815,f15997,f16001,f16274,f16278,f16282,f16286,f16290,f16294,f16298,f16302,f16584,f16598,f16602,f16726,f16730,f16734,f16738,f16742,f16746,f16750,f17072,f17076,f17080,f17084,f17088,f17296,f17300,f17304,f17308,f17319,f17323,f17642,f17646,f17650,f17822,f17918,f17922,f17926,f17930,f17934,f17938,f18291,f18295,f18299,f18306,f18310,f18590,f18596,f18958,f18991,f18995,f19003,f19007,f19015,f19267,f19337,f19341,f19422,f19426,f19430,f19434,f19438,f19447,f19451,f19455,f19469,f19473,f19477,f19528,f19635,f19639,f19643,f19647,f19651,f19656,f19660,f19664,f19668,f19672,f19676,f19680,f19684,f19688,f19692,f19696,f19774,f19837,f19841,f19845,f19849,f19853,f19857,f19862,f19866,f19870,f19874,f19878,f19882,f19886,f19890,f19894,f19898,f19936,f19940,f19944,f20269,f20286,f20290,f20294,f20298,f20302,f20306,f20310,f20314,f20335,f20340,f20344,f20470,f20506,f20510,f20514,f20518,f20522,f20526,f20533,f20537,f20541,f20545,f20549,f20553,f20557,f20561,f20565,f20569,f20573,f20577,f20581,f20585,f20589,f20995,f21116,f21120,f21124,f21128,f21132,f21136,f21143,f21147,f21151,f21155,f21159,f21163,f21167,f21171,f21175,f21179,f21183,f21187,f21191,f21195,f21199,f21203,f21207,f21211,f21215,f21219,f21223,f21260,f21264,f21268,f21272,f21276,f21280,f21284,f21288,f21382,f22604,f22707,f22711,f22715,f22719,f22723,f22727,f22731,f22735,f22739,f22743,f22747,f22751,f22755,f22759,f22763,f22767,f22771,f22775,f22779,f22794,f22798,f22802,f22806,f22810,f22814,f22818,f22822,f22826,f22830,f22834,f22838,f22842,f22846,f22850,f22854,f22858,f22862,f22866,f22870,f22874,f22879,f22883,f22887,f22891,f22895,f22899,f22903,f22907,f22911,f22915,f22919,f22923,f22927,f22931,f22935,f22939,f22943,f22947,f22951,f22955,f22959,f23025,f23045,f23049,f23053,f23057,f23061,f23065,f23069,f23073,f23077,f23081,f23085,f23089,f23093,f23097,f23101,f23105,f23109,f23113,f23127,f23131,f23135,f23139,f23143,f23147,f23151,f23155,f23159,f23163,f23167,f23171,f23175,f23179,f23183,f23187,f23191,f23195,f23199,f23203,f23207,f23213,f23217,f23258,f23815,f25414,f25715,f25903,f26352,f27058,f27062,f27069,f27073,f27077,f27081,f27085,f27089,f27093,f27097,f27101,f27105,f27109,f27113,f27117,f27121,f27125,f27129,f27133,f27137,f27141,f27145,f27149,f27154,f27158,f27162,f27166,f27170,f27174,f27178,f27182,f27186,f27190,f27194,f27198,f27202,f27206,f27210,f27214,f27218,f27222,f27226,f27230,f27234,f27238,f27242,f27246,f27250,f27254,f27258,f27262,f27266,f27270,f27274,f27278,f27282,f27908,f28372,f28574,f28811,f28815,f28819,f28823,f28828,f28832,f28836,f28840,f28844,f28848,f28852,f28856,f28860,f28864,f28869,f28873,f28877,f28881,f28885,f28889,f28893,f28897,f28901,f28905,f28909,f28973,f28977,f28981,f28985,f28989,f28993,f28997,f29001,f29005,f29009,f29013,f29017,f29021,f29025,f29029,f29033,f29037,f29041,f29045,f29049,f29053,f29057,f29061,f29065,f29069,f29073,f29077,f29081,f29085,f29089,f29093,f29097,f29101,f29583,f30324,f30786,f31786,f31942,f31946,f31950,f31954,f31958,f31962,f31968,f31972,f31976,f31980,f31984,f31988,f31992,f31996,f32000,f32004,f32008,f32012,f32016,f32020,f32024,f32028,f32032,f32036,f32040,f32044,f32048,f32099,f32103,f32107,f32111,f32115,f32119,f32123,f32127,f32131,f32135,f32139,f32143,f32147,f32151,f32155,f32159,f32163,f32167,f32171,f32175,f32179,f32188,f32192,f32196,f32200,f32204,f32208,f32212,f32216,f32220,f32225,f32231,f32235,f32239,f32243,f35080,f35715,f35829,f35833,f35837,f35841,f35845,f35849,f35853,f35857,f35861,f35883,f35887,f35891,f35895,f35899,f35903,f35907,f35911,f35915,f35919,f35924,f35928,f35932,f35936,f35940,f35944,f35948,f35952,f35956,f35960,f35964,f35968,f35972,f35976,f35980,f35984,f35988,f35992,f35996,f36000,f36004,f36008,f36012,f36016,f36020,f36024,f36028,f36032,f36036,f36040,f36044,f36048,f36052,f36056,f36060,f36064,f36068,f36072,f36076,f36080,f36084,f36088,f36094,f36098,f36102,f36106,f36110,f36114,f36118,f36122,f36126,f36130,f36136,f36140,f36144,f36148,f36152,f36156,f36160,f36164,f36168,f36172,f36176,f36180,f36184,f36188,f36192,f36196,f36200,f36204,f36208,f36212,f36216,f36220,f36224,f36228,f36232,f36236,f36240,f36244,f36248,f36252,f36256,f36264,f36288,f36292,f37743,f38596,f39102,f39470,f40046,f42930,f42934,f42938,f42942,f42946,f42950,f42954,f42958,f42962,f42966,f42970,f42974,f42978,f42982,f42986,f42990,f42994,f42998,f43002,f43006,f43010,f43014,f43018,f43022,f43026,f43030,f43034,f43080,f43084,f43088,f43092,f43096,f43100,f43104,f43108,f43112,f43116,f43120,f43124,f43128,f43132,f43136,f43140,f43144,f43148,f43152,f43156,f43160,f43164,f43168,f43172,f43176,f43180,f43184,f43188,f43192,f43196,f43200,f43204,f43208,f43212,f43216,f43220,f43224,f43228,f43232,f43236,f43240,f43244,f43248,f43252,f43256,f43260,f43264,f43268,f43272,f43276,f43280,f43284,f43288,f43292,f43296,f43300,f43304,f43308,f43312,f43316,f43320,f43324,f43328,f43332,f43336,f43337]) ).
fof(f43337,plain,
( ~ spl0_63
| ~ spl0_10
| ~ spl0_103
| ~ spl0_503 ),
inference(avatar_split_clause,[],[f11619,f10139,f1340,f896,f1112]) ).
fof(f1112,plain,
( spl0_63
<=> c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f896,plain,
( spl0_10
<=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1340,plain,
( spl0_103
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f10139,plain,
( spl0_503
<=> ! [X0,X1,X40] :
( ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f11619,plain,
( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_103
| ~ spl0_503 ),
inference(resolution,[],[f10140,f1342]) ).
fof(f1342,plain,
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f10140,plain,
( ! [X40,X0,X1] :
( ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_503 ),
inference(avatar_component_clause,[],[f10139]) ).
fof(f43336,plain,
( spl0_1267
| ~ spl0_110
| ~ spl0_111
| ~ spl0_500 ),
inference(avatar_split_clause,[],[f11509,f10127,f1398,f1394,f43334]) ).
fof(f43334,plain,
( spl0_1267
<=> ! [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_1267])]) ).
fof(f1394,plain,
( spl0_110
<=> ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1398,plain,
( spl0_111
<=> ! [X9,X2] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f10127,plain,
( spl0_500
<=> ! [X9,X11,X5,X2] : c_HOL_Ominus__class_Ominus(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f11509,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_110
| ~ spl0_111
| ~ spl0_500 ),
inference(forward_demodulation,[],[f11437,f1399]) ).
fof(f1399,plain,
( ! [X2,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) = X9
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1398]) ).
fof(f11437,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_110
| ~ spl0_500 ),
inference(superposition,[],[f10128,f1395]) ).
fof(f1395,plain,
( ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X5,tc_fun(X2,tc_bool))
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1394]) ).
fof(f10128,plain,
( ! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_500 ),
inference(avatar_component_clause,[],[f10127]) ).
fof(f43332,plain,
( spl0_1266
| ~ spl0_110
| ~ spl0_112
| ~ spl0_496 ),
inference(avatar_split_clause,[],[f11055,f10109,f1402,f1394,f43330]) ).
fof(f43330,plain,
( spl0_1266
<=> ! [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_1266])]) ).
fof(f1402,plain,
( spl0_112
<=> ! [X2,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f10109,plain,
( spl0_496
<=> ! [X9,X11,X5,X2] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f11055,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_110
| ~ spl0_112
| ~ spl0_496 ),
inference(forward_demodulation,[],[f10996,f1403]) ).
fof(f1403,plain,
( ! [X2,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1402]) ).
fof(f10996,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_110
| ~ spl0_496 ),
inference(superposition,[],[f10110,f1395]) ).
fof(f10110,plain,
( ! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_496 ),
inference(avatar_component_clause,[],[f10109]) ).
fof(f43328,plain,
( spl0_1265
| ~ spl0_110
| ~ spl0_111
| ~ spl0_496 ),
inference(avatar_split_clause,[],[f11051,f10109,f1398,f1394,f43326]) ).
fof(f43326,plain,
( spl0_1265
<=> ! [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_1265])]) ).
fof(f11051,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_110
| ~ spl0_111
| ~ spl0_496 ),
inference(forward_demodulation,[],[f10988,f1399]) ).
fof(f10988,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_110
| ~ spl0_496 ),
inference(superposition,[],[f10110,f1395]) ).
fof(f43324,plain,
( spl0_1264
| ~ spl0_53
| ~ spl0_493 ),
inference(avatar_split_clause,[],[f10682,f10097,f1072,f43322]) ).
fof(f43322,plain,
( spl0_1264
<=> ! [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_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f1072,plain,
( spl0_53
<=> ! [X2,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X5,tc_fun(X2,tc_bool)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f10097,plain,
( spl0_493
<=> ! [X9,X11,X5,X2] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f10682,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_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool))
| ~ spl0_53
| ~ spl0_493 ),
inference(superposition,[],[f10098,f1073]) ).
fof(f1073,plain,
( ! [X2,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X5,tc_fun(X2,tc_bool)) = X5
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f10098,plain,
( ! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool))
| ~ spl0_493 ),
inference(avatar_component_clause,[],[f10097]) ).
fof(f43320,plain,
( spl0_1263
| ~ spl0_173
| ~ spl0_491 ),
inference(avatar_split_clause,[],[f10008,f9982,f1836,f43318]) ).
fof(f43318,plain,
( spl0_1263
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(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)),X2)
| c_in(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f1836,plain,
( spl0_173
<=> ! [X9,X5,X19,X2] :
( c_in(X19,X9,X2)
| ~ c_in(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f9982,plain,
( spl0_491
<=> ! [X9,X11,X5,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f10008,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(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)),X2)
| c_in(X4,X3,X2) )
| ~ spl0_173
| ~ spl0_491 ),
inference(superposition,[],[f1837,f9983]) ).
fof(f9983,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool))
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f9982]) ).
fof(f1837,plain,
( ! [X2,X19,X9,X5] :
( ~ c_in(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2)
| c_in(X19,X9,X2) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1836]) ).
fof(f43316,plain,
( spl0_1262
| ~ spl0_167
| ~ spl0_491 ),
inference(avatar_split_clause,[],[f10006,f9982,f1812,f43314]) ).
fof(f43314,plain,
( spl0_1262
<=> ! [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_1262])]) ).
fof(f1812,plain,
( spl0_167
<=> ! [X6,X9,X5,X2] :
( hBOOL(hAPP(X9,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f10006,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_167
| ~ spl0_491 ),
inference(superposition,[],[f1813,f9983]) ).
fof(f1813,plain,
( ! [X2,X6,X9,X5] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X6))
| hBOOL(hAPP(X9,X6)) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1812]) ).
fof(f43312,plain,
( spl0_1261
| ~ spl0_135
| ~ spl0_464 ),
inference(avatar_split_clause,[],[f9172,f8843,f1494,f43310]) ).
fof(f43310,plain,
( spl0_1261
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(c_Relation_OId(t_a),t_a),t_a)
| hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_OId(t_a)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f1494,plain,
( spl0_135
<=> ! [X2,X0] : c_in(c_Pair(X0,X0,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f8843,plain,
( spl0_464
<=> ! [X18,X4,X7,X6] :
( hBOOL(hAPP(X18,X7))
| hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X7,v_sko__Wellfounded__Xacc__Xinducts__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f9172,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(c_Relation_OId(t_a),t_a),t_a)
| hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_OId(t_a)))) )
| ~ spl0_135
| ~ spl0_464 ),
inference(resolution,[],[f8844,f1495]) ).
fof(f1495,plain,
( ! [X2,X0] : c_in(c_Pair(X0,X0,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2))
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1494]) ).
fof(f8844,plain,
( ! [X18,X6,X7,X4] :
( ~ c_in(c_Pair(X7,v_sko__Wellfounded__Xacc__Xinducts__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| hBOOL(hAPP(X18,X7)) )
| ~ spl0_464 ),
inference(avatar_component_clause,[],[f8843]) ).
fof(f43308,plain,
( spl0_1260
| ~ spl0_135
| ~ spl0_463 ),
inference(avatar_split_clause,[],[f9143,f8839,f1494,f43306]) ).
fof(f43306,plain,
( spl0_1260
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(c_Relation_OId(t_a),t_a),t_a)
| hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Relation_OId(t_a)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f8839,plain,
( spl0_463
<=> ! [X18,X4,X7,X6] :
( hBOOL(hAPP(X18,X7))
| hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X7,v_sko__Wellfounded__Xacc__Xinduct__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f9143,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(c_Relation_OId(t_a),t_a),t_a)
| hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Relation_OId(t_a)))) )
| ~ spl0_135
| ~ spl0_463 ),
inference(resolution,[],[f8840,f1495]) ).
fof(f8840,plain,
( ! [X18,X6,X7,X4] :
( ~ c_in(c_Pair(X7,v_sko__Wellfounded__Xacc__Xinduct__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| hBOOL(hAPP(X18,X7)) )
| ~ spl0_463 ),
inference(avatar_component_clause,[],[f8839]) ).
fof(f43304,plain,
( spl0_1259
| ~ spl0_332
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f8415,f7935,f4035,f43302]) ).
fof(f43302,plain,
( spl0_1259
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Product__Type_OSigma(X1,X2,X3,X4),X3,X4),X4,X3),X3)
| c_in(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f4035,plain,
( spl0_332
<=> ! [X3,X9,X0,X5,X2,X1] :
( c_in(X0,X5,X2)
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f7935,plain,
( spl0_444
<=> ! [X4,X0,X3,X2] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,X4,X2,X3),X2,X3),X4,tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f8415,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Product__Type_OSigma(X1,X2,X3,X4),X3,X4),X4,X3),X3)
| c_in(X0,X1,X3) )
| ~ spl0_332
| ~ spl0_444 ),
inference(resolution,[],[f7936,f4036]) ).
fof(f4036,plain,
( ! [X2,X3,X0,X1,X9,X5] :
( ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3))
| c_in(X0,X5,X2) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f4035]) ).
fof(f7936,plain,
( ! [X2,X3,X0,X4] :
( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,X4,X2,X3),X2,X3),X4,tc_prod(X2,X3))
| ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2) )
| ~ spl0_444 ),
inference(avatar_component_clause,[],[f7935]) ).
fof(f43300,plain,
( spl0_1258
| ~ spl0_346
| ~ spl0_870 ),
inference(avatar_split_clause,[],[f26713,f23201,f4509,f43298]) ).
fof(f43298,plain,
( spl0_1258
<=> ! [X0] : v_a____ = c_ATP__Linkup_Osko__Relation__XImageE__1__1(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____,c_Relation_OId(X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f4509,plain,
( spl0_346
<=> ! [X0] : c_in(v_a____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f23201,plain,
( spl0_870
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X2,X1)
| c_ATP__Linkup_Osko__Relation__XImageE__1__1(X2,X0,c_Relation_OId(X1),X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f26713,plain,
( ! [X0] : v_a____ = c_ATP__Linkup_Osko__Relation__XImageE__1__1(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____,c_Relation_OId(X0),X0,X0)
| ~ spl0_346
| ~ spl0_870 ),
inference(resolution,[],[f23202,f4510]) ).
fof(f4510,plain,
( ! [X0] : c_in(v_a____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f4509]) ).
fof(f23202,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X2,X1)
| c_ATP__Linkup_Osko__Relation__XImageE__1__1(X2,X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_870 ),
inference(avatar_component_clause,[],[f23201]) ).
fof(f43296,plain,
( spl0_1257
| ~ spl0_334
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f8405,f7935,f4043,f43294]) ).
fof(f43294,plain,
( spl0_1257
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f4043,plain,
( spl0_334
<=> ! [X5,X4,X7,X6,X2] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_in(X6,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f8405,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) )
| ~ spl0_334
| ~ spl0_444 ),
inference(resolution,[],[f7936,f4044]) ).
fof(f4044,plain,
( ! [X2,X6,X7,X4,X5] :
( ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| c_in(X6,X5,X2)
| ~ c_Relation_Orefl__on(X5,X4,X2) )
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f4043]) ).
fof(f43292,plain,
( spl0_1256
| ~ spl0_331
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f8403,f7935,f4031,f43290]) ).
fof(f43290,plain,
( spl0_1256
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f4031,plain,
( spl0_331
<=> ! [X5,X4,X7,X6,X2] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_in(X6,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f8403,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) )
| ~ spl0_331
| ~ spl0_444 ),
inference(resolution,[],[f7936,f4032]) ).
fof(f4032,plain,
( ! [X2,X6,X7,X4,X5] :
( ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| c_in(X6,X5,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2) )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f4031]) ).
fof(f43288,plain,
( spl0_1255
| ~ spl0_18
| ~ spl0_55
| ~ spl0_270
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f7794,f6643,f3187,f1080,f929,f43286]) ).
fof(f43286,plain,
( spl0_1255
<=> ! [X0,X1] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Relation_Osym(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f929,plain,
( spl0_18
<=> ! [X2,X4] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X4,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1080,plain,
( spl0_55
<=> ! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| c_Transitive__Closure_Otrancl(X4,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f3187,plain,
( spl0_270
<=> ! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f6643,plain,
( spl0_425
<=> ! [X2,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X4,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f7794,plain,
( ! [X0,X1] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Relation_Osym(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_18
| ~ spl0_55
| ~ spl0_270
| ~ spl0_425 ),
inference(forward_demodulation,[],[f7749,f1130]) ).
fof(f1130,plain,
( ! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1)
| ~ spl0_18
| ~ spl0_55 ),
inference(resolution,[],[f1081,f930]) ).
fof(f930,plain,
( ! [X2,X4] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X4,X2),X2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f929]) ).
fof(f1081,plain,
( ! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| c_Transitive__Closure_Otrancl(X4,X2) = X4 )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1080]) ).
fof(f7749,plain,
( ! [X0,X1] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),X1)
| ~ c_Relation_Osym(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_270
| ~ spl0_425 ),
inference(superposition,[],[f3188,f6644]) ).
fof(f6644,plain,
( ! [X2,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X4,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_425 ),
inference(avatar_component_clause,[],[f6643]) ).
fof(f3188,plain,
( ! [X2,X4] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2)
| ~ c_Relation_Osym(X4,X2) )
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f3187]) ).
fof(f43284,plain,
( spl0_1254
| ~ spl0_18
| ~ spl0_55
| ~ spl0_269
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f7793,f6643,f3183,f1080,f929,f43282]) ).
fof(f43282,plain,
( spl0_1254
<=> ! [X0,X1] :
( c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f3183,plain,
( spl0_269
<=> ! [X2,X4] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f7793,plain,
( ! [X0,X1] :
( c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_18
| ~ spl0_55
| ~ spl0_269
| ~ spl0_425 ),
inference(forward_demodulation,[],[f7748,f1130]) ).
fof(f7748,plain,
( ! [X0,X1] :
( c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),X1)
| ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_269
| ~ spl0_425 ),
inference(superposition,[],[f3184,f6644]) ).
fof(f3184,plain,
( ! [X2,X4] :
( c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2)
| ~ c_Wellfounded_Oacyclic(X4,X2) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f3183]) ).
fof(f43280,plain,
( spl0_1253
| ~ spl0_221
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f7747,f6643,f2393,f43278]) ).
fof(f43278,plain,
( spl0_1253
<=> ! [X0,X1] :
( c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Relation_Oantisym(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f2393,plain,
( spl0_221
<=> ! [X2,X4] :
( ~ c_Relation_Oantisym(X4,X2)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f7747,plain,
( ! [X0,X1] :
( c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Relation_Oantisym(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_221
| ~ spl0_425 ),
inference(superposition,[],[f2394,f6644]) ).
fof(f2394,plain,
( ! [X2,X4] :
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X4,X2) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2393]) ).
fof(f43276,plain,
( spl0_1252
| ~ spl0_174
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7411,f6606,f1840,f43274]) ).
fof(f43274,plain,
( spl0_1252
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(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)),X3)
| c_in(X4,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f1840,plain,
( spl0_174
<=> ! [X9,X5,X19,X2] :
( c_in(X19,X5,X2)
| ~ c_in(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f6606,plain,
( spl0_416
<=> ! [X9,X11,X5,X2] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f7411,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(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)),X3)
| c_in(X4,X0,X3) )
| ~ spl0_174
| ~ spl0_416 ),
inference(superposition,[],[f1841,f6607]) ).
fof(f6607,plain,
( ! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_416 ),
inference(avatar_component_clause,[],[f6606]) ).
fof(f1841,plain,
( ! [X2,X19,X9,X5] :
( ~ c_in(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2)
| c_in(X19,X5,X2) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1840]) ).
fof(f43272,plain,
( spl0_1251
| ~ spl0_168
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7409,f6606,f1816,f43270]) ).
fof(f43270,plain,
( spl0_1251
<=> ! [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_1251])]) ).
fof(f1816,plain,
( spl0_168
<=> ! [X5,X9,X6,X2] :
( hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f7409,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_168
| ~ spl0_416 ),
inference(superposition,[],[f1817,f6607]) ).
fof(f1817,plain,
( ! [X2,X6,X9,X5] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X6))
| hBOOL(hAPP(X5,X6)) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f43268,plain,
( spl0_1250
| ~ spl0_174
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f7097,f6582,f1840,f43266]) ).
fof(f43266,plain,
( spl0_1250
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(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)),X3)
| c_in(X4,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f6582,plain,
( spl0_410
<=> ! [X9,X11,X5,X2] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f7097,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(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)),X3)
| c_in(X4,X0,X3) )
| ~ spl0_174
| ~ spl0_410 ),
inference(superposition,[],[f1841,f6583]) ).
fof(f6583,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f6582]) ).
fof(f43264,plain,
( spl0_1249
| ~ spl0_168
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f7095,f6582,f1816,f43262]) ).
fof(f43262,plain,
( spl0_1249
<=> ! [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_1249])]) ).
fof(f7095,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_168
| ~ spl0_410 ),
inference(superposition,[],[f1817,f6583]) ).
fof(f43260,plain,
( spl0_1248
| ~ spl0_173
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6998,f6571,f1836,f43258]) ).
fof(f43258,plain,
( spl0_1248
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(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)),X2)
| c_in(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f6571,plain,
( spl0_409
<=> ! [X9,X11,X5,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f6998,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(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)),X2)
| c_in(X4,X3,X2) )
| ~ spl0_173
| ~ spl0_409 ),
inference(superposition,[],[f1837,f6572]) ).
fof(f6572,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_409 ),
inference(avatar_component_clause,[],[f6571]) ).
fof(f43256,plain,
( spl0_1247
| ~ spl0_346
| ~ spl0_867 ),
inference(avatar_split_clause,[],[f26561,f23189,f4509,f43254]) ).
fof(f43254,plain,
( spl0_1247
<=> ! [X0] : v_a____ = c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_a____,c_Relation_OId__on(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f23189,plain,
( spl0_867
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f26561,plain,
( ! [X0] : v_a____ = c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_a____,c_Relation_OId__on(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X0,X0)
| ~ spl0_346
| ~ spl0_867 ),
inference(resolution,[],[f23190,f4510]) ).
fof(f23190,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_867 ),
inference(avatar_component_clause,[],[f23189]) ).
fof(f43252,plain,
( spl0_1246
| ~ spl0_167
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6996,f6571,f1812,f43250]) ).
fof(f43250,plain,
( spl0_1246
<=> ! [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_1246])]) ).
fof(f6996,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_167
| ~ spl0_409 ),
inference(superposition,[],[f1813,f6572]) ).
fof(f43248,plain,
( spl0_1245
| ~ spl0_170
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f6840,f6563,f1824,f43246]) ).
fof(f43246,plain,
( spl0_1245
<=> ! [X4,X0,X3,X2,X1] :
( c_in(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)
| ~ c_in(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f1824,plain,
( spl0_170
<=> ! [X9,X5,X19,X2] :
( ~ c_in(X19,X9,X2)
| c_in(X19,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f6563,plain,
( spl0_407
<=> ! [X9,X11,X5,X2] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f6840,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(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)
| ~ c_in(X4,X3,X2) )
| ~ spl0_170
| ~ spl0_407 ),
inference(superposition,[],[f1825,f6564]) ).
fof(f6564,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool))
| ~ spl0_407 ),
inference(avatar_component_clause,[],[f6563]) ).
fof(f1825,plain,
( ! [X2,X19,X9,X5] :
( c_in(X19,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X19,X9,X2) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1824]) ).
fof(f43244,plain,
( spl0_1244
| ~ spl0_153
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f6835,f6563,f1752,f43242]) ).
fof(f43242,plain,
( spl0_1244
<=> ! [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_1244])]) ).
fof(f1752,plain,
( spl0_153
<=> ! [X6,X9,X5,X2] :
( ~ hBOOL(hAPP(X9,X6))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f6835,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_153
| ~ spl0_407 ),
inference(superposition,[],[f1753,f6564]) ).
fof(f1753,plain,
( ! [X2,X6,X9,X5] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X6))
| ~ hBOOL(hAPP(X9,X6)) )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1752]) ).
fof(f43240,plain,
( spl0_1243
| ~ spl0_169
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f6701,f6559,f1820,f43238]) ).
fof(f43238,plain,
( spl0_1243
<=> ! [X4,X0,X3,X2,X1] :
( c_in(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)
| ~ c_in(X4,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f1820,plain,
( spl0_169
<=> ! [X9,X5,X19,X2] :
( ~ c_in(X19,X5,X2)
| c_in(X19,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f6559,plain,
( spl0_406
<=> ! [X9,X11,X5,X2] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f6701,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(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)
| ~ c_in(X4,X0,X3) )
| ~ spl0_169
| ~ spl0_406 ),
inference(superposition,[],[f1821,f6560]) ).
fof(f6560,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_406 ),
inference(avatar_component_clause,[],[f6559]) ).
fof(f1821,plain,
( ! [X2,X19,X9,X5] :
( c_in(X19,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X19,X5,X2) )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1820]) ).
fof(f43236,plain,
( spl0_1242
| ~ spl0_154
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f6698,f6559,f1756,f43234]) ).
fof(f43234,plain,
( spl0_1242
<=> ! [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_1242])]) ).
fof(f1756,plain,
( spl0_154
<=> ! [X5,X9,X6,X2] :
( ~ hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f6698,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_154
| ~ spl0_406 ),
inference(superposition,[],[f1757,f6560]) ).
fof(f1757,plain,
( ! [X2,X6,X9,X5] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X6))
| ~ hBOOL(hAPP(X5,X6)) )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1756]) ).
fof(f43232,plain,
( spl0_1241
| ~ spl0_268
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f6451,f6203,f3179,f43230]) ).
fof(f43230,plain,
( spl0_1241
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,c_Relation_OId__on(X2,X3),X1,X3,X4),X1)
| ~ c_in(X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f3179,plain,
( spl0_268
<=> ! [X6,X2,X5] :
( ~ c_in(X6,X5,X2)
| c_in(c_Pair(X6,X6,X2,X2),c_Relation_OId__on(X5,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f6203,plain,
( spl0_401
<=> ! [X3,X4,X0,X12,X6,X2] :
( ~ c_in(c_Pair(X6,X0,X2,X2),X4,tc_prod(X2,X2))
| hAPP(X12,X6) = hAPP(c_Recdef_Ocut(X12,X4,X0,X2,X3),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f6451,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,c_Relation_OId__on(X2,X3),X1,X3,X4),X1)
| ~ c_in(X1,X2,X3) )
| ~ spl0_268
| ~ spl0_401 ),
inference(resolution,[],[f6204,f3180]) ).
fof(f3180,plain,
( ! [X2,X6,X5] :
( c_in(c_Pair(X6,X6,X2,X2),c_Relation_OId__on(X5,X2),tc_prod(X2,X2))
| ~ c_in(X6,X5,X2) )
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f3179]) ).
fof(f6204,plain,
( ! [X2,X3,X0,X6,X4,X12] :
( ~ c_in(c_Pair(X6,X0,X2,X2),X4,tc_prod(X2,X2))
| hAPP(X12,X6) = hAPP(c_Recdef_Ocut(X12,X4,X0,X2,X3),X6) )
| ~ spl0_401 ),
inference(avatar_component_clause,[],[f6203]) ).
fof(f43228,plain,
( spl0_1240
| ~ spl0_62
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f6372,f6191,f1108,f43226]) ).
fof(f43226,plain,
( spl0_1240
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f1108,plain,
( spl0_62
<=> ! [X13,X2,X6] :
( ~ c_in(X6,X13,X2)
| hBOOL(hAPP(X13,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f6191,plain,
( spl0_398
<=> ! [X6,X40,X7] :
( X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Obelow(X40,X6,X7),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f6372,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2))) )
| ~ spl0_62
| ~ spl0_398 ),
inference(resolution,[],[f6192,f1109]) ).
fof(f1109,plain,
( ! [X2,X6,X13] :
( ~ c_in(X6,X13,X2)
| hBOOL(hAPP(X13,X6)) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1108]) ).
fof(f6192,plain,
( ! [X40,X6,X7] :
( c_in(c_Arrow__Order__Mirabelle_Obelow(X40,X6,X7),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X6 = X7 )
| ~ spl0_398 ),
inference(avatar_component_clause,[],[f6191]) ).
fof(f43224,plain,
( spl0_1239
| ~ spl0_62
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f6365,f6187,f1108,f43222]) ).
fof(f43222,plain,
( spl0_1239
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f6187,plain,
( spl0_397
<=> ! [X6,X40,X7] :
( X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Oabove(X40,X6,X7),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f6365,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2))) )
| ~ spl0_62
| ~ spl0_397 ),
inference(resolution,[],[f6188,f1109]) ).
fof(f6188,plain,
( ! [X40,X6,X7] :
( c_in(c_Arrow__Order__Mirabelle_Oabove(X40,X6,X7),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X6 = X7 )
| ~ spl0_397 ),
inference(avatar_component_clause,[],[f6187]) ).
fof(f43220,plain,
( spl0_1238
| ~ spl0_48
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5785,f5531,f1050,f43218]) ).
fof(f43218,plain,
( spl0_1238
<=> ! [X2,X6,X4,X0,X5,X3,X1] : hAPP(c_split(c_COMBK(X0,X1,X2),X3,X4,X6),X5) = hAPP(X0,hAPP(c_snd(X3,X4),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f1050,plain,
( spl0_48
<=> ! [X18,X3,X2,X26] : hAPP(c_COMBK(X18,X2,X3),X26) = X18 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f5531,plain,
( spl0_382
<=> ! [X2,X18,X10,X3,X22] : hAPP(c_split(X18,X3,X10,X2),X22) = hAPP(hAPP(X18,hAPP(c_fst(X3,X10),X22)),hAPP(c_snd(X3,X10),X22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f5785,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hAPP(c_split(c_COMBK(X0,X1,X2),X3,X4,X6),X5) = hAPP(X0,hAPP(c_snd(X3,X4),X5))
| ~ spl0_48
| ~ spl0_382 ),
inference(superposition,[],[f5532,f1051]) ).
fof(f1051,plain,
( ! [X2,X3,X18,X26] : hAPP(c_COMBK(X18,X2,X3),X26) = X18
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1050]) ).
fof(f5532,plain,
( ! [X2,X3,X10,X18,X22] : hAPP(c_split(X18,X3,X10,X2),X22) = hAPP(hAPP(X18,hAPP(c_fst(X3,X10),X22)),hAPP(c_snd(X3,X10),X22))
| ~ spl0_382 ),
inference(avatar_component_clause,[],[f5531]) ).
fof(f43216,plain,
( spl0_1237
| ~ spl0_308
| ~ spl0_376
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5508,f5102,f5098,f3505,f43214]) ).
fof(f43214,plain,
( spl0_1237
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f3505,plain,
( spl0_308
<=> ! [X2,X4] : c_Relation_ORange(c_Relation_Oconverse(X4,X2,X2),X2,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X2),X2,X2),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f5098,plain,
( spl0_376
<=> ! [X6,X2,X8] : c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f5102,plain,
( spl0_377
<=> ! [X6,X4,X0,X3,X2] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2)
| ~ c_in(c_Pair(X0,X6,X2,X3),X4,tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f5508,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),X2)
| ~ spl0_308
| ~ spl0_376
| ~ spl0_377 ),
inference(forward_demodulation,[],[f5490,f3506]) ).
fof(f3506,plain,
( ! [X2,X4] : c_Relation_ORange(c_Relation_Oconverse(X4,X2,X2),X2,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X2),X2,X2),X2,X2)
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f3505]) ).
fof(f5490,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2),X2,X2),X2)
| ~ spl0_376
| ~ spl0_377 ),
inference(resolution,[],[f5103,f5099]) ).
fof(f5099,plain,
( ! [X2,X8,X6] : c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f5098]) ).
fof(f5103,plain,
( ! [X2,X3,X0,X6,X4] :
( ~ c_in(c_Pair(X0,X6,X2,X3),X4,tc_prod(X2,X3))
| c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f5102]) ).
fof(f43212,plain,
( spl0_1236
| ~ spl0_346
| ~ spl0_866 ),
inference(avatar_split_clause,[],[f26451,f23185,f4509,f43210]) ).
fof(f43210,plain,
( spl0_1236
<=> ! [X0] : v_a____ = c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_a____,c_Relation_OId__on(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f23185,plain,
( spl0_866
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f26451,plain,
( ! [X0] : v_a____ = c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_a____,c_Relation_OId__on(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X0,X0)
| ~ spl0_346
| ~ spl0_866 ),
inference(resolution,[],[f23186,f4510]) ).
fof(f23186,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_866 ),
inference(avatar_component_clause,[],[f23185]) ).
fof(f43208,plain,
( spl0_1235
| ~ spl0_288
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5477,f5098,f3425,f43206]) ).
fof(f43206,plain,
( spl0_1235
<=> ! [X2,X0,X1] : c_in(c_Pair(X2,X2,X1,X1),c_Transitive__Closure_Otrancl(c_Set_Oinsert(X0,c_Relation_OId(X1),tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f3425,plain,
( spl0_288
<=> ! [X2,X5,X0] : c_Set_Oinsert(X0,X5,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f5477,plain,
( ! [X2,X0,X1] : c_in(c_Pair(X2,X2,X1,X1),c_Transitive__Closure_Otrancl(c_Set_Oinsert(X0,c_Relation_OId(X1),tc_prod(X1,X1)),X1),tc_prod(X1,X1))
| ~ spl0_288
| ~ spl0_376 ),
inference(superposition,[],[f5099,f3426]) ).
fof(f3426,plain,
( ! [X2,X0,X5] : c_Set_Oinsert(X0,X5,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X5,tc_fun(X2,tc_bool))
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3425]) ).
fof(f43204,plain,
( spl0_1234
| ~ spl0_62
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5467,f5098,f1108,f43202]) ).
fof(f43202,plain,
( spl0_1234
<=> ! [X2,X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Pair(X2,X2,X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f5467,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Pair(X2,X2,X1,X1)))
| ~ spl0_62
| ~ spl0_376 ),
inference(resolution,[],[f5099,f1109]) ).
fof(f43200,plain,
( spl0_1233
| ~ spl0_331
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5459,f5098,f4031,f43198]) ).
fof(f43198,plain,
( spl0_1233
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X3,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f5459,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X3,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) )
| ~ spl0_331
| ~ spl0_376 ),
inference(resolution,[],[f5099,f4032]) ).
fof(f43196,plain,
( spl0_1232
| ~ spl0_334
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5457,f5098,f4043,f43194]) ).
fof(f43194,plain,
( spl0_1232
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X3,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f5457,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X3,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) )
| ~ spl0_334
| ~ spl0_376 ),
inference(resolution,[],[f5099,f4044]) ).
fof(f43192,plain,
( spl0_1231
| ~ spl0_3
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f5171,f5046,f861,f43190]) ).
fof(f43190,plain,
( spl0_1231
<=> ! [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_1231])]) ).
fof(f861,plain,
( spl0_3
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f5046,plain,
( spl0_363
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f5171,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_3
| ~ spl0_363 ),
inference(resolution,[],[f5047,f863]) ).
fof(f863,plain,
( class_Lattices_Odistrib__lattice(tc_bool)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f5047,plain,
( ! [X2,X6,X7,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2) )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f5046]) ).
fof(f43188,plain,
( spl0_1230
| ~ spl0_3
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f5169,f5042,f861,f43186]) ).
fof(f43186,plain,
( spl0_1230
<=> ! [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_1230])]) ).
fof(f5042,plain,
( spl0_362
<=> ! [X7,X22,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X6,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2),c_Lattices_Oupper__semilattice__class_Osup(X22,X6,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f5169,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_3
| ~ spl0_362 ),
inference(resolution,[],[f5043,f863]) ).
fof(f5043,plain,
( ! [X2,X6,X7,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X6,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2),c_Lattices_Oupper__semilattice__class_Osup(X22,X6,X2),X2) )
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f5042]) ).
fof(f43184,plain,
( spl0_1229
| ~ spl0_3
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f5167,f5034,f861,f43182]) ).
fof(f43182,plain,
( spl0_1229
<=> ! [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_1229])]) ).
fof(f5034,plain,
( spl0_360
<=> ! [X7,X22,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2),c_Lattices_Olower__semilattice__class_Oinf(X22,X6,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f5167,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_3
| ~ spl0_360 ),
inference(resolution,[],[f5035,f863]) ).
fof(f5035,plain,
( ! [X2,X6,X7,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2),c_Lattices_Olower__semilattice__class_Oinf(X22,X6,X2),X2) )
| ~ spl0_360 ),
inference(avatar_component_clause,[],[f5034]) ).
fof(f43180,plain,
( spl0_1228
| ~ spl0_3
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f5165,f5030,f861,f43178]) ).
fof(f43178,plain,
( spl0_1228
<=> ! [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_1228])]) ).
fof(f5030,plain,
( spl0_359
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f5165,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_3
| ~ spl0_359 ),
inference(resolution,[],[f5031,f863]) ).
fof(f5031,plain,
( ! [X2,X6,X7,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2) )
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f5030]) ).
fof(f43176,plain,
( spl0_1227
| ~ spl0_82
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4983,f4537,f1204,f43174]) ).
fof(f43174,plain,
( spl0_1227
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Wellfounded_Oacc(X0,tc_prod(X1,X2)),X1,X2),X3),X4))
| ~ c_Wellfounded_Owf(X0,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f1204,plain,
( spl0_82
<=> ! [X6,X2,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_in(X6,c_Wellfounded_Oacc(X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f4537,plain,
( spl0_353
<=> ! [X3,X7,X8,X6,X2] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X8,X2,X3),X6),X7))
| ~ c_in(c_Pair(X6,X7,X2,X3),X8,tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f4983,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Wellfounded_Oacc(X0,tc_prod(X1,X2)),X1,X2),X3),X4))
| ~ c_Wellfounded_Owf(X0,tc_prod(X1,X2)) )
| ~ spl0_82
| ~ spl0_353 ),
inference(resolution,[],[f4538,f1205]) ).
fof(f1205,plain,
( ! [X2,X6,X4] :
( c_in(X6,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_Wellfounded_Owf(X4,X2) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f4538,plain,
( ! [X2,X3,X8,X6,X7] :
( ~ c_in(c_Pair(X6,X7,X2,X3),X8,tc_prod(X2,X3))
| hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X8,X2,X3),X6),X7)) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f4537]) ).
fof(f43172,plain,
( spl0_1226
| ~ spl0_352
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4967,f4537,f4533,f43170]) ).
fof(f43170,plain,
( spl0_1226
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X2,X1)),X2))
| c_in(X2,c_Wellfounded_Oacc(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f4533,plain,
( spl0_352
<=> ! [X6,X2,X4] :
( c_in(X6,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X4,X6,X2),X6,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f4967,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X2,X1)),X2))
| c_in(X2,c_Wellfounded_Oacc(X0,X1),X1) )
| ~ spl0_352
| ~ spl0_353 ),
inference(resolution,[],[f4538,f4534]) ).
fof(f4534,plain,
( ! [X2,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X4,X6,X2),X6,X2,X2),X4,tc_prod(X2,X2))
| c_in(X6,c_Wellfounded_Oacc(X4,X2),X2) )
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f4533]) ).
fof(f43168,plain,
( spl0_1225
| ~ spl0_427
| ~ spl0_752 ),
inference(avatar_split_clause,[],[f22497,f21189,f7626,f43166]) ).
fof(f43166,plain,
( spl0_1225
<=> ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_b____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f7626,plain,
( spl0_427
<=> ! [X0] : c_in(v_b____,c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f21189,plain,
( spl0_752
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,tc_prod(X2,X2))
| hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f22497,plain,
( ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_b____))
| ~ spl0_427
| ~ spl0_752 ),
inference(resolution,[],[f21190,f7627]) ).
fof(f7627,plain,
( ! [X0] : c_in(v_b____,c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)
| ~ spl0_427 ),
inference(avatar_component_clause,[],[f7626]) ).
fof(f21190,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,tc_prod(X2,X2))
| hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),X0)) )
| ~ spl0_752 ),
inference(avatar_component_clause,[],[f21189]) ).
fof(f43164,plain,
( spl0_1224
| ~ spl0_351
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4966,f4537,f4529,f43162]) ).
fof(f43162,plain,
( spl0_1224
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X2,X1)),X2))
| c_in(X2,c_Wellfounded_Oacc(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f4529,plain,
( spl0_351
<=> ! [X6,X2,X8] :
( c_in(X6,c_Wellfounded_Oacc(X8,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X8,X6,X2),X6,X2,X2),X8,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f4966,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X2,X1)),X2))
| c_in(X2,c_Wellfounded_Oacc(X0,X1),X1) )
| ~ spl0_351
| ~ spl0_353 ),
inference(resolution,[],[f4538,f4530]) ).
fof(f4530,plain,
( ! [X2,X8,X6] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X8,X6,X2),X6,X2,X2),X8,tc_prod(X2,X2))
| c_in(X6,c_Wellfounded_Oacc(X8,X2),X2) )
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f4529]) ).
fof(f43160,plain,
( spl0_1223
| ~ spl0_292
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4851,f4513,f3441,f43158]) ).
fof(f43158,plain,
( spl0_1223
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Transitive__Closure_Otrancl(X0,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f3441,plain,
( spl0_292
<=> ! [X9,X11,X5,X2] :
( c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f4513,plain,
( spl0_347
<=> ! [X2,X4] : c_Transitive__Closure_Otrancl(X4,X2) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X4,X2),X4,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f4851,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Transitive__Closure_Otrancl(X0,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)) )
| ~ spl0_292
| ~ spl0_347 ),
inference(superposition,[],[f3442,f4514]) ).
fof(f4514,plain,
( ! [X2,X4] : c_Transitive__Closure_Otrancl(X4,X2) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X4,X2),X4,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f4513]) ).
fof(f3442,plain,
( ! [X2,X11,X9,X5] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool))
| c_lessequals(X5,X11,tc_fun(X2,tc_bool)) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3441]) ).
fof(f43156,plain,
( spl0_1222
| ~ spl0_285
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4849,f4513,f3413,f43154]) ).
fof(f43154,plain,
( spl0_1222
<=> ! [X0,X1] :
( c_Transitive__Closure_Otrancl(X0,X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f3413,plain,
( spl0_285
<=> ! [X2,X5,X9] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f4849,plain,
( ! [X0,X1] :
( c_Transitive__Closure_Otrancl(X0,X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) = X0 )
| ~ spl0_285
| ~ spl0_347 ),
inference(superposition,[],[f3414,f4514]) ).
fof(f3414,plain,
( ! [X2,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5 )
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f3413]) ).
fof(f43152,plain,
( spl0_1221
| ~ spl0_239
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4468,f4043,f2893,f43150]) ).
fof(f43150,plain,
( spl0_1221
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X1,X2,tc_prod(X0,X0))
| c_in(hAPP(c_fst(X0,X0),X1),X3,X0)
| ~ c_Relation_Orefl__on(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f2893,plain,
( spl0_239
<=> ! [X2,X3,X15] : c_Pair(hAPP(c_fst(X2,X3),X15),hAPP(c_snd(X2,X3),X15),X2,X3) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f4468,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X1,X2,tc_prod(X0,X0))
| c_in(hAPP(c_fst(X0,X0),X1),X3,X0)
| ~ c_Relation_Orefl__on(X3,X2,X0) )
| ~ spl0_239
| ~ spl0_334 ),
inference(superposition,[],[f4044,f2894]) ).
fof(f2894,plain,
( ! [X2,X3,X15] : c_Pair(hAPP(c_fst(X2,X3),X15),hAPP(c_snd(X2,X3),X15),X2,X3) = X15
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2893]) ).
fof(f43148,plain,
( spl0_1220
| ~ spl0_239
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4450,f4039,f2893,f43146]) ).
fof(f43146,plain,
( spl0_1220
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X1,X2,tc_prod(X0,X0))
| c_in(hAPP(c_snd(X0,X0),X1),X3,X0)
| ~ c_Relation_Orefl__on(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f4039,plain,
( spl0_333
<=> ! [X6,X4,X7,X5,X2] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_in(X7,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f4450,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X1,X2,tc_prod(X0,X0))
| c_in(hAPP(c_snd(X0,X0),X1),X3,X0)
| ~ c_Relation_Orefl__on(X3,X2,X0) )
| ~ spl0_239
| ~ spl0_333 ),
inference(superposition,[],[f4040,f2894]) ).
fof(f4040,plain,
( ! [X2,X6,X7,X4,X5] :
( ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| c_in(X7,X5,X2)
| ~ c_Relation_Orefl__on(X5,X4,X2) )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f4039]) ).
fof(f43144,plain,
( spl0_1219
| ~ spl0_239
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4431,f4035,f2893,f43142]) ).
fof(f43142,plain,
( spl0_1219
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_in(X2,c_Product__Type_OSigma(X3,X4,X0,X1),tc_prod(X0,X1))
| c_in(hAPP(c_fst(X0,X1),X2),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f4431,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X2,c_Product__Type_OSigma(X3,X4,X0,X1),tc_prod(X0,X1))
| c_in(hAPP(c_fst(X0,X1),X2),X3,X0) )
| ~ spl0_239
| ~ spl0_332 ),
inference(superposition,[],[f4036,f2894]) ).
fof(f43140,plain,
( spl0_1218
| ~ spl0_239
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f4427,f4031,f2893,f43138]) ).
fof(f43138,plain,
( spl0_1218
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X1,X2,tc_prod(X0,X0))
| c_in(hAPP(c_fst(X0,X0),X1),X3,X0)
| ~ c_Equiv__Relations_Oequiv(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f4427,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X1,X2,tc_prod(X0,X0))
| c_in(hAPP(c_fst(X0,X0),X1),X3,X0)
| ~ c_Equiv__Relations_Oequiv(X3,X2,X0) )
| ~ spl0_239
| ~ spl0_331 ),
inference(superposition,[],[f4032,f2894]) ).
fof(f43136,plain,
( spl0_1217
| ~ spl0_239
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4409,f4027,f2893,f43134]) ).
fof(f43134,plain,
( spl0_1217
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X1,X2,tc_prod(X0,X0))
| c_in(hAPP(c_snd(X0,X0),X1),X3,X0)
| ~ c_Equiv__Relations_Oequiv(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f4027,plain,
( spl0_330
<=> ! [X6,X4,X7,X5,X2] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_in(X7,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f4409,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X1,X2,tc_prod(X0,X0))
| c_in(hAPP(c_snd(X0,X0),X1),X3,X0)
| ~ c_Equiv__Relations_Oequiv(X3,X2,X0) )
| ~ spl0_239
| ~ spl0_330 ),
inference(superposition,[],[f4028,f2894]) ).
fof(f4028,plain,
( ! [X2,X6,X7,X4,X5] :
( ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| c_in(X7,X5,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2) )
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f4027]) ).
fof(f43132,plain,
( spl0_1216
| ~ spl0_170
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4175,f3986,f1824,f43130]) ).
fof(f43130,plain,
( spl0_1216
<=> ! [X0,X3,X2,X1] :
( c_in(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X3,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f3986,plain,
( spl0_320
<=> ! [X2,X5,X9] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f4175,plain,
( ! [X2,X3,X0,X1] :
( c_in(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X3,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_170
| ~ spl0_320 ),
inference(superposition,[],[f1825,f3987]) ).
fof(f3987,plain,
( ! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f3986]) ).
fof(f43128,plain,
( spl0_1215
| ~ spl0_153
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4172,f3986,f1752,f43126]) ).
fof(f43126,plain,
( spl0_1215
<=> ! [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_1215])]) ).
fof(f4172,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_153
| ~ spl0_320 ),
inference(superposition,[],[f1753,f3987]) ).
fof(f43124,plain,
( spl0_1214
| ~ spl0_309
| ~ spl0_752 ),
inference(avatar_split_clause,[],[f22491,f21189,f3509,f43122]) ).
fof(f43122,plain,
( spl0_1214
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(v_Lab____,X0),c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f3509,plain,
( spl0_309
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1),v_Lab____,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f22491,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(v_Lab____,X0),c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2) )
| ~ spl0_309
| ~ spl0_752 ),
inference(resolution,[],[f21190,f3510]) ).
fof(f3510,plain,
( ! [X2,X0,X1] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1),v_Lab____,X2)
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f3509]) ).
fof(f43120,plain,
( spl0_1213
| ~ spl0_169
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f4137,f3982,f1820,f43118]) ).
fof(f43118,plain,
( spl0_1213
<=> ! [X0,X3,X2,X1] :
( c_in(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f3982,plain,
( spl0_319
<=> ! [X2,X5,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f4137,plain,
( ! [X2,X3,X0,X1] :
( c_in(X3,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_169
| ~ spl0_319 ),
inference(superposition,[],[f1821,f3983]) ).
fof(f3983,plain,
( ! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X2,tc_bool))
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f3982]) ).
fof(f43116,plain,
( spl0_1212
| ~ spl0_154
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f4134,f3982,f1756,f43114]) ).
fof(f43114,plain,
( spl0_1212
<=> ! [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_1212])]) ).
fof(f4134,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_154
| ~ spl0_319 ),
inference(superposition,[],[f1757,f3983]) ).
fof(f43112,plain,
( spl0_1211
| ~ spl0_164
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f4129,f3982,f1800,f43110]) ).
fof(f43110,plain,
( spl0_1211
<=> ! [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_1211])]) ).
fof(f1800,plain,
( spl0_164
<=> ! [X2,X5,X9] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f4129,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_164
| ~ spl0_319 ),
inference(superposition,[],[f3983,f1801]) ).
fof(f1801,plain,
( ! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X2,tc_bool))
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1800]) ).
fof(f43108,plain,
( spl0_1210
| ~ spl0_152
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f4090,f3974,f1748,f43106]) ).
fof(f43106,plain,
( spl0_1210
<=> ! [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_1210])]) ).
fof(f1748,plain,
( spl0_152
<=> ! [X2,X5,X9] : c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X9,X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f3974,plain,
( spl0_317
<=> ! [X2,X5,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f4090,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_152
| ~ spl0_317 ),
inference(superposition,[],[f3975,f1749]) ).
fof(f1749,plain,
( ! [X2,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X9,X5,tc_fun(X2,tc_bool))
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1748]) ).
fof(f3975,plain,
( ! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f3974]) ).
fof(f43104,plain,
( spl0_1209
| ~ spl0_156
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4063,f3966,f1768,f43102]) ).
fof(f43102,plain,
( spl0_1209
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)) = c_Relation_Orel__comp(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X2,X0,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f1768,plain,
( spl0_156
<=> ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f3966,plain,
( spl0_315
<=> ! [X10,X8,X3,X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X10),tc_bool)),X8,X2,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f4063,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)) = c_Relation_Orel__comp(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X2,X0,X0,X1)
| ~ spl0_156
| ~ spl0_315 ),
inference(superposition,[],[f3967,f1769]) ).
fof(f1769,plain,
( ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1768]) ).
fof(f3967,plain,
( ! [X2,X3,X10,X8] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X10),tc_bool)),X8,X2,X10,X3)
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f3966]) ).
fof(f43100,plain,
( spl0_1208
| ~ spl0_156
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4054,f3962,f1768,f43098]) ).
fof(f43098,plain,
( spl0_1208
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X0),tc_bool)) = c_Relation_Orel__comp(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X2,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f3962,plain,
( spl0_314
<=> ! [X2,X8,X3,X10] : c_Relation_Orel__comp(X8,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X3),tc_bool)),X2,X10,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f4054,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X0),tc_bool)) = c_Relation_Orel__comp(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X2,X0,X0)
| ~ spl0_156
| ~ spl0_314 ),
inference(superposition,[],[f3963,f1769]) ).
fof(f3963,plain,
( ! [X2,X3,X10,X8] : c_Relation_Orel__comp(X8,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X3),tc_bool)),X2,X10,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| ~ spl0_314 ),
inference(avatar_component_clause,[],[f3962]) ).
fof(f43096,plain,
( spl0_1207
| ~ spl0_102
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3901,f3493,f1336,f43094]) ).
fof(f43094,plain,
( spl0_1207
<=> ! [X0,X3,X2,X1] : c_Relation_Oinv__image(c_Relation_OId__on(X0,X1),X2,X1,X3) = c_Relation_Oconverse(c_Relation_Oinv__image(c_Relation_OId__on(X0,X1),X2,X1,X3),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f1336,plain,
( spl0_102
<=> ! [X2,X5] : c_Relation_OId__on(X5,X2) = c_Relation_Oconverse(c_Relation_OId__on(X5,X2),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f3493,plain,
( spl0_305
<=> ! [X3,X8,X12,X2] : c_Relation_Oconverse(c_Relation_Oinv__image(X8,X12,X3,X2),X2,X2) = c_Relation_Oinv__image(c_Relation_Oconverse(X8,X3,X3),X12,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f3901,plain,
( ! [X2,X3,X0,X1] : c_Relation_Oinv__image(c_Relation_OId__on(X0,X1),X2,X1,X3) = c_Relation_Oconverse(c_Relation_Oinv__image(c_Relation_OId__on(X0,X1),X2,X1,X3),X3,X3)
| ~ spl0_102
| ~ spl0_305 ),
inference(superposition,[],[f3494,f1337]) ).
fof(f1337,plain,
( ! [X2,X5] : c_Relation_OId__on(X5,X2) = c_Relation_Oconverse(c_Relation_OId__on(X5,X2),X2,X2)
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1336]) ).
fof(f3494,plain,
( ! [X2,X3,X8,X12] : c_Relation_Oconverse(c_Relation_Oinv__image(X8,X12,X3,X2),X2,X2) = c_Relation_Oinv__image(c_Relation_Oconverse(X8,X3,X3),X12,X3,X2)
| ~ spl0_305 ),
inference(avatar_component_clause,[],[f3493]) ).
fof(f43092,plain,
( spl0_1206
| ~ spl0_61
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3866,f3473,f1104,f43090]) ).
fof(f43090,plain,
( spl0_1206
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( ~ hBOOL(hAPP(hAPP(X0,X4),X5))
| c_in(c_Pair(X4,X5,X1,X2),c_split(X0,X1,X2,X3),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f1104,plain,
( spl0_61
<=> ! [X6,X2,X13] :
( ~ hBOOL(hAPP(X13,X6))
| c_in(X6,X13,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f3473,plain,
( spl0_300
<=> ! [X10,X0,X12,X3,X2,X1] : hAPP(hAPP(X12,X0),X1) = hAPP(c_split(X12,X2,X3,X10),c_Pair(X0,X1,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3866,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(X0,X4),X5))
| c_in(c_Pair(X4,X5,X1,X2),c_split(X0,X1,X2,X3),X6) )
| ~ spl0_61
| ~ spl0_300 ),
inference(superposition,[],[f1105,f3474]) ).
fof(f3474,plain,
( ! [X2,X3,X10,X0,X1,X12] : hAPP(hAPP(X12,X0),X1) = hAPP(c_split(X12,X2,X3,X10),c_Pair(X0,X1,X2,X3))
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f3473]) ).
fof(f1105,plain,
( ! [X2,X6,X13] :
( ~ hBOOL(hAPP(X13,X6))
| c_in(X6,X13,X2) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f43088,plain,
( spl0_1205
| ~ spl0_203
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3695,f3425,f2311,f43086]) ).
fof(f43086,plain,
( spl0_1205
<=> ! [X2,X0,X1] :
( c_Set_Oinsert(X0,X2,X1) != X2
| c_lessequals(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X2,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f2311,plain,
( spl0_203
<=> ! [X2,X5,X9] :
( c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) != X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f3695,plain,
( ! [X2,X0,X1] :
( c_Set_Oinsert(X0,X2,X1) != X2
| c_lessequals(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X2,tc_fun(X1,tc_bool)) )
| ~ spl0_203
| ~ spl0_288 ),
inference(superposition,[],[f2312,f3426]) ).
fof(f2312,plain,
( ! [X2,X9,X5] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) != X9
| c_lessequals(X5,X9,tc_fun(X2,tc_bool)) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2311]) ).
fof(f43084,plain,
( spl0_1204
| ~ spl0_164
| ~ spl0_200
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3320,f3151,f2299,f1800,f43082]) ).
fof(f43082,plain,
( spl0_1204
<=> ! [X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Orel__comp(X0,X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)) = X0
| ~ c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f2299,plain,
( spl0_200
<=> ! [X2,X5,X9] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f3151,plain,
( spl0_261
<=> ! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| c_lessequals(c_Relation_Orel__comp(X4,X4,X2,X2,X2),X4,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f3320,plain,
( ! [X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Orel__comp(X0,X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)) = X0
| ~ c_Relation_Otrans(X0,X1) )
| ~ spl0_164
| ~ spl0_200
| ~ spl0_261 ),
inference(forward_demodulation,[],[f3301,f1801]) ).
fof(f3301,plain,
( ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)) = X0 )
| ~ spl0_200
| ~ spl0_261 ),
inference(resolution,[],[f3152,f2300]) ).
fof(f2300,plain,
( ! [X2,X9,X5] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = X9 )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2299]) ).
fof(f3152,plain,
( ! [X2,X4] :
( c_lessequals(c_Relation_Orel__comp(X4,X4,X2,X2,X2),X4,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Otrans(X4,X2) )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f3151]) ).
fof(f43080,plain,
( spl0_1203
| ~ spl0_298
| ~ spl0_752 ),
inference(avatar_split_clause,[],[f22490,f21189,f3465,f43078]) ).
fof(f43078,plain,
( spl0_1203
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(v_Lab____,X0),c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f3465,plain,
( spl0_298
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1),v_Lab____,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f22490,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(v_Lab____,X0),c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2) )
| ~ spl0_298
| ~ spl0_752 ),
inference(resolution,[],[f21190,f3466]) ).
fof(f3466,plain,
( ! [X2,X0,X1] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1),v_Lab____,X2)
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f3465]) ).
fof(f43034,plain,
( ~ spl0_9
| spl0_1202
| ~ spl0_259
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3306,f3151,f3143,f43032,f891]) ).
fof(f891,plain,
( spl0_9
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f43032,plain,
( spl0_1202
<=> ! [X2,X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_lessequals(hAPP(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X2),hAPP(X0,X2),tc_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f3143,plain,
( spl0_259
<=> ! [X6,X3,X12,X36,X2] :
( ~ class_HOL_Oord(X3)
| ~ c_lessequals(X12,X36,tc_fun(X2,X3))
| c_lessequals(hAPP(X12,X6),hAPP(X36,X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f3306,plain,
( ! [X2,X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X2),hAPP(X0,X2),tc_bool) )
| ~ spl0_259
| ~ spl0_261 ),
inference(resolution,[],[f3152,f3144]) ).
fof(f3144,plain,
( ! [X2,X3,X36,X6,X12] :
( ~ c_lessequals(X12,X36,tc_fun(X2,X3))
| ~ class_HOL_Oord(X3)
| c_lessequals(hAPP(X12,X6),hAPP(X36,X6),X3) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f3143]) ).
fof(f43030,plain,
( spl0_1201
| ~ spl0_230
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3038,f2893,f2429,f43028]) ).
fof(f43028,plain,
( spl0_1201
<=> ! [X0,X1] :
( ~ c_in(X1,c_Relation_OId(X0),tc_prod(X0,X0))
| hAPP(c_fst(X0,X0),X1) = hAPP(c_snd(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f2429,plain,
( spl0_230
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f3038,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_Relation_OId(X0),tc_prod(X0,X0))
| hAPP(c_fst(X0,X0),X1) = hAPP(c_snd(X0,X0),X1) )
| ~ spl0_230
| ~ spl0_239 ),
inference(superposition,[],[f2430,f2894]) ).
fof(f2430,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2))
| X0 = X1 )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2429]) ).
fof(f43026,plain,
( spl0_1200
| ~ spl0_235
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2990,f2881,f2877,f43024]) ).
fof(f43024,plain,
( spl0_1200
<=> ! [X4,X0,X3,X2,X1] :
( c_lessequals(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X4,X0,X3),X2,tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f2877,plain,
( spl0_235
<=> ! [X9,X5,X2,X1] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_lessequals(X5,c_Set_Oinsert(X1,X9,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2881,plain,
( spl0_236
<=> ! [X6,X2,X5,X9] :
( c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2990,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X4,X0,X3),X2,tc_fun(X3,tc_bool)) )
| ~ spl0_235
| ~ spl0_236 ),
inference(resolution,[],[f2882,f2878]) ).
fof(f2878,plain,
( ! [X2,X1,X9,X5] :
( c_lessequals(X5,c_Set_Oinsert(X1,X9,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool)) )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2877]) ).
fof(f2882,plain,
( ! [X2,X6,X9,X5] :
( ~ c_lessequals(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool))
| c_lessequals(X5,X9,tc_fun(X2,tc_bool)) )
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2881]) ).
fof(f43022,plain,
( spl0_1199
| ~ spl0_135
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2865,f2425,f1494,f43020]) ).
fof(f43020,plain,
( spl0_1199
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1))
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(c_Relation_OId(X1),X0,tc_prod(X1,X1)),c_Relation_OId(X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f2425,plain,
( spl0_229
<=> ! [X8,X6,X2,X26] :
( ~ c_Wellfounded_Owf(X8,X2)
| ~ c_in(X6,X26,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X26,X8,X2),X26,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2865,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1))
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(c_Relation_OId(X1),X0,tc_prod(X1,X1)),c_Relation_OId(X1),tc_prod(X1,X1)) )
| ~ spl0_135
| ~ spl0_229 ),
inference(resolution,[],[f2426,f1495]) ).
fof(f2426,plain,
( ! [X2,X8,X6,X26] :
( ~ c_in(X6,X26,X2)
| ~ c_Wellfounded_Owf(X8,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X26,X8,X2),X26,X2) )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2425]) ).
fof(f43018,plain,
( spl0_1198
| ~ spl0_135
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2852,f2421,f1494,f43016]) ).
fof(f43016,plain,
( spl0_1198
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(c_Relation_OId(X1),X0,tc_prod(X1,X1)),c_Relation_OId(X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f2421,plain,
( spl0_228
<=> ! [X4,X27,X2,X26] :
( ~ c_Wellfounded_Owf(X4,X2)
| ~ c_in(X27,X26,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X26,X4,X2),X26,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2852,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(c_Relation_OId(X1),X0,tc_prod(X1,X1)),c_Relation_OId(X1),tc_prod(X1,X1)) )
| ~ spl0_135
| ~ spl0_228 ),
inference(resolution,[],[f2422,f1495]) ).
fof(f2422,plain,
( ! [X2,X26,X27,X4] :
( ~ c_in(X27,X26,X2)
| ~ c_Wellfounded_Owf(X4,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X26,X4,X2),X26,X2) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2421]) ).
fof(f43014,plain,
( spl0_1197
| ~ spl0_124
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2838,f2413,f1450,f43012]) ).
fof(f43012,plain,
( spl0_1197
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( c_in(X3,c_Set_Oimage(c_snd(X0,X1),X4,X5,X6),X6)
| ~ c_in(c_Pair(X2,X3,X0,X1),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1450,plain,
( spl0_124
<=> ! [X3,X7,X6,X2] : hAPP(c_snd(X3,X2),c_Pair(X6,X7,X3,X2)) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f2413,plain,
( spl0_226
<=> ! [X5,X44,X12,X6,X2] :
( ~ c_in(X6,X5,X44)
| c_in(hAPP(X12,X6),c_Set_Oimage(X12,X5,X44,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2838,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_in(X3,c_Set_Oimage(c_snd(X0,X1),X4,X5,X6),X6)
| ~ c_in(c_Pair(X2,X3,X0,X1),X4,X5) )
| ~ spl0_124
| ~ spl0_226 ),
inference(superposition,[],[f2414,f1451]) ).
fof(f1451,plain,
( ! [X2,X3,X6,X7] : hAPP(c_snd(X3,X2),c_Pair(X6,X7,X3,X2)) = X7
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1450]) ).
fof(f2414,plain,
( ! [X2,X6,X44,X5,X12] :
( c_in(hAPP(X12,X6),c_Set_Oimage(X12,X5,X44,X2),X2)
| ~ c_in(X6,X5,X44) )
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2413]) ).
fof(f43010,plain,
( spl0_1196
| ~ spl0_123
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2837,f2413,f1446,f43008]) ).
fof(f43008,plain,
( spl0_1196
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( c_in(X2,c_Set_Oimage(c_fst(X0,X1),X4,X5,X6),X6)
| ~ c_in(c_Pair(X2,X3,X0,X1),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1446,plain,
( spl0_123
<=> ! [X0,X3,X2,X1] : hAPP(c_fst(X2,X3),c_Pair(X0,X1,X2,X3)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f2837,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_in(X2,c_Set_Oimage(c_fst(X0,X1),X4,X5,X6),X6)
| ~ c_in(c_Pair(X2,X3,X0,X1),X4,X5) )
| ~ spl0_123
| ~ spl0_226 ),
inference(superposition,[],[f2414,f1447]) ).
fof(f1447,plain,
( ! [X2,X3,X0,X1] : hAPP(c_fst(X2,X3),c_Pair(X0,X1,X2,X3)) = X0
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1446]) ).
fof(f43006,plain,
( spl0_1195
| ~ spl0_98
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2825,f2397,f1320,f43004]) ).
fof(f43004,plain,
( spl0_1195
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,tc_prod(X2,X2))
| c_Transitive__Closure_Otrancl(X1,X2) = c_Set_Oinsert(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1320,plain,
( spl0_98
<=> ! [X2,X5,X0] :
( ~ c_in(X0,X5,X2)
| c_Set_Oinsert(X0,X5,X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f2397,plain,
( spl0_222
<=> ! [X2,X16,X4] :
( ~ c_in(X16,X4,tc_prod(X2,X2))
| c_in(X16,c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2825,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,tc_prod(X2,X2))
| c_Transitive__Closure_Otrancl(X1,X2) = c_Set_Oinsert(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) )
| ~ spl0_98
| ~ spl0_222 ),
inference(resolution,[],[f2398,f1321]) ).
fof(f1321,plain,
( ! [X2,X0,X5] :
( ~ c_in(X0,X5,X2)
| c_Set_Oinsert(X0,X5,X2) = X5 )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f2398,plain,
( ! [X2,X16,X4] :
( c_in(X16,c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(X16,X4,tc_prod(X2,X2)) )
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2397]) ).
fof(f43002,plain,
( spl0_1194
| ~ spl0_106
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2589,f2303,f1375,f43000]) ).
fof(f43000,plain,
( spl0_1194
<=> ! [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_1194])]) ).
fof(f1375,plain,
( spl0_106
<=> ! [X2,X5,X9] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2303,plain,
( spl0_201
<=> ! [X2,X5,X9] :
( ~ c_lessequals(X9,X5,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2589,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_106
| ~ spl0_201 ),
inference(resolution,[],[f2304,f1376]) ).
fof(f1376,plain,
( ! [X2,X9,X5] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f2304,plain,
( ! [X2,X9,X5] :
( ~ c_lessequals(X9,X5,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = X5 )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2303]) ).
fof(f42998,plain,
( spl0_1193
| ~ spl0_353
| ~ spl0_750 ),
inference(avatar_split_clause,[],[f21244,f21181,f4537,f42996]) ).
fof(f42996,plain,
( spl0_1193
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f21181,plain,
( spl0_750
<=> ! [X2,X0,X1] : c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Set_Oinsert(X0,v_Lab____,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f21244,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____))
| ~ spl0_353
| ~ spl0_750 ),
inference(resolution,[],[f21182,f4538]) ).
fof(f21182,plain,
( ! [X2,X0,X1] : c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Set_Oinsert(X0,v_Lab____,X1),X2)
| ~ spl0_750 ),
inference(avatar_component_clause,[],[f21181]) ).
fof(f42994,plain,
( spl0_1192
| ~ spl0_105
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2588,f2303,f1371,f42992]) ).
fof(f42992,plain,
( spl0_1192
<=> ! [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_1192])]) ).
fof(f1371,plain,
( spl0_105
<=> ! [X2,X5,X9] : c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f2588,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_105
| ~ spl0_201 ),
inference(resolution,[],[f2304,f1372]) ).
fof(f1372,plain,
( ! [X2,X9,X5] : c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1371]) ).
fof(f42990,plain,
( spl0_1191
| ~ spl0_105
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2565,f2299,f1371,f42988]) ).
fof(f42988,plain,
( spl0_1191
<=> ! [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_1191])]) ).
fof(f2565,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_105
| ~ spl0_200 ),
inference(resolution,[],[f2300,f1372]) ).
fof(f42986,plain,
( spl0_1190
| ~ spl0_117
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2501,f2279,f1422,f42984]) ).
fof(f42984,plain,
( spl0_1190
<=> ! [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_1190])]) ).
fof(f1422,plain,
( spl0_117
<=> ! [X2,X5,X9] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f2279,plain,
( spl0_195
<=> ! [X2,X5,X9] :
( ~ c_lessequals(X9,X5,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2501,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_117
| ~ spl0_195 ),
inference(resolution,[],[f2280,f1423]) ).
fof(f1423,plain,
( ! [X2,X9,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool))
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1422]) ).
fof(f2280,plain,
( ! [X2,X9,X5] :
( ~ c_lessequals(X9,X5,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = X9 )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2279]) ).
fof(f42982,plain,
( spl0_1189
| ~ spl0_116
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2494,f2279,f1418,f42980]) ).
fof(f42980,plain,
( spl0_1189
<=> ! [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_1189])]) ).
fof(f1418,plain,
( spl0_116
<=> ! [X2,X5,X9] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f2494,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_116
| ~ spl0_195 ),
inference(resolution,[],[f2280,f1419]) ).
fof(f1419,plain,
( ! [X2,X9,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool))
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1418]) ).
fof(f42978,plain,
( spl0_1188
| ~ spl0_117
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2478,f2275,f1422,f42976]) ).
fof(f42976,plain,
( spl0_1188
<=> ! [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_1188])]) ).
fof(f2275,plain,
( spl0_194
<=> ! [X2,X5,X9] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f2478,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_117
| ~ spl0_194 ),
inference(resolution,[],[f2276,f1423]) ).
fof(f2276,plain,
( ! [X2,X9,X5] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = X5 )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2275]) ).
fof(f42974,plain,
( spl0_1187
| ~ spl0_116
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2471,f2275,f1418,f42972]) ).
fof(f42972,plain,
( spl0_1187
<=> ! [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_1187])]) ).
fof(f2471,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_116
| ~ spl0_194 ),
inference(resolution,[],[f2276,f1419]) ).
fof(f42970,plain,
( spl0_1186
| ~ spl0_115
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2470,f2275,f1414,f42968]) ).
fof(f42968,plain,
( spl0_1186
<=> ! [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_1186])]) ).
fof(f1414,plain,
( spl0_115
<=> ! [X2,X5,X9] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f2470,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_115
| ~ spl0_194 ),
inference(resolution,[],[f2276,f1415]) ).
fof(f1415,plain,
( ! [X2,X9,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool))
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1414]) ).
fof(f42966,plain,
( spl0_1185
| ~ spl0_122
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2258,f1901,f1442,f42964]) ).
fof(f42964,plain,
( spl0_1185
<=> ! [X0,X3,X2,X1] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(X0,X1,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f1442,plain,
( spl0_122
<=> ! [X0,X9,X2,X1] :
( ~ c_in(X0,X9,X2)
| c_in(X0,c_Set_Oinsert(X1,X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1901,plain,
( spl0_188
<=> ! [X2,X0,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| ~ c_in(c_Pair(X0,X0,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f2258,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(X0,X1,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) )
| ~ spl0_122
| ~ spl0_188 ),
inference(resolution,[],[f1902,f1443]) ).
fof(f1443,plain,
( ! [X2,X0,X1,X9] :
( c_in(X0,c_Set_Oinsert(X1,X9,X2),X2)
| ~ c_in(X0,X9,X2) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1442]) ).
fof(f1902,plain,
( ! [X2,X0,X4] :
( ~ c_in(c_Pair(X0,X0,X2,X2),X4,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X4,X2) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1901]) ).
fof(f42962,plain,
( spl0_1184
| ~ spl0_122
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2239,f1889,f1442,f42960]) ).
fof(f42960,plain,
( spl0_1184
<=> ! [X0,X3,X2,X1] :
( ~ c_Relation_Oirrefl(c_Set_Oinsert(X0,X1,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f1889,plain,
( spl0_185
<=> ! [X6,X2,X4] :
( ~ c_Relation_Oirrefl(X4,X2)
| ~ c_in(c_Pair(X6,X6,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f2239,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Relation_Oirrefl(c_Set_Oinsert(X0,X1,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) )
| ~ spl0_122
| ~ spl0_185 ),
inference(resolution,[],[f1890,f1443]) ).
fof(f1890,plain,
( ! [X2,X6,X4] :
( ~ c_in(c_Pair(X6,X6,X2,X2),X4,tc_prod(X2,X2))
| ~ c_Relation_Oirrefl(X4,X2) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1889]) ).
fof(f42958,plain,
( spl0_1183
| ~ spl0_145
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2157,f1861,f1605,f42956]) ).
fof(f42956,plain,
( spl0_1183
<=> ! [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_1183])]) ).
fof(f1605,plain,
( spl0_145
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1861,plain,
( spl0_178
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X6,X0,X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f2157,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_145
| ~ spl0_178 ),
inference(duplicate_literal_removal,[],[f2145]) ).
fof(f2145,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_145
| ~ spl0_178 ),
inference(resolution,[],[f1862,f1606]) ).
fof(f1606,plain,
( ! [X2,X6,X7] :
( ~ c_lessequals(X6,X7,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X7 )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1605]) ).
fof(f1862,plain,
( ! [X2,X0,X1,X6] :
( c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X2)
| ~ c_lessequals(X6,X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1861]) ).
fof(f42954,plain,
( spl0_1182
| ~ spl0_143
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2156,f1861,f1597,f42952]) ).
fof(f42952,plain,
( spl0_1182
<=> ! [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_1182])]) ).
fof(f1597,plain,
( spl0_143
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f2156,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_143
| ~ spl0_178 ),
inference(duplicate_literal_removal,[],[f2146]) ).
fof(f2146,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_143
| ~ spl0_178 ),
inference(resolution,[],[f1862,f1598]) ).
fof(f1598,plain,
( ! [X2,X6,X7] :
( ~ c_lessequals(X7,X6,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X6 )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1597]) ).
fof(f42950,plain,
( spl0_1181
| ~ spl0_145
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2143,f1857,f1605,f42948]) ).
fof(f42948,plain,
( spl0_1181
<=> ! [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_1181])]) ).
fof(f1857,plain,
( spl0_177
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X6,X1,X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f2143,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_145
| ~ spl0_177 ),
inference(duplicate_literal_removal,[],[f2131]) ).
fof(f2131,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_145
| ~ spl0_177 ),
inference(resolution,[],[f1858,f1606]) ).
fof(f1858,plain,
( ! [X2,X0,X1,X6] :
( c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X2)
| ~ c_lessequals(X6,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1857]) ).
fof(f42946,plain,
( spl0_1180
| ~ spl0_143
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2142,f1857,f1597,f42944]) ).
fof(f42944,plain,
( spl0_1180
<=> ! [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_1180])]) ).
fof(f2142,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_143
| ~ spl0_177 ),
inference(duplicate_literal_removal,[],[f2132]) ).
fof(f2132,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_143
| ~ spl0_177 ),
inference(resolution,[],[f1858,f1598]) ).
fof(f42942,plain,
( spl0_1179
| ~ spl0_142
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2036,f1792,f1589,f42940]) ).
fof(f42940,plain,
( spl0_1179
<=> ! [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_1179])]) ).
fof(f1589,plain,
( spl0_142
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1792,plain,
( spl0_162
<=> ! [X6,X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,X6,X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f2036,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_142
| ~ spl0_162 ),
inference(duplicate_literal_removal,[],[f2027]) ).
fof(f2027,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_142
| ~ spl0_162 ),
inference(resolution,[],[f1793,f1590]) ).
fof(f1590,plain,
( ! [X2,X6,X7] :
( ~ c_lessequals(X7,X6,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X7 )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1589]) ).
fof(f1793,plain,
( ! [X2,X0,X1,X6] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X6,X2)
| ~ c_lessequals(X1,X6,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f42938,plain,
( spl0_1178
| ~ spl0_140
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2035,f1792,f1581,f42936]) ).
fof(f42936,plain,
( spl0_1178
<=> ! [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_1178])]) ).
fof(f1581,plain,
( spl0_140
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f2035,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_140
| ~ spl0_162 ),
inference(duplicate_literal_removal,[],[f2028]) ).
fof(f2028,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_140
| ~ spl0_162 ),
inference(resolution,[],[f1793,f1582]) ).
fof(f1582,plain,
( ! [X2,X6,X7] :
( ~ c_lessequals(X6,X7,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X6 )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1581]) ).
fof(f42934,plain,
( spl0_1177
| ~ spl0_142
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2023,f1788,f1589,f42932]) ).
fof(f42932,plain,
( spl0_1177
<=> ! [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_1177])]) ).
fof(f1788,plain,
( spl0_161
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,X6,X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2023,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_142
| ~ spl0_161 ),
inference(duplicate_literal_removal,[],[f2014]) ).
fof(f2014,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_142
| ~ spl0_161 ),
inference(resolution,[],[f1789,f1590]) ).
fof(f1789,plain,
( ! [X2,X0,X1,X6] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X6,X2)
| ~ c_lessequals(X0,X6,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1788]) ).
fof(f42930,plain,
( spl0_1176
| ~ spl0_140
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2022,f1788,f1581,f42928]) ).
fof(f42928,plain,
( spl0_1176
<=> ! [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_1176])]) ).
fof(f2022,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_140
| ~ spl0_161 ),
inference(duplicate_literal_removal,[],[f2015]) ).
fof(f2015,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_140
| ~ spl0_161 ),
inference(resolution,[],[f1789,f1582]) ).
fof(f40046,plain,
( spl0_1175
| ~ spl0_202
| ~ spl0_930 ),
inference(avatar_split_clause,[],[f28599,f27260,f2307,f40044]) ).
fof(f40044,plain,
( spl0_1175
<=> ! [X0] : ~ c_lessequals(v_Lab____,c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omkbot(X0,v_a____),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f2307,plain,
( spl0_202
<=> ! [X0,X1] :
( ~ c_lessequals(v_Lab____,X1,tc_fun(X0,tc_bool))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f27260,plain,
( spl0_930
<=> ! [X2,X0,X1] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f28599,plain,
( ! [X0] : ~ c_lessequals(v_Lab____,c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omkbot(X0,v_a____),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_202
| ~ spl0_930 ),
inference(resolution,[],[f27261,f2308]) ).
fof(f2308,plain,
( ! [X0,X1] :
( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,X0)
| ~ c_lessequals(v_Lab____,X1,tc_fun(X0,tc_bool)) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2307]) ).
fof(f27261,plain,
( ! [X2,X0,X1] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_930 ),
inference(avatar_component_clause,[],[f27260]) ).
fof(f39470,plain,
( spl0_1174
| ~ spl0_202
| ~ spl0_929 ),
inference(avatar_split_clause,[],[f28576,f27256,f2307,f39468]) ).
fof(f39468,plain,
( spl0_1174
<=> ! [X0] : ~ c_lessequals(v_Lab____,c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f27256,plain,
( spl0_929
<=> ! [X2,X0,X1] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f28576,plain,
( ! [X0] : ~ c_lessequals(v_Lab____,c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_202
| ~ spl0_929 ),
inference(resolution,[],[f27257,f2308]) ).
fof(f27257,plain,
( ! [X2,X0,X1] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_929 ),
inference(avatar_component_clause,[],[f27256]) ).
fof(f39102,plain,
( spl0_1173
| ~ spl0_311
| ~ spl0_879 ),
inference(avatar_split_clause,[],[f27064,f26350,f3517,f39100]) ).
fof(f39100,plain,
( spl0_1173
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Relation_ORange(c_Relation_Oconverse(v_Lab____,X0,X1),X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f3517,plain,
( spl0_311
<=> ! [X2,X8,X3] : c_Set_Oimage(c_fst(X2,X3),X8,tc_prod(X2,X3),X2) = c_Relation_ORange(c_Relation_Oconverse(X8,X2,X3),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f26350,plain,
( spl0_879
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_Lab____,X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f27064,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Relation_ORange(c_Relation_Oconverse(v_Lab____,X0,X1),X1,X0)
| ~ spl0_311
| ~ spl0_879 ),
inference(superposition,[],[f26351,f3518]) ).
fof(f3518,plain,
( ! [X2,X3,X8] : c_Set_Oimage(c_fst(X2,X3),X8,tc_prod(X2,X3),X2) = c_Relation_ORange(c_Relation_Oconverse(X8,X2,X3),X3,X2)
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f3517]) ).
fof(f26351,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_Lab____,X0,X2)
| ~ spl0_879 ),
inference(avatar_component_clause,[],[f26350]) ).
fof(f38596,plain,
( spl0_1172
| ~ spl0_752
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f22995,f22917,f21189,f38594]) ).
fof(f38594,plain,
( spl0_1172
<=> ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(v_Lab____,X0),X1),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f22917,plain,
( spl0_821
<=> ! [X0,X1] : c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(v_Lab____,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f22995,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(v_Lab____,X0),X1),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_752
| ~ spl0_821 ),
inference(resolution,[],[f22918,f21190]) ).
fof(f22918,plain,
( ! [X0,X1] : c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(v_Lab____,X0),X1)
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f22917]) ).
fof(f37743,plain,
( spl0_1171
| ~ spl0_377
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f22982,f22917,f5102,f37741]) ).
fof(f37741,plain,
( spl0_1171
<=> ! [X0] : c_in(v_b____,c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f22982,plain,
( ! [X0] : c_in(v_b____,c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_377
| ~ spl0_821 ),
inference(resolution,[],[f22918,f5103]) ).
fof(f36292,plain,
( spl0_1170
| ~ spl0_148
| ~ spl0_519 ),
inference(avatar_split_clause,[],[f12237,f12043,f1618,f36290]) ).
fof(f36290,plain,
( spl0_1170
<=> ! [X4,X0,X3,X2,X1] : c_Recdef_Ocut(X0,c_Arrow__Order__Mirabelle_Omkbot(X1,X2),X2,tc_Arrow__Order__Mirabelle_Oalt,X3) = c_Recdef_Ocut(X4,c_Arrow__Order__Mirabelle_Omkbot(X1,X2),X2,tc_Arrow__Order__Mirabelle_Oalt,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f1618,plain,
( spl0_148
<=> ! [X6,X27,X40] : ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f12043,plain,
( spl0_519
<=> ! [X3,X4,X36,X12,X6,X2] :
( c_Recdef_Ocut(X12,X4,X6,X2,X3) = c_Recdef_Ocut(X36,X4,X6,X2,X3)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X12,X36,X4,X6,X2,X3),X6,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f12237,plain,
( ! [X2,X3,X0,X1,X4] : c_Recdef_Ocut(X0,c_Arrow__Order__Mirabelle_Omkbot(X1,X2),X2,tc_Arrow__Order__Mirabelle_Oalt,X3) = c_Recdef_Ocut(X4,c_Arrow__Order__Mirabelle_Omkbot(X1,X2),X2,tc_Arrow__Order__Mirabelle_Oalt,X3)
| ~ spl0_148
| ~ spl0_519 ),
inference(resolution,[],[f12044,f1619]) ).
fof(f1619,plain,
( ! [X40,X6,X27] : ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1618]) ).
fof(f12044,plain,
( ! [X2,X3,X36,X6,X4,X12] :
( c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X12,X36,X4,X6,X2,X3),X6,X2,X2),X4,tc_prod(X2,X2))
| c_Recdef_Ocut(X12,X4,X6,X2,X3) = c_Recdef_Ocut(X36,X4,X6,X2,X3) )
| ~ spl0_519 ),
inference(avatar_component_clause,[],[f12043]) ).
fof(f36288,plain,
( spl0_1169
| ~ spl0_187
| ~ spl0_506 ),
inference(avatar_split_clause,[],[f11694,f10151,f1897,f36286]) ).
fof(f36286,plain,
( spl0_1169
<=> ! [X4,X0,X3,X2,X1] :
( c_in(c_Pair(X0,X0,X1,X1),c_Relation_Oinv__image(X2,X3,X4,X1),tc_prod(X1,X1))
| ~ c_Nitpick_Orefl_H(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f1897,plain,
( spl0_187
<=> ! [X6,X2,X4] :
( ~ c_Nitpick_Orefl_H(X4,X2)
| c_in(c_Pair(X6,X6,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f10151,plain,
( spl0_506
<=> ! [X2,X6,X4,X7,X12,X3] :
( ~ c_in(c_Pair(hAPP(X12,X6),hAPP(X12,X7),X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X6,X7,X2,X2),c_Relation_Oinv__image(X4,X12,X3,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f11694,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X0,X0,X1,X1),c_Relation_Oinv__image(X2,X3,X4,X1),tc_prod(X1,X1))
| ~ c_Nitpick_Orefl_H(X2,X4) )
| ~ spl0_187
| ~ spl0_506 ),
inference(resolution,[],[f10152,f1898]) ).
fof(f1898,plain,
( ! [X2,X6,X4] :
( c_in(c_Pair(X6,X6,X2,X2),X4,tc_prod(X2,X2))
| ~ c_Nitpick_Orefl_H(X4,X2) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1897]) ).
fof(f10152,plain,
( ! [X2,X3,X6,X7,X4,X12] :
( ~ c_in(c_Pair(hAPP(X12,X6),hAPP(X12,X7),X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X6,X7,X2,X2),c_Relation_Oinv__image(X4,X12,X3,X2),tc_prod(X2,X2)) )
| ~ spl0_506 ),
inference(avatar_component_clause,[],[f10151]) ).
fof(f36264,plain,
( spl0_1167
| ~ spl0_1168
| ~ spl0_103
| ~ spl0_482 ),
inference(avatar_split_clause,[],[f9914,f9334,f1340,f36261,f36258]) ).
fof(f36258,plain,
( spl0_1167
<=> ! [X0] :
( ~ c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f36261,plain,
( spl0_1168
<=> c_Relation_Osingle__valued(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f9334,plain,
( spl0_482
<=> ! [X2,X6,X4,X7,X3,X22] :
( X7 = X22
| ~ c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_in(c_Pair(X6,X7,X2,X3),X4,tc_prod(X2,X3))
| ~ c_in(c_Pair(X6,X22,X2,X3),X4,tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f9914,plain,
( ! [X0] :
( ~ c_Relation_Osingle__valued(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X0 )
| ~ spl0_103
| ~ spl0_482 ),
inference(resolution,[],[f9335,f1342]) ).
fof(f9335,plain,
( ! [X2,X3,X6,X7,X4,X22] :
( ~ c_in(c_Pair(X6,X22,X2,X3),X4,tc_prod(X2,X3))
| ~ c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_in(c_Pair(X6,X7,X2,X3),X4,tc_prod(X2,X3))
| X7 = X22 )
| ~ spl0_482 ),
inference(avatar_component_clause,[],[f9334]) ).
fof(f36256,plain,
( spl0_1166
| ~ spl0_185
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f8357,f7931,f1889,f36254]) ).
fof(f36254,plain,
( spl0_1166
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,hAPP(X1,X0),X2)
| ~ c_in(X0,X3,X2)
| ~ c_Relation_Oirrefl(c_Product__Type_OSigma(X3,X1,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f7931,plain,
( spl0_443
<=> ! [X3,X9,X0,X5,X2,X1] :
( ~ c_in(X0,X5,X2)
| ~ c_in(X1,hAPP(X9,X0),X3)
| c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f8357,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,hAPP(X1,X0),X2)
| ~ c_in(X0,X3,X2)
| ~ c_Relation_Oirrefl(c_Product__Type_OSigma(X3,X1,X2,X2),X2) )
| ~ spl0_185
| ~ spl0_443 ),
inference(resolution,[],[f7932,f1890]) ).
fof(f7932,plain,
( ! [X2,X3,X0,X1,X9,X5] :
( c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3))
| ~ c_in(X1,hAPP(X9,X0),X3)
| ~ c_in(X0,X5,X2) )
| ~ spl0_443 ),
inference(avatar_component_clause,[],[f7931]) ).
fof(f36252,plain,
( spl0_1165
| ~ spl0_188
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f8356,f7931,f1901,f36250]) ).
fof(f36250,plain,
( spl0_1165
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,hAPP(X1,X0),X2)
| ~ c_in(X0,X3,X2)
| ~ c_Wellfounded_Owf(c_Product__Type_OSigma(X3,X1,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f8356,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,hAPP(X1,X0),X2)
| ~ c_in(X0,X3,X2)
| ~ c_Wellfounded_Owf(c_Product__Type_OSigma(X3,X1,X2,X2),X2) )
| ~ spl0_188
| ~ spl0_443 ),
inference(resolution,[],[f7932,f1902]) ).
fof(f36248,plain,
( spl0_1164
| ~ spl0_187
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f8181,f7899,f1897,f36246]) ).
fof(f36246,plain,
( spl0_1164
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f7899,plain,
( spl0_435
<=> ! [X40,X0,X6,X1] :
( X0 = X1
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f8181,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_187
| ~ spl0_435 ),
inference(resolution,[],[f7900,f1898]) ).
fof(f7900,plain,
( ! [X40,X0,X1,X6] :
( ~ c_in(c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X0 = X1 )
| ~ spl0_435 ),
inference(avatar_component_clause,[],[f7899]) ).
fof(f36244,plain,
( spl0_1163
| ~ spl0_299
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f8180,f7899,f3469,f36242]) ).
fof(f36242,plain,
( spl0_1163
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| c_Relation_Oirrefl(c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f3469,plain,
( spl0_299
<=> ! [X2,X4] :
( c_Relation_Oirrefl(X4,X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X4,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f8180,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| c_Relation_Oirrefl(c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_299
| ~ spl0_435 ),
inference(resolution,[],[f7900,f3470]) ).
fof(f3470,plain,
( ! [X2,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X4,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X4,X2),X2,X2),X4,tc_prod(X2,X2))
| c_Relation_Oirrefl(X4,X2) )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f3469]) ).
fof(f36240,plain,
( spl0_1162
| ~ spl0_187
| ~ spl0_434 ),
inference(avatar_split_clause,[],[f8173,f7895,f1897,f36238]) ).
fof(f36238,plain,
( spl0_1162
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f7895,plain,
( spl0_434
<=> ! [X40,X0,X6,X1] :
( X0 = X1
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f8173,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_187
| ~ spl0_434 ),
inference(resolution,[],[f7896,f1898]) ).
fof(f7896,plain,
( ! [X40,X0,X1,X6] :
( ~ c_in(c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X0 = X1 )
| ~ spl0_434 ),
inference(avatar_component_clause,[],[f7895]) ).
fof(f36236,plain,
( spl0_1161
| ~ spl0_299
| ~ spl0_434 ),
inference(avatar_split_clause,[],[f8172,f7895,f3469,f36234]) ).
fof(f36234,plain,
( spl0_1161
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| c_Relation_Oirrefl(c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f8172,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| c_Relation_Oirrefl(c_Arrow__Order__Mirabelle_Oabove(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_299
| ~ spl0_434 ),
inference(resolution,[],[f7896,f3470]) ).
fof(f36232,plain,
( spl0_1160
| ~ spl0_53
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f8005,f7866,f1072,f36230]) ).
fof(f36230,plain,
( spl0_1160
<=> ! [X0,X3,X2,X1] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X1,tc_bool)),X0,X1)
| ~ c_Relation_Orefl__on(X3,X0,X1)
| ~ c_Relation_Orefl__on(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f7866,plain,
( spl0_429
<=> ! [X4,X9,X14,X5,X2] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| ~ c_Relation_Orefl__on(X9,X14,X2)
| c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f8005,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X1,tc_bool)),X0,X1)
| ~ c_Relation_Orefl__on(X3,X0,X1)
| ~ c_Relation_Orefl__on(X2,X0,X1) )
| ~ spl0_53
| ~ spl0_429 ),
inference(superposition,[],[f7867,f1073]) ).
fof(f7867,plain,
( ! [X2,X9,X14,X4,X5] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Orefl__on(X9,X14,X2)
| ~ c_Relation_Orefl__on(X5,X4,X2) )
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f7866]) ).
fof(f36228,plain,
( spl0_1159
| ~ spl0_46
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f7970,f7862,f1042,f36226]) ).
fof(f36226,plain,
( spl0_1159
<=> ! [X0,X3,X2,X1] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)),X0,X1)
| ~ c_Relation_Orefl__on(X3,X0,X1)
| ~ c_Relation_Orefl__on(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f1042,plain,
( spl0_46
<=> ! [X2,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_fun(X2,tc_bool)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f7862,plain,
( spl0_428
<=> ! [X4,X9,X14,X5,X2] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| ~ c_Relation_Orefl__on(X9,X14,X2)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f7970,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)),X0,X1)
| ~ c_Relation_Orefl__on(X3,X0,X1)
| ~ c_Relation_Orefl__on(X2,X0,X1) )
| ~ spl0_46
| ~ spl0_428 ),
inference(superposition,[],[f7863,f1043]) ).
fof(f1043,plain,
( ! [X2,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_fun(X2,tc_bool)) = X5
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f7863,plain,
( ! [X2,X9,X14,X4,X5] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Orefl__on(X9,X14,X2)
| ~ c_Relation_Orefl__on(X5,X4,X2) )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f7862]) ).
fof(f36224,plain,
( spl0_1158
| ~ spl0_250
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f6511,f6211,f2937,f36222]) ).
fof(f36222,plain,
( spl0_1158
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_OImage(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(X1,X2,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f2937,plain,
( spl0_250
<=> ! [X0,X1] :
( X0 = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f6211,plain,
( spl0_403
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_in(X0,X5,X2)
| c_in(X1,c_Relation_OImage(X4,X5,X2,X3),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f6511,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_OImage(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(X1,X2,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1 )
| ~ spl0_250
| ~ spl0_403 ),
inference(resolution,[],[f6212,f2938]) ).
fof(f2938,plain,
( ! [X0,X1] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2937]) ).
fof(f6212,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))
| c_in(X1,c_Relation_OImage(X4,X5,X2,X3),X3)
| ~ c_in(X0,X5,X2) )
| ~ spl0_403 ),
inference(avatar_component_clause,[],[f6211]) ).
fof(f36220,plain,
( spl0_1157
| ~ spl0_61
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f36131,f36046,f1104,f36218]) ).
fof(f36218,plain,
( spl0_1157
<=> ! [X2,X0,X1] : c_in(v_a____,c_Transitive__Closure_Otrancl(c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f36046,plain,
( spl0_1115
<=> ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f36131,plain,
( ! [X2,X0,X1] : c_in(v_a____,c_Transitive__Closure_Otrancl(c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)
| ~ spl0_61
| ~ spl0_1115 ),
inference(resolution,[],[f36047,f1105]) ).
fof(f36047,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),v_a____))
| ~ spl0_1115 ),
inference(avatar_component_clause,[],[f36046]) ).
fof(f36216,plain,
( spl0_1156
| ~ spl0_253
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f6510,f6211,f2949,f36214]) ).
fof(f36214,plain,
( spl0_1156
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Relation_OImage(c_Arrow__Order__Mirabelle_Omktop(X1,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(X3,X2,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f2949,plain,
( spl0_253
<=> ! [X6,X27,X40] :
( X6 = X27
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f6510,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Relation_OImage(c_Arrow__Order__Mirabelle_Omktop(X1,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(X3,X2,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 )
| ~ spl0_253
| ~ spl0_403 ),
inference(resolution,[],[f6212,f2950]) ).
fof(f2950,plain,
( ! [X40,X6,X27] :
( c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X27 )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2949]) ).
fof(f36212,plain,
( spl0_1155
| ~ spl0_252
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f6509,f6211,f2945,f36210]) ).
fof(f36210,plain,
( spl0_1155
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Relation_OImage(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(X2,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f2945,plain,
( spl0_252
<=> ! [X6,X40,X7] :
( X6 = X7
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f6509,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Relation_OImage(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(X2,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 )
| ~ spl0_252
| ~ spl0_403 ),
inference(resolution,[],[f6212,f2946]) ).
fof(f2946,plain,
( ! [X40,X6,X7] :
( c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X7 )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2945]) ).
fof(f36208,plain,
( spl0_1154
| ~ spl0_250
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f6455,f6203,f2937,f36206]) ).
fof(f36206,plain,
( spl0_1154
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),X2,tc_Arrow__Order__Mirabelle_Oalt,X3),X1)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f6455,plain,
( ! [X2,X3,X0,X1] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),X2,tc_Arrow__Order__Mirabelle_Oalt,X3),X1)
| X1 = X2 )
| ~ spl0_250
| ~ spl0_401 ),
inference(resolution,[],[f6204,f2938]) ).
fof(f36204,plain,
( spl0_1153
| ~ spl0_253
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f6454,f6203,f2949,f36202]) ).
fof(f36202,plain,
( spl0_1153
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,c_Arrow__Order__Mirabelle_Omktop(X2,X3),X3,tc_Arrow__Order__Mirabelle_Oalt,X4),X1)
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f6454,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,c_Arrow__Order__Mirabelle_Omktop(X2,X3),X3,tc_Arrow__Order__Mirabelle_Oalt,X4),X1)
| X1 = X3 )
| ~ spl0_253
| ~ spl0_401 ),
inference(resolution,[],[f6204,f2950]) ).
fof(f36200,plain,
( spl0_1152
| ~ spl0_252
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f6453,f6203,f2945,f36198]) ).
fof(f36198,plain,
( spl0_1152
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,c_Arrow__Order__Mirabelle_Omkbot(X2,X1),X3,tc_Arrow__Order__Mirabelle_Oalt,X4),X1)
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f6453,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,c_Arrow__Order__Mirabelle_Omkbot(X2,X1),X3,tc_Arrow__Order__Mirabelle_Oalt,X4),X1)
| X1 = X3 )
| ~ spl0_252
| ~ spl0_401 ),
inference(resolution,[],[f6204,f2946]) ).
fof(f36196,plain,
( spl0_1151
| ~ spl0_130
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f6435,f6199,f1474,f36194]) ).
fof(f36194,plain,
( spl0_1151
<=> ! [X0,X1] :
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1,X1),X1)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f1474,plain,
( spl0_130
<=> ! [X2,X8] :
( ~ c_Wellfounded_Owf(X8,X2)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X2,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f6199,plain,
( spl0_400
<=> ! [X4,X10,X14,X3,X2] : c_Relation_Oconverse(c_Relation_Orel__comp(X4,X14,X3,X10,X2),X3,X2) = c_Relation_Orel__comp(c_Relation_Oconverse(X14,X10,X2),c_Relation_Oconverse(X4,X3,X10),X2,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f6435,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1,X1),X1)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1) )
| ~ spl0_130
| ~ spl0_400 ),
inference(superposition,[],[f1475,f6200]) ).
fof(f6200,plain,
( ! [X2,X3,X10,X14,X4] : c_Relation_Oconverse(c_Relation_Orel__comp(X4,X14,X3,X10,X2),X3,X2) = c_Relation_Orel__comp(c_Relation_Oconverse(X14,X10,X2),c_Relation_Oconverse(X4,X3,X10),X2,X10,X3)
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f6199]) ).
fof(f1475,plain,
( ! [X2,X8] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X2,X2,X2),X2)
| ~ c_Wellfounded_Owf(X8,X2) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1474]) ).
fof(f36192,plain,
( spl0_1150
| ~ spl0_131
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f6434,f6199,f1478,f36190]) ).
fof(f36190,plain,
( spl0_1150
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1,X1),X1)
| c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f1478,plain,
( spl0_131
<=> ! [X2,X8] :
( c_Wellfounded_Owf(X8,X2)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X2,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f6434,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1,X1),X1)
| c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1) )
| ~ spl0_131
| ~ spl0_400 ),
inference(superposition,[],[f1479,f6200]) ).
fof(f1479,plain,
( ! [X2,X8] :
( ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X2,X2,X2),X2)
| c_Wellfounded_Owf(X8,X2) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1478]) ).
fof(f36188,plain,
( spl0_1149
| ~ spl0_116
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f6237,f6167,f1418,f36186]) ).
fof(f36186,plain,
( spl0_1149
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2),c_Set_Oinsert(X0,X3,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f6167,plain,
( spl0_392
<=> ! [X9,X0,X5,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X5,X2),c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f6237,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2),c_Set_Oinsert(X0,X3,X2),tc_fun(X2,tc_bool))
| ~ spl0_116
| ~ spl0_392 ),
inference(superposition,[],[f1419,f6168]) ).
fof(f6168,plain,
( ! [X2,X0,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X5,X2),c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2)
| ~ spl0_392 ),
inference(avatar_component_clause,[],[f6167]) ).
fof(f36184,plain,
( spl0_1148
| ~ spl0_115
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f6236,f6167,f1414,f36182]) ).
fof(f36182,plain,
( spl0_1148
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2),c_Set_Oinsert(X0,X1,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f6236,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2),c_Set_Oinsert(X0,X1,X2),tc_fun(X2,tc_bool))
| ~ spl0_115
| ~ spl0_392 ),
inference(superposition,[],[f1415,f6168]) ).
fof(f36180,plain,
( spl0_1147
| ~ spl0_163
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5804,f5535,f1796,f36178]) ).
fof(f36178,plain,
( spl0_1147
<=> ! [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_1147])]) ).
fof(f1796,plain,
( spl0_163
<=> ! [X7,X22,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X7,X2)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f5535,plain,
( spl0_383
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f5804,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_163
| ~ spl0_383 ),
inference(resolution,[],[f5536,f1797]) ).
fof(f1797,plain,
( ! [X2,X6,X7,X22] :
( ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2)
| c_lessequals(X6,X7,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1796]) ).
fof(f5536,plain,
( ! [X2,X6,X7,X22] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2),X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f5535]) ).
fof(f36176,plain,
( spl0_1146
| ~ spl0_61
| ~ spl0_1104 ),
inference(avatar_split_clause,[],[f36089,f36002,f1104,f36174]) ).
fof(f36174,plain,
( spl0_1146
<=> ! [X2,X0,X1] : c_in(v_a____,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f36002,plain,
( spl0_1104
<=> ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f36089,plain,
( ! [X2,X0,X1] : c_in(v_a____,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),X2)
| ~ spl0_61
| ~ spl0_1104 ),
inference(resolution,[],[f36003,f1105]) ).
fof(f36003,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),v_a____))
| ~ spl0_1104 ),
inference(avatar_component_clause,[],[f36002]) ).
fof(f36172,plain,
( spl0_1145
| ~ spl0_179
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5801,f5535,f1865,f36170]) ).
fof(f36170,plain,
( spl0_1145
<=> ! [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_1145])]) ).
fof(f1865,plain,
( spl0_179
<=> ! [X6,X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X1,X6,X2)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f5801,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_179
| ~ spl0_383 ),
inference(resolution,[],[f5536,f1866]) ).
fof(f1866,plain,
( ! [X2,X0,X1,X6] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X6,X2)
| c_lessequals(X1,X6,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1865]) ).
fof(f36168,plain,
( spl0_1144
| ~ spl0_180
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5800,f5535,f1869,f36166]) ).
fof(f36166,plain,
( spl0_1144
<=> ! [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_1144])]) ).
fof(f1869,plain,
( spl0_180
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X0,X6,X2)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f5800,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_180
| ~ spl0_383 ),
inference(resolution,[],[f5536,f1870]) ).
fof(f1870,plain,
( ! [X2,X0,X1,X6] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X6,X2)
| c_lessequals(X0,X6,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1869]) ).
fof(f36164,plain,
( spl0_1143
| ~ spl0_160
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f5606,f5526,f1784,f36162]) ).
fof(f36162,plain,
( spl0_1143
<=> ! [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_1143])]) ).
fof(f1784,plain,
( spl0_160
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X1,X2)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f5526,plain,
( spl0_381
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f5606,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_160
| ~ spl0_381 ),
inference(resolution,[],[f5527,f1785]) ).
fof(f1785,plain,
( ! [X2,X0,X1,X6] :
( ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| c_lessequals(X6,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1784]) ).
fof(f5527,plain,
( ! [X2,X6,X7,X22] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2),X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_381 ),
inference(avatar_component_clause,[],[f5526]) ).
fof(f36160,plain,
( spl0_1142
| ~ spl0_163
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f5605,f5526,f1796,f36158]) ).
fof(f36158,plain,
( spl0_1142
<=> ! [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_1142])]) ).
fof(f5605,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_163
| ~ spl0_381 ),
inference(resolution,[],[f5527,f1797]) ).
fof(f36156,plain,
( spl0_1141
| ~ spl0_180
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f5601,f5526,f1869,f36154]) ).
fof(f36154,plain,
( spl0_1141
<=> ! [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_1141])]) ).
fof(f5601,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_180
| ~ spl0_381 ),
inference(resolution,[],[f5527,f1870]) ).
fof(f36152,plain,
( spl0_1140
| ~ spl0_72
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f5393,f5078,f1163,f36150]) ).
fof(f36150,plain,
( spl0_1140
<=> ! [X2,X4,X0,X5,X3,X1] :
( c_in(hAPP(X0,X1),c_Set_Oinsert(X2,c_Set_Oimage(X0,X3,X4,X5),X5),X5)
| ~ c_in(X1,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f1163,plain,
( spl0_72
<=> ! [X2,X0,X9] : c_lessequals(X9,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f5078,plain,
( spl0_371
<=> ! [X5,X3,X9,X12,X6,X2] :
( ~ c_in(X6,X5,X3)
| c_in(hAPP(X12,X6),X9,X2)
| ~ c_lessequals(c_Set_Oimage(X12,X5,X3,X2),X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f5393,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_in(hAPP(X0,X1),c_Set_Oinsert(X2,c_Set_Oimage(X0,X3,X4,X5),X5),X5)
| ~ c_in(X1,X3,X4) )
| ~ spl0_72
| ~ spl0_371 ),
inference(resolution,[],[f5079,f1164]) ).
fof(f1164,plain,
( ! [X2,X0,X9] : c_lessequals(X9,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool))
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f5079,plain,
( ! [X2,X3,X6,X9,X5,X12] :
( ~ c_lessequals(c_Set_Oimage(X12,X5,X3,X2),X9,tc_fun(X2,tc_bool))
| c_in(hAPP(X12,X6),X9,X2)
| ~ c_in(X6,X5,X3) )
| ~ spl0_371 ),
inference(avatar_component_clause,[],[f5078]) ).
fof(f36148,plain,
( spl0_1139
| ~ spl0_62
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f5004,f4541,f1108,f36146]) ).
fof(f36146,plain,
( spl0_1139
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X2),X3),X4))
| hBOOL(hAPP(X0,c_Pair(X3,X4,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f4541,plain,
( spl0_354
<=> ! [X3,X7,X8,X6,X2] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X8,X2,X3),X6),X7))
| c_in(c_Pair(X6,X7,X2,X3),X8,tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f5004,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X2),X3),X4))
| hBOOL(hAPP(X0,c_Pair(X3,X4,X1,X2))) )
| ~ spl0_62
| ~ spl0_354 ),
inference(resolution,[],[f4542,f1109]) ).
fof(f4542,plain,
( ! [X2,X3,X8,X6,X7] :
( c_in(c_Pair(X6,X7,X2,X3),X8,tc_prod(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X8,X2,X3),X6),X7)) )
| ~ spl0_354 ),
inference(avatar_component_clause,[],[f4541]) ).
fof(f36144,plain,
( spl0_1138
| ~ spl0_332
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4996,f4541,f4035,f36142]) ).
fof(f36142,plain,
( spl0_1138
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Product__Type_OSigma(X0,X1,X2,X3),X2,X3),X4),X5))
| c_in(X4,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f4996,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Product__Type_OSigma(X0,X1,X2,X3),X2,X3),X4),X5))
| c_in(X4,X0,X2) )
| ~ spl0_332
| ~ spl0_354 ),
inference(resolution,[],[f4542,f4036]) ).
fof(f36140,plain,
( spl0_1137
| ~ spl0_330
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4993,f4541,f4027,f36138]) ).
fof(f36138,plain,
( spl0_1137
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X3))
| c_in(X3,X4,X1)
| ~ c_Equiv__Relations_Oequiv(X4,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f4993,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X3))
| c_in(X3,X4,X1)
| ~ c_Equiv__Relations_Oequiv(X4,X0,X1) )
| ~ spl0_330
| ~ spl0_354 ),
inference(resolution,[],[f4542,f4028]) ).
fof(f36136,plain,
( spl0_1136
| ~ spl0_331
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4992,f4541,f4031,f36134]) ).
fof(f36134,plain,
( spl0_1136
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X3))
| c_in(X2,X4,X1)
| ~ c_Equiv__Relations_Oequiv(X4,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f4992,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X3))
| c_in(X2,X4,X1)
| ~ c_Equiv__Relations_Oequiv(X4,X0,X1) )
| ~ spl0_331
| ~ spl0_354 ),
inference(resolution,[],[f4542,f4032]) ).
fof(f36130,plain,
( spl0_1135
| ~ spl0_333
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4991,f4541,f4039,f36128]) ).
fof(f36128,plain,
( spl0_1135
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X3))
| c_in(X3,X4,X1)
| ~ c_Relation_Orefl__on(X4,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f4991,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X3))
| c_in(X3,X4,X1)
| ~ c_Relation_Orefl__on(X4,X0,X1) )
| ~ spl0_333
| ~ spl0_354 ),
inference(resolution,[],[f4542,f4040]) ).
fof(f36126,plain,
( spl0_1134
| ~ spl0_334
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4990,f4541,f4043,f36124]) ).
fof(f36124,plain,
( spl0_1134
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X3))
| c_in(X2,X4,X1)
| ~ c_Relation_Orefl__on(X4,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f4990,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X3))
| c_in(X2,X4,X1)
| ~ c_Relation_Orefl__on(X4,X0,X1) )
| ~ spl0_334
| ~ spl0_354 ),
inference(resolution,[],[f4542,f4044]) ).
fof(f36122,plain,
( spl0_1133
| ~ spl0_62
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4946,f4533,f1108,f36120]) ).
fof(f36120,plain,
( spl0_1133
<=> ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| hBOOL(hAPP(X1,c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),X0,X2,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f4946,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| hBOOL(hAPP(X1,c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),X0,X2,X2))) )
| ~ spl0_62
| ~ spl0_352 ),
inference(resolution,[],[f4534,f1109]) ).
fof(f36118,plain,
( spl0_1132
| ~ spl0_331
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4939,f4533,f4031,f36116]) ).
fof(f36116,plain,
( spl0_1132
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f4939,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) )
| ~ spl0_331
| ~ spl0_352 ),
inference(resolution,[],[f4534,f4032]) ).
fof(f36114,plain,
( spl0_1131
| ~ spl0_334
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4937,f4533,f4043,f36112]) ).
fof(f36112,plain,
( spl0_1131
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f4937,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) )
| ~ spl0_334
| ~ spl0_352 ),
inference(resolution,[],[f4534,f4044]) ).
fof(f36110,plain,
( spl0_1130
| ~ spl0_267
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4935,f4533,f3175,f36108]) ).
fof(f36108,plain,
( spl0_1130
<=> ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId__on(X1,X2),X0,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f3175,plain,
( spl0_267
<=> ! [X5,X7,X6,X2] :
( c_in(X6,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Relation_OId__on(X5,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f4935,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId__on(X1,X2),X0,X2),X1,X2) )
| ~ spl0_267
| ~ spl0_352 ),
inference(resolution,[],[f4534,f3176]) ).
fof(f3176,plain,
( ! [X2,X6,X7,X5] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Relation_OId__on(X5,X2),tc_prod(X2,X2))
| c_in(X6,X5,X2) )
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f3175]) ).
fof(f36106,plain,
( spl0_1129
| ~ spl0_62
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4914,f4529,f1108,f36104]) ).
fof(f36104,plain,
( spl0_1129
<=> ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| hBOOL(hAPP(X1,c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X0,X2),X0,X2,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f4914,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| hBOOL(hAPP(X1,c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X0,X2),X0,X2,X2))) )
| ~ spl0_62
| ~ spl0_351 ),
inference(resolution,[],[f4530,f1109]) ).
fof(f36102,plain,
( spl0_1128
| ~ spl0_331
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4907,f4529,f4031,f36100]) ).
fof(f36100,plain,
( spl0_1128
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X0,X2),X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f4907,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X0,X2),X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) )
| ~ spl0_331
| ~ spl0_351 ),
inference(resolution,[],[f4530,f4032]) ).
fof(f36098,plain,
( spl0_1127
| ~ spl0_334
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4905,f4529,f4043,f36096]) ).
fof(f36096,plain,
( spl0_1127
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X0,X2),X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f4905,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X0,X2),X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) )
| ~ spl0_334
| ~ spl0_351 ),
inference(resolution,[],[f4530,f4044]) ).
fof(f36094,plain,
( spl0_1126
| ~ spl0_267
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4903,f4529,f3175,f36092]) ).
fof(f36092,plain,
( spl0_1126
<=> ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId__on(X1,X2),X0,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f4903,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId__on(X1,X2),X0,X2),X1,X2) )
| ~ spl0_267
| ~ spl0_351 ),
inference(resolution,[],[f4530,f3176]) ).
fof(f36088,plain,
( spl0_1125
| ~ spl0_153
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4842,f4513,f1752,f36086]) ).
fof(f36086,plain,
( spl0_1125
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X1),X2))
| ~ hBOOL(hAPP(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f4842,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X1),X2))
| ~ hBOOL(hAPP(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),X2)) )
| ~ spl0_153
| ~ spl0_347 ),
inference(superposition,[],[f1753,f4514]) ).
fof(f36084,plain,
( spl0_1124
| ~ spl0_105
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4840,f4513,f1371,f36082]) ).
fof(f36082,plain,
( spl0_1124
<=> ! [X0,X1] : c_lessequals(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f4840,plain,
( ! [X0,X1] : c_lessequals(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool))
| ~ spl0_105
| ~ spl0_347 ),
inference(superposition,[],[f1372,f4514]) ).
fof(f36080,plain,
( spl0_1123
| ~ spl0_72
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f4751,f4497,f1163,f36078]) ).
fof(f36078,plain,
( spl0_1123
<=> ! [X4,X0,X3,X2,X1] : c_lessequals(c_Set_Oimage(X0,X2,X3,X4),c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),tc_fun(X4,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f4497,plain,
( spl0_343
<=> ! [X3,X0,X12,X9,X2] : c_Set_Oimage(X12,c_Set_Oinsert(X0,X9,X3),X3,X2) = c_Set_Oinsert(hAPP(X12,X0),c_Set_Oimage(X12,X9,X3,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f4751,plain,
( ! [X2,X3,X0,X1,X4] : c_lessequals(c_Set_Oimage(X0,X2,X3,X4),c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),tc_fun(X4,tc_bool))
| ~ spl0_72
| ~ spl0_343 ),
inference(superposition,[],[f1164,f4498]) ).
fof(f4498,plain,
( ! [X2,X3,X0,X9,X12] : c_Set_Oimage(X12,c_Set_Oinsert(X0,X9,X3),X3,X2) = c_Set_Oinsert(hAPP(X12,X0),c_Set_Oimage(X12,X9,X3,X2),X2)
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f4497]) ).
fof(f36076,plain,
( spl0_1122
| ~ spl0_215
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4696,f4485,f2369,f36074]) ).
fof(f36074,plain,
( spl0_1122
<=> ! [X0,X1] :
( c_Wellfounded_Owf(c_Relation_OId__on(X0,X1),X1)
| ~ c_Wellfounded_Owf(c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f2369,plain,
( spl0_215
<=> ! [X2,X16,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(X16,X2)
| ~ c_lessequals(X16,X4,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f4485,plain,
( spl0_340
<=> ! [X2,X5] : c_lessequals(c_Relation_OId__on(X5,X2),c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f4696,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(c_Relation_OId__on(X0,X1),X1)
| ~ c_Wellfounded_Owf(c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),X1) )
| ~ spl0_215
| ~ spl0_340 ),
inference(resolution,[],[f4486,f2370]) ).
fof(f2370,plain,
( ! [X2,X16,X4] :
( ~ c_lessequals(X16,X4,tc_fun(tc_prod(X2,X2),tc_bool))
| c_Wellfounded_Owf(X16,X2)
| ~ c_Wellfounded_Owf(X4,X2) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2369]) ).
fof(f4486,plain,
( ! [X2,X5] : c_lessequals(c_Relation_OId__on(X5,X2),c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f4485]) ).
fof(f36072,plain,
( spl0_1121
| ~ spl0_217
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4694,f4485,f2377,f36070]) ).
fof(f36070,plain,
( spl0_1121
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(c_Relation_OId__on(X0,X1),X1)
| ~ c_Wellfounded_Oacyclic(c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f2377,plain,
( spl0_217
<=> ! [X2,X4,X14] :
( ~ c_Wellfounded_Oacyclic(X14,X2)
| c_Wellfounded_Oacyclic(X4,X2)
| ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f4694,plain,
( ! [X0,X1] :
( c_Wellfounded_Oacyclic(c_Relation_OId__on(X0,X1),X1)
| ~ c_Wellfounded_Oacyclic(c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),X1) )
| ~ spl0_217
| ~ spl0_340 ),
inference(resolution,[],[f4486,f2378]) ).
fof(f2378,plain,
( ! [X2,X14,X4] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_Wellfounded_Oacyclic(X4,X2)
| ~ c_Wellfounded_Oacyclic(X14,X2) )
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f2377]) ).
fof(f36068,plain,
( spl0_1120
| ~ spl0_106
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4629,f4477,f1375,f36066]) ).
fof(f36066,plain,
( spl0_1120
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Set_Oinsert(X0,X1,X2),c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f4477,plain,
( spl0_338
<=> ! [X11,X0,X9,X2] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,X9,X2),X11,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f4629,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Set_Oinsert(X0,X1,X2),c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool))
| ~ spl0_106
| ~ spl0_338 ),
inference(superposition,[],[f1376,f4478]) ).
fof(f4478,plain,
( ! [X2,X0,X11,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,X9,X2),X11,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),X2)
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f4477]) ).
fof(f36064,plain,
( spl0_1119
| ~ spl0_105
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f4562,f4473,f1371,f36062]) ).
fof(f36062,plain,
( spl0_1119
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f4473,plain,
( spl0_337
<=> ! [X9,X0,X5,X2] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f4562,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))
| ~ spl0_105
| ~ spl0_337 ),
inference(superposition,[],[f1372,f4474]) ).
fof(f4474,plain,
( ! [X2,X0,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2)
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f4473]) ).
fof(f36060,plain,
( spl0_1118
| ~ spl0_82
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4449,f4039,f1204,f36058]) ).
fof(f36058,plain,
( spl0_1118
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Owf(X3,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f4449,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Owf(X3,tc_prod(X2,X2)) )
| ~ spl0_82
| ~ spl0_333 ),
inference(resolution,[],[f4040,f1205]) ).
fof(f36056,plain,
( spl0_1117
| ~ spl0_299
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4428,f4035,f3469,f36054]) ).
fof(f36054,plain,
( spl0_1117
<=> ! [X2,X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Product__Type_OSigma(X0,X1,X2,X2),X2),X0,X2)
| c_Relation_Oirrefl(c_Product__Type_OSigma(X0,X1,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f4428,plain,
( ! [X2,X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Product__Type_OSigma(X0,X1,X2,X2),X2),X0,X2)
| c_Relation_Oirrefl(c_Product__Type_OSigma(X0,X1,X2,X2),X2) )
| ~ spl0_299
| ~ spl0_332 ),
inference(resolution,[],[f4036,f3470]) ).
fof(f36052,plain,
( spl0_1116
| ~ spl0_82
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4408,f4027,f1204,f36050]) ).
fof(f36050,plain,
( spl0_1116
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Owf(X3,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f4408,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Owf(X3,tc_prod(X2,X2)) )
| ~ spl0_82
| ~ spl0_330 ),
inference(resolution,[],[f4028,f1205]) ).
fof(f36048,plain,
( spl0_1115
| ~ spl0_752
| ~ spl0_874 ),
inference(avatar_split_clause,[],[f23295,f23256,f21189,f36046]) ).
fof(f23256,plain,
( spl0_874
<=> ! [X0,X1] : c_in(v_a____,c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f23295,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),v_a____))
| ~ spl0_752
| ~ spl0_874 ),
inference(resolution,[],[f23257,f21190]) ).
fof(f23257,plain,
( ! [X0,X1] : c_in(v_a____,c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1)
| ~ spl0_874 ),
inference(avatar_component_clause,[],[f23256]) ).
fof(f36044,plain,
( spl0_1114
| ~ spl0_117
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4328,f4002,f1422,f36042]) ).
fof(f36042,plain,
( spl0_1114
<=> ! [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_1114])]) ).
fof(f4002,plain,
( spl0_324
<=> ! [X9,X11,X5,X2] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X11,tc_fun(X2,tc_bool))
| c_lessequals(X5,X11,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f4328,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_117
| ~ spl0_324 ),
inference(resolution,[],[f4003,f1423]) ).
fof(f4003,plain,
( ! [X2,X11,X9,X5] :
( ~ c_lessequals(X9,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_lessequals(X5,X11,tc_fun(X2,tc_bool)) )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f4002]) ).
fof(f36040,plain,
( spl0_1113
| ~ spl0_106
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4311,f4002,f1375,f36038]) ).
fof(f36038,plain,
( spl0_1113
<=> ! [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_1113])]) ).
fof(f4311,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_106
| ~ spl0_324 ),
inference(resolution,[],[f4003,f1376]) ).
fof(f36036,plain,
( spl0_1112
| ~ spl0_105
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4310,f4002,f1371,f36034]) ).
fof(f36034,plain,
( spl0_1112
<=> ! [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_1112])]) ).
fof(f4310,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_105
| ~ spl0_324 ),
inference(resolution,[],[f4003,f1372]) ).
fof(f36032,plain,
( spl0_1111
| ~ spl0_293
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f4107,f3974,f3445,f36030]) ).
fof(f36030,plain,
( spl0_1111
<=> ! [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_1111])]) ).
fof(f3445,plain,
( spl0_293
<=> ! [X2,X5,X11,X9] :
( c_lessequals(X9,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f4107,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_293
| ~ spl0_317 ),
inference(superposition,[],[f3446,f3975]) ).
fof(f3446,plain,
( ! [X2,X11,X9,X5] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool))
| c_lessequals(X9,X11,tc_fun(X2,tc_bool)) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3445]) ).
fof(f36028,plain,
( spl0_1110
| ~ spl0_292
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f4106,f3974,f3441,f36026]) ).
fof(f36026,plain,
( spl0_1110
<=> ! [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_1110])]) ).
fof(f4106,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_292
| ~ spl0_317 ),
inference(superposition,[],[f3442,f3975]) ).
fof(f36024,plain,
( spl0_1109
| ~ spl0_285
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f4104,f3974,f3413,f36022]) ).
fof(f36022,plain,
( spl0_1109
<=> ! [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_1109])]) ).
fof(f4104,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_285
| ~ spl0_317 ),
inference(superposition,[],[f3414,f3975]) ).
fof(f36020,plain,
( spl0_1108
| ~ spl0_284
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f4103,f3974,f3409,f36018]) ).
fof(f36018,plain,
( spl0_1108
<=> ! [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_1108])]) ).
fof(f3409,plain,
( spl0_284
<=> ! [X9,X5,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X9
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f4103,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_284
| ~ spl0_317 ),
inference(superposition,[],[f3410,f3975]) ).
fof(f3410,plain,
( ! [X2,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X9 )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f3409]) ).
fof(f36016,plain,
( spl0_1107
| ~ spl0_94
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3913,f3493,f1252,f36014]) ).
fof(f36014,plain,
( spl0_1107
<=> ! [X0,X3,X2,X1] :
( c_Relation_Oantisym(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| ~ c_Relation_Oantisym(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f1252,plain,
( spl0_94
<=> ! [X2,X4] :
( ~ c_Relation_Oantisym(X4,X2)
| c_Relation_Oantisym(c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f3913,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Oantisym(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| ~ c_Relation_Oantisym(c_Relation_Oinv__image(X0,X1,X2,X3),X3) )
| ~ spl0_94
| ~ spl0_305 ),
inference(superposition,[],[f1253,f3494]) ).
fof(f1253,plain,
( ! [X2,X4] :
( c_Relation_Oantisym(c_Relation_Oconverse(X4,X2,X2),X2)
| ~ c_Relation_Oantisym(X4,X2) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1252]) ).
fof(f36012,plain,
( spl0_1106
| ~ spl0_93
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3912,f3493,f1248,f36010]) ).
fof(f36010,plain,
( spl0_1106
<=> ! [X0,X3,X2,X1] :
( ~ c_Relation_Oantisym(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| c_Relation_Oantisym(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f1248,plain,
( spl0_93
<=> ! [X2,X4] :
( c_Relation_Oantisym(X4,X2)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f3912,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Relation_Oantisym(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| c_Relation_Oantisym(c_Relation_Oinv__image(X0,X1,X2,X3),X3) )
| ~ spl0_93
| ~ spl0_305 ),
inference(superposition,[],[f1249,f3494]) ).
fof(f1249,plain,
( ! [X2,X4] :
( ~ c_Relation_Oantisym(c_Relation_Oconverse(X4,X2,X2),X2)
| c_Relation_Oantisym(X4,X2) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1248]) ).
fof(f36008,plain,
( spl0_1105
| ~ spl0_90
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3911,f3493,f1236,f36006]) ).
fof(f36006,plain,
( spl0_1105
<=> ! [X0,X3,X2,X1] :
( c_Relation_Otrans(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| ~ c_Relation_Otrans(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f1236,plain,
( spl0_90
<=> ! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| c_Relation_Otrans(c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f3911,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Otrans(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| ~ c_Relation_Otrans(c_Relation_Oinv__image(X0,X1,X2,X3),X3) )
| ~ spl0_90
| ~ spl0_305 ),
inference(superposition,[],[f1237,f3494]) ).
fof(f1237,plain,
( ! [X2,X4] :
( c_Relation_Otrans(c_Relation_Oconverse(X4,X2,X2),X2)
| ~ c_Relation_Otrans(X4,X2) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1236]) ).
fof(f36004,plain,
( spl0_1104
| ~ spl0_752
| ~ spl0_779 ),
inference(avatar_split_clause,[],[f22790,f22737,f21189,f36002]) ).
fof(f22737,plain,
( spl0_779
<=> ! [X0,X1] : c_in(v_a____,c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f22790,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),v_a____))
| ~ spl0_752
| ~ spl0_779 ),
inference(resolution,[],[f22738,f21190]) ).
fof(f22738,plain,
( ! [X0,X1] : c_in(v_a____,c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)
| ~ spl0_779 ),
inference(avatar_component_clause,[],[f22737]) ).
fof(f36000,plain,
( spl0_1103
| ~ spl0_89
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3910,f3493,f1232,f35998]) ).
fof(f35998,plain,
( spl0_1103
<=> ! [X0,X3,X2,X1] :
( ~ c_Relation_Otrans(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| c_Relation_Otrans(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1232,plain,
( spl0_89
<=> ! [X2,X4] :
( c_Relation_Otrans(X4,X2)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f3910,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Relation_Otrans(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| c_Relation_Otrans(c_Relation_Oinv__image(X0,X1,X2,X3),X3) )
| ~ spl0_89
| ~ spl0_305 ),
inference(superposition,[],[f1233,f3494]) ).
fof(f1233,plain,
( ! [X2,X4] :
( ~ c_Relation_Otrans(c_Relation_Oconverse(X4,X2,X2),X2)
| c_Relation_Otrans(X4,X2) )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f35996,plain,
( spl0_1102
| ~ spl0_84
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3908,f3493,f1212,f35994]) ).
fof(f35994,plain,
( spl0_1102
<=> ! [X0,X3,X2,X1] :
( c_Relation_Osym(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| ~ c_Relation_Osym(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1212,plain,
( spl0_84
<=> ! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Osym(c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f3908,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Osym(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| ~ c_Relation_Osym(c_Relation_Oinv__image(X0,X1,X2,X3),X3) )
| ~ spl0_84
| ~ spl0_305 ),
inference(superposition,[],[f1213,f3494]) ).
fof(f1213,plain,
( ! [X2,X4] :
( c_Relation_Osym(c_Relation_Oconverse(X4,X2,X2),X2)
| ~ c_Relation_Osym(X4,X2) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f35992,plain,
( spl0_1101
| ~ spl0_83
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3907,f3493,f1208,f35990]) ).
fof(f35990,plain,
( spl0_1101
<=> ! [X0,X3,X2,X1] :
( ~ c_Relation_Osym(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| c_Relation_Osym(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f1208,plain,
( spl0_83
<=> ! [X2,X4] :
( c_Relation_Osym(X4,X2)
| ~ c_Relation_Osym(c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f3907,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Relation_Osym(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| c_Relation_Osym(c_Relation_Oinv__image(X0,X1,X2,X3),X3) )
| ~ spl0_83
| ~ spl0_305 ),
inference(superposition,[],[f1209,f3494]) ).
fof(f1209,plain,
( ! [X2,X4] :
( ~ c_Relation_Osym(c_Relation_Oconverse(X4,X2,X2),X2)
| c_Relation_Osym(X4,X2) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1208]) ).
fof(f35988,plain,
( spl0_1100
| ~ spl0_76
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3906,f3493,f1179,f35986]) ).
fof(f35986,plain,
( spl0_1100
<=> ! [X0,X3,X2,X1] :
( c_Wellfounded_Oacyclic(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f1179,plain,
( spl0_76
<=> ! [X2,X4] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f3906,plain,
( ! [X2,X3,X0,X1] :
( c_Wellfounded_Oacyclic(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X1,X2,X3),X3) )
| ~ spl0_76
| ~ spl0_305 ),
inference(superposition,[],[f1180,f3494]) ).
fof(f1180,plain,
( ! [X2,X4] :
( c_Wellfounded_Oacyclic(c_Relation_Oconverse(X4,X2,X2),X2)
| ~ c_Wellfounded_Oacyclic(X4,X2) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1179]) ).
fof(f35984,plain,
( spl0_1099
| ~ spl0_75
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3905,f3493,f1175,f35982]) ).
fof(f35982,plain,
( spl0_1099
<=> ! [X0,X3,X2,X1] :
( ~ c_Wellfounded_Oacyclic(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f1175,plain,
( spl0_75
<=> ! [X2,X4] :
( c_Wellfounded_Oacyclic(X4,X2)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f3905,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),X3)
| c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X1,X2,X3),X3) )
| ~ spl0_75
| ~ spl0_305 ),
inference(superposition,[],[f1176,f3494]) ).
fof(f1176,plain,
( ! [X2,X4] :
( ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X4,X2,X2),X2)
| c_Wellfounded_Oacyclic(X4,X2) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1175]) ).
fof(f35980,plain,
( spl0_1098
| ~ spl0_91
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3902,f3493,f1240,f35978]) ).
fof(f35978,plain,
( spl0_1098
<=> ! [X0,X3,X2,X1] : c_Relation_Oinv__image(X0,X2,X1,X3) = c_Relation_Oconverse(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X1,X1),X2,X1,X3),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f1240,plain,
( spl0_91
<=> ! [X4,X2,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X4,X2,X3),X3,X2) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f3902,plain,
( ! [X2,X3,X0,X1] : c_Relation_Oinv__image(X0,X2,X1,X3) = c_Relation_Oconverse(c_Relation_Oinv__image(c_Relation_Oconverse(X0,X1,X1),X2,X1,X3),X3,X3)
| ~ spl0_91
| ~ spl0_305 ),
inference(superposition,[],[f3494,f1241]) ).
fof(f1241,plain,
( ! [X2,X3,X4] : c_Relation_Oconverse(c_Relation_Oconverse(X4,X2,X3),X3,X2) = X4
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1240]) ).
fof(f35976,plain,
( spl0_1097
| ~ spl0_61
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3810,f3449,f1104,f35974]) ).
fof(f35974,plain,
( spl0_1097
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X2,X1))
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X3,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f3449,plain,
( spl0_294
<=> ! [X5,X9,X6,X2] :
( ~ hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(X9,X6))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3810,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X2,X1))
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X3,tc_bool)),X4) )
| ~ spl0_61
| ~ spl0_294 ),
inference(resolution,[],[f3450,f1105]) ).
fof(f3450,plain,
( ! [X2,X6,X9,X5] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X6))
| ~ hBOOL(hAPP(X9,X6))
| ~ hBOOL(hAPP(X5,X6)) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3449]) ).
fof(f35972,plain,
( spl0_1096
| ~ spl0_62
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3758,f3437,f1108,f35970]) ).
fof(f35970,plain,
( spl0_1096
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_in(X0,X3,X2)
| hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f3437,plain,
( spl0_291
<=> ! [X9,X5,X19,X2] :
( ~ c_in(X19,X5,X2)
| c_in(X19,X9,X2)
| c_in(X19,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f3758,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_in(X0,X3,X2)
| hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X0)) )
| ~ spl0_62
| ~ spl0_291 ),
inference(resolution,[],[f3438,f1109]) ).
fof(f3438,plain,
( ! [X2,X19,X9,X5] :
( c_in(X19,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2)
| c_in(X19,X9,X2)
| ~ c_in(X19,X5,X2) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f3437]) ).
fof(f35968,plain,
( spl0_1095
| ~ spl0_62
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3728,f3429,f1108,f35966]) ).
fof(f35966,plain,
( spl0_1095
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_in(X0,X3,X2)
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f3429,plain,
( spl0_289
<=> ! [X9,X5,X19,X2] :
( ~ c_in(X19,X5,X2)
| ~ c_in(X19,X9,X2)
| c_in(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f3728,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_in(X0,X3,X2)
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X0)) )
| ~ spl0_62
| ~ spl0_289 ),
inference(resolution,[],[f3430,f1109]) ).
fof(f3430,plain,
( ! [X2,X19,X9,X5] :
( c_in(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X19,X9,X2)
| ~ c_in(X19,X5,X2) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f3429]) ).
fof(f35964,plain,
( spl0_1094
| ~ spl0_169
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3693,f3425,f1820,f35962]) ).
fof(f35962,plain,
( spl0_1094
<=> ! [X0,X3,X2,X1] :
( c_in(X3,c_Set_Oinsert(X0,X2,X1),X1)
| ~ c_in(X3,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f3693,plain,
( ! [X2,X3,X0,X1] :
( c_in(X3,c_Set_Oinsert(X0,X2,X1),X1)
| ~ c_in(X3,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) )
| ~ spl0_169
| ~ spl0_288 ),
inference(superposition,[],[f1821,f3426]) ).
fof(f35960,plain,
( spl0_1093
| ~ spl0_154
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3690,f3425,f1756,f35958]) ).
fof(f35958,plain,
( spl0_1093
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X0,X2,X1),X3))
| ~ hBOOL(hAPP(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f3690,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X0,X2,X1),X3))
| ~ hBOOL(hAPP(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X3)) )
| ~ spl0_154
| ~ spl0_288 ),
inference(superposition,[],[f1757,f3426]) ).
fof(f35956,plain,
( spl0_1092
| ~ spl0_164
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3684,f3425,f1800,f35954]) ).
fof(f35954,plain,
( spl0_1092
<=> ! [X2,X0,X1] : c_Set_Oinsert(X0,X2,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f3684,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X0,X2,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))
| ~ spl0_164
| ~ spl0_288 ),
inference(superposition,[],[f3426,f1801]) ).
fof(f35952,plain,
( spl0_1091
| ~ spl0_35
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3261,f3143,f997,f35950]) ).
fof(f35950,plain,
( spl0_1091
<=> ! [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_1091])]) ).
fof(f997,plain,
( spl0_35
<=> ! [X6,X2] :
( ~ class_Orderings_Obot(X2)
| c_lessequals(c_Orderings_Obot__class_Obot(X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f3261,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_35
| ~ spl0_259 ),
inference(resolution,[],[f3144,f998]) ).
fof(f998,plain,
( ! [X2,X6] :
( c_lessequals(c_Orderings_Obot__class_Obot(X2),X6,X2)
| ~ class_Orderings_Obot(X2) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f35948,plain,
( spl0_1090
| ~ spl0_122
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f3014,f2889,f1442,f35946]) ).
fof(f35946,plain,
( spl0_1090
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X4,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3)
| ~ c_in(X4,c_Set_Oinsert(X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f2889,plain,
( spl0_238
<=> ! [X5,X7,X6,X2] : c_Set_Oinsert(X6,c_Set_Oinsert(X7,X5,X2),X2) = c_Set_Oinsert(X7,c_Set_Oinsert(X6,X5,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f3014,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X4,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3)
| ~ c_in(X4,c_Set_Oinsert(X1,X2,X3),X3) )
| ~ spl0_122
| ~ spl0_238 ),
inference(superposition,[],[f1443,f2890]) ).
fof(f2890,plain,
( ! [X2,X6,X7,X5] : c_Set_Oinsert(X6,c_Set_Oinsert(X7,X5,X2),X2) = c_Set_Oinsert(X7,c_Set_Oinsert(X6,X5,X2),X2)
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2889]) ).
fof(f35944,plain,
( spl0_1089
| ~ spl0_118
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f3013,f2889,f1426,f35942]) ).
fof(f35942,plain,
( spl0_1089
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f1426,plain,
( spl0_118
<=> ! [X6,X2,X5,X7] :
( ~ hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(c_Set_Oinsert(X7,X5,X2),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f3013,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) )
| ~ spl0_118
| ~ spl0_238 ),
inference(superposition,[],[f1427,f2890]) ).
fof(f1427,plain,
( ! [X2,X6,X7,X5] :
( hBOOL(hAPP(c_Set_Oinsert(X7,X5,X2),X6))
| ~ hBOOL(hAPP(X5,X6)) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1426]) ).
fof(f35940,plain,
( spl0_1088
| ~ spl0_194
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2957,f2877,f2275,f35938]) ).
fof(f35938,plain,
( spl0_1088
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X3,X1,X2),tc_fun(X2,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f2957,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X3,X1,X2),tc_fun(X2,tc_bool)) = X0 )
| ~ spl0_194
| ~ spl0_235 ),
inference(resolution,[],[f2878,f2276]) ).
fof(f35936,plain,
( spl0_1087
| ~ spl0_195
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2956,f2877,f2279,f35934]) ).
fof(f35934,plain,
( spl0_1087
<=> ! [X2,X0,X1,X3] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X1,X2),X0,tc_fun(X2,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f2956,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X1,X2),X0,tc_fun(X2,tc_bool)) = X0 )
| ~ spl0_195
| ~ spl0_235 ),
inference(resolution,[],[f2878,f2280]) ).
fof(f35932,plain,
( spl0_1086
| ~ spl0_208
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2953,f2877,f2331,f35930]) ).
fof(f35930,plain,
( spl0_1086
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_in(X3,c_Set_Oinsert(X4,X1,X2),X2)
| ~ c_in(X3,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f2331,plain,
( spl0_208
<=> ! [X5,X9,X6,X2] :
( ~ c_in(X6,X5,X2)
| c_in(X6,X9,X2)
| ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f2953,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_in(X3,c_Set_Oinsert(X4,X1,X2),X2)
| ~ c_in(X3,X0,X2) )
| ~ spl0_208
| ~ spl0_235 ),
inference(resolution,[],[f2878,f2332]) ).
fof(f2332,plain,
( ! [X2,X6,X9,X5] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_in(X6,X9,X2)
| ~ c_in(X6,X5,X2) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f2331]) ).
fof(f35928,plain,
( spl0_1085
| ~ spl0_214
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2952,f2877,f2365,f35926]) ).
fof(f35926,plain,
( spl0_1085
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X2),X4))
| ~ hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f2365,plain,
( spl0_214
<=> ! [X18,X6,X2,X26] :
( ~ hBOOL(hAPP(X18,X6))
| hBOOL(hAPP(X26,X6))
| ~ c_lessequals(X18,X26,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2952,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X2),X4))
| ~ hBOOL(hAPP(X0,X4)) )
| ~ spl0_214
| ~ spl0_235 ),
inference(resolution,[],[f2878,f2366]) ).
fof(f2366,plain,
( ! [X2,X18,X6,X26] :
( ~ c_lessequals(X18,X26,tc_fun(X2,tc_bool))
| hBOOL(hAPP(X26,X6))
| ~ hBOOL(hAPP(X18,X6)) )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2365]) ).
fof(f35924,plain,
( spl0_1084
| ~ spl0_225
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2840,f2413,f2409,f35922]) ).
fof(f35922,plain,
( spl0_1084
<=> ! [X0,X3,X2,X1] :
( c_in(hAPP(c_snd(X0,X1),X3),c_Relation_ORange(X2,X0,X1),X1)
| ~ c_in(X3,X2,tc_prod(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f2409,plain,
( spl0_225
<=> ! [X2,X8,X3] : c_Set_Oimage(c_snd(X3,X2),X8,tc_prod(X3,X2),X2) = c_Relation_ORange(X8,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2840,plain,
( ! [X2,X3,X0,X1] :
( c_in(hAPP(c_snd(X0,X1),X3),c_Relation_ORange(X2,X0,X1),X1)
| ~ c_in(X3,X2,tc_prod(X0,X1)) )
| ~ spl0_225
| ~ spl0_226 ),
inference(superposition,[],[f2414,f2410]) ).
fof(f2410,plain,
( ! [X2,X3,X8] : c_Set_Oimage(c_snd(X3,X2),X8,tc_prod(X3,X2),X2) = c_Relation_ORange(X8,X3,X2)
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2409]) ).
fof(f35919,plain,
( spl0_1083
| ~ spl0_140
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2148,f1861,f1581,f35917]) ).
fof(f35917,plain,
( spl0_1083
<=> ! [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_1083])]) ).
fof(f2148,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_140
| ~ spl0_178 ),
inference(resolution,[],[f1862,f1582]) ).
fof(f35915,plain,
( spl0_1082
| ~ spl0_142
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2147,f1861,f1589,f35913]) ).
fof(f35913,plain,
( spl0_1082
<=> ! [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_1082])]) ).
fof(f2147,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_142
| ~ spl0_178 ),
inference(resolution,[],[f1862,f1590]) ).
fof(f35911,plain,
( spl0_1081
| ~ spl0_140
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2134,f1857,f1581,f35909]) ).
fof(f35909,plain,
( spl0_1081
<=> ! [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_1081])]) ).
fof(f2134,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_140
| ~ spl0_177 ),
inference(resolution,[],[f1858,f1582]) ).
fof(f35907,plain,
( spl0_1080
| ~ spl0_142
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2133,f1857,f1589,f35905]) ).
fof(f35905,plain,
( spl0_1080
<=> ! [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_1080])]) ).
fof(f2133,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_142
| ~ spl0_177 ),
inference(resolution,[],[f1858,f1590]) ).
fof(f35903,plain,
( spl0_1079
| ~ spl0_156
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2090,f1808,f1768,f35901]) ).
fof(f35901,plain,
( spl0_1079
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f1808,plain,
( spl0_166
<=> ! [X2,X12,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Set_Oimage(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2090,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0),X1)
| ~ spl0_156
| ~ spl0_166 ),
inference(superposition,[],[f1809,f1769]) ).
fof(f1809,plain,
( ! [X2,X3,X12] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Set_Oimage(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2)
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1808]) ).
fof(f35899,plain,
( spl0_1078
| ~ spl0_143
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2026,f1792,f1597,f35897]) ).
fof(f35897,plain,
( spl0_1078
<=> ! [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_1078])]) ).
fof(f2026,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_143
| ~ spl0_162 ),
inference(resolution,[],[f1793,f1598]) ).
fof(f35895,plain,
( spl0_1077
| ~ spl0_145
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2025,f1792,f1605,f35893]) ).
fof(f35893,plain,
( spl0_1077
<=> ! [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_1077])]) ).
fof(f2025,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_145
| ~ spl0_162 ),
inference(resolution,[],[f1793,f1606]) ).
fof(f35891,plain,
( spl0_1076
| ~ spl0_143
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2013,f1788,f1597,f35889]) ).
fof(f35889,plain,
( spl0_1076
<=> ! [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_1076])]) ).
fof(f2013,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_143
| ~ spl0_161 ),
inference(resolution,[],[f1789,f1598]) ).
fof(f35887,plain,
( spl0_1075
| ~ spl0_145
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2012,f1788,f1605,f35885]) ).
fof(f35885,plain,
( spl0_1075
<=> ! [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_1075])]) ).
fof(f2012,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_145
| ~ spl0_161 ),
inference(resolution,[],[f1789,f1606]) ).
fof(f35883,plain,
( spl0_1074
| ~ spl0_150
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1958,f1768,f1740,f35881]) ).
fof(f35881,plain,
( spl0_1074
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_OImage(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f1740,plain,
( spl0_150
<=> ! [X2,X8,X3] : c_Relation_OImage(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1958,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_OImage(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0),X2)
| ~ spl0_150
| ~ spl0_156 ),
inference(superposition,[],[f1741,f1769]) ).
fof(f1741,plain,
( ! [X2,X3,X8] : c_Relation_OImage(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1740]) ).
fof(f35861,plain,
( spl0_1073
| ~ spl0_79
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1943,f1764,f1191,f35859]) ).
fof(f35859,plain,
( spl0_1073
<=> ! [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_1073])]) ).
fof(f1191,plain,
( spl0_79
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1764,plain,
( spl0_155
<=> ! [X6,X2,X7] :
( ~ class_Orderings_Oorder(X2)
| X6 = X7
| ~ c_lessequals(X6,X7,X2)
| ~ c_lessequals(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1943,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_79
| ~ spl0_155 ),
inference(resolution,[],[f1765,f1192]) ).
fof(f1192,plain,
( ! [X2,X6,X7] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f1765,plain,
( ! [X2,X6,X7] :
( ~ c_lessequals(X7,X6,X2)
| X6 = X7
| ~ c_lessequals(X6,X7,X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f35857,plain,
( spl0_1072
| ~ spl0_80
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1942,f1764,f1195,f35855]) ).
fof(f35855,plain,
( spl0_1072
<=> ! [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_1072])]) ).
fof(f1195,plain,
( spl0_80
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1942,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_80
| ~ spl0_155 ),
inference(resolution,[],[f1765,f1196]) ).
fof(f1196,plain,
( ! [X2,X6,X7] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f35853,plain,
( spl0_1071
| ~ spl0_78
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1941,f1764,f1187,f35851]) ).
fof(f35851,plain,
( spl0_1071
<=> ! [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_1071])]) ).
fof(f1187,plain,
( spl0_78
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1941,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_78
| ~ spl0_155 ),
inference(resolution,[],[f1765,f1188]) ).
fof(f1188,plain,
( ! [X2,X6,X7] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1187]) ).
fof(f35849,plain,
( spl0_1070
| ~ spl0_81
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1940,f1764,f1199,f35847]) ).
fof(f35847,plain,
( spl0_1070
<=> ! [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_1070])]) ).
fof(f1199,plain,
( spl0_81
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1940,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_81
| ~ spl0_155 ),
inference(resolution,[],[f1765,f1200]) ).
fof(f1200,plain,
( ! [X2,X6,X7] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2)
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f35845,plain,
( spl0_1069
| ~ spl0_68
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1934,f1764,f1146,f35843]) ).
fof(f35843,plain,
( spl0_1069
<=> ! [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_1069])]) ).
fof(f1146,plain,
( spl0_68
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1934,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_68
| ~ spl0_155 ),
inference(resolution,[],[f1765,f1147]) ).
fof(f1147,plain,
( ! [X2,X6,X7] :
( c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f35841,plain,
( spl0_1068
| ~ spl0_69
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1933,f1764,f1150,f35839]) ).
fof(f35839,plain,
( spl0_1068
<=> ! [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_1068])]) ).
fof(f1150,plain,
( spl0_69
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1933,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_69
| ~ spl0_155 ),
inference(resolution,[],[f1765,f1151]) ).
fof(f1151,plain,
( ! [X2,X6,X7] :
( c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1150]) ).
fof(f35837,plain,
( spl0_1067
| ~ spl0_67
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1932,f1764,f1142,f35835]) ).
fof(f35835,plain,
( spl0_1067
<=> ! [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_1067])]) ).
fof(f1142,plain,
( spl0_67
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1932,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_67
| ~ spl0_155 ),
inference(resolution,[],[f1765,f1143]) ).
fof(f1143,plain,
( ! [X2,X6,X7] :
( c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f35833,plain,
( spl0_1066
| ~ spl0_70
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1931,f1764,f1154,f35831]) ).
fof(f35831,plain,
( spl0_1066
<=> ! [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_1066])]) ).
fof(f1154,plain,
( spl0_70
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1931,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_70
| ~ spl0_155 ),
inference(resolution,[],[f1765,f1155]) ).
fof(f1155,plain,
( ! [X2,X6,X7] :
( c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2)
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f35829,plain,
( spl0_1065
| ~ spl0_87
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1355,f1328,f1224,f35827]) ).
fof(f35827,plain,
( spl0_1065
<=> ! [X0,X3,X2,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Oinv__image(X0,X2,X1,X3) = c_Relation_Oconverse(c_Relation_Oinv__image(X0,X2,X1,X3),X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f1224,plain,
( spl0_87
<=> ! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Oconverse(X4,X2,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1328,plain,
( spl0_100
<=> ! [X3,X4,X12,X2] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Osym(c_Relation_Oinv__image(X4,X12,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1355,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Oinv__image(X0,X2,X1,X3) = c_Relation_Oconverse(c_Relation_Oinv__image(X0,X2,X1,X3),X3,X3) )
| ~ spl0_87
| ~ spl0_100 ),
inference(resolution,[],[f1329,f1225]) ).
fof(f1225,plain,
( ! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Oconverse(X4,X2,X2) = X4 )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1224]) ).
fof(f1329,plain,
( ! [X2,X3,X4,X12] :
( c_Relation_Osym(c_Relation_Oinv__image(X4,X12,X2,X3),X3)
| ~ c_Relation_Osym(X4,X2) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f35715,plain,
( spl0_1064
| ~ spl0_427
| ~ spl0_988 ),
inference(avatar_split_clause,[],[f31662,f29067,f7626,f35713]) ).
fof(f35713,plain,
( spl0_1064
<=> ! [X0] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f29067,plain,
( spl0_988
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,c_Relation_ORange(X1,X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f31662,plain,
( ! [X0] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_427
| ~ spl0_988 ),
inference(resolution,[],[f29068,f7627]) ).
fof(f29068,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(X1,X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) )
| ~ spl0_988 ),
inference(avatar_component_clause,[],[f29067]) ).
fof(f35080,plain,
( spl0_1063
| ~ spl0_427
| ~ spl0_987 ),
inference(avatar_split_clause,[],[f31603,f29063,f7626,f35078]) ).
fof(f35078,plain,
( spl0_1063
<=> ! [X0] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f29063,plain,
( spl0_987
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,c_Relation_ORange(X1,X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f31603,plain,
( ! [X0] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_427
| ~ spl0_987 ),
inference(resolution,[],[f29064,f7627]) ).
fof(f29064,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(X1,X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) )
| ~ spl0_987 ),
inference(avatar_component_clause,[],[f29063]) ).
fof(f32243,plain,
( spl0_1062
| ~ spl0_110
| ~ spl0_197
| ~ spl0_499 ),
inference(avatar_split_clause,[],[f11380,f10123,f2287,f1394,f32241]) ).
fof(f32241,plain,
( spl0_1062
<=> ! [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_1062])]) ).
fof(f2287,plain,
( spl0_197
<=> ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f10123,plain,
( spl0_499
<=> ! [X9,X11,X5,X2] : c_HOL_Ominus__class_Ominus(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f11380,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_110
| ~ spl0_197
| ~ spl0_499 ),
inference(forward_demodulation,[],[f11302,f2288]) ).
fof(f2288,plain,
( ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2287]) ).
fof(f11302,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_110
| ~ spl0_499 ),
inference(superposition,[],[f10124,f1395]) ).
fof(f10124,plain,
( ! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_499 ),
inference(avatar_component_clause,[],[f10123]) ).
fof(f32239,plain,
( spl0_1061
| ~ spl0_110
| ~ spl0_196
| ~ spl0_499 ),
inference(avatar_split_clause,[],[f11370,f10123,f2283,f1394,f32237]) ).
fof(f32237,plain,
( spl0_1061
<=> ! [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_1061])]) ).
fof(f2283,plain,
( spl0_196
<=> ! [X2,X9] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f11370,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_110
| ~ spl0_196
| ~ spl0_499 ),
inference(forward_demodulation,[],[f11294,f2284]) ).
fof(f2284,plain,
( ! [X2,X9] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool))
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f2283]) ).
fof(f11294,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_110
| ~ spl0_499 ),
inference(superposition,[],[f10124,f1395]) ).
fof(f32235,plain,
( spl0_1060
| ~ spl0_127
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f9368,f9274,f1462,f32233]) ).
fof(f32233,plain,
( spl0_1060
<=> ! [X2,X0,X1] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_Relation_OId(X2),tc_prod(X2,X2)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f1462,plain,
( spl0_127
<=> ! [X2,X4] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f9274,plain,
( spl0_467
<=> ! [X9,X0,X5,X2] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f9368,plain,
( ! [X2,X0,X1] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_Relation_OId(X2),tc_prod(X2,X2)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_127
| ~ spl0_467 ),
inference(superposition,[],[f1463,f9275]) ).
fof(f9275,plain,
( ! [X2,X0,X9,X5] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool))
| ~ spl0_467 ),
inference(avatar_component_clause,[],[f9274]) ).
fof(f1463,plain,
( ! [X2,X4] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f32231,plain,
( spl0_1059
| ~ spl0_171
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f9354,f9274,f1828,f32229]) ).
fof(f32229,plain,
( spl0_1059
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X4,c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,X3,X2),tc_fun(X2,tc_bool)),X2)
| ~ c_in(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f1828,plain,
( spl0_171
<=> ! [X9,X5,X19,X2] :
( ~ c_in(X19,X9,X2)
| ~ c_in(X19,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f9354,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X4,c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,X3,X2),tc_fun(X2,tc_bool)),X2)
| ~ c_in(X4,X3,X2) )
| ~ spl0_171
| ~ spl0_467 ),
inference(superposition,[],[f1829,f9275]) ).
fof(f1829,plain,
( ! [X2,X19,X9,X5] :
( ~ c_in(X19,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X19,X9,X2) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1828]) ).
fof(f32225,plain,
( ~ spl0_1058
| ~ spl0_10
| spl0_313
| ~ spl0_103
| ~ spl0_465 ),
inference(avatar_split_clause,[],[f9212,f8847,f1340,f3878,f896,f32222]) ).
fof(f32222,plain,
( spl0_1058
<=> c_Relation_Oantisym(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f3878,plain,
( spl0_313
<=> v_a____ = v_b____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f8847,plain,
( spl0_465
<=> ! [X4,X7,X6,X2] :
( ~ c_Relation_Oantisym(X4,X2)
| X6 = X7
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f9212,plain,
( v_a____ = v_b____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_103
| ~ spl0_465 ),
inference(resolution,[],[f8848,f1342]) ).
fof(f8848,plain,
( ! [X2,X6,X7,X4] :
( ~ c_in(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2))
| X6 = X7
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| ~ c_Relation_Oantisym(X4,X2) )
| ~ spl0_465 ),
inference(avatar_component_clause,[],[f8847]) ).
fof(f32220,plain,
( spl0_1057
| ~ spl0_57
| ~ spl0_230
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f8504,f7939,f2429,f1088,f32218]) ).
fof(f32218,plain,
( spl0_1057
<=> ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f1088,plain,
( spl0_57
<=> ! [X2] : c_Relation_OId(X2) = c_Relation_Oconverse(c_Relation_OId(X2),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f7939,plain,
( spl0_445
<=> ! [X4,X0,X3,X2] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,X4,X2,X3),X2,X3),X4,tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f8504,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_57
| ~ spl0_230
| ~ spl0_445 ),
inference(forward_demodulation,[],[f8459,f1089]) ).
fof(f1089,plain,
( ! [X2] : c_Relation_OId(X2) = c_Relation_Oconverse(c_Relation_OId(X2),X2,X2)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f8459,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId(X1),X1,X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_230
| ~ spl0_445 ),
inference(resolution,[],[f7940,f2430]) ).
fof(f7940,plain,
( ! [X2,X3,X0,X4] :
( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,X4,X2,X3),X2,X3),X4,tc_prod(X2,X3))
| ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2) )
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f7939]) ).
fof(f32216,plain,
( spl0_1056
| ~ spl0_57
| ~ spl0_230
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f8444,f7935,f2429,f1088,f32214]) ).
fof(f32214,plain,
( spl0_1056
<=> ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f8444,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_57
| ~ spl0_230
| ~ spl0_444 ),
inference(forward_demodulation,[],[f8399,f1089]) ).
fof(f8399,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId(X1),X1,X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_230
| ~ spl0_444 ),
inference(resolution,[],[f7936,f2430]) ).
fof(f32212,plain,
( spl0_1055
| ~ spl0_187
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f7664,f6631,f1897,f32210]) ).
fof(f32210,plain,
( spl0_1055
<=> ! [X2,X0,X1] :
( c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Nitpick_Orefl_H(c_Relation_Oconverse(X2,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f6631,plain,
( spl0_422
<=> ! [X4,X0,X3,X2,X1] :
( c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f7664,plain,
( ! [X2,X0,X1] :
( c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Nitpick_Orefl_H(c_Relation_Oconverse(X2,X1,X1),X1) )
| ~ spl0_187
| ~ spl0_422 ),
inference(resolution,[],[f6632,f1898]) ).
fof(f6632,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3))
| c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2)) )
| ~ spl0_422 ),
inference(avatar_component_clause,[],[f6631]) ).
fof(f32208,plain,
( spl0_1054
| ~ spl0_185
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f7640,f6627,f1889,f32206]) ).
fof(f32206,plain,
( spl0_1054
<=> ! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Relation_Oirrefl(c_Relation_Oconverse(X2,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f6627,plain,
( spl0_421
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
| c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f7640,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Relation_Oirrefl(c_Relation_Oconverse(X2,X1,X1),X1) )
| ~ spl0_185
| ~ spl0_421 ),
inference(resolution,[],[f6628,f1890]) ).
fof(f6628,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3))
| ~ c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2)) )
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f6627]) ).
fof(f32204,plain,
( spl0_1053
| ~ spl0_188
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f7639,f6627,f1901,f32202]) ).
fof(f32202,plain,
( spl0_1053
<=> ! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X2,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f7639,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X2,X1,X1),X1) )
| ~ spl0_188
| ~ spl0_421 ),
inference(resolution,[],[f6628,f1902]) ).
fof(f32200,plain,
( spl0_1052
| ~ spl0_330
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f7538,f6614,f4027,f32198]) ).
fof(f32198,plain,
( spl0_1052
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X3),X3)
| c_in(X0,X4,X3)
| ~ c_Equiv__Relations_Oequiv(X4,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f6614,plain,
( spl0_418
<=> ! [X3,X4,X5,X2,X1] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X5,X1,X4,X3,X2),X1,X3,X2),X4,tc_prod(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f7538,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X3),X3)
| c_in(X0,X4,X3)
| ~ c_Equiv__Relations_Oequiv(X4,X1,X3) )
| ~ spl0_330
| ~ spl0_418 ),
inference(resolution,[],[f6615,f4028]) ).
fof(f6615,plain,
( ! [X2,X3,X1,X4,X5] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X5,X1,X4,X3,X2),X1,X3,X2),X4,tc_prod(X3,X2))
| ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2) )
| ~ spl0_418 ),
inference(avatar_component_clause,[],[f6614]) ).
fof(f32196,plain,
( spl0_1051
| ~ spl0_333
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f7536,f6614,f4039,f32194]) ).
fof(f32194,plain,
( spl0_1051
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X3),X3)
| c_in(X0,X4,X3)
| ~ c_Relation_Orefl__on(X4,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f7536,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X3),X3)
| c_in(X0,X4,X3)
| ~ c_Relation_Orefl__on(X4,X1,X3) )
| ~ spl0_333
| ~ spl0_418 ),
inference(resolution,[],[f6615,f4040]) ).
fof(f32192,plain,
( spl0_1050
| ~ spl0_110
| ~ spl0_197
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7443,f6606,f2287,f1394,f32190]) ).
fof(f32190,plain,
( spl0_1050
<=> ! [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_1050])]) ).
fof(f7443,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_110
| ~ spl0_197
| ~ spl0_416 ),
inference(forward_demodulation,[],[f7393,f2288]) ).
fof(f7393,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_110
| ~ spl0_416 ),
inference(superposition,[],[f6607,f1395]) ).
fof(f32188,plain,
( spl0_1049
| ~ spl0_257
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7396,f6606,f3135,f32186]) ).
fof(f32186,plain,
( spl0_1049
<=> ! [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_1049])]) ).
fof(f3135,plain,
( spl0_257
<=> ! [X2,X5,X9] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f7396,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_257
| ~ spl0_416 ),
inference(superposition,[],[f6607,f3136]) ).
fof(f3136,plain,
( ! [X2,X9,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f3135]) ).
fof(f32179,plain,
( spl0_1048
| ~ spl0_21
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f6303,f6175,f941,f32177]) ).
fof(f32177,plain,
( spl0_1048
<=> ! [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_1048])]) ).
fof(f941,plain,
( spl0_21
<=> ! [X2,X5] : c_lessequals(X5,X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f6175,plain,
( spl0_394
<=> ! [X9,X11,X5,X2] :
( ~ c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f6303,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_21
| ~ spl0_394 ),
inference(resolution,[],[f6176,f942]) ).
fof(f942,plain,
( ! [X2,X5] : c_lessequals(X5,X5,tc_fun(X2,tc_bool))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f941]) ).
fof(f6176,plain,
( ! [X2,X11,X9,X5] :
( ~ c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) )
| ~ spl0_394 ),
inference(avatar_component_clause,[],[f6175]) ).
fof(f32175,plain,
( spl0_1047
| ~ spl0_230
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f6103,f5559,f2429,f32173]) ).
fof(f32173,plain,
( spl0_1047
<=> ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f5559,plain,
( spl0_389
<=> ! [X4,X0,X3,X2] :
( ~ c_in(X0,c_Relation_ORange(X4,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X4,X2,X3),X0,X3,X2),X4,tc_prod(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f6103,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_230
| ~ spl0_389 ),
inference(resolution,[],[f5560,f2430]) ).
fof(f5560,plain,
( ! [X2,X3,X0,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X4,X2,X3),X0,X3,X2),X4,tc_prod(X3,X2))
| ~ c_in(X0,c_Relation_ORange(X4,X3,X2),X2) )
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f5559]) ).
fof(f32171,plain,
( spl0_1046
| ~ spl0_230
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6062,f5555,f2429,f32169]) ).
fof(f32169,plain,
( spl0_1046
<=> ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f5555,plain,
( spl0_388
<=> ! [X4,X3,X2,X1] :
( ~ c_in(X1,c_Relation_ORange(X4,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X4,X2,X3),X1,X3,X2),X4,tc_prod(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f6062,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_230
| ~ spl0_388 ),
inference(resolution,[],[f5556,f2430]) ).
fof(f5556,plain,
( ! [X2,X3,X1,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X4,X2,X3),X1,X3,X2),X4,tc_prod(X3,X2))
| ~ c_in(X1,c_Relation_ORange(X4,X3,X2),X2) )
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f5555]) ).
fof(f32167,plain,
( spl0_1045
| ~ spl0_296
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f5000,f4541,f3457,f32165]) ).
fof(f32165,plain,
( spl0_1045
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1)),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1)))
| c_Nitpick_Orefl_H(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f3457,plain,
( spl0_296
<=> ! [X2,X4] :
( c_Nitpick_Orefl_H(X4,X2)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X4,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f5000,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1)),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1)))
| c_Nitpick_Orefl_H(X0,X1) )
| ~ spl0_296
| ~ spl0_354 ),
inference(resolution,[],[f4542,f3458]) ).
fof(f3458,plain,
( ! [X2,X4] :
( ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X4,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X4,X2),X2,X2),X4,tc_prod(X2,X2))
| c_Nitpick_Orefl_H(X4,X2) )
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f3457]) ).
fof(f32163,plain,
( spl0_1044
| ~ spl0_307
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4995,f4541,f3501,f32161]) ).
fof(f32161,plain,
( spl0_1044
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X2),X3),X4))
| c_in(X4,c_Relation_ORange(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f3501,plain,
( spl0_307
<=> ! [X6,X4,X0,X3,X2] :
( c_in(X0,c_Relation_ORange(X4,X3,X2),X2)
| ~ c_in(c_Pair(X6,X0,X3,X2),X4,tc_prod(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f4995,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X2),X3),X4))
| c_in(X4,c_Relation_ORange(X0,X1,X2),X2) )
| ~ spl0_307
| ~ spl0_354 ),
inference(resolution,[],[f4542,f3502]) ).
fof(f3502,plain,
( ! [X2,X3,X0,X6,X4] :
( ~ c_in(c_Pair(X6,X0,X3,X2),X4,tc_prod(X3,X2))
| c_in(X0,c_Relation_ORange(X4,X3,X2),X2) )
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f3501]) ).
fof(f32159,plain,
( spl0_1043
| ~ spl0_299
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4965,f4537,f3469,f32157]) ).
fof(f32157,plain,
( spl0_1043
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1)),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1)))
| c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f4965,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1)),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1)))
| c_Relation_Oirrefl(X0,X1) )
| ~ spl0_299
| ~ spl0_353 ),
inference(resolution,[],[f4538,f3470]) ).
fof(f32155,plain,
( spl0_1042
| ~ spl0_249
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4936,f4533,f2933,f32153]) ).
fof(f32153,plain,
( spl0_1042
<=> ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
| c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId__on(X1,X2),X0,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f2933,plain,
( spl0_249
<=> ! [X5,X7,X6,X2] :
( X6 = X7
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Relation_OId__on(X5,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f4936,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
| c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId__on(X1,X2),X0,X2) = X0 )
| ~ spl0_249
| ~ spl0_352 ),
inference(resolution,[],[f4534,f2934]) ).
fof(f2934,plain,
( ! [X2,X6,X7,X5] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Relation_OId__on(X5,X2),tc_prod(X2,X2))
| X6 = X7 )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2933]) ).
fof(f32151,plain,
( spl0_1041
| ~ spl0_249
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4904,f4529,f2933,f32149]) ).
fof(f32149,plain,
( spl0_1041
<=> ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
| c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId__on(X1,X2),X0,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f4904,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
| c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId__on(X1,X2),X0,X2) = X0 )
| ~ spl0_249
| ~ spl0_351 ),
inference(resolution,[],[f4530,f2934]) ).
fof(f32147,plain,
( spl0_1040
| ~ spl0_170
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4635,f4477,f1824,f32145]) ).
fof(f32145,plain,
( spl0_1040
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X4,c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2),X2)
| ~ c_in(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f4635,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X4,c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2),X2)
| ~ c_in(X4,X3,X2) )
| ~ spl0_170
| ~ spl0_338 ),
inference(superposition,[],[f1825,f4478]) ).
fof(f32143,plain,
( spl0_1039
| ~ spl0_153
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4630,f4477,f1752,f32141]) ).
fof(f32141,plain,
( spl0_1039
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f4630,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(X3,X4)) )
| ~ spl0_153
| ~ spl0_338 ),
inference(superposition,[],[f1753,f4478]) ).
fof(f32139,plain,
( spl0_1038
| ~ spl0_61
| ~ spl0_938 ),
inference(avatar_split_clause,[],[f28865,f28572,f1104,f32137]) ).
fof(f32137,plain,
( spl0_1038
<=> ! [X0,X1] : c_in(v_a____,hAPP(c_FunDef_Oin__rel(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f28572,plain,
( spl0_938
<=> ! [X0] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f28865,plain,
( ! [X0,X1] : c_in(v_a____,hAPP(c_FunDef_Oin__rel(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X1)
| ~ spl0_61
| ~ spl0_938 ),
inference(resolution,[],[f28573,f1105]) ).
fof(f28573,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____))
| ~ spl0_938 ),
inference(avatar_component_clause,[],[f28572]) ).
fof(f32135,plain,
( spl0_1037
| ~ spl0_169
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f4568,f4473,f1820,f32133]) ).
fof(f32133,plain,
( spl0_1037
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X4,c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X3),X3)
| ~ c_in(X4,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f4568,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X4,c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X3),X3)
| ~ c_in(X4,X0,X3) )
| ~ spl0_169
| ~ spl0_337 ),
inference(superposition,[],[f1821,f4474]) ).
fof(f32131,plain,
( spl0_1036
| ~ spl0_154
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f4565,f4473,f1756,f32129]) ).
fof(f32129,plain,
( spl0_1036
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f4565,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X0,X4)) )
| ~ spl0_154
| ~ spl0_337 ),
inference(superposition,[],[f1757,f4474]) ).
fof(f32127,plain,
( spl0_1035
| ~ spl0_105
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4170,f3986,f1371,f32125]) ).
fof(f32125,plain,
( spl0_1035
<=> ! [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_1035])]) ).
fof(f4170,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_105
| ~ spl0_320 ),
inference(superposition,[],[f1372,f3987]) ).
fof(f32123,plain,
( spl0_1034
| ~ spl0_106
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f4132,f3982,f1375,f32121]) ).
fof(f32121,plain,
( spl0_1034
<=> ! [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_1034])]) ).
fof(f4132,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_106
| ~ spl0_319 ),
inference(superposition,[],[f1376,f3983]) ).
fof(f32119,plain,
( spl0_1033
| ~ spl0_295
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3955,f3513,f3453,f32117]) ).
fof(f32117,plain,
( spl0_1033
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X0),tc_bool)) = c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f3453,plain,
( spl0_295
<=> ! [X4,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)) = X4
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ORange(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f3513,plain,
( spl0_310
<=> ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f3955,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X0),tc_bool)) = c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X0,X1)
| ~ spl0_295
| ~ spl0_310 ),
inference(trivial_inequality_removal,[],[f3954]) ).
fof(f3954,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X0),tc_bool)) = c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X0,X1) )
| ~ spl0_295
| ~ spl0_310 ),
inference(superposition,[],[f3454,f3514]) ).
fof(f3514,plain,
( ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2)
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f3513]) ).
fof(f3454,plain,
( ! [X2,X3,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ORange(X4,X3,X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)) = X4 )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f3453]) ).
fof(f32115,plain,
( spl0_1032
| ~ spl0_82
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3944,f3501,f1204,f32113]) ).
fof(f32113,plain,
( spl0_1032
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Relation_ORange(c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),X2,X3),X3)
| ~ c_Wellfounded_Owf(X1,tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f3944,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),X2,X3),X3)
| ~ c_Wellfounded_Owf(X1,tc_prod(X2,X3)) )
| ~ spl0_82
| ~ spl0_307 ),
inference(resolution,[],[f3502,f1205]) ).
fof(f32111,plain,
( spl0_1031
| ~ spl0_99
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3924,f3493,f1324,f32109]) ).
fof(f32109,plain,
( spl0_1031
<=> ! [X0,X3,X2,X1] :
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Oinv__image(X0,X2,X1,X3),X3,X3),X3)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1324,plain,
( spl0_99
<=> ! [X3,X4,X12,X2] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X4,X12,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f3924,plain,
( ! [X2,X3,X0,X1] :
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Oinv__image(X0,X2,X1,X3),X3,X3),X3)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1) )
| ~ spl0_99
| ~ spl0_305 ),
inference(superposition,[],[f1325,f3494]) ).
fof(f1325,plain,
( ! [X2,X3,X4,X12] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X4,X12,X2,X3),X3)
| ~ c_Wellfounded_Owf(X4,X2) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1324]) ).
fof(f32107,plain,
( spl0_1030
| ~ spl0_100
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3923,f3493,f1328,f32105]) ).
fof(f32105,plain,
( spl0_1030
<=> ! [X0,X3,X2,X1] :
( c_Relation_Osym(c_Relation_Oconverse(c_Relation_Oinv__image(X0,X2,X1,X3),X3,X3),X3)
| ~ c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f3923,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Osym(c_Relation_Oconverse(c_Relation_Oinv__image(X0,X2,X1,X3),X3,X3),X3)
| ~ c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) )
| ~ spl0_100
| ~ spl0_305 ),
inference(superposition,[],[f1329,f3494]) ).
fof(f32103,plain,
( spl0_1029
| ~ spl0_101
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3922,f3493,f1332,f32101]) ).
fof(f32101,plain,
( spl0_1029
<=> ! [X0,X3,X2,X1] :
( c_Relation_Otrans(c_Relation_Oconverse(c_Relation_Oinv__image(X0,X2,X1,X3),X3,X3),X3)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f1332,plain,
( spl0_101
<=> ! [X3,X4,X12,X2] :
( ~ c_Relation_Otrans(X4,X2)
| c_Relation_Otrans(c_Relation_Oinv__image(X4,X12,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f3922,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Otrans(c_Relation_Oconverse(c_Relation_Oinv__image(X0,X2,X1,X3),X3,X3),X3)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1) )
| ~ spl0_101
| ~ spl0_305 ),
inference(superposition,[],[f1333,f3494]) ).
fof(f1333,plain,
( ! [X2,X3,X4,X12] :
( c_Relation_Otrans(c_Relation_Oinv__image(X4,X12,X2,X3),X3)
| ~ c_Relation_Otrans(X4,X2) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1332]) ).
fof(f32099,plain,
( spl0_1028
| ~ spl0_57
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3903,f3493,f1088,f32097]) ).
fof(f32097,plain,
( spl0_1028
<=> ! [X2,X0,X1] : c_Relation_Oinv__image(c_Relation_OId(X0),X1,X0,X2) = c_Relation_Oconverse(c_Relation_Oinv__image(c_Relation_OId(X0),X1,X0,X2),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f3903,plain,
( ! [X2,X0,X1] : c_Relation_Oinv__image(c_Relation_OId(X0),X1,X0,X2) = c_Relation_Oconverse(c_Relation_Oinv__image(c_Relation_OId(X0),X1,X0,X2),X2,X2)
| ~ spl0_57
| ~ spl0_305 ),
inference(superposition,[],[f3494,f1089]) ).
fof(f32048,plain,
( spl0_1027
| ~ spl0_59
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3825,f3453,f1096,f32046]) ).
fof(f32046,plain,
( spl0_1027
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| c_Relation_OId__on(X0,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1096,plain,
( spl0_59
<=> ! [X2,X5] : c_Relation_ORange(c_Relation_OId__on(X5,X2),X2,X2) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f3825,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| c_Relation_OId__on(X0,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) )
| ~ spl0_59
| ~ spl0_295 ),
inference(superposition,[],[f3454,f1097]) ).
fof(f1097,plain,
( ! [X2,X5] : c_Relation_ORange(c_Relation_OId__on(X5,X2),X2,X2) = X5
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f32044,plain,
( spl0_1026
| ~ spl0_105
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3794,f3445,f1371,f32042]) ).
fof(f32042,plain,
( spl0_1026
<=> ! [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_1026])]) ).
fof(f3794,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_105
| ~ spl0_293 ),
inference(resolution,[],[f3446,f1372]) ).
fof(f32040,plain,
( spl0_1025
| ~ spl0_105
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3771,f3441,f1371,f32038]) ).
fof(f32038,plain,
( spl0_1025
<=> ! [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_1025])]) ).
fof(f3771,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_105
| ~ spl0_292 ),
inference(resolution,[],[f3442,f1372]) ).
fof(f32036,plain,
( spl0_1024
| ~ spl0_117
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f3671,f3421,f1422,f32034]) ).
fof(f32034,plain,
( spl0_1024
<=> ! [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_1024])]) ).
fof(f3421,plain,
( spl0_287
<=> ! [X9,X11,X5,X2] :
( c_lessequals(X11,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f3671,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_117
| ~ spl0_287 ),
inference(resolution,[],[f3422,f1423]) ).
fof(f3422,plain,
( ! [X2,X11,X9,X5] :
( ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(X11,X5,tc_fun(X2,tc_bool)) )
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f3421]) ).
fof(f32032,plain,
( spl0_1023
| ~ spl0_115
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3655,f3417,f1414,f32030]) ).
fof(f32030,plain,
( spl0_1023
<=> ! [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_1023])]) ).
fof(f3417,plain,
( spl0_286
<=> ! [X9,X11,X5,X2] :
( c_lessequals(X11,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f3655,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_115
| ~ spl0_286 ),
inference(forward_demodulation,[],[f3638,f117]) ).
fof(f117,axiom,
! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
fof(f3638,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_115
| ~ spl0_286 ),
inference(resolution,[],[f3418,f1415]) ).
fof(f3418,plain,
( ! [X2,X11,X9,X5] :
( ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(X11,X9,tc_fun(X2,tc_bool)) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f3417]) ).
fof(f32028,plain,
( spl0_1022
| ~ spl0_117
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3646,f3417,f1422,f32026]) ).
fof(f32026,plain,
( spl0_1022
<=> ! [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_1022])]) ).
fof(f3646,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_117
| ~ spl0_286 ),
inference(resolution,[],[f3418,f1423]) ).
fof(f32024,plain,
( spl0_1021
| ~ spl0_116
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3639,f3417,f1418,f32022]) ).
fof(f32022,plain,
( spl0_1021
<=> ! [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_1021])]) ).
fof(f3639,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_116
| ~ spl0_286 ),
inference(resolution,[],[f3418,f1419]) ).
fof(f32020,plain,
( spl0_1020
| ~ spl0_164
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f3357,f3187,f1800,f32018]) ).
fof(f32018,plain,
( spl0_1020
<=> ! [X0,X1] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Relation_Osym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f3357,plain,
( ! [X0,X1] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Relation_Osym(X0,X1) )
| ~ spl0_164
| ~ spl0_270 ),
inference(superposition,[],[f3188,f1801]) ).
fof(f32016,plain,
( spl0_1019
| ~ spl0_164
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3350,f3183,f1800,f32014]) ).
fof(f32014,plain,
( spl0_1019
<=> ! [X0,X1] :
( c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Wellfounded_Oacyclic(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f3350,plain,
( ! [X0,X1] :
( c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl0_164
| ~ spl0_269 ),
inference(superposition,[],[f3184,f1801]) ).
fof(f32012,plain,
( spl0_1018
| ~ spl0_239
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3339,f3175,f2893,f32010]) ).
fof(f32010,plain,
( spl0_1018
<=> ! [X2,X0,X1] :
( ~ c_in(X1,c_Relation_OId__on(X2,X0),tc_prod(X0,X0))
| c_in(hAPP(c_fst(X0,X0),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f3339,plain,
( ! [X2,X0,X1] :
( ~ c_in(X1,c_Relation_OId__on(X2,X0),tc_prod(X0,X0))
| c_in(hAPP(c_fst(X0,X0),X1),X2,X0) )
| ~ spl0_239
| ~ spl0_267 ),
inference(superposition,[],[f3176,f2894]) ).
fof(f32008,plain,
( spl0_1017
| ~ spl0_61
| ~ spl0_1000 ),
inference(avatar_split_clause,[],[f31963,f31784,f1104,f32006]) ).
fof(f32006,plain,
( spl0_1017
<=> ! [X3,X4,X0,X5,X2,X1] : c_in(X0,c_Set_Oimage(c_COMBK(X0,X1,X2),v_Lab____,X3,X4),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f31784,plain,
( spl0_1000
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),v_Lab____,X3,X4),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f31963,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_in(X0,c_Set_Oimage(c_COMBK(X0,X1,X2),v_Lab____,X3,X4),X5)
| ~ spl0_61
| ~ spl0_1000 ),
inference(resolution,[],[f31785,f1105]) ).
fof(f31785,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),v_Lab____,X3,X4),X0))
| ~ spl0_1000 ),
inference(avatar_component_clause,[],[f31784]) ).
fof(f32004,plain,
( spl0_1016
| ~ spl0_214
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3304,f3151,f2365,f32002]) ).
fof(f32002,plain,
( spl0_1016
<=> ! [X2,X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f3304,plain,
( ! [X2,X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X2)) )
| ~ spl0_214
| ~ spl0_261 ),
inference(resolution,[],[f3152,f2366]) ).
fof(f32000,plain,
( spl0_1015
| ~ spl0_260
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3298,f3151,f3147,f31998]) ).
fof(f31998,plain,
( spl0_1015
<=> ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1,X1)
| ~ c_Relation_Osingle__valued(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f3147,plain,
( spl0_260
<=> ! [X4,X14,X3,X2] :
( ~ c_Relation_Osingle__valued(X14,X2,X3)
| c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X3),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f3298,plain,
( ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1,X1)
| ~ c_Relation_Osingle__valued(X0,X1,X1) )
| ~ spl0_260
| ~ spl0_261 ),
inference(resolution,[],[f3152,f3148]) ).
fof(f3148,plain,
( ! [X2,X3,X14,X4] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_Relation_Osingle__valued(X14,X2,X3) )
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f3147]) ).
fof(f31996,plain,
( spl0_1014
| ~ spl0_157
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f3016,f2889,f1772,f31994]) ).
fof(f31994,plain,
( spl0_1014
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X4,tc_fun(X3,tc_bool))
| c_in(X0,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f1772,plain,
( spl0_157
<=> ! [X5,X9,X6,X2] :
( c_in(X6,X9,X2)
| ~ c_lessequals(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f3016,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X4,tc_fun(X3,tc_bool))
| c_in(X0,X4,X3) )
| ~ spl0_157
| ~ spl0_238 ),
inference(superposition,[],[f1773,f2890]) ).
fof(f1773,plain,
( ! [X2,X6,X9,X5] :
( ~ c_lessequals(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool))
| c_in(X6,X9,X2) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f31992,plain,
( spl0_1013
| ~ spl0_157
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2968,f2877,f1772,f31990]) ).
fof(f31990,plain,
( spl0_1013
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| c_in(X0,c_Set_Oinsert(X4,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f2968,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| c_in(X0,c_Set_Oinsert(X4,X3,X2),X2) )
| ~ spl0_157
| ~ spl0_235 ),
inference(resolution,[],[f2878,f1773]) ).
fof(f31988,plain,
( spl0_1012
| ~ spl0_178
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2205,f1869,f1861,f31986]) ).
fof(f31986,plain,
( spl0_1012
<=> ! [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_1012])]) ).
fof(f2205,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_178
| ~ spl0_180 ),
inference(duplicate_literal_removal,[],[f2195]) ).
fof(f2195,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_178
| ~ spl0_180 ),
inference(resolution,[],[f1870,f1862]) ).
fof(f31984,plain,
( spl0_1011
| ~ spl0_177
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2204,f1869,f1857,f31982]) ).
fof(f31982,plain,
( spl0_1011
<=> ! [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_1011])]) ).
fof(f2204,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_177
| ~ spl0_180 ),
inference(duplicate_literal_removal,[],[f2196]) ).
fof(f2196,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_177
| ~ spl0_180 ),
inference(resolution,[],[f1870,f1858]) ).
fof(f31980,plain,
( spl0_1010
| ~ spl0_178
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2182,f1865,f1861,f31978]) ).
fof(f31978,plain,
( spl0_1010
<=> ! [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_1010])]) ).
fof(f2182,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_178
| ~ spl0_179 ),
inference(duplicate_literal_removal,[],[f2172]) ).
fof(f2172,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_178
| ~ spl0_179 ),
inference(resolution,[],[f1866,f1862]) ).
fof(f31976,plain,
( spl0_1009
| ~ spl0_177
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2181,f1865,f1857,f31974]) ).
fof(f31974,plain,
( spl0_1009
<=> ! [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_1009])]) ).
fof(f2181,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_177
| ~ spl0_179 ),
inference(duplicate_literal_removal,[],[f2173]) ).
fof(f2173,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_177
| ~ spl0_179 ),
inference(resolution,[],[f1866,f1858]) ).
fof(f31972,plain,
( spl0_1008
| ~ spl0_162
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f2057,f1796,f1792,f31970]) ).
fof(f31970,plain,
( spl0_1008
<=> ! [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_1008])]) ).
fof(f2057,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_162
| ~ spl0_163 ),
inference(duplicate_literal_removal,[],[f2047]) ).
fof(f2047,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_162
| ~ spl0_163 ),
inference(resolution,[],[f1797,f1793]) ).
fof(f31968,plain,
( spl0_1007
| ~ spl0_161
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f2056,f1796,f1788,f31966]) ).
fof(f31966,plain,
( spl0_1007
<=> ! [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_1007])]) ).
fof(f2056,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_161
| ~ spl0_163 ),
inference(duplicate_literal_removal,[],[f2048]) ).
fof(f2048,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_161
| ~ spl0_163 ),
inference(resolution,[],[f1797,f1789]) ).
fof(f31962,plain,
( spl0_1006
| ~ spl0_160
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2034,f1792,f1784,f31960]) ).
fof(f31960,plain,
( spl0_1006
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X0,X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f2034,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X0,X3),X2,X3) )
| ~ spl0_160
| ~ spl0_162 ),
inference(duplicate_literal_removal,[],[f2029]) ).
fof(f2029,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X0,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_160
| ~ spl0_162 ),
inference(resolution,[],[f1793,f1785]) ).
fof(f31958,plain,
( spl0_1005
| ~ spl0_160
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2021,f1788,f1784,f31956]) ).
fof(f31956,plain,
( spl0_1005
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f2021,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,X3),X2,X3) )
| ~ spl0_160
| ~ spl0_161 ),
inference(duplicate_literal_removal,[],[f2016]) ).
fof(f2016,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_160
| ~ spl0_161 ),
inference(resolution,[],[f1789,f1785]) ).
fof(f31954,plain,
( spl0_1004
| ~ spl0_98
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1540,f1442,f1320,f31952]) ).
fof(f31952,plain,
( spl0_1004
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| c_Set_Oinsert(X3,X1,X2) = c_Set_Oinsert(X0,c_Set_Oinsert(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f1540,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_Set_Oinsert(X3,X1,X2) = c_Set_Oinsert(X0,c_Set_Oinsert(X3,X1,X2),X2) )
| ~ spl0_98
| ~ spl0_122 ),
inference(resolution,[],[f1443,f1321]) ).
fof(f31950,plain,
( spl0_1003
| ~ spl0_55
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1356,f1332,f1080,f31948]) ).
fof(f31948,plain,
( spl0_1003
<=> ! [X0,X3,X2,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Relation_Oinv__image(X0,X2,X1,X3) = c_Transitive__Closure_Otrancl(c_Relation_Oinv__image(X0,X2,X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f1356,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Relation_Oinv__image(X0,X2,X1,X3) = c_Transitive__Closure_Otrancl(c_Relation_Oinv__image(X0,X2,X1,X3),X3) )
| ~ spl0_55
| ~ spl0_101 ),
inference(resolution,[],[f1333,f1081]) ).
fof(f31946,plain,
( spl0_1002
| ~ spl0_29
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1347,f1316,f973,f31944]) ).
fof(f31944,plain,
( spl0_1002
<=> ! [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_1002])]) ).
fof(f973,plain,
( spl0_29
<=> ! [X55,X56] :
( ~ class_Lattices_Obounded__lattice(X56)
| class_Lattices_Obounded__lattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1316,plain,
( spl0_97
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1347,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_29
| ~ spl0_97 ),
inference(resolution,[],[f1317,f974]) ).
fof(f974,plain,
( ! [X56,X55] :
( class_Lattices_Obounded__lattice(tc_fun(X55,X56))
| ~ class_Lattices_Obounded__lattice(X56) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f1317,plain,
( ! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X6,X2) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f31942,plain,
( spl0_1001
| ~ spl0_29
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1345,f1311,f973,f31940]) ).
fof(f31940,plain,
( spl0_1001
<=> ! [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_1001])]) ).
fof(f1311,plain,
( spl0_96
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1345,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_29
| ~ spl0_96 ),
inference(resolution,[],[f1312,f974]) ).
fof(f1312,plain,
( ! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X2),X2) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1311]) ).
fof(f31786,plain,
( spl0_1000
| ~ spl0_62
| ~ spl0_999 ),
inference(avatar_split_clause,[],[f31374,f30784,f1108,f31784]) ).
fof(f30784,plain,
( spl0_999
<=> ! [X4,X0,X3,X2,X1] : c_in(X0,c_Set_Oimage(c_COMBK(X0,X1,X2),v_Lab____,X3,X4),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f31374,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),v_Lab____,X3,X4),X0))
| ~ spl0_62
| ~ spl0_999 ),
inference(resolution,[],[f30785,f1109]) ).
fof(f30785,plain,
( ! [X2,X3,X0,X1,X4] : c_in(X0,c_Set_Oimage(c_COMBK(X0,X1,X2),v_Lab____,X3,X4),X4)
| ~ spl0_999 ),
inference(avatar_component_clause,[],[f30784]) ).
fof(f30786,plain,
( spl0_999
| ~ spl0_92
| ~ spl0_959 ),
inference(avatar_split_clause,[],[f30477,f28891,f1244,f30784]) ).
fof(f1244,plain,
( spl0_92
<=> ! [X0] : c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f28891,plain,
( spl0_959
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( c_in(X0,c_Set_Oimage(c_COMBK(X0,X1,X2),X4,X5,X6),X6)
| ~ c_in(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f30477,plain,
( ! [X2,X3,X0,X1,X4] : c_in(X0,c_Set_Oimage(c_COMBK(X0,X1,X2),v_Lab____,X3,X4),X4)
| ~ spl0_92
| ~ spl0_959 ),
inference(resolution,[],[f28892,f1245]) ).
fof(f1245,plain,
( ! [X0] : c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,X0)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1244]) ).
fof(f28892,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_in(X3,X4,X5)
| c_in(X0,c_Set_Oimage(c_COMBK(X0,X1,X2),X4,X5,X6),X6) )
| ~ spl0_959 ),
inference(avatar_component_clause,[],[f28891]) ).
fof(f30324,plain,
( spl0_998
| ~ spl0_61
| ~ spl0_937 ),
inference(avatar_split_clause,[],[f28824,f28370,f1104,f30322]) ).
fof(f30322,plain,
( spl0_998
<=> ! [X0,X1] : c_in(v_a____,c_Transitive__Closure_Otrancl(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f28370,plain,
( spl0_937
<=> ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X0),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f28824,plain,
( ! [X0,X1] : c_in(v_a____,c_Transitive__Closure_Otrancl(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X0),X1)
| ~ spl0_61
| ~ spl0_937 ),
inference(resolution,[],[f28371,f1105]) ).
fof(f28371,plain,
( ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X0),v_a____))
| ~ spl0_937 ),
inference(avatar_component_clause,[],[f28370]) ).
fof(f29583,plain,
( spl0_997
| ~ spl0_334
| ~ spl0_750 ),
inference(avatar_split_clause,[],[f21228,f21181,f4043,f29581]) ).
fof(f29581,plain,
( spl0_997
<=> ! [X2,X0,X1] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Set_Oinsert(X1,v_Lab____,X2),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f21228,plain,
( ! [X2,X0,X1] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Set_Oinsert(X1,v_Lab____,X2),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_334
| ~ spl0_750 ),
inference(resolution,[],[f21182,f4044]) ).
fof(f29101,plain,
( spl0_996
| ~ spl0_46
| ~ spl0_347
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f13392,f12817,f4513,f1042,f29099]) ).
fof(f29099,plain,
( spl0_996
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),X1)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f12817,plain,
( spl0_542
<=> ! [X13,X2,X8] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f13392,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),X1)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_46
| ~ spl0_347
| ~ spl0_542 ),
inference(forward_demodulation,[],[f13357,f1043]) ).
fof(f13357,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_347
| ~ spl0_542 ),
inference(superposition,[],[f12818,f4514]) ).
fof(f12818,plain,
( ! [X2,X8,X13] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) )
| ~ spl0_542 ),
inference(avatar_component_clause,[],[f12817]) ).
fof(f29097,plain,
( spl0_995
| ~ spl0_333
| ~ spl0_750 ),
inference(avatar_split_clause,[],[f21227,f21181,f4039,f29095]) ).
fof(f29095,plain,
( spl0_995
<=> ! [X2,X0,X1] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Set_Oinsert(X1,v_Lab____,X2),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f21227,plain,
( ! [X2,X0,X1] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Set_Oinsert(X1,v_Lab____,X2),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_333
| ~ spl0_750 ),
inference(resolution,[],[f21182,f4040]) ).
fof(f29093,plain,
( spl0_994
| ~ spl0_46
| ~ spl0_347
| ~ spl0_541 ),
inference(avatar_split_clause,[],[f13329,f12813,f4513,f1042,f29091]) ).
fof(f29091,plain,
( spl0_994
<=> ! [X0,X1] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),X1)
| ~ c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f12813,plain,
( spl0_541
<=> ! [X13,X2,X8] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f13329,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),X1)
| ~ c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_46
| ~ spl0_347
| ~ spl0_541 ),
inference(forward_demodulation,[],[f13294,f1043]) ).
fof(f13294,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_347
| ~ spl0_541 ),
inference(superposition,[],[f12814,f4514]) ).
fof(f12814,plain,
( ! [X2,X8,X13] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) )
| ~ spl0_541 ),
inference(avatar_component_clause,[],[f12813]) ).
fof(f29089,plain,
( spl0_993
| ~ spl0_135
| ~ spl0_506 ),
inference(avatar_split_clause,[],[f11700,f10151,f1494,f29087]) ).
fof(f29087,plain,
( spl0_993
<=> ! [X0,X3,X2,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_Oinv__image(c_Relation_OId(X2),X3,X2,X1),tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f11700,plain,
( ! [X2,X3,X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_Oinv__image(c_Relation_OId(X2),X3,X2,X1),tc_prod(X1,X1))
| ~ spl0_135
| ~ spl0_506 ),
inference(resolution,[],[f10152,f1495]) ).
fof(f29085,plain,
( spl0_992
| ~ spl0_66
| ~ spl0_473 ),
inference(avatar_split_clause,[],[f9592,f9298,f1138,f29083]) ).
fof(f29083,plain,
( spl0_992
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X2,X0,X1),X3,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f1138,plain,
( spl0_66
<=> ! [X2,X5] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f9298,plain,
( spl0_473
<=> ! [X5,X3,X4,X11,X9,X2] :
( c_lessequals(c_Relation_OImage(X4,X11,X2,X3),X9,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X9,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f9592,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X2,X0,X1),X3,tc_fun(X1,tc_bool))
| ~ spl0_66
| ~ spl0_473 ),
inference(resolution,[],[f9299,f1139]) ).
fof(f1139,plain,
( ! [X2,X5] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool))
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1138]) ).
fof(f9299,plain,
( ! [X2,X3,X11,X9,X4,X5] :
( ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X9,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool))
| c_lessequals(c_Relation_OImage(X4,X11,X2,X3),X9,tc_fun(X3,tc_bool)) )
| ~ spl0_473 ),
inference(avatar_component_clause,[],[f9298]) ).
fof(f29081,plain,
( spl0_991
| ~ spl0_307
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f7542,f6614,f3501,f29079]) ).
fof(f29079,plain,
( spl0_991
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
| c_in(X0,c_Relation_ORange(X1,X3,X4),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f7542,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
| c_in(X0,c_Relation_ORange(X1,X3,X4),X4) )
| ~ spl0_307
| ~ spl0_418 ),
inference(resolution,[],[f6615,f3502]) ).
fof(f29077,plain,
( spl0_990
| ~ spl0_187
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f6504,f6211,f1897,f29075]) ).
fof(f29075,plain,
( spl0_990
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Relation_OImage(X1,X2,X3,X3),X3)
| ~ c_in(X0,X2,X3)
| ~ c_Nitpick_Orefl_H(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f6504,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Relation_OImage(X1,X2,X3,X3),X3)
| ~ c_in(X0,X2,X3)
| ~ c_Nitpick_Orefl_H(X1,X3) )
| ~ spl0_187
| ~ spl0_403 ),
inference(resolution,[],[f6212,f1898]) ).
fof(f29073,plain,
( spl0_989
| ~ spl0_187
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f6448,f6203,f1897,f29071]) ).
fof(f29071,plain,
( spl0_989
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,X2,X1,X3,X4),X1)
| ~ c_Nitpick_Orefl_H(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f6448,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,X2,X1,X3,X4),X1)
| ~ c_Nitpick_Orefl_H(X2,X3) )
| ~ spl0_187
| ~ spl0_401 ),
inference(resolution,[],[f6204,f1898]) ).
fof(f29069,plain,
( spl0_988
| ~ spl0_330
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6068,f5555,f4027,f29067]) ).
fof(f6068,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(X1,X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) )
| ~ spl0_330
| ~ spl0_388 ),
inference(resolution,[],[f5556,f4028]) ).
fof(f29065,plain,
( spl0_987
| ~ spl0_333
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6066,f5555,f4039,f29063]) ).
fof(f6066,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(X1,X2,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) )
| ~ spl0_333
| ~ spl0_388 ),
inference(resolution,[],[f5556,f4040]) ).
fof(f29061,plain,
( spl0_986
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5788,f5531,f29059]) ).
fof(f29059,plain,
( spl0_986
<=> ! [X3,X4,X0,X5,X2,X1] : hAPP(c_split(X0,X1,X2,X4),X3) = hAPP(c_split(X0,X1,X2,X5),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f5788,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(c_split(X0,X1,X2,X4),X3) = hAPP(c_split(X0,X1,X2,X5),X3)
| ~ spl0_382 ),
inference(superposition,[],[f5532,f5532]) ).
fof(f29057,plain,
( spl0_985
| ~ spl0_250
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5495,f5102,f2937,f29055]) ).
fof(f29055,plain,
( spl0_985
<=> ! [X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f5495,plain,
( ! [X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1 )
| ~ spl0_250
| ~ spl0_377 ),
inference(resolution,[],[f5103,f2938]) ).
fof(f29053,plain,
( spl0_984
| ~ spl0_331
| ~ spl0_750 ),
inference(avatar_split_clause,[],[f21226,f21181,f4031,f29051]) ).
fof(f29051,plain,
( spl0_984
<=> ! [X2,X0,X1] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Set_Oinsert(X1,v_Lab____,X2),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f21226,plain,
( ! [X2,X0,X1] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Set_Oinsert(X1,v_Lab____,X2),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_331
| ~ spl0_750 ),
inference(resolution,[],[f21182,f4032]) ).
fof(f29049,plain,
( spl0_983
| ~ spl0_253
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5494,f5102,f2949,f29047]) ).
fof(f29047,plain,
( spl0_983
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Arrow__Order__Mirabelle_Omktop(X1,X2),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f5494,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Arrow__Order__Mirabelle_Omktop(X1,X2),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 )
| ~ spl0_253
| ~ spl0_377 ),
inference(resolution,[],[f5103,f2950]) ).
fof(f29045,plain,
( spl0_982
| ~ spl0_252
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5493,f5102,f2945,f29043]) ).
fof(f29043,plain,
( spl0_982
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f5493,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 )
| ~ spl0_252
| ~ spl0_377 ),
inference(resolution,[],[f5103,f2946]) ).
fof(f29041,plain,
( spl0_981
| ~ spl0_299
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5484,f5102,f3469,f29039]) ).
fof(f29039,plain,
( spl0_981
<=> ! [X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1),X1)
| c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f5484,plain,
( ! [X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1),X1)
| c_Relation_Oirrefl(X0,X1) )
| ~ spl0_299
| ~ spl0_377 ),
inference(resolution,[],[f5103,f3470]) ).
fof(f29037,plain,
( spl0_980
| ~ spl0_132
| ~ spl0_307
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5481,f5098,f3501,f1482,f29035]) ).
fof(f29035,plain,
( spl0_980
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f1482,plain,
( spl0_132
<=> ! [X2,X4] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X4,X2),X2,X2) = c_Relation_ORange(X4,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f5481,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2)
| ~ spl0_132
| ~ spl0_307
| ~ spl0_376 ),
inference(forward_demodulation,[],[f5462,f1483]) ).
fof(f1483,plain,
( ! [X2,X4] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X4,X2),X2,X2) = c_Relation_ORange(X4,X2,X2)
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1482]) ).
fof(f5462,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2),X2)
| ~ spl0_307
| ~ spl0_376 ),
inference(resolution,[],[f5099,f3502]) ).
fof(f29033,plain,
( spl0_979
| ~ spl0_267
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4988,f4541,f3175,f29031]) ).
fof(f29031,plain,
( spl0_979
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),X1,X1),X2),X3))
| c_in(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f4988,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),X1,X1),X2),X3))
| c_in(X2,X0,X1) )
| ~ spl0_267
| ~ spl0_354 ),
inference(resolution,[],[f4542,f3176]) ).
fof(f29029,plain,
( spl0_978
| ~ spl0_268
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4970,f4537,f3179,f29027]) ).
fof(f29027,plain,
( spl0_978
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),X1,X1),X2),X2))
| ~ c_in(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f4970,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),X1,X1),X2),X2))
| ~ c_in(X2,X0,X1) )
| ~ spl0_268
| ~ spl0_353 ),
inference(resolution,[],[f4538,f3180]) ).
fof(f29025,plain,
( spl0_977
| ~ spl0_62
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3851,f3469,f1108,f29023]) ).
fof(f29023,plain,
( spl0_977
<=> ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| hBOOL(hAPP(X0,c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f3851,plain,
( ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| hBOOL(hAPP(X0,c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X1,X1))) )
| ~ spl0_62
| ~ spl0_299 ),
inference(resolution,[],[f3470,f1109]) ).
fof(f29021,plain,
( spl0_976
| ~ spl0_106
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3688,f3425,f1375,f29019]) ).
fof(f29019,plain,
( spl0_976
<=> ! [X2,X0,X1] : c_lessequals(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_Set_Oinsert(X0,X2,X1),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f3688,plain,
( ! [X2,X0,X1] : c_lessequals(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_Set_Oinsert(X0,X2,X1),tc_fun(X1,tc_bool))
| ~ spl0_106
| ~ spl0_288 ),
inference(superposition,[],[f1376,f3426]) ).
fof(f29017,plain,
( spl0_975
| ~ spl0_196
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3654,f3417,f2283,f29015]) ).
fof(f29015,plain,
( spl0_975
<=> ! [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_975])]) ).
fof(f3654,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_196
| ~ spl0_286 ),
inference(superposition,[],[f3418,f2284]) ).
fof(f29013,plain,
( spl0_974
| ~ spl0_6
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3574,f3393,f876,f29011]) ).
fof(f29011,plain,
( spl0_974
<=> ! [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_974])]) ).
fof(f876,plain,
( spl0_6
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f3393,plain,
( spl0_280
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f3574,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_6
| ~ spl0_280 ),
inference(resolution,[],[f3394,f878]) ).
fof(f878,plain,
( class_Lattices_Olattice(tc_bool)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f3394,plain,
( ! [X2,X6,X7,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2) )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f3393]) ).
fof(f29009,plain,
( spl0_973
| ~ spl0_330
| ~ spl0_750 ),
inference(avatar_split_clause,[],[f21225,f21181,f4027,f29007]) ).
fof(f29007,plain,
( spl0_973
<=> ! [X2,X0,X1] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Set_Oinsert(X1,v_Lab____,X2),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f21225,plain,
( ! [X2,X0,X1] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Set_Oinsert(X1,v_Lab____,X2),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_330
| ~ spl0_750 ),
inference(resolution,[],[f21182,f4028]) ).
fof(f29005,plain,
( spl0_972
| ~ spl0_6
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3572,f3389,f876,f29003]) ).
fof(f29003,plain,
( spl0_972
<=> ! [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_972])]) ).
fof(f3389,plain,
( spl0_279
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X22,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f3572,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_6
| ~ spl0_279 ),
inference(resolution,[],[f3390,f878]) ).
fof(f3390,plain,
( ! [X2,X6,X7,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X22,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f3389]) ).
fof(f29001,plain,
( spl0_971
| ~ spl0_1
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3522,f3368,f851,f28999]) ).
fof(f28999,plain,
( spl0_971
<=> ! [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_971])]) ).
fof(f851,plain,
( spl0_1
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f3368,plain,
( spl0_274
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f3522,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_1
| ~ spl0_274 ),
inference(resolution,[],[f3369,f853]) ).
fof(f853,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f851]) ).
fof(f3369,plain,
( ! [X2,X6,X7,X22] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f3368]) ).
fof(f28997,plain,
( spl0_970
| ~ spl0_1
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3520,f3364,f851,f28995]) ).
fof(f28995,plain,
( spl0_970
<=> ! [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_970])]) ).
fof(f3364,plain,
( spl0_273
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X22,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f3520,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_1
| ~ spl0_273 ),
inference(resolution,[],[f3365,f853]) ).
fof(f3365,plain,
( ! [X2,X6,X7,X22] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X22,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f3364]) ).
fof(f28993,plain,
( spl0_969
| ~ spl0_243
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3344,f3179,f2909,f28991]) ).
fof(f28991,plain,
( spl0_969
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,c_Pair(X0,X0,X2,X2),X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f2909,plain,
( spl0_243
<=> ! [X2,X5,X19] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X5,X19,X2),X5,X2)
| ~ c_in(X19,c_Relation_OId__on(X5,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f3344,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,c_Pair(X0,X0,X2,X2),X2),X1,X2) )
| ~ spl0_243
| ~ spl0_268 ),
inference(resolution,[],[f3180,f2910]) ).
fof(f2910,plain,
( ! [X2,X19,X5] :
( ~ c_in(X19,c_Relation_OId__on(X5,X2),tc_prod(X2,X2))
| c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X5,X19,X2),X5,X2) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2909]) ).
fof(f28989,plain,
( spl0_968
| ~ spl0_117
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3294,f3147,f1422,f28987]) ).
fof(f28987,plain,
( spl0_968
<=> ! [X0,X3,X2,X1] :
( c_Relation_Osingle__valued(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3)
| ~ c_Relation_Osingle__valued(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f3294,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Osingle__valued(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3)
| ~ c_Relation_Osingle__valued(X0,X2,X3) )
| ~ spl0_117
| ~ spl0_260 ),
inference(resolution,[],[f3148,f1423]) ).
fof(f28985,plain,
( spl0_967
| ~ spl0_116
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3287,f3147,f1418,f28983]) ).
fof(f28983,plain,
( spl0_967
<=> ! [X0,X3,X2,X1] :
( c_Relation_Osingle__valued(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3)
| ~ c_Relation_Osingle__valued(X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f3287,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Osingle__valued(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3)
| ~ c_Relation_Osingle__valued(X1,X2,X3) )
| ~ spl0_116
| ~ spl0_260 ),
inference(resolution,[],[f3148,f1419]) ).
fof(f28981,plain,
( spl0_966
| ~ spl0_115
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3286,f3147,f1414,f28979]) ).
fof(f28979,plain,
( spl0_966
<=> ! [X0,X3,X2,X1] :
( c_Relation_Osingle__valued(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3)
| ~ c_Relation_Osingle__valued(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f3286,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Osingle__valued(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3)
| ~ c_Relation_Osingle__valued(X0,X2,X3) )
| ~ spl0_115
| ~ spl0_260 ),
inference(resolution,[],[f3148,f1415]) ).
fof(f28977,plain,
( spl0_965
| ~ spl0_106
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3275,f3147,f1375,f28975]) ).
fof(f28975,plain,
( spl0_965
<=> ! [X0,X3,X2,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| ~ c_Relation_Osingle__valued(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f3275,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| ~ c_Relation_Osingle__valued(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) )
| ~ spl0_106
| ~ spl0_260 ),
inference(resolution,[],[f3148,f1376]) ).
fof(f28973,plain,
( spl0_964
| ~ spl0_105
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3274,f3147,f1371,f28971]) ).
fof(f28971,plain,
( spl0_964
<=> ! [X2,X0,X1,X3] :
( c_Relation_Osingle__valued(X0,X1,X2)
| ~ c_Relation_Osingle__valued(c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f3274,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| ~ c_Relation_Osingle__valued(c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) )
| ~ spl0_105
| ~ spl0_260 ),
inference(resolution,[],[f3148,f1372]) ).
fof(f28909,plain,
( spl0_963
| ~ spl0_611
| ~ spl0_730 ),
inference(avatar_split_clause,[],[f21096,f20579,f16740,f28907]) ).
fof(f28907,plain,
( spl0_963
<=> ! [X0,X1] : ~ c_in(v_b____,hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f16740,plain,
( spl0_611
<=> ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f20579,plain,
( spl0_730
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f21096,plain,
( ! [X0,X1] : ~ c_in(v_b____,hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_611
| ~ spl0_730 ),
inference(resolution,[],[f20580,f16741]) ).
fof(f16741,plain,
( ! [X0] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_611 ),
inference(avatar_component_clause,[],[f16740]) ).
fof(f20580,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2))
| ~ spl0_730 ),
inference(avatar_component_clause,[],[f20579]) ).
fof(f28905,plain,
( spl0_962
| ~ spl0_9
| ~ spl0_105
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3250,f3143,f1371,f891,f28903]) ).
fof(f28903,plain,
( spl0_962
<=> ! [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_962])]) ).
fof(f3250,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_105
| ~ spl0_259 ),
inference(resolution,[],[f3144,f1372]) ).
fof(f28901,plain,
( spl0_961
| ~ spl0_72
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f3052,f2897,f1163,f28899]) ).
fof(f28899,plain,
( spl0_961
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool))
| c_Set_Oinsert(X0,X1,X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2897,plain,
( spl0_240
<=> ! [X9,X5,X2] :
( X5 = X9
| ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X5,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f3052,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool))
| c_Set_Oinsert(X0,X1,X2) = X1 )
| ~ spl0_72
| ~ spl0_240 ),
inference(resolution,[],[f2898,f1164]) ).
fof(f2898,plain,
( ! [X2,X9,X5] :
( ~ c_lessequals(X9,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| X5 = X9 )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2897]) ).
fof(f28897,plain,
( spl0_960
| ~ spl0_72
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f3011,f2889,f1163,f28895]) ).
fof(f28895,plain,
( spl0_960
<=> ! [X0,X3,X2,X1] : c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f3011,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),tc_fun(X3,tc_bool))
| ~ spl0_72
| ~ spl0_238 ),
inference(superposition,[],[f1164,f2890]) ).
fof(f28893,plain,
( spl0_959
| ~ spl0_48
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2836,f2413,f1050,f28891]) ).
fof(f2836,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_in(X0,c_Set_Oimage(c_COMBK(X0,X1,X2),X4,X5,X6),X6)
| ~ c_in(X3,X4,X5) )
| ~ spl0_48
| ~ spl0_226 ),
inference(superposition,[],[f2414,f1051]) ).
fof(f28889,plain,
( spl0_958
| ~ spl0_185
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2828,f2397,f1889,f28887]) ).
fof(f28887,plain,
( spl0_958
<=> ! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2828,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(X2,X1),X1) )
| ~ spl0_185
| ~ spl0_222 ),
inference(resolution,[],[f2398,f1890]) ).
fof(f28885,plain,
( spl0_957
| ~ spl0_188
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2827,f2397,f1901,f28883]) ).
fof(f28883,plain,
( spl0_957
<=> ! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2827,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))
| ~ c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X2,X1),X1) )
| ~ spl0_188
| ~ spl0_222 ),
inference(resolution,[],[f2398,f1902]) ).
fof(f28881,plain,
( spl0_956
| ~ spl0_79
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2709,f2361,f1191,f28879]) ).
fof(f28879,plain,
( spl0_956
<=> ! [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_956])]) ).
fof(f2361,plain,
( spl0_213
<=> ! [X7,X22,X6,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X6,X7,X2)
| ~ c_lessequals(X7,X22,X2)
| c_lessequals(X6,X22,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f2709,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_79
| ~ spl0_213 ),
inference(resolution,[],[f2362,f1192]) ).
fof(f2362,plain,
( ! [X2,X6,X7,X22] :
( ~ c_lessequals(X7,X22,X2)
| ~ c_lessequals(X6,X7,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X6,X22,X2) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2361]) ).
fof(f28877,plain,
( spl0_955
| ~ spl0_78
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2707,f2361,f1187,f28875]) ).
fof(f28875,plain,
( spl0_955
<=> ! [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_955])]) ).
fof(f2707,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_78
| ~ spl0_213 ),
inference(resolution,[],[f2362,f1188]) ).
fof(f28873,plain,
( spl0_954
| ~ spl0_69
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2697,f2361,f1150,f28871]) ).
fof(f28871,plain,
( spl0_954
<=> ! [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_954])]) ).
fof(f2697,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_69
| ~ spl0_213 ),
inference(resolution,[],[f2362,f1151]) ).
fof(f28869,plain,
( spl0_953
| ~ spl0_70
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2695,f2361,f1154,f28867]) ).
fof(f28867,plain,
( spl0_953
<=> ! [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_953])]) ).
fof(f2695,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_70
| ~ spl0_213 ),
inference(resolution,[],[f2362,f1155]) ).
fof(f28864,plain,
( spl0_952
| ~ spl0_79
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2680,f2347,f1191,f28862]) ).
fof(f28862,plain,
( spl0_952
<=> ! [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_952])]) ).
fof(f2347,plain,
( spl0_212
<=> ! [X7,X22,X6,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X7,X6,X2)
| ~ c_lessequals(X22,X7,X2)
| c_lessequals(X22,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2680,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_79
| ~ spl0_212 ),
inference(resolution,[],[f2348,f1192]) ).
fof(f2348,plain,
( ! [X2,X6,X7,X22] :
( ~ c_lessequals(X22,X7,X2)
| ~ c_lessequals(X7,X6,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X22,X6,X2) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2347]) ).
fof(f28860,plain,
( spl0_951
| ~ spl0_78
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2678,f2347,f1187,f28858]) ).
fof(f28858,plain,
( spl0_951
<=> ! [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_951])]) ).
fof(f2678,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_78
| ~ spl0_212 ),
inference(resolution,[],[f2348,f1188]) ).
fof(f28856,plain,
( spl0_950
| ~ spl0_69
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2668,f2347,f1150,f28854]) ).
fof(f28854,plain,
( spl0_950
<=> ! [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_950])]) ).
fof(f2668,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_69
| ~ spl0_212 ),
inference(resolution,[],[f2348,f1151]) ).
fof(f28852,plain,
( spl0_949
| ~ spl0_70
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2666,f2347,f1154,f28850]) ).
fof(f28850,plain,
( spl0_949
<=> ! [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_949])]) ).
fof(f2666,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_70
| ~ spl0_212 ),
inference(resolution,[],[f2348,f1155]) ).
fof(f28848,plain,
( spl0_948
| ~ spl0_112
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2613,f2311,f1402,f28846]) ).
fof(f28846,plain,
( spl0_948
<=> ! [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_948])]) ).
fof(f2613,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_112
| ~ spl0_203 ),
inference(superposition,[],[f2312,f1403]) ).
fof(f28844,plain,
( spl0_947
| ~ spl0_98
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2245,f1897,f1320,f28842]) ).
fof(f28842,plain,
( spl0_947
<=> ! [X2,X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| c_Set_Oinsert(c_Pair(X2,X2,X1,X1),X0,tc_prod(X1,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f2245,plain,
( ! [X2,X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| c_Set_Oinsert(c_Pair(X2,X2,X1,X1),X0,tc_prod(X1,X1)) = X0 )
| ~ spl0_98
| ~ spl0_187 ),
inference(resolution,[],[f1898,f1321]) ).
fof(f28840,plain,
( spl0_946
| ~ spl0_98
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f2235,f1885,f1320,f28838]) ).
fof(f28838,plain,
( spl0_946
<=> ! [X0,X1] :
( X0 = X1
| c_Arrow__Order__Mirabelle_OLin = c_Set_Oinsert(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f1885,plain,
( spl0_184
<=> ! [X0,X1] :
( X0 = X1
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f2235,plain,
( ! [X0,X1] :
( X0 = X1
| c_Arrow__Order__Mirabelle_OLin = c_Set_Oinsert(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_98
| ~ spl0_184 ),
inference(resolution,[],[f1886,f1321]) ).
fof(f1886,plain,
( ! [X0,X1] :
( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X0 = X1 )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1885]) ).
fof(f28836,plain,
( spl0_945
| ~ spl0_112
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1956,f1768,f1402,f28834]) ).
fof(f28834,plain,
( spl0_945
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f1956,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool)) = X1
| ~ spl0_112
| ~ spl0_156 ),
inference(superposition,[],[f1403,f1769]) ).
fof(f28832,plain,
( spl0_944
| ~ spl0_111
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1955,f1768,f1398,f28830]) ).
fof(f28830,plain,
( spl0_944
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1,tc_fun(tc_prod(X0,X0),tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f1955,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1,tc_fun(tc_prod(X0,X0),tc_bool)) = X1
| ~ spl0_111
| ~ spl0_156 ),
inference(superposition,[],[f1399,f1769]) ).
fof(f28828,plain,
( spl0_943
| ~ spl0_109
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1954,f1768,f1387,f28826]) ).
fof(f28826,plain,
( spl0_943
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1387,plain,
( spl0_109
<=> ! [X2,X5] : c_HOL_Ominus__class_Ominus(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1954,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool)) = X1
| ~ spl0_109
| ~ spl0_156 ),
inference(superposition,[],[f1388,f1769]) ).
fof(f1388,plain,
( ! [X2,X5] : c_HOL_Ominus__class_Ominus(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1387]) ).
fof(f28823,plain,
( spl0_942
| ~ spl0_26
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1537,f1430,f961,f28821]) ).
fof(f28821,plain,
( spl0_942
<=> ! [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_942])]) ).
fof(f961,plain,
( spl0_26
<=> ! [X55,X56] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Oupper__semilattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1430,plain,
( spl0_119
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1537,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_26
| ~ spl0_119 ),
inference(resolution,[],[f1431,f962]) ).
fof(f962,plain,
( ! [X56,X55] :
( class_Lattices_Oupper__semilattice(tc_fun(X55,X56))
| ~ class_Lattices_Olattice(X56) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f961]) ).
fof(f1431,plain,
( ! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1430]) ).
fof(f28819,plain,
( spl0_941
| ~ spl0_31
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1527,f1410,f981,f28817]) ).
fof(f28817,plain,
( spl0_941
<=> ! [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_941])]) ).
fof(f981,plain,
( spl0_31
<=> ! [X55,X56] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Olattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1410,plain,
( spl0_114
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1527,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_31
| ~ spl0_114 ),
inference(resolution,[],[f1411,f982]) ).
fof(f982,plain,
( ! [X56,X55] :
( class_Lattices_Olattice(tc_fun(X55,X56))
| ~ class_Lattices_Olattice(X56) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f1411,plain,
( ! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) = X6 )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1410]) ).
fof(f28815,plain,
( spl0_940
| ~ spl0_31
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1525,f1406,f981,f28813]) ).
fof(f28813,plain,
( spl0_940
<=> ! [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_940])]) ).
fof(f1406,plain,
( spl0_113
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1525,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_31
| ~ spl0_113 ),
inference(resolution,[],[f1407,f982]) ).
fof(f1407,plain,
( ! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) = X6 )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1406]) ).
fof(f28811,plain,
( spl0_939
| ~ spl0_27
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1505,f1379,f965,f28809]) ).
fof(f28809,plain,
( spl0_939
<=> ! [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_939])]) ).
fof(f965,plain,
( spl0_27
<=> ! [X55,X56] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Olower__semilattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1379,plain,
( spl0_107
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1505,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_27
| ~ spl0_107 ),
inference(resolution,[],[f1380,f966]) ).
fof(f966,plain,
( ! [X56,X55] :
( class_Lattices_Olower__semilattice(tc_fun(X55,X56))
| ~ class_Lattices_Olattice(X56) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f1380,plain,
( ! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1379]) ).
fof(f28574,plain,
( spl0_938
| ~ spl0_353
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f22983,f22917,f4537,f28572]) ).
fof(f22983,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____))
| ~ spl0_353
| ~ spl0_821 ),
inference(resolution,[],[f22918,f4538]) ).
fof(f28372,plain,
( spl0_937
| ~ spl0_391
| ~ spl0_752 ),
inference(avatar_split_clause,[],[f22494,f21189,f5598,f28370]) ).
fof(f5598,plain,
( spl0_391
<=> ! [X0] : c_in(v_a____,hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f22494,plain,
( ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X0),v_a____))
| ~ spl0_391
| ~ spl0_752 ),
inference(resolution,[],[f21190,f5599]) ).
fof(f5599,plain,
( ! [X0] : c_in(v_a____,hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X0)
| ~ spl0_391 ),
inference(avatar_component_clause,[],[f5598]) ).
fof(f27908,plain,
( spl0_936
| ~ spl0_61
| ~ spl0_933 ),
inference(avatar_split_clause,[],[f27356,f27272,f1104,f27906]) ).
fof(f27906,plain,
( spl0_936
<=> ! [X2,X0,X1] : c_in(v_a____,c_Relation_ORange(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f27272,plain,
( spl0_933
<=> ! [X0,X1] : hBOOL(hAPP(c_Relation_ORange(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f27356,plain,
( ! [X2,X0,X1] : c_in(v_a____,c_Relation_ORange(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2)
| ~ spl0_61
| ~ spl0_933 ),
inference(resolution,[],[f27273,f1105]) ).
fof(f27273,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_ORange(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____))
| ~ spl0_933 ),
inference(avatar_component_clause,[],[f27272]) ).
fof(f27282,plain,
( spl0_935
| ~ spl0_111
| ~ spl0_197
| ~ spl0_516 ),
inference(avatar_split_clause,[],[f12082,f12031,f2287,f1398,f27280]) ).
fof(f27280,plain,
( spl0_935
<=> ! [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_935])]) ).
fof(f12031,plain,
( spl0_516
<=> ! [X9,X11,X5,X2] :
( c_lessequals(X11,X5,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f12082,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_111
| ~ spl0_197
| ~ spl0_516 ),
inference(forward_demodulation,[],[f12054,f1399]) ).
fof(f12054,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_197
| ~ spl0_516 ),
inference(superposition,[],[f12032,f2288]) ).
fof(f12032,plain,
( ! [X2,X11,X9,X5] :
( c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool))
| c_lessequals(X11,X5,tc_fun(X2,tc_bool)) )
| ~ spl0_516 ),
inference(avatar_component_clause,[],[f12031]) ).
fof(f27278,plain,
( spl0_934
| ~ spl0_380
| ~ spl0_473 ),
inference(avatar_split_clause,[],[f9587,f9298,f5522,f27276]) ).
fof(f27276,plain,
( spl0_934
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Relation_OImage(X0,X1,X2,X2),X3,tc_fun(X2,tc_bool))
| ~ c_Relation_Orefl__on(X3,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f5522,plain,
( spl0_380
<=> ! [X2,X5,X4] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f9587,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Relation_OImage(X0,X1,X2,X2),X3,tc_fun(X2,tc_bool))
| ~ c_Relation_Orefl__on(X3,X0,X2) )
| ~ spl0_380
| ~ spl0_473 ),
inference(resolution,[],[f9299,f5523]) ).
fof(f5523,plain,
( ! [X2,X4,X5] :
( c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Orefl__on(X5,X4,X2) )
| ~ spl0_380 ),
inference(avatar_component_clause,[],[f5522]) ).
fof(f27274,plain,
( spl0_933
| ~ spl0_62
| ~ spl0_769 ),
inference(avatar_split_clause,[],[f22192,f21380,f1108,f27272]) ).
fof(f21380,plain,
( spl0_769
<=> ! [X0,X1] : c_in(v_a____,c_Relation_ORange(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f22192,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_ORange(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____))
| ~ spl0_62
| ~ spl0_769 ),
inference(resolution,[],[f21381,f1109]) ).
fof(f21381,plain,
( ! [X0,X1] : c_in(v_a____,c_Relation_ORange(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_769 ),
inference(avatar_component_clause,[],[f21380]) ).
fof(f27270,plain,
( spl0_932
| ~ spl0_386
| ~ spl0_473 ),
inference(avatar_split_clause,[],[f9586,f9298,f5547,f27268]) ).
fof(f27268,plain,
( spl0_932
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Relation_OImage(X0,X1,X2,X2),X3,tc_fun(X2,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X3,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f5547,plain,
( spl0_386
<=> ! [X2,X5,X4] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f9586,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Relation_OImage(X0,X1,X2,X2),X3,tc_fun(X2,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X3,X0,X2) )
| ~ spl0_386
| ~ spl0_473 ),
inference(resolution,[],[f9299,f5548]) ).
fof(f5548,plain,
( ! [X2,X4,X5] :
( c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2) )
| ~ spl0_386 ),
inference(avatar_component_clause,[],[f5547]) ).
fof(f27266,plain,
( spl0_931
| ~ spl0_110
| ~ spl0_364
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f9373,f9274,f5050,f1394,f27264]) ).
fof(f27264,plain,
( spl0_931
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f5050,plain,
( spl0_364
<=> ! [X5,X2,X0] : c_Set_Oinsert(X0,X5,X2) = c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f9373,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool))
| ~ spl0_110
| ~ spl0_364
| ~ spl0_467 ),
inference(forward_demodulation,[],[f9350,f5051]) ).
fof(f5051,plain,
( ! [X2,X0,X5] : c_Set_Oinsert(X0,X5,X2) = c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f5050]) ).
fof(f9350,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool))
| ~ spl0_110
| ~ spl0_467 ),
inference(superposition,[],[f9275,f1395]) ).
fof(f27262,plain,
( spl0_930
| ~ spl0_148
| ~ spl0_462 ),
inference(avatar_split_clause,[],[f9064,f8835,f1618,f27260]) ).
fof(f8835,plain,
( spl0_462
<=> ! [X7,X8,X6,X2] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X8,X6,X7,X2),X7,X2,X2),X8,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f9064,plain,
( ! [X2,X0,X1] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_148
| ~ spl0_462 ),
inference(resolution,[],[f8836,f1619]) ).
fof(f8836,plain,
( ! [X2,X8,X6,X7] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X8,X6,X7,X2),X7,X2,X2),X8,tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2)) )
| ~ spl0_462 ),
inference(avatar_component_clause,[],[f8835]) ).
fof(f27258,plain,
( spl0_929
| ~ spl0_147
| ~ spl0_461 ),
inference(avatar_split_clause,[],[f8997,f8831,f1614,f27256]) ).
fof(f1614,plain,
( spl0_147
<=> ! [X6,X40,X7] : ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f8831,plain,
( spl0_461
<=> ! [X7,X8,X6,X2] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X8,X6,X7,X2),X2,X2),X8,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f8997,plain,
( ! [X2,X0,X1] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_147
| ~ spl0_461 ),
inference(resolution,[],[f8832,f1615]) ).
fof(f1615,plain,
( ! [X40,X6,X7] : ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1614]) ).
fof(f8832,plain,
( ! [X2,X8,X6,X7] :
( c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X8,X6,X7,X2),X2,X2),X8,tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2)) )
| ~ spl0_461 ),
inference(avatar_component_clause,[],[f8831]) ).
fof(f27254,plain,
( spl0_928
| ~ spl0_59
| ~ spl0_267
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f6138,f5559,f3175,f1096,f27252]) ).
fof(f27252,plain,
( spl0_928
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f6138,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2),X1,X2) )
| ~ spl0_59
| ~ spl0_267
| ~ spl0_389 ),
inference(forward_demodulation,[],[f6104,f1097]) ).
fof(f6104,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2),X2)
| c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2),X1,X2) )
| ~ spl0_267
| ~ spl0_389 ),
inference(resolution,[],[f5560,f3176]) ).
fof(f27250,plain,
( spl0_927
| ~ spl0_59
| ~ spl0_267
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6097,f5555,f3175,f1096,f27248]) ).
fof(f27248,plain,
( spl0_927
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f6097,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2),X1,X2) )
| ~ spl0_59
| ~ spl0_267
| ~ spl0_388 ),
inference(forward_demodulation,[],[f6063,f1097]) ).
fof(f6063,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2),X2)
| c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2),X1,X2) )
| ~ spl0_267
| ~ spl0_388 ),
inference(resolution,[],[f5556,f3176]) ).
fof(f27246,plain,
( spl0_926
| ~ spl0_38
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f5007,f4541,f1009,f27244]) ).
fof(f27244,plain,
( spl0_926
<=> ! [X0,X3,X2,X1] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X0,X1),X2),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f1009,plain,
( spl0_38
<=> ! [X6,X2] : ~ c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f5007,plain,
( ! [X2,X3,X0,X1] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X0,X1),X2),X3))
| ~ spl0_38
| ~ spl0_354 ),
inference(resolution,[],[f4542,f1010]) ).
fof(f1010,plain,
( ! [X2,X6] : ~ c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1009]) ).
fof(f27242,plain,
( spl0_925
| ~ spl0_244
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4999,f4541,f2913,f27240]) ).
fof(f27240,plain,
( spl0_925
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X2),X2))
| ~ c_Wellfounded_Oacyclic(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f2913,plain,
( spl0_244
<=> ! [X6,X2,X4] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| ~ c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f4999,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X2),X2))
| ~ c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl0_244
| ~ spl0_354 ),
inference(resolution,[],[f4542,f2914]) ).
fof(f2914,plain,
( ! [X2,X6,X4] :
( ~ c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_Wellfounded_Oacyclic(X4,X2) )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2913]) ).
fof(f27238,plain,
( spl0_924
| ~ spl0_249
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4989,f4541,f2933,f27236]) ).
fof(f27236,plain,
( spl0_924
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),X1,X1),X2),X3))
| X2 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f4989,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),X1,X1),X2),X3))
| X2 = X3 )
| ~ spl0_249
| ~ spl0_354 ),
inference(resolution,[],[f4542,f2934]) ).
fof(f27234,plain,
( spl0_923
| ~ spl0_250
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4974,f4537,f2937,f27232]) ).
fof(f27232,plain,
( spl0_923
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f4974,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))
| X0 = X1 )
| ~ spl0_250
| ~ spl0_353 ),
inference(resolution,[],[f4538,f2938]) ).
fof(f27230,plain,
( spl0_922
| ~ spl0_253
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4973,f4537,f2949,f27228]) ).
fof(f27228,plain,
( spl0_922
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f4973,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1))
| X1 = X2 )
| ~ spl0_253
| ~ spl0_353 ),
inference(resolution,[],[f4538,f2950]) ).
fof(f27226,plain,
( spl0_921
| ~ spl0_252
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4972,f4537,f2945,f27224]) ).
fof(f27224,plain,
( spl0_921
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f4972,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2))
| X1 = X2 )
| ~ spl0_252
| ~ spl0_353 ),
inference(resolution,[],[f4538,f2946]) ).
fof(f27222,plain,
( spl0_920
| ~ spl0_230
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4934,f4533,f2429,f27220]) ).
fof(f27220,plain,
( spl0_920
<=> ! [X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId(X1),X1),X1)
| c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId(X1),X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f4934,plain,
( ! [X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId(X1),X1),X1)
| c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId(X1),X0,X1) = X0 )
| ~ spl0_230
| ~ spl0_352 ),
inference(resolution,[],[f4534,f2430]) ).
fof(f27218,plain,
( spl0_919
| ~ spl0_330
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4908,f4529,f4027,f27216]) ).
fof(f27216,plain,
( spl0_919
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f4908,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) )
| ~ spl0_330
| ~ spl0_351 ),
inference(resolution,[],[f4530,f4028]) ).
fof(f27214,plain,
( spl0_918
| ~ spl0_333
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4906,f4529,f4039,f27212]) ).
fof(f27212,plain,
( spl0_918
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f4906,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(X0,X3,X2)
| ~ c_Relation_Orefl__on(X3,X1,X2) )
| ~ spl0_333
| ~ spl0_351 ),
inference(resolution,[],[f4530,f4040]) ).
fof(f27210,plain,
( spl0_917
| ~ spl0_230
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4902,f4529,f2429,f27208]) ).
fof(f27208,plain,
( spl0_917
<=> ! [X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId(X1),X1),X1)
| c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId(X1),X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f4902,plain,
( ! [X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId(X1),X1),X1)
| c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId(X1),X0,X1) = X0 )
| ~ spl0_230
| ~ spl0_351 ),
inference(resolution,[],[f4530,f2430]) ).
fof(f27206,plain,
( spl0_916
| ~ spl0_322
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4853,f4513,f3994,f27204]) ).
fof(f27204,plain,
( spl0_916
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Transitive__Closure_Otrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f3994,plain,
( spl0_322
<=> ! [X2,X5,X9] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f4853,plain,
( ! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Transitive__Closure_Otrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool))
| ~ spl0_322
| ~ spl0_347 ),
inference(superposition,[],[f3995,f4514]) ).
fof(f3995,plain,
( ! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f3994]) ).
fof(f27202,plain,
( spl0_915
| ~ spl0_53
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f4683,f4481,f1072,f27200]) ).
fof(f27200,plain,
( spl0_915
<=> ! [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_915])]) ).
fof(f4481,plain,
( spl0_339
<=> ! [X2,X5,X9] :
( c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f4683,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_53
| ~ spl0_339 ),
inference(superposition,[],[f4482,f1073]) ).
fof(f4482,plain,
( ! [X2,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)) = X5 )
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f4481]) ).
fof(f27198,plain,
( spl0_914
| ~ spl0_268
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4436,f4039,f3179,f27196]) ).
fof(f27196,plain,
( spl0_914
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,c_Relation_OId__on(X3,X2),X2)
| ~ c_in(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f4436,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,c_Relation_OId__on(X3,X2),X2)
| ~ c_in(X0,X3,X2) )
| ~ spl0_268
| ~ spl0_333 ),
inference(resolution,[],[f4040,f3180]) ).
fof(f27194,plain,
( spl0_913
| ~ spl0_268
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4395,f4027,f3179,f27192]) ).
fof(f27192,plain,
( spl0_913
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_OId__on(X3,X2),X2)
| ~ c_in(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f4395,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_OId__on(X3,X2),X2)
| ~ c_in(X0,X3,X2) )
| ~ spl0_268
| ~ spl0_330 ),
inference(resolution,[],[f4028,f3180]) ).
fof(f27190,plain,
( spl0_912
| ~ spl0_62
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f4391,f4023,f1108,f27188]) ).
fof(f27188,plain,
( spl0_912
<=> ! [X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omktop(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f4023,plain,
( spl0_329
<=> ! [X6,X40] :
( ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(X40,X6),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f4391,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omktop(X0,X1))) )
| ~ spl0_62
| ~ spl0_329 ),
inference(resolution,[],[f4024,f1109]) ).
fof(f4024,plain,
( ! [X40,X6] :
( c_in(c_Arrow__Order__Mirabelle_Omktop(X40,X6),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f4023]) ).
fof(f27186,plain,
( spl0_911
| ~ spl0_62
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4387,f4019,f1108,f27184]) ).
fof(f27184,plain,
( spl0_911
<=> ! [X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omkbot(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f4019,plain,
( spl0_328
<=> ! [X6,X40] :
( ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omkbot(X40,X6),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f4387,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Omkbot(X0,X1))) )
| ~ spl0_62
| ~ spl0_328 ),
inference(resolution,[],[f4020,f1109]) ).
fof(f4020,plain,
( ! [X40,X6] :
( c_in(c_Arrow__Order__Mirabelle_Omkbot(X40,X6),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_328 ),
inference(avatar_component_clause,[],[f4019]) ).
fof(f27182,plain,
( spl0_910
| ~ spl0_56
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3891,f3485,f1084,f27180]) ).
fof(f27180,plain,
( spl0_910
<=> ! [X2,X0,X1] :
( ~ c_in(X2,X1,X0)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X1,X2,c_Relation_OId(X0),X0,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1084,plain,
( spl0_56
<=> ! [X2,X5] : c_Relation_OImage(c_Relation_OId(X2),X5,X2,X2) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f3485,plain,
( spl0_303
<=> ! [X3,X4,X5,X2,X1] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X5,X1,X4,X3,X2),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f3891,plain,
( ! [X2,X0,X1] :
( ~ c_in(X2,X1,X0)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X1,X2,c_Relation_OId(X0),X0,X0),X1,X0) )
| ~ spl0_56
| ~ spl0_303 ),
inference(superposition,[],[f3486,f1085]) ).
fof(f1085,plain,
( ! [X2,X5] : c_Relation_OImage(c_Relation_OId(X2),X5,X2,X2) = X5
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f3486,plain,
( ! [X2,X3,X1,X4,X5] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X5,X1,X4,X3,X2),X5,X3) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f3485]) ).
fof(f27178,plain,
( spl0_909
| ~ spl0_56
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3870,f3477,f1084,f27176]) ).
fof(f27176,plain,
( spl0_909
<=> ! [X2,X0,X1] :
( ~ c_in(X2,X1,X0)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X1,X2,c_Relation_OId(X0),X0,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f3477,plain,
( spl0_301
<=> ! [X3,X4,X5,X2,X1] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X5,X1,X4,X3,X2),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f3870,plain,
( ! [X2,X0,X1] :
( ~ c_in(X2,X1,X0)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X1,X2,c_Relation_OId(X0),X0,X0),X1,X0) )
| ~ spl0_56
| ~ spl0_301 ),
inference(superposition,[],[f3478,f1085]) ).
fof(f3478,plain,
( ! [X2,X3,X1,X4,X5] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X5,X1,X4,X3,X2),X5,X3) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f3477]) ).
fof(f27174,plain,
( spl0_908
| ~ spl0_62
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3348,f3179,f1108,f27172]) ).
fof(f27172,plain,
( spl0_908
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Relation_OId__on(X1,X2),c_Pair(X0,X0,X2,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f3348,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Relation_OId__on(X1,X2),c_Pair(X0,X0,X2,X2))) )
| ~ spl0_62
| ~ spl0_268 ),
inference(resolution,[],[f3180,f1109]) ).
fof(f27170,plain,
( spl0_907
| ~ spl0_110
| ~ spl0_156
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3331,f3163,f1768,f1394,f27168]) ).
fof(f27168,plain,
( spl0_907
<=> ! [X0,X1] :
( c_Relation_Ototal__on(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| ~ c_Relation_Ototal__on(X1,c_Relation_OId(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f3163,plain,
( spl0_264
<=> ! [X2,X5,X4] :
( ~ c_Relation_Ototal__on(X5,X4,X2)
| c_Relation_Ototal__on(X5,c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f3331,plain,
( ! [X0,X1] :
( c_Relation_Ototal__on(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| ~ c_Relation_Ototal__on(X1,c_Relation_OId(X0),X0) )
| ~ spl0_110
| ~ spl0_156
| ~ spl0_264 ),
inference(forward_demodulation,[],[f3329,f1769]) ).
fof(f3329,plain,
( ! [X0,X1] :
( c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Relation_Ototal__on(X1,c_Relation_OId(X0),X0) )
| ~ spl0_110
| ~ spl0_264 ),
inference(superposition,[],[f3164,f1395]) ).
fof(f3164,plain,
( ! [X2,X4,X5] :
( c_Relation_Ototal__on(X5,c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Ototal__on(X5,X4,X2) )
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f3163]) ).
fof(f27166,plain,
( spl0_906
| ~ spl0_110
| ~ spl0_156
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3326,f3155,f1768,f1394,f27164]) ).
fof(f27164,plain,
( spl0_906
<=> ! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| c_Relation_Ototal__on(X1,c_Relation_OId(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f3155,plain,
( spl0_262
<=> ! [X2,X5,X4] :
( c_Relation_Ototal__on(X5,X4,X2)
| ~ c_Relation_Ototal__on(X5,c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f3326,plain,
( ! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| c_Relation_Ototal__on(X1,c_Relation_OId(X0),X0) )
| ~ spl0_110
| ~ spl0_156
| ~ spl0_262 ),
inference(forward_demodulation,[],[f3324,f1769]) ).
fof(f3324,plain,
( ! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Relation_Ototal__on(X1,c_Relation_OId(X0),X0) )
| ~ spl0_110
| ~ spl0_262 ),
inference(superposition,[],[f3156,f1395]) ).
fof(f3156,plain,
( ! [X2,X4,X5] :
( ~ c_Relation_Ototal__on(X5,c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Relation_Ototal__on(X5,X4,X2) )
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f3155]) ).
fof(f27162,plain,
( spl0_905
| ~ spl0_216
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3296,f3151,f2373,f27160]) ).
fof(f27160,plain,
( spl0_905
<=> ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Relation_Oantisym(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1)
| ~ c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2373,plain,
( spl0_216
<=> ! [X2,X4,X14] :
( ~ c_Relation_Oantisym(X14,X2)
| c_Relation_Oantisym(X4,X2)
| ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f3296,plain,
( ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Relation_Oantisym(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1)
| ~ c_Relation_Oantisym(X0,X1) )
| ~ spl0_216
| ~ spl0_261 ),
inference(resolution,[],[f3152,f2374]) ).
fof(f2374,plain,
( ! [X2,X14,X4] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_Relation_Oantisym(X4,X2)
| ~ c_Relation_Oantisym(X14,X2) )
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f2373]) ).
fof(f27158,plain,
( spl0_904
| ~ spl0_217
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3295,f3151,f2377,f27156]) ).
fof(f27156,plain,
( spl0_904
<=> ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1)
| ~ c_Wellfounded_Oacyclic(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f3295,plain,
( ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1)
| ~ c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl0_217
| ~ spl0_261 ),
inference(resolution,[],[f3152,f2378]) ).
fof(f27154,plain,
( spl0_903
| ~ spl0_22
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3249,f3143,f945,f27152]) ).
fof(f27152,plain,
( spl0_903
<=> ! [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_903])]) ).
fof(f945,plain,
( spl0_22
<=> ! [X6,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X6,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f3249,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_22
| ~ spl0_259 ),
inference(resolution,[],[f3144,f946]) ).
fof(f946,plain,
( ! [X2,X6] :
( c_lessequals(X6,X6,X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f27149,plain,
( spl0_902
| ~ spl0_23
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3248,f3143,f949,f27147]) ).
fof(f27147,plain,
( spl0_902
<=> ! [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_902])]) ).
fof(f949,plain,
( spl0_23
<=> ! [X6,X2] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X6,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f3248,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_23
| ~ spl0_259 ),
inference(resolution,[],[f3144,f950]) ).
fof(f950,plain,
( ! [X2,X6] :
( c_lessequals(X6,X6,X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f949]) ).
fof(f27145,plain,
( spl0_901
| ~ spl0_231
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3036,f2893,f2433,f27143]) ).
fof(f27143,plain,
( spl0_901
<=> ! [X4,X0,X3,X2,X1] :
( c_Pair(X3,X4,X0,X1) != X2
| hAPP(c_snd(X0,X1),X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f2433,plain,
( spl0_231
<=> ! [X54,X53,X0,X3,X2,X1] :
( X1 = X54
| c_Pair(X0,X1,X2,X3) != c_Pair(X53,X54,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f3036,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Pair(X3,X4,X0,X1) != X2
| hAPP(c_snd(X0,X1),X2) = X4 )
| ~ spl0_231
| ~ spl0_239 ),
inference(superposition,[],[f2434,f2894]) ).
fof(f2434,plain,
( ! [X2,X3,X0,X1,X54,X53] :
( c_Pair(X0,X1,X2,X3) != c_Pair(X53,X54,X2,X3)
| X1 = X54 )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2433]) ).
fof(f27141,plain,
( spl0_900
| ~ spl0_232
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3034,f2893,f2437,f27139]) ).
fof(f27139,plain,
( spl0_900
<=> ! [X4,X0,X3,X2,X1] :
( c_Pair(X3,X4,X0,X1) != X2
| hAPP(c_fst(X0,X1),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f2437,plain,
( spl0_232
<=> ! [X53,X0,X54,X3,X2,X1] :
( X0 = X53
| c_Pair(X0,X1,X2,X3) != c_Pair(X53,X54,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f3034,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Pair(X3,X4,X0,X1) != X2
| hAPP(c_fst(X0,X1),X2) = X3 )
| ~ spl0_232
| ~ spl0_239 ),
inference(superposition,[],[f2438,f2894]) ).
fof(f2438,plain,
( ! [X2,X3,X0,X1,X54,X53] :
( c_Pair(X0,X1,X2,X3) != c_Pair(X53,X54,X2,X3)
| X0 = X53 )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2437]) ).
fof(f27137,plain,
( spl0_899
| ~ spl0_106
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2995,f2881,f1375,f27135]) ).
fof(f27135,plain,
( spl0_899
<=> ! [X0,X3,X2,X1] : c_lessequals(X0,c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2995,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool))
| ~ spl0_106
| ~ spl0_236 ),
inference(forward_demodulation,[],[f2982,f15]) ).
fof(f15,axiom,
! [X2,X0,X11,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,X9,X2),X11,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
fof(f2982,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X0,X2),X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_106
| ~ spl0_236 ),
inference(resolution,[],[f2882,f1376]) ).
fof(f27133,plain,
( spl0_898
| ~ spl0_105
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2994,f2881,f1371,f27131]) ).
fof(f27131,plain,
( spl0_898
<=> ! [X0,X3,X2,X1] : c_lessequals(X0,c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f2994,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))
| ~ spl0_105
| ~ spl0_236 ),
inference(forward_demodulation,[],[f2981,f14]) ).
fof(f14,axiom,
! [X2,X0,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
fof(f2981,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X0,X3),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ spl0_105
| ~ spl0_236 ),
inference(resolution,[],[f2882,f1372]) ).
fof(f27129,plain,
( spl0_897
| ~ spl0_20
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2841,f2417,f937,f27127]) ).
fof(f27127,plain,
( spl0_897
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f937,plain,
( spl0_20
<=> ! [X2,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Oacyclic(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f2417,plain,
( spl0_227
<=> ! [X2,X4] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X4,X2,X2),X2)
| c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X2),X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f2841,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1) )
| ~ spl0_20
| ~ spl0_227 ),
inference(resolution,[],[f2418,f938]) ).
fof(f938,plain,
( ! [X2,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Oacyclic(X4,X2) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f937]) ).
fof(f2418,plain,
( ! [X2,X4] :
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X2),X2,X2),X2)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X4,X2,X2),X2) )
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2417]) ).
fof(f27125,plain,
( spl0_896
| ~ spl0_62
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2835,f2413,f1108,f27123]) ).
fof(f27123,plain,
( spl0_896
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Set_Oimage(X3,X1,X2,X4),hAPP(X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f2835,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Set_Oimage(X3,X1,X2,X4),hAPP(X3,X0))) )
| ~ spl0_62
| ~ spl0_226 ),
inference(resolution,[],[f2414,f1109]) ).
fof(f27121,plain,
( spl0_895
| ~ spl0_164
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2822,f2393,f1800,f27119]) ).
fof(f27119,plain,
( spl0_895
<=> ! [X0,X1] :
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f2822,plain,
( ! [X0,X1] :
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Oantisym(X0,X1) )
| ~ spl0_164
| ~ spl0_221 ),
inference(superposition,[],[f2394,f1801]) ).
fof(f27117,plain,
( spl0_894
| ~ spl0_164
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2816,f2381,f1800,f27115]) ).
fof(f27115,plain,
( spl0_894
<=> ! [X0,X1] :
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f2381,plain,
( spl0_218
<=> ! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2816,plain,
( ! [X0,X1] :
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Otrans(X0,X1) )
| ~ spl0_164
| ~ spl0_218 ),
inference(superposition,[],[f2382,f1801]) ).
fof(f2382,plain,
( ! [X2,X4] :
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X4,X2) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2381]) ).
fof(f27113,plain,
( spl0_893
| ~ spl0_164
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2614,f2311,f1800,f27111]) ).
fof(f27111,plain,
( spl0_893
<=> ! [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_893])]) ).
fof(f2614,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_164
| ~ spl0_203 ),
inference(superposition,[],[f2312,f1801]) ).
fof(f27109,plain,
( spl0_892
| ~ spl0_225
| ~ spl0_879 ),
inference(avatar_split_clause,[],[f27063,f26350,f2409,f27107]) ).
fof(f27107,plain,
( spl0_892
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Relation_ORange(v_Lab____,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f27063,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Relation_ORange(v_Lab____,X0,X1)
| ~ spl0_225
| ~ spl0_879 ),
inference(superposition,[],[f26351,f2410]) ).
fof(f27105,plain,
( spl0_891
| ~ spl0_72
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2596,f2303,f1163,f27103]) ).
fof(f27103,plain,
( spl0_891
<=> ! [X2,X0,X1] : c_Set_Oinsert(X0,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2596,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X0,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool))
| ~ spl0_72
| ~ spl0_201 ),
inference(resolution,[],[f2304,f1164]) ).
fof(f27101,plain,
( spl0_890
| ~ spl0_72
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2573,f2299,f1163,f27099]) ).
fof(f27099,plain,
( spl0_890
<=> ! [X2,X0,X1] : c_Set_Oinsert(X1,X0,X2) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f2573,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X1,X0,X2) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool))
| ~ spl0_72
| ~ spl0_200 ),
inference(resolution,[],[f2300,f1164]) ).
fof(f27097,plain,
( spl0_889
| ~ spl0_54
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2230,f1881,f1076,f27095]) ).
fof(f27095,plain,
( spl0_889
<=> ! [X0,X1] :
( c_Relation_Osym(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1)
| ~ c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f1076,plain,
( spl0_54
<=> ! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1881,plain,
( spl0_183
<=> ! [X2,X4] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X2),X2,X2) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X2,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f2230,plain,
( ! [X0,X1] :
( c_Relation_Osym(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1)
| ~ c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) )
| ~ spl0_54
| ~ spl0_183 ),
inference(superposition,[],[f1077,f1882]) ).
fof(f1882,plain,
( ! [X2,X4] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X2),X2,X2) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X2,X2),X2)
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1881]) ).
fof(f1077,plain,
( ! [X2,X4] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X4,X2),X2)
| ~ c_Relation_Osym(X4,X2) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1076]) ).
fof(f27093,plain,
( spl0_888
| ~ spl0_65
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1951,f1768,f1123,f27091]) ).
fof(f27091,plain,
( spl0_888
<=> ! [X0] : c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0)),tc_prod(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f1123,plain,
( spl0_65
<=> ! [X2] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1951,plain,
( ! [X0] : c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0)),tc_prod(X0,X0))
| ~ spl0_65
| ~ spl0_156 ),
inference(superposition,[],[f1124,f1769]) ).
fof(f1124,plain,
( ! [X2] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f27089,plain,
( spl0_887
| ~ spl0_68
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1733,f1605,f1146,f27087]) ).
fof(f27087,plain,
( spl0_887
<=> ! [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_887])]) ).
fof(f1733,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_68
| ~ spl0_145 ),
inference(duplicate_literal_removal,[],[f1720]) ).
fof(f1720,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_68
| ~ spl0_145 ),
inference(resolution,[],[f1606,f1147]) ).
fof(f27085,plain,
( spl0_886
| ~ spl0_67
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1704,f1597,f1142,f27083]) ).
fof(f27083,plain,
( spl0_886
<=> ! [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_886])]) ).
fof(f1704,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_67
| ~ spl0_143 ),
inference(duplicate_literal_removal,[],[f1688]) ).
fof(f1688,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_67
| ~ spl0_143 ),
inference(resolution,[],[f1598,f1143]) ).
fof(f27081,plain,
( spl0_885
| ~ spl0_68
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1703,f1597,f1146,f27079]) ).
fof(f27079,plain,
( spl0_885
<=> ! [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_885])]) ).
fof(f1703,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_68
| ~ spl0_143 ),
inference(duplicate_literal_removal,[],[f1690]) ).
fof(f1690,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_68
| ~ spl0_143 ),
inference(resolution,[],[f1598,f1147]) ).
fof(f27077,plain,
( spl0_884
| ~ spl0_80
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1674,f1589,f1195,f27075]) ).
fof(f27075,plain,
( spl0_884
<=> ! [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_884])]) ).
fof(f1674,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_80
| ~ spl0_142 ),
inference(duplicate_literal_removal,[],[f1669]) ).
fof(f1669,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_80
| ~ spl0_142 ),
inference(resolution,[],[f1590,f1196]) ).
fof(f27073,plain,
( spl0_883
| ~ spl0_81
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1648,f1581,f1199,f27071]) ).
fof(f27071,plain,
( spl0_883
<=> ! [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_883])]) ).
fof(f1648,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_81
| ~ spl0_140 ),
inference(duplicate_literal_removal,[],[f1640]) ).
fof(f1640,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_81
| ~ spl0_140 ),
inference(resolution,[],[f1582,f1200]) ).
fof(f27069,plain,
( spl0_882
| ~ spl0_80
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1647,f1581,f1195,f27067]) ).
fof(f27067,plain,
( spl0_882
<=> ! [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_882])]) ).
fof(f1647,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_80
| ~ spl0_140 ),
inference(duplicate_literal_removal,[],[f1642]) ).
fof(f1642,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_80
| ~ spl0_140 ),
inference(resolution,[],[f1582,f1196]) ).
fof(f27062,plain,
( spl0_881
| ~ spl0_98
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1574,f1494,f1320,f27060]) ).
fof(f27060,plain,
( spl0_881
<=> ! [X0,X1] : c_Relation_OId(X1) = c_Set_Oinsert(c_Pair(X0,X0,X1,X1),c_Relation_OId(X1),tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f1574,plain,
( ! [X0,X1] : c_Relation_OId(X1) = c_Set_Oinsert(c_Pair(X0,X0,X1,X1),c_Relation_OId(X1),tc_prod(X1,X1))
| ~ spl0_98
| ~ spl0_135 ),
inference(resolution,[],[f1495,f1321]) ).
fof(f27058,plain,
( spl0_880
| ~ spl0_55
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1295,f1236,f1080,f27056]) ).
fof(f27056,plain,
( spl0_880
<=> ! [X0,X1] :
( c_Relation_Oconverse(X0,X1,X1) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1)
| ~ c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f1295,plain,
( ! [X0,X1] :
( c_Relation_Oconverse(X0,X1,X1) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1)
| ~ c_Relation_Otrans(X0,X1) )
| ~ spl0_55
| ~ spl0_90 ),
inference(forward_demodulation,[],[f1293,f552]) ).
fof(f552,axiom,
! [X2,X4] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X2),X2,X2) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X2,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
fof(f1293,plain,
( ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Relation_Oconverse(X0,X1,X1) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1) )
| ~ spl0_55
| ~ spl0_90 ),
inference(resolution,[],[f1237,f1081]) ).
fof(f26352,plain,
( spl0_879
| ~ spl0_104
| ~ spl0_857 ),
inference(avatar_split_clause,[],[f26141,f23149,f1351,f26350]) ).
fof(f1351,plain,
( spl0_104
<=> ! [X0] : v_Lab____ = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f23149,plain,
( spl0_857
<=> ! [X4,X0,X3,X2,X1] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f26141,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_Lab____,X0,X2)
| ~ spl0_104
| ~ spl0_857 ),
inference(superposition,[],[f23150,f1352]) ).
fof(f1352,plain,
( ! [X0] : v_Lab____ = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,X0)
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f23150,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ spl0_857 ),
inference(avatar_component_clause,[],[f23149]) ).
fof(f25903,plain,
( spl0_878
| ~ spl0_334
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f22967,f22917,f4043,f25901]) ).
fof(f25901,plain,
( spl0_878
<=> ! [X0,X1] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f22967,plain,
( ! [X0,X1] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_334
| ~ spl0_821 ),
inference(resolution,[],[f22918,f4044]) ).
fof(f25715,plain,
( spl0_877
| ~ spl0_333
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f22966,f22917,f4039,f25713]) ).
fof(f25713,plain,
( spl0_877
<=> ! [X0,X1] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f22966,plain,
( ! [X0,X1] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_333
| ~ spl0_821 ),
inference(resolution,[],[f22918,f4040]) ).
fof(f25414,plain,
( spl0_876
| ~ spl0_331
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f22965,f22917,f4031,f25412]) ).
fof(f25412,plain,
( spl0_876
<=> ! [X0,X1] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Transitive__Closure_Otrancl(v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f22965,plain,
( ! [X0,X1] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Transitive__Closure_Otrancl(v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_331
| ~ spl0_821 ),
inference(resolution,[],[f22918,f4032]) ).
fof(f23815,plain,
( spl0_875
| ~ spl0_330
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f22964,f22917,f4027,f23813]) ).
fof(f23813,plain,
( spl0_875
<=> ! [X0,X1] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Transitive__Closure_Otrancl(v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f22964,plain,
( ! [X0,X1] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,c_Transitive__Closure_Otrancl(v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_330
| ~ spl0_821 ),
inference(resolution,[],[f22918,f4028]) ).
fof(f23258,plain,
( spl0_874
| ~ spl0_61
| ~ spl0_861 ),
inference(avatar_split_clause,[],[f23208,f23165,f1104,f23256]) ).
fof(f23165,plain,
( spl0_861
<=> ! [X0] : hBOOL(hAPP(c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f23208,plain,
( ! [X0,X1] : c_in(v_a____,c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1)
| ~ spl0_61
| ~ spl0_861 ),
inference(resolution,[],[f23166,f1105]) ).
fof(f23166,plain,
( ! [X0] : hBOOL(hAPP(c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____))
| ~ spl0_861 ),
inference(avatar_component_clause,[],[f23165]) ).
fof(f23217,plain,
( spl0_873
| ~ spl0_59
| ~ spl0_102
| ~ spl0_249
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f8508,f7939,f2933,f1336,f1096,f23215]) ).
fof(f23215,plain,
( spl0_873
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f8508,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_59
| ~ spl0_102
| ~ spl0_249
| ~ spl0_445 ),
inference(forward_demodulation,[],[f8507,f1097]) ).
fof(f8507,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2),X2)
| c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_102
| ~ spl0_249
| ~ spl0_445 ),
inference(forward_demodulation,[],[f8461,f1337]) ).
fof(f8461,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2),X2)
| c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_249
| ~ spl0_445 ),
inference(resolution,[],[f7940,f2934]) ).
fof(f23213,plain,
( spl0_872
| ~ spl0_59
| ~ spl0_102
| ~ spl0_249
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f8448,f7935,f2933,f1336,f1096,f23211]) ).
fof(f23211,plain,
( spl0_872
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f8448,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_59
| ~ spl0_102
| ~ spl0_249
| ~ spl0_444 ),
inference(forward_demodulation,[],[f8447,f1097]) ).
fof(f8447,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2),X2)
| c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_102
| ~ spl0_249
| ~ spl0_444 ),
inference(forward_demodulation,[],[f8401,f1337]) ).
fof(f8401,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2),X2)
| c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_249
| ~ spl0_444 ),
inference(resolution,[],[f7936,f2934]) ).
fof(f23207,plain,
( spl0_871
| ~ spl0_56
| ~ spl0_230
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f7618,f6618,f2429,f1084,f23205]) ).
fof(f23205,plain,
( spl0_871
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X2,X1)
| c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X2,X0,c_Relation_OId(X1),X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f6618,plain,
( spl0_419
<=> ! [X3,X4,X5,X2,X1] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X5,X1,X4,X3,X2),X1,X3,X2),X4,tc_prod(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f7618,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X2,X1)
| c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X2,X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_56
| ~ spl0_230
| ~ spl0_419 ),
inference(forward_demodulation,[],[f7578,f1085]) ).
fof(f7578,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X2,X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_230
| ~ spl0_419 ),
inference(resolution,[],[f6619,f2430]) ).
fof(f6619,plain,
( ! [X2,X3,X1,X4,X5] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X5,X1,X4,X3,X2),X1,X3,X2),X4,tc_prod(X3,X2))
| ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2) )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f6618]) ).
fof(f23203,plain,
( spl0_870
| ~ spl0_56
| ~ spl0_230
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f7570,f6614,f2429,f1084,f23201]) ).
fof(f7570,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X2,X1)
| c_ATP__Linkup_Osko__Relation__XImageE__1__1(X2,X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_56
| ~ spl0_230
| ~ spl0_418 ),
inference(forward_demodulation,[],[f7530,f1085]) ).
fof(f7530,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1),X1)
| c_ATP__Linkup_Osko__Relation__XImageE__1__1(X2,X0,c_Relation_OId(X1),X1,X1) = X0 )
| ~ spl0_230
| ~ spl0_418 ),
inference(resolution,[],[f6615,f2430]) ).
fof(f23199,plain,
( spl0_869
| ~ spl0_38
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f7556,f6614,f1009,f23197]) ).
fof(f23197,plain,
( spl0_869
<=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X3,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f7556,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X3,X1,X2),X2)
| ~ spl0_38
| ~ spl0_418 ),
inference(resolution,[],[f6615,f1010]) ).
fof(f23195,plain,
( spl0_868
| ~ spl0_135
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f6452,f6203,f1494,f23193]) ).
fof(f23193,plain,
( spl0_868
<=> ! [X0,X3,X2,X1] : hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,c_Relation_OId(X2),X1,X2,X3),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f6452,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,c_Relation_OId(X2),X1,X2,X3),X1)
| ~ spl0_135
| ~ spl0_401 ),
inference(resolution,[],[f6204,f1495]) ).
fof(f23191,plain,
( spl0_867
| ~ spl0_59
| ~ spl0_249
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f6139,f5559,f2933,f1096,f23189]) ).
fof(f6139,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_59
| ~ spl0_249
| ~ spl0_389 ),
inference(forward_demodulation,[],[f6105,f1097]) ).
fof(f6105,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2),X2)
| c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_249
| ~ spl0_389 ),
inference(resolution,[],[f5560,f2934]) ).
fof(f23187,plain,
( spl0_866
| ~ spl0_59
| ~ spl0_249
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6098,f5555,f2933,f1096,f23185]) ).
fof(f6098,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_59
| ~ spl0_249
| ~ spl0_388 ),
inference(forward_demodulation,[],[f6064,f1097]) ).
fof(f6064,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2),X2)
| c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
| ~ spl0_249
| ~ spl0_388 ),
inference(resolution,[],[f5556,f2934]) ).
fof(f23183,plain,
( spl0_865
| ~ spl0_187
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5488,f5102,f1897,f23181]) ).
fof(f23181,plain,
( spl0_865
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2)
| ~ c_Nitpick_Orefl_H(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f5488,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2)
| ~ c_Nitpick_Orefl_H(X1,X2) )
| ~ spl0_187
| ~ spl0_377 ),
inference(resolution,[],[f5103,f1898]) ).
fof(f23179,plain,
( spl0_864
| ~ spl0_296
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5466,f5098,f3457,f23177]) ).
fof(f23177,plain,
( spl0_864
<=> ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f5466,plain,
( ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ spl0_296
| ~ spl0_376 ),
inference(resolution,[],[f5099,f3458]) ).
fof(f23175,plain,
( spl0_863
| ~ spl0_185
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5465,f5098,f1889,f23173]) ).
fof(f23173,plain,
( spl0_863
<=> ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f5465,plain,
( ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ spl0_185
| ~ spl0_376 ),
inference(resolution,[],[f5099,f1890]) ).
fof(f23171,plain,
( spl0_862
| ~ spl0_188
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5464,f5098,f1901,f23169]) ).
fof(f23169,plain,
( spl0_862
<=> ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f5464,plain,
( ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ spl0_188
| ~ spl0_376 ),
inference(resolution,[],[f5099,f1902]) ).
fof(f23167,plain,
( spl0_861
| ~ spl0_62
| ~ spl0_840 ),
inference(avatar_split_clause,[],[f23114,f23071,f1108,f23165]) ).
fof(f23071,plain,
( spl0_840
<=> ! [X0] : c_in(v_a____,c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f23114,plain,
( ! [X0] : hBOOL(hAPP(c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____))
| ~ spl0_62
| ~ spl0_840 ),
inference(resolution,[],[f23072,f1109]) ).
fof(f23072,plain,
( ! [X0] : c_in(v_a____,c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_840 ),
inference(avatar_component_clause,[],[f23071]) ).
fof(f23163,plain,
( spl0_860
| ~ spl0_187
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f5416,f5086,f1897,f23161]) ).
fof(f23161,plain,
( spl0_860
<=> ! [X2,X0,X1,X3] :
( c_in(X0,hAPP(X1,X0),X2)
| ~ c_Nitpick_Orefl_H(c_Product__Type_OSigma(X3,X1,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f5086,plain,
( spl0_373
<=> ! [X2,X3,X0,X9,X5,X1] :
( c_in(X1,hAPP(X9,X0),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f5416,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,hAPP(X1,X0),X2)
| ~ c_Nitpick_Orefl_H(c_Product__Type_OSigma(X3,X1,X2,X2),X2) )
| ~ spl0_187
| ~ spl0_373 ),
inference(resolution,[],[f5087,f1898]) ).
fof(f5087,plain,
( ! [X2,X3,X0,X1,X9,X5] :
( ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3))
| c_in(X1,hAPP(X9,X0),X3) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f5086]) ).
fof(f23159,plain,
( spl0_859
| ~ spl0_230
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4987,f4541,f2429,f23157]) ).
fof(f23157,plain,
( spl0_859
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId(X0),X0,X0),X1),X2))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f4987,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId(X0),X0,X0),X1),X2))
| X1 = X2 )
| ~ spl0_230
| ~ spl0_354 ),
inference(resolution,[],[f4542,f2430]) ).
fof(f23155,plain,
( spl0_858
| ~ spl0_307
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4909,f4529,f3501,f23153]) ).
fof(f23153,plain,
( spl0_858
<=> ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(X0,c_Relation_ORange(X1,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f4909,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
| c_in(X0,c_Relation_ORange(X1,X2,X2),X2) )
| ~ spl0_307
| ~ spl0_351 ),
inference(resolution,[],[f4530,f3502]) ).
fof(f23151,plain,
( spl0_857
| ~ spl0_77
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f4752,f4497,f1183,f23149]) ).
fof(f1183,plain,
( spl0_77
<=> ! [X2,X5,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X0,X5,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f4752,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ spl0_77
| ~ spl0_343 ),
inference(superposition,[],[f1184,f4498]) ).
fof(f1184,plain,
( ! [X2,X0,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X0,X5,X2)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1183]) ).
fof(f23147,plain,
( spl0_856
| ~ spl0_41
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f4750,f4497,f1021,f23145]) ).
fof(f23145,plain,
( spl0_856
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),hAPP(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f1021,plain,
( spl0_41
<=> ! [X6,X2,X5] : hBOOL(hAPP(c_Set_Oinsert(X6,X5,X2),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f4750,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),hAPP(X0,X1)))
| ~ spl0_41
| ~ spl0_343 ),
inference(superposition,[],[f1022,f4498]) ).
fof(f1022,plain,
( ! [X2,X6,X5] : hBOOL(hAPP(c_Set_Oinsert(X6,X5,X2),X6))
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f23143,plain,
( spl0_855
| ~ spl0_257
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f4691,f4481,f3135,f23141]) ).
fof(f23141,plain,
( spl0_855
<=> ! [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_855])]) ).
fof(f4691,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_257
| ~ spl0_339 ),
inference(trivial_inequality_removal,[],[f4688]) ).
fof(f4688,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_257
| ~ spl0_339 ),
inference(superposition,[],[f4482,f3136]) ).
fof(f23139,plain,
( spl0_854
| ~ spl0_250
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4458,f4043,f2937,f23137]) ).
fof(f23137,plain,
( spl0_854
<=> ! [X2,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X2),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f4458,plain,
( ! [X2,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X2),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 )
| ~ spl0_250
| ~ spl0_334 ),
inference(resolution,[],[f4044,f2938]) ).
fof(f23135,plain,
( spl0_853
| ~ spl0_253
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4457,f4043,f2949,f23133]) ).
fof(f23133,plain,
( spl0_853
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f4457,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 )
| ~ spl0_253
| ~ spl0_334 ),
inference(resolution,[],[f4044,f2950]) ).
fof(f23131,plain,
( spl0_852
| ~ spl0_252
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4456,f4043,f2945,f23129]) ).
fof(f23129,plain,
( spl0_852
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,c_Arrow__Order__Mirabelle_Omkbot(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f4456,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,c_Arrow__Order__Mirabelle_Omkbot(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 )
| ~ spl0_252
| ~ spl0_334 ),
inference(resolution,[],[f4044,f2946]) ).
fof(f23127,plain,
( spl0_851
| ~ spl0_250
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4440,f4039,f2937,f23125]) ).
fof(f23125,plain,
( spl0_851
<=> ! [X2,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f4440,plain,
( ! [X2,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 )
| ~ spl0_250
| ~ spl0_333 ),
inference(resolution,[],[f4040,f2938]) ).
fof(f23113,plain,
( spl0_850
| ~ spl0_253
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4439,f4039,f2949,f23111]) ).
fof(f23111,plain,
( spl0_850
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f4439,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 )
| ~ spl0_253
| ~ spl0_333 ),
inference(resolution,[],[f4040,f2950]) ).
fof(f23109,plain,
( spl0_849
| ~ spl0_252
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4438,f4039,f2945,f23107]) ).
fof(f23107,plain,
( spl0_849
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f4438,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X1,c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 )
| ~ spl0_252
| ~ spl0_333 ),
inference(resolution,[],[f4040,f2946]) ).
fof(f23105,plain,
( spl0_848
| ~ spl0_299
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4433,f4039,f3469,f23103]) ).
fof(f23103,plain,
( spl0_848
<=> ! [X2,X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X2,X1)
| ~ c_Relation_Orefl__on(X2,X0,X1)
| c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f4433,plain,
( ! [X2,X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X2,X1)
| ~ c_Relation_Orefl__on(X2,X0,X1)
| c_Relation_Oirrefl(X0,X1) )
| ~ spl0_299
| ~ spl0_333 ),
inference(resolution,[],[f4040,f3470]) ).
fof(f23101,plain,
( spl0_847
| ~ spl0_250
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f4417,f4031,f2937,f23099]) ).
fof(f23099,plain,
( spl0_847
<=> ! [X2,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X2),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f4417,plain,
( ! [X2,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X2),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 )
| ~ spl0_250
| ~ spl0_331 ),
inference(resolution,[],[f4032,f2938]) ).
fof(f23097,plain,
( spl0_846
| ~ spl0_253
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f4416,f4031,f2949,f23095]) ).
fof(f23095,plain,
( spl0_846
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f4416,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 )
| ~ spl0_253
| ~ spl0_331 ),
inference(resolution,[],[f4032,f2950]) ).
fof(f23093,plain,
( spl0_845
| ~ spl0_252
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f4415,f4031,f2945,f23091]) ).
fof(f23091,plain,
( spl0_845
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,c_Arrow__Order__Mirabelle_Omkbot(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f4415,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,c_Arrow__Order__Mirabelle_Omkbot(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 )
| ~ spl0_252
| ~ spl0_331 ),
inference(resolution,[],[f4032,f2946]) ).
fof(f23089,plain,
( spl0_844
| ~ spl0_250
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4399,f4027,f2937,f23087]) ).
fof(f23087,plain,
( spl0_844
<=> ! [X2,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f4399,plain,
( ! [X2,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 )
| ~ spl0_250
| ~ spl0_330 ),
inference(resolution,[],[f4028,f2938]) ).
fof(f23085,plain,
( spl0_843
| ~ spl0_253
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4398,f4027,f2949,f23083]) ).
fof(f23083,plain,
( spl0_843
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f4398,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 )
| ~ spl0_253
| ~ spl0_330 ),
inference(resolution,[],[f4028,f2950]) ).
fof(f23081,plain,
( spl0_842
| ~ spl0_252
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4397,f4027,f2945,f23079]) ).
fof(f23079,plain,
( spl0_842
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f4397,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X3 )
| ~ spl0_252
| ~ spl0_330 ),
inference(resolution,[],[f4028,f2946]) ).
fof(f23077,plain,
( spl0_841
| ~ spl0_299
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4392,f4027,f3469,f23075]) ).
fof(f23075,plain,
( spl0_841
<=> ! [X2,X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X2,X1)
| ~ c_Equiv__Relations_Oequiv(X2,X0,X1)
| c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f4392,plain,
( ! [X2,X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X2,X1)
| ~ c_Equiv__Relations_Oequiv(X2,X0,X1)
| c_Relation_Oirrefl(X0,X1) )
| ~ spl0_299
| ~ spl0_330 ),
inference(resolution,[],[f4028,f3470]) ).
fof(f23073,plain,
( spl0_840
| ~ spl0_307
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f22984,f22917,f3501,f23071]) ).
fof(f22984,plain,
( ! [X0] : c_in(v_a____,c_Relation_ORange(c_Transitive__Closure_Otrancl(v_Lab____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_307
| ~ spl0_821 ),
inference(resolution,[],[f22918,f3502]) ).
fof(f23069,plain,
( spl0_839
| ~ spl0_267
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3843,f3469,f3175,f23067]) ).
fof(f23067,plain,
( spl0_839
<=> ! [X0,X1] :
( c_Relation_Oirrefl(c_Relation_OId__on(X0,X1),X1)
| c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f3843,plain,
( ! [X0,X1] :
( c_Relation_Oirrefl(c_Relation_OId__on(X0,X1),X1)
| c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),X0,X1) )
| ~ spl0_267
| ~ spl0_299 ),
inference(resolution,[],[f3470,f3176]) ).
fof(f23065,plain,
( spl0_838
| ~ spl0_268
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3829,f3457,f3179,f23063]) ).
fof(f23063,plain,
( spl0_838
<=> ! [X0,X1] :
( c_Nitpick_Orefl_H(c_Relation_OId__on(X0,X1),X1)
| ~ c_in(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(c_Relation_OId__on(X0,X1),X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f3829,plain,
( ! [X0,X1] :
( c_Nitpick_Orefl_H(c_Relation_OId__on(X0,X1),X1)
| ~ c_in(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(c_Relation_OId__on(X0,X1),X1),X0,X1) )
| ~ spl0_268
| ~ spl0_296 ),
inference(resolution,[],[f3458,f3180]) ).
fof(f23061,plain,
( spl0_837
| ~ spl0_85
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3361,f3191,f1216,f23059]) ).
fof(f23059,plain,
( spl0_837
<=> ! [X0] :
( c_Relation_OId(X0) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
| c_Wellfounded_Owf(c_Relation_OId(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f1216,plain,
( spl0_85
<=> ! [X2,X8,X3] : c_Relation_Orel__comp(c_Relation_OId(X2),X8,X2,X2,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f3191,plain,
( spl0_271
<=> ! [X2,X8] :
( c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Relation_Orel__comp(X8,X8,X2,X2,X2)
| c_Wellfounded_Owf(X8,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f3361,plain,
( ! [X0] :
( c_Relation_OId(X0) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
| c_Wellfounded_Owf(c_Relation_OId(X0),X0) )
| ~ spl0_85
| ~ spl0_271 ),
inference(superposition,[],[f3192,f1217]) ).
fof(f1217,plain,
( ! [X2,X3,X8] : c_Relation_Orel__comp(c_Relation_OId(X2),X8,X2,X2,X3) = X8
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1216]) ).
fof(f3192,plain,
( ! [X2,X8] :
( c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Relation_Orel__comp(X8,X8,X2,X2,X2)
| c_Wellfounded_Owf(X8,X2) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f3191]) ).
fof(f23057,plain,
( spl0_836
| ~ spl0_82
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3334,f3171,f1204,f23055]) ).
fof(f23055,plain,
( spl0_836
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1)))
| hBOOL(hAPP(X0,X2))
| ~ c_Wellfounded_Owf(X1,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f3171,plain,
( spl0_266
<=> ! [X6,X18,X4] :
( hBOOL(hAPP(X18,X6))
| ~ hBOOL(hAPP(X18,v_sko__Wellfounded__Xacc__Xinduct__1(X18,X4)))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f3334,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1)))
| hBOOL(hAPP(X0,X2))
| ~ c_Wellfounded_Owf(X1,t_a) )
| ~ spl0_82
| ~ spl0_266 ),
inference(resolution,[],[f3172,f1205]) ).
fof(f3172,plain,
( ! [X18,X6,X4] :
( ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ hBOOL(hAPP(X18,v_sko__Wellfounded__Xacc__Xinduct__1(X18,X4)))
| hBOOL(hAPP(X18,X6)) )
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f3171]) ).
fof(f23053,plain,
( spl0_835
| ~ spl0_82
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3332,f3167,f1204,f23051]) ).
fof(f23051,plain,
( spl0_835
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1)))
| hBOOL(hAPP(X0,X2))
| ~ c_Wellfounded_Owf(X1,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f3167,plain,
( spl0_265
<=> ! [X6,X18,X4] :
( hBOOL(hAPP(X18,X6))
| ~ hBOOL(hAPP(X18,v_sko__Wellfounded__Xacc__Xinducts__1(X18,X4)))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f3332,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1)))
| hBOOL(hAPP(X0,X2))
| ~ c_Wellfounded_Owf(X1,t_a) )
| ~ spl0_82
| ~ spl0_265 ),
inference(resolution,[],[f3168,f1205]) ).
fof(f3168,plain,
( ! [X18,X6,X4] :
( ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ hBOOL(hAPP(X18,v_sko__Wellfounded__Xacc__Xinducts__1(X18,X4)))
| hBOOL(hAPP(X18,X6)) )
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f3167]) ).
fof(f23049,plain,
( spl0_834
| ~ spl0_66
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3284,f3147,f1138,f23047]) ).
fof(f23047,plain,
( spl0_834
<=> ! [X2,X0,X1] :
( c_Relation_Osingle__valued(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X0,X1)
| ~ c_Relation_Osingle__valued(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f3284,plain,
( ! [X2,X0,X1] :
( c_Relation_Osingle__valued(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X0,X1)
| ~ c_Relation_Osingle__valued(X2,X0,X1) )
| ~ spl0_66
| ~ spl0_260 ),
inference(resolution,[],[f3148,f1139]) ).
fof(f23045,plain,
( spl0_833
| ~ spl0_72
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3282,f3147,f1163,f23043]) ).
fof(f23043,plain,
( spl0_833
<=> ! [X2,X0,X1,X3] :
( c_Relation_Osingle__valued(X0,X1,X2)
| ~ c_Relation_Osingle__valued(c_Set_Oinsert(X3,X0,tc_prod(X1,X2)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f3282,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| ~ c_Relation_Osingle__valued(c_Set_Oinsert(X3,X0,tc_prod(X1,X2)),X1,X2) )
| ~ spl0_72
| ~ spl0_260 ),
inference(resolution,[],[f3148,f1164]) ).
fof(f23025,plain,
( spl0_832
| ~ spl0_9
| ~ spl0_66
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3260,f3143,f1138,f891,f23023]) ).
fof(f23023,plain,
( spl0_832
<=> ! [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_832])]) ).
fof(f3260,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_66
| ~ spl0_259 ),
inference(resolution,[],[f3144,f1139]) ).
fof(f22959,plain,
( spl0_831
| ~ spl0_9
| ~ spl0_72
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3258,f3143,f1163,f891,f22957]) ).
fof(f22957,plain,
( spl0_831
<=> ! [X0,X3,X2,X1] : c_lessequals(hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X0,X3),X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f3258,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X0,X3),X1),tc_bool) )
| ~ spl0_72
| ~ spl0_259 ),
inference(resolution,[],[f3144,f1164]) ).
fof(f22955,plain,
( spl0_830
| ~ spl0_62
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3120,f2949,f1108,f22953]) ).
fof(f22953,plain,
( spl0_830
<=> ! [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_830])]) ).
fof(f3120,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_62
| ~ spl0_253 ),
inference(resolution,[],[f2950,f1109]) ).
fof(f22951,plain,
( spl0_829
| ~ spl0_62
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3108,f2945,f1108,f22949]) ).
fof(f22949,plain,
( spl0_829
<=> ! [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_829])]) ).
fof(f3108,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_62
| ~ spl0_252 ),
inference(resolution,[],[f2946,f1109]) ).
fof(f22947,plain,
( spl0_828
| ~ spl0_62
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3100,f2937,f1108,f22945]) ).
fof(f22945,plain,
( spl0_828
<=> ! [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_828])]) ).
fof(f3100,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_62
| ~ spl0_250 ),
inference(resolution,[],[f2938,f1109]) ).
fof(f22943,plain,
( spl0_827
| ~ spl0_222
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f3088,f2913,f2397,f22941]) ).
fof(f22941,plain,
( spl0_827
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| ~ c_in(c_Pair(X2,X2,X1,X1),X0,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f3088,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| ~ c_in(c_Pair(X2,X2,X1,X1),X0,tc_prod(X1,X1)) )
| ~ spl0_222
| ~ spl0_244 ),
inference(resolution,[],[f2914,f2398]) ).
fof(f22939,plain,
( spl0_826
| ~ spl0_37
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2830,f2405,f1005,f22937]) ).
fof(f22937,plain,
( spl0_826
<=> ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1)
| c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f1005,plain,
( spl0_37
<=> ! [X2,X4] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f2405,plain,
( spl0_224
<=> ! [X2,X5,X4] :
( ~ c_Relation_Oirrefl(X4,X2)
| ~ c_Relation_Otrans(X4,X2)
| ~ c_Relation_Ototal__on(X5,X4,X2)
| c_Order__Relation_Ostrict__linear__order__on(X5,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2830,plain,
( ! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1)
| c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0,X1) )
| ~ spl0_37
| ~ spl0_224 ),
inference(resolution,[],[f2406,f1006]) ).
fof(f1006,plain,
( ! [X2,X4] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,X2)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f2406,plain,
( ! [X2,X4,X5] :
( ~ c_Relation_Ototal__on(X5,X4,X2)
| ~ c_Relation_Otrans(X4,X2)
| ~ c_Relation_Oirrefl(X4,X2)
| c_Order__Relation_Ostrict__linear__order__on(X5,X4,X2) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2405]) ).
fof(f22935,plain,
( spl0_825
| ~ spl0_117
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2811,f2377,f1422,f22933]) ).
fof(f22933,plain,
( spl0_825
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Oacyclic(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f2811,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Oacyclic(X0,X2) )
| ~ spl0_117
| ~ spl0_217 ),
inference(resolution,[],[f2378,f1423]) ).
fof(f22931,plain,
( spl0_824
| ~ spl0_116
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2804,f2377,f1418,f22929]) ).
fof(f22929,plain,
( spl0_824
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f2804,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) )
| ~ spl0_116
| ~ spl0_217 ),
inference(resolution,[],[f2378,f1419]) ).
fof(f22927,plain,
( spl0_823
| ~ spl0_115
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2803,f2377,f1414,f22925]) ).
fof(f22925,plain,
( spl0_823
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Oacyclic(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f2803,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Oacyclic(X0,X2) )
| ~ spl0_115
| ~ spl0_217 ),
inference(resolution,[],[f2378,f1415]) ).
fof(f22923,plain,
( spl0_822
| ~ spl0_106
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2793,f2377,f1375,f22921]) ).
fof(f22921,plain,
( spl0_822
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f2793,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) )
| ~ spl0_106
| ~ spl0_217 ),
inference(resolution,[],[f2378,f1376]) ).
fof(f22919,plain,
( spl0_821
| ~ spl0_61
| ~ spl0_800 ),
inference(avatar_split_clause,[],[f22875,f22832,f1104,f22917]) ).
fof(f22832,plain,
( spl0_800
<=> ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(v_Lab____,X0),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f22875,plain,
( ! [X0,X1] : c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(v_Lab____,X0),X1)
| ~ spl0_61
| ~ spl0_800 ),
inference(resolution,[],[f22833,f1105]) ).
fof(f22833,plain,
( ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(v_Lab____,X0),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_800 ),
inference(avatar_component_clause,[],[f22832]) ).
fof(f22915,plain,
( spl0_820
| ~ spl0_105
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2792,f2377,f1371,f22913]) ).
fof(f22913,plain,
( spl0_820
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f2792,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1) )
| ~ spl0_105
| ~ spl0_217 ),
inference(resolution,[],[f2378,f1372]) ).
fof(f22911,plain,
( spl0_819
| ~ spl0_117
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2786,f2373,f1422,f22909]) ).
fof(f22909,plain,
( spl0_819
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f2786,plain,
( ! [X2,X0,X1] :
( c_Relation_Oantisym(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X0,X2) )
| ~ spl0_117
| ~ spl0_216 ),
inference(resolution,[],[f2374,f1423]) ).
fof(f22907,plain,
( spl0_818
| ~ spl0_116
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2779,f2373,f1418,f22905]) ).
fof(f22905,plain,
( spl0_818
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f2779,plain,
( ! [X2,X0,X1] :
( c_Relation_Oantisym(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2) )
| ~ spl0_116
| ~ spl0_216 ),
inference(resolution,[],[f2374,f1419]) ).
fof(f22903,plain,
( spl0_817
| ~ spl0_115
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2778,f2373,f1414,f22901]) ).
fof(f22901,plain,
( spl0_817
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2778,plain,
( ! [X2,X0,X1] :
( c_Relation_Oantisym(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X0,X2) )
| ~ spl0_115
| ~ spl0_216 ),
inference(resolution,[],[f2374,f1415]) ).
fof(f22899,plain,
( spl0_816
| ~ spl0_106
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2768,f2373,f1375,f22897]) ).
fof(f22897,plain,
( spl0_816
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f2768,plain,
( ! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) )
| ~ spl0_106
| ~ spl0_216 ),
inference(resolution,[],[f2374,f1376]) ).
fof(f22895,plain,
( spl0_815
| ~ spl0_105
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2767,f2373,f1371,f22893]) ).
fof(f22893,plain,
( spl0_815
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2767,plain,
( ! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1) )
| ~ spl0_105
| ~ spl0_216 ),
inference(resolution,[],[f2374,f1372]) ).
fof(f22891,plain,
( spl0_814
| ~ spl0_117
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2761,f2369,f1422,f22889]) ).
fof(f22889,plain,
( spl0_814
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f2761,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X0,X2) )
| ~ spl0_117
| ~ spl0_215 ),
inference(resolution,[],[f2370,f1423]) ).
fof(f22887,plain,
( spl0_813
| ~ spl0_106
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2743,f2369,f1375,f22885]) ).
fof(f22885,plain,
( spl0_813
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f2743,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) )
| ~ spl0_106
| ~ spl0_215 ),
inference(resolution,[],[f2370,f1376]) ).
fof(f22883,plain,
( spl0_812
| ~ spl0_105
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2742,f2369,f1371,f22881]) ).
fof(f22881,plain,
( spl0_812
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f2742,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1) )
| ~ spl0_105
| ~ spl0_215 ),
inference(resolution,[],[f2370,f1372]) ).
fof(f22879,plain,
( spl0_811
| ~ spl0_117
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2738,f2365,f1422,f22877]) ).
fof(f22877,plain,
( spl0_811
<=> ! [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_811])]) ).
fof(f2738,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_117
| ~ spl0_214 ),
inference(resolution,[],[f2366,f1423]) ).
fof(f22874,plain,
( spl0_810
| ~ spl0_35
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2704,f2361,f997,f22872]) ).
fof(f22872,plain,
( spl0_810
<=> ! [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_810])]) ).
fof(f2704,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_35
| ~ spl0_213 ),
inference(resolution,[],[f2362,f998]) ).
fof(f22870,plain,
( spl0_809
| ~ spl0_117
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2607,f2303,f1422,f22868]) ).
fof(f22868,plain,
( spl0_809
<=> ! [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_809])]) ).
fof(f2607,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_117
| ~ spl0_201 ),
inference(resolution,[],[f2304,f1423]) ).
fof(f22866,plain,
( spl0_808
| ~ spl0_116
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2600,f2303,f1418,f22864]) ).
fof(f22864,plain,
( spl0_808
<=> ! [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_808])]) ).
fof(f2600,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_116
| ~ spl0_201 ),
inference(resolution,[],[f2304,f1419]) ).
fof(f22862,plain,
( spl0_807
| ~ spl0_115
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2599,f2303,f1414,f22860]) ).
fof(f22860,plain,
( spl0_807
<=> ! [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_807])]) ).
fof(f2599,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_115
| ~ spl0_201 ),
inference(resolution,[],[f2304,f1415]) ).
fof(f22858,plain,
( spl0_806
| ~ spl0_117
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2584,f2299,f1422,f22856]) ).
fof(f22856,plain,
( spl0_806
<=> ! [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_806])]) ).
fof(f2584,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_117
| ~ spl0_200 ),
inference(resolution,[],[f2300,f1423]) ).
fof(f22854,plain,
( spl0_805
| ~ spl0_116
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2577,f2299,f1418,f22852]) ).
fof(f22852,plain,
( spl0_805
<=> ! [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_805])]) ).
fof(f2577,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_116
| ~ spl0_200 ),
inference(resolution,[],[f2300,f1419]) ).
fof(f22850,plain,
( spl0_804
| ~ spl0_115
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2576,f2299,f1414,f22848]) ).
fof(f22848,plain,
( spl0_804
<=> ! [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_804])]) ).
fof(f2576,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_115
| ~ spl0_200 ),
inference(resolution,[],[f2300,f1415]) ).
fof(f22846,plain,
( spl0_803
| ~ spl0_106
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2483,f2279,f1375,f22844]) ).
fof(f22844,plain,
( spl0_803
<=> ! [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_803])]) ).
fof(f2483,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_106
| ~ spl0_195 ),
inference(resolution,[],[f2280,f1376]) ).
fof(f22842,plain,
( spl0_802
| ~ spl0_105
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2482,f2279,f1371,f22840]) ).
fof(f22840,plain,
( spl0_802
<=> ! [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_802])]) ).
fof(f2482,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_105
| ~ spl0_195 ),
inference(resolution,[],[f2280,f1372]) ).
fof(f22838,plain,
( spl0_801
| ~ spl0_106
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2460,f2275,f1375,f22836]) ).
fof(f22836,plain,
( spl0_801
<=> ! [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_801])]) ).
fof(f2460,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_106
| ~ spl0_194 ),
inference(resolution,[],[f2276,f1376]) ).
fof(f22834,plain,
( spl0_800
| ~ spl0_92
| ~ spl0_752 ),
inference(avatar_split_clause,[],[f22486,f21189,f1244,f22832]) ).
fof(f22486,plain,
( ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(v_Lab____,X0),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_92
| ~ spl0_752 ),
inference(resolution,[],[f21190,f1245]) ).
fof(f22830,plain,
( spl0_799
| ~ spl0_105
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2459,f2275,f1371,f22828]) ).
fof(f22828,plain,
( spl0_799
<=> ! [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_799])]) ).
fof(f2459,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_105
| ~ spl0_194 ),
inference(resolution,[],[f2276,f1372]) ).
fof(f22826,plain,
( spl0_798
| ~ spl0_20
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2126,f1853,f937,f22824]) ).
fof(f22824,plain,
( spl0_798
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f1853,plain,
( spl0_176
<=> ! [X2,X23,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X23,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2126,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1) )
| ~ spl0_20
| ~ spl0_176 ),
inference(resolution,[],[f1854,f938]) ).
fof(f1854,plain,
( ! [X2,X4,X23] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X23,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X4,X2) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1853]) ).
fof(f22822,plain,
( spl0_797
| ~ spl0_20
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f2122,f1844,f937,f22820]) ).
fof(f22820,plain,
( spl0_797
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f1844,plain,
( spl0_175
<=> ! [X2,X23,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X4,X23,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f2122,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) )
| ~ spl0_20
| ~ spl0_175 ),
inference(resolution,[],[f1845,f938]) ).
fof(f1845,plain,
( ! [X2,X4,X23] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X4,X23,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X4,X2) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1844]) ).
fof(f22818,plain,
( spl0_796
| ~ spl0_62
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f2106,f1824,f1108,f22816]) ).
fof(f22816,plain,
( spl0_796
<=> ! [X2,X0,X1,X3] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2106,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),X0)) )
| ~ spl0_62
| ~ spl0_170 ),
inference(resolution,[],[f1825,f1109]) ).
fof(f22814,plain,
( spl0_795
| ~ spl0_62
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2099,f1820,f1108,f22812]) ).
fof(f22812,plain,
( spl0_795
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f2099,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X0)) )
| ~ spl0_62
| ~ spl0_169 ),
inference(resolution,[],[f1821,f1109]) ).
fof(f22810,plain,
( spl0_794
| ~ spl0_77
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1953,f1768,f1183,f22808]) ).
fof(f22808,plain,
( spl0_794
<=> ! [X2,X0,X1] : c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X1,X2,tc_prod(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f1953,plain,
( ! [X2,X0,X1] : c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X1,X2,tc_prod(X0,X0))
| ~ spl0_77
| ~ spl0_156 ),
inference(superposition,[],[f1184,f1769]) ).
fof(f22806,plain,
( spl0_793
| ~ spl0_66
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1952,f1768,f1138,f22804]) ).
fof(f22804,plain,
( spl0_793
<=> ! [X0,X1] : c_lessequals(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1,tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f1952,plain,
( ! [X0,X1] : c_lessequals(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_66
| ~ spl0_156 ),
inference(superposition,[],[f1139,f1769]) ).
fof(f22802,plain,
( spl0_792
| ~ spl0_35
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1938,f1764,f997,f22800]) ).
fof(f22800,plain,
( spl0_792
<=> ! [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_792])]) ).
fof(f1938,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_35
| ~ spl0_155 ),
inference(resolution,[],[f1765,f998]) ).
fof(f22798,plain,
( spl0_791
| ~ spl0_61
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1923,f1756,f1104,f22796]) ).
fof(f22796,plain,
( spl0_791
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f1923,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X4) )
| ~ spl0_61
| ~ spl0_154 ),
inference(resolution,[],[f1757,f1105]) ).
fof(f22794,plain,
( spl0_790
| ~ spl0_61
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1919,f1752,f1104,f22792]) ).
fof(f22792,plain,
( spl0_790
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X3,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f1919,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X3,tc_bool)),X4) )
| ~ spl0_61
| ~ spl0_153 ),
inference(resolution,[],[f1753,f1105]) ).
fof(f22779,plain,
( spl0_789
| ~ spl0_79
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1729,f1605,f1191,f22777]) ).
fof(f22777,plain,
( spl0_789
<=> ! [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_789])]) ).
fof(f1729,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_79
| ~ spl0_145 ),
inference(resolution,[],[f1606,f1192]) ).
fof(f22775,plain,
( spl0_788
| ~ spl0_80
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1728,f1605,f1195,f22773]) ).
fof(f22773,plain,
( spl0_788
<=> ! [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_788])]) ).
fof(f1728,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_80
| ~ spl0_145 ),
inference(resolution,[],[f1606,f1196]) ).
fof(f22771,plain,
( spl0_787
| ~ spl0_78
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1727,f1605,f1187,f22769]) ).
fof(f22769,plain,
( spl0_787
<=> ! [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_787])]) ).
fof(f1727,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_78
| ~ spl0_145 ),
inference(resolution,[],[f1606,f1188]) ).
fof(f22767,plain,
( spl0_786
| ~ spl0_81
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1726,f1605,f1199,f22765]) ).
fof(f22765,plain,
( spl0_786
<=> ! [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_786])]) ).
fof(f1726,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_81
| ~ spl0_145 ),
inference(resolution,[],[f1606,f1200]) ).
fof(f22763,plain,
( spl0_785
| ~ spl0_79
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1699,f1597,f1191,f22761]) ).
fof(f22761,plain,
( spl0_785
<=> ! [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_785])]) ).
fof(f1699,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_79
| ~ spl0_143 ),
inference(resolution,[],[f1598,f1192]) ).
fof(f22759,plain,
( spl0_784
| ~ spl0_80
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1698,f1597,f1195,f22757]) ).
fof(f22757,plain,
( spl0_784
<=> ! [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_784])]) ).
fof(f1698,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_80
| ~ spl0_143 ),
inference(resolution,[],[f1598,f1196]) ).
fof(f22755,plain,
( spl0_783
| ~ spl0_81
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1696,f1597,f1199,f22753]) ).
fof(f22753,plain,
( spl0_783
<=> ! [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_783])]) ).
fof(f1696,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_81
| ~ spl0_143 ),
inference(resolution,[],[f1598,f1200]) ).
fof(f22751,plain,
( spl0_782
| ~ spl0_68
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1661,f1589,f1146,f22749]) ).
fof(f22749,plain,
( spl0_782
<=> ! [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_782])]) ).
fof(f1661,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_68
| ~ spl0_142 ),
inference(resolution,[],[f1590,f1147]) ).
fof(f22747,plain,
( spl0_781
| ~ spl0_69
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1660,f1589,f1150,f22745]) ).
fof(f22745,plain,
( spl0_781
<=> ! [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_781])]) ).
fof(f1660,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_69
| ~ spl0_142 ),
inference(resolution,[],[f1590,f1151]) ).
fof(f22743,plain,
( spl0_780
| ~ spl0_67
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1659,f1589,f1142,f22741]) ).
fof(f22741,plain,
( spl0_780
<=> ! [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_780])]) ).
fof(f1659,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_67
| ~ spl0_142 ),
inference(resolution,[],[f1590,f1143]) ).
fof(f22739,plain,
( spl0_779
| ~ spl0_61
| ~ spl0_770 ),
inference(avatar_split_clause,[],[f22693,f22602,f1104,f22737]) ).
fof(f22602,plain,
( spl0_770
<=> ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f22693,plain,
( ! [X0,X1] : c_in(v_a____,c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)
| ~ spl0_61
| ~ spl0_770 ),
inference(resolution,[],[f22603,f1105]) ).
fof(f22603,plain,
( ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_a____))
| ~ spl0_770 ),
inference(avatar_component_clause,[],[f22602]) ).
fof(f22735,plain,
( spl0_778
| ~ spl0_70
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1658,f1589,f1154,f22733]) ).
fof(f22733,plain,
( spl0_778
<=> ! [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_778])]) ).
fof(f1658,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_70
| ~ spl0_142 ),
inference(resolution,[],[f1590,f1155]) ).
fof(f22731,plain,
( spl0_777
| ~ spl0_68
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1634,f1581,f1146,f22729]) ).
fof(f22729,plain,
( spl0_777
<=> ! [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_777])]) ).
fof(f1634,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_68
| ~ spl0_140 ),
inference(resolution,[],[f1582,f1147]) ).
fof(f22727,plain,
( spl0_776
| ~ spl0_69
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1633,f1581,f1150,f22725]) ).
fof(f22725,plain,
( spl0_776
<=> ! [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_776])]) ).
fof(f1633,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_69
| ~ spl0_140 ),
inference(resolution,[],[f1582,f1151]) ).
fof(f22723,plain,
( spl0_775
| ~ spl0_67
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1632,f1581,f1142,f22721]) ).
fof(f22721,plain,
( spl0_775
<=> ! [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_775])]) ).
fof(f1632,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_67
| ~ spl0_140 ),
inference(resolution,[],[f1582,f1143]) ).
fof(f22719,plain,
( spl0_774
| ~ spl0_82
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1348,f1320,f1204,f22717]) ).
fof(f22717,plain,
( spl0_774
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacc(X1,X2) = c_Set_Oinsert(X0,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f1348,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacc(X1,X2) = c_Set_Oinsert(X0,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) )
| ~ spl0_82
| ~ spl0_98 ),
inference(resolution,[],[f1321,f1205]) ).
fof(f22715,plain,
( spl0_773
| ~ spl0_54
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1284,f1224,f1076,f22713]) ).
fof(f22713,plain,
( spl0_773
<=> ! [X0,X1] :
( c_Transitive__Closure_Otrancl(X0,X1) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1)
| ~ c_Relation_Osym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f1284,plain,
( ! [X0,X1] :
( c_Transitive__Closure_Otrancl(X0,X1) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1)
| ~ c_Relation_Osym(X0,X1) )
| ~ spl0_54
| ~ spl0_87 ),
inference(resolution,[],[f1225,f1077]) ).
fof(f22711,plain,
( spl0_772
| ~ spl0_29
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1266,f1171,f973,f22709]) ).
fof(f22709,plain,
( spl0_772
<=> ! [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_772])]) ).
fof(f1171,plain,
( spl0_74
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X6,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1266,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_29
| ~ spl0_74 ),
inference(resolution,[],[f1172,f974]) ).
fof(f1172,plain,
( ! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X6,X2) = X6 )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f22707,plain,
( spl0_771
| ~ spl0_29
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f1264,f1167,f973,f22705]) ).
fof(f22705,plain,
( spl0_771
<=> ! [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_771])]) ).
fof(f1167,plain,
( spl0_73
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X2),X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1264,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_29
| ~ spl0_73 ),
inference(resolution,[],[f1168,f974]) ).
fof(f1168,plain,
( ! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X2),X2) = X6 )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1167]) ).
fof(f22604,plain,
( spl0_770
| ~ spl0_346
| ~ spl0_752 ),
inference(avatar_split_clause,[],[f22493,f21189,f4509,f22602]) ).
fof(f22493,plain,
( ! [X0] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_a____))
| ~ spl0_346
| ~ spl0_752 ),
inference(resolution,[],[f21190,f4510]) ).
fof(f21382,plain,
( spl0_769
| ~ spl0_307
| ~ spl0_750 ),
inference(avatar_split_clause,[],[f21245,f21181,f3501,f21380]) ).
fof(f21245,plain,
( ! [X0,X1] : c_in(v_a____,c_Relation_ORange(c_Set_Oinsert(X0,v_Lab____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_307
| ~ spl0_750 ),
inference(resolution,[],[f21182,f3502]) ).
fof(f21288,plain,
( spl0_768
| ~ spl0_376
| ~ spl0_538 ),
inference(avatar_split_clause,[],[f13137,f12801,f5098,f21286]) ).
fof(f21286,plain,
( spl0_768
<=> ! [X2,X0,X1] : ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f12801,plain,
( spl0_538
<=> ! [X4,X7,X6,X2] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f13137,plain,
( ! [X2,X0,X1] : ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)),X1)
| ~ spl0_376
| ~ spl0_538 ),
inference(resolution,[],[f12802,f5099]) ).
fof(f12802,plain,
( ! [X2,X6,X7,X4] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2) )
| ~ spl0_538 ),
inference(avatar_component_clause,[],[f12801]) ).
fof(f21284,plain,
( spl0_767
| ~ spl0_147
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f8398,f7935,f1614,f21282]) ).
fof(f21282,plain,
( spl0_767
<=> ! [X0,X1] : ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Arrow__Order__Mirabelle_Omktop(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f8398,plain,
( ! [X0,X1] : ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(c_Arrow__Order__Mirabelle_Omktop(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_147
| ~ spl0_444 ),
inference(resolution,[],[f7936,f1615]) ).
fof(f21280,plain,
( spl0_766
| ~ spl0_103
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f6512,f6211,f1340,f21278]) ).
fof(f21278,plain,
( spl0_766
<=> ! [X0] :
( c_in(v_b____,c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f6512,plain,
( ! [X0] :
( c_in(v_b____,c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_103
| ~ spl0_403 ),
inference(resolution,[],[f6212,f1342]) ).
fof(f21276,plain,
( spl0_765
| ~ spl0_103
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f6456,f6203,f1340,f21274]) ).
fof(f21274,plain,
( spl0_765
<=> ! [X0,X1] : hAPP(X0,v_a____) = hAPP(c_Recdef_Ocut(X0,v_Lab____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,X1),v_a____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f6456,plain,
( ! [X0,X1] : hAPP(X0,v_a____) = hAPP(c_Recdef_Ocut(X0,v_Lab____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,X1),v_a____)
| ~ spl0_103
| ~ spl0_401 ),
inference(resolution,[],[f6204,f1342]) ).
fof(f21272,plain,
( spl0_764
| ~ spl0_59
| ~ spl0_102
| ~ spl0_156
| ~ spl0_314
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6158,f5563,f3962,f1768,f1336,f1096,f21270]) ).
fof(f21270,plain,
( spl0_764
<=> ! [X0] : c_Equiv__Relations_Oequiv(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f5563,plain,
( spl0_390
<=> ! [X2,X4] :
( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X4,X2,X2),X2,X2),X4,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f6158,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| ~ spl0_59
| ~ spl0_102
| ~ spl0_156
| ~ spl0_314
| ~ spl0_390 ),
inference(forward_demodulation,[],[f6157,f1097]) ).
fof(f6157,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| ~ spl0_102
| ~ spl0_156
| ~ spl0_314
| ~ spl0_390 ),
inference(forward_demodulation,[],[f6156,f1337]) ).
fof(f6156,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),X0,X0),c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| ~ spl0_156
| ~ spl0_314
| ~ spl0_390 ),
inference(forward_demodulation,[],[f6149,f1769]) ).
fof(f6149,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0,X0),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_314
| ~ spl0_390 ),
inference(trivial_inequality_removal,[],[f6148]) ).
fof(f6148,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool))
| c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0,X0),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) )
| ~ spl0_314
| ~ spl0_390 ),
inference(superposition,[],[f5564,f3963]) ).
fof(f5564,plain,
( ! [X2,X4] :
( c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2) != X4
| c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X4,X2,X2),X2,X2),X4,X2) )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f5563]) ).
fof(f21268,plain,
( spl0_763
| ~ spl0_185
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4998,f4541,f1889,f21266]) ).
fof(f21266,plain,
( spl0_763
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X2))
| ~ c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f4998,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X2))
| ~ c_Relation_Oirrefl(X0,X1) )
| ~ spl0_185
| ~ spl0_354 ),
inference(resolution,[],[f4542,f1890]) ).
fof(f21264,plain,
( spl0_762
| ~ spl0_188
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4997,f4541,f1901,f21262]) ).
fof(f21262,plain,
( spl0_762
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X2))
| ~ c_Wellfounded_Owf(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f4997,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X2))
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_188
| ~ spl0_354 ),
inference(resolution,[],[f4542,f1902]) ).
fof(f21260,plain,
( spl0_761
| ~ spl0_187
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4969,f4537,f1897,f21258]) ).
fof(f21258,plain,
( spl0_761
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X2))
| ~ c_Nitpick_Orefl_H(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f4969,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X1),X2),X2))
| ~ c_Nitpick_Orefl_H(X0,X1) )
| ~ spl0_187
| ~ spl0_353 ),
inference(resolution,[],[f4538,f1898]) ).
fof(f21223,plain,
( spl0_760
| ~ spl0_250
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3935,f3501,f2937,f21221]) ).
fof(f21221,plain,
( spl0_760
<=> ! [X0,X1] :
( c_in(X0,c_Relation_ORange(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f3935,plain,
( ! [X0,X1] :
( c_in(X0,c_Relation_ORange(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1 )
| ~ spl0_250
| ~ spl0_307 ),
inference(resolution,[],[f3502,f2938]) ).
fof(f21219,plain,
( spl0_759
| ~ spl0_253
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3934,f3501,f2949,f21217]) ).
fof(f21217,plain,
( spl0_759
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Arrow__Order__Mirabelle_Omktop(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f3934,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Arrow__Order__Mirabelle_Omktop(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 )
| ~ spl0_253
| ~ spl0_307 ),
inference(resolution,[],[f3502,f2950]) ).
fof(f21215,plain,
( spl0_758
| ~ spl0_252
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3933,f3501,f2945,f21213]) ).
fof(f21213,plain,
( spl0_758
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f3933,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X2 )
| ~ spl0_252
| ~ spl0_307 ),
inference(resolution,[],[f3502,f2946]) ).
fof(f21211,plain,
( spl0_757
| ~ spl0_299
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3928,f3501,f3469,f21209]) ).
fof(f21209,plain,
( spl0_757
<=> ! [X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_Relation_ORange(X0,X1,X1),X1)
| c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f3928,plain,
( ! [X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_Relation_ORange(X0,X1,X1),X1)
| c_Relation_Oirrefl(X0,X1) )
| ~ spl0_299
| ~ spl0_307 ),
inference(resolution,[],[f3502,f3470]) ).
fof(f21207,plain,
( spl0_756
| ~ spl0_82
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3837,f3457,f1204,f21205]) ).
fof(f21205,plain,
( spl0_756
<=> ! [X0,X1] :
( c_Nitpick_Orefl_H(c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),X1)
| ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f3837,plain,
( ! [X0,X1] :
( c_Nitpick_Orefl_H(c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),X1)
| ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1)) )
| ~ spl0_82
| ~ spl0_296 ),
inference(resolution,[],[f3458,f1205]) ).
fof(f21203,plain,
( spl0_755
| ~ spl0_147
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3040,f2893,f1614,f21201]) ).
fof(f21201,plain,
( spl0_755
<=> ! [X0,X1] : ~ c_in(X0,c_Arrow__Order__Mirabelle_Omktop(X1,hAPP(c_fst(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f3040,plain,
( ! [X0,X1] : ~ c_in(X0,c_Arrow__Order__Mirabelle_Omktop(X1,hAPP(c_fst(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_147
| ~ spl0_239 ),
inference(superposition,[],[f1615,f2894]) ).
fof(f21199,plain,
( spl0_754
| ~ spl0_148
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3039,f2893,f1618,f21197]) ).
fof(f21197,plain,
( spl0_754
<=> ! [X0,X1] : ~ c_in(X0,c_Arrow__Order__Mirabelle_Omkbot(X1,hAPP(c_snd(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f3039,plain,
( ! [X0,X1] : ~ c_in(X0,c_Arrow__Order__Mirabelle_Omkbot(X1,hAPP(c_snd(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_148
| ~ spl0_239 ),
inference(superposition,[],[f1619,f2894]) ).
fof(f21195,plain,
( spl0_753
| ~ spl0_72
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2989,f2881,f1163,f21193]) ).
fof(f21193,plain,
( spl0_753
<=> ! [X0,X3,X2,X1] : c_lessequals(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,X0,X3),X3),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f2989,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,X0,X3),X3),tc_fun(X3,tc_bool))
| ~ spl0_72
| ~ spl0_236 ),
inference(resolution,[],[f2882,f1164]) ).
fof(f21191,plain,
( spl0_752
| ~ spl0_62
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2826,f2397,f1108,f21189]) ).
fof(f2826,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,tc_prod(X2,X2))
| hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),X0)) )
| ~ spl0_62
| ~ spl0_222 ),
inference(resolution,[],[f2398,f1109]) ).
fof(f21187,plain,
( spl0_751
| ~ spl0_6
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2658,f2339,f876,f21185]) ).
fof(f21185,plain,
( spl0_751
<=> ! [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_751])]) ).
fof(f2339,plain,
( spl0_210
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f2658,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_6
| ~ spl0_210 ),
inference(resolution,[],[f2340,f878]) ).
fof(f2340,plain,
( ! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f2339]) ).
fof(f21183,plain,
( spl0_750
| ~ spl0_61
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f21137,f20993,f1104,f21181]) ).
fof(f20993,plain,
( spl0_733
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_Lab____,X0),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f21137,plain,
( ! [X2,X0,X1] : c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Set_Oinsert(X0,v_Lab____,X1),X2)
| ~ spl0_61
| ~ spl0_733 ),
inference(resolution,[],[f20994,f1105]) ).
fof(f20994,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_Lab____,X0),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_733 ),
inference(avatar_component_clause,[],[f20993]) ).
fof(f21179,plain,
( spl0_749
| ~ spl0_1
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2620,f2319,f851,f21177]) ).
fof(f21177,plain,
( spl0_749
<=> ! [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_749])]) ).
fof(f2319,plain,
( spl0_205
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2620,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_1
| ~ spl0_205 ),
inference(resolution,[],[f2320,f853]) ).
fof(f2320,plain,
( ! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2319]) ).
fof(f21175,plain,
( spl0_748
| ~ spl0_82
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2257,f1901,f1204,f21173]) ).
fof(f21173,plain,
( spl0_748
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),X1)
| ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f2257,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),X1)
| ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1)) )
| ~ spl0_82
| ~ spl0_188 ),
inference(resolution,[],[f1902,f1205]) ).
fof(f21171,plain,
( spl0_747
| ~ spl0_82
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2238,f1889,f1204,f21169]) ).
fof(f21169,plain,
( spl0_747
<=> ! [X0,X1] :
( ~ c_Relation_Oirrefl(c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),X1)
| ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f2238,plain,
( ! [X0,X1] :
( ~ c_Relation_Oirrefl(c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),X1)
| ~ c_Wellfounded_Owf(X0,tc_prod(X1,X1)) )
| ~ spl0_82
| ~ spl0_185 ),
inference(resolution,[],[f1890,f1205]) ).
fof(f21167,plain,
( spl0_746
| ~ spl0_67
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2207,f1869,f1142,f21165]) ).
fof(f21165,plain,
( spl0_746
<=> ! [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_746])]) ).
fof(f2207,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_67
| ~ spl0_180 ),
inference(duplicate_literal_removal,[],[f2190]) ).
fof(f2190,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_67
| ~ spl0_180 ),
inference(resolution,[],[f1870,f1143]) ).
fof(f21163,plain,
( spl0_745
| ~ spl0_68
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2206,f1869,f1146,f21161]) ).
fof(f21161,plain,
( spl0_745
<=> ! [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_745])]) ).
fof(f2206,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_68
| ~ spl0_180 ),
inference(duplicate_literal_removal,[],[f2192]) ).
fof(f2192,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_68
| ~ spl0_180 ),
inference(resolution,[],[f1870,f1147]) ).
fof(f21159,plain,
( spl0_744
| ~ spl0_67
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2184,f1865,f1142,f21157]) ).
fof(f21157,plain,
( spl0_744
<=> ! [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_744])]) ).
fof(f2184,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_67
| ~ spl0_179 ),
inference(duplicate_literal_removal,[],[f2167]) ).
fof(f2167,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_67
| ~ spl0_179 ),
inference(resolution,[],[f1866,f1143]) ).
fof(f21155,plain,
( spl0_743
| ~ spl0_68
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2183,f1865,f1146,f21153]) ).
fof(f21153,plain,
( spl0_743
<=> ! [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_743])]) ).
fof(f2183,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_68
| ~ spl0_179 ),
inference(duplicate_literal_removal,[],[f2169]) ).
fof(f2169,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_68
| ~ spl0_179 ),
inference(resolution,[],[f1866,f1147]) ).
fof(f21151,plain,
( spl0_742
| ~ spl0_81
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f2059,f1796,f1199,f21149]) ).
fof(f21149,plain,
( spl0_742
<=> ! [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_742])]) ).
fof(f2059,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_81
| ~ spl0_163 ),
inference(duplicate_literal_removal,[],[f2043]) ).
fof(f2043,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_81
| ~ spl0_163 ),
inference(resolution,[],[f1797,f1200]) ).
fof(f21147,plain,
( spl0_741
| ~ spl0_80
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f2058,f1796,f1195,f21145]) ).
fof(f21145,plain,
( spl0_741
<=> ! [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_741])]) ).
fof(f2058,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_80
| ~ spl0_163 ),
inference(duplicate_literal_removal,[],[f2045]) ).
fof(f2045,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_80
| ~ spl0_163 ),
inference(resolution,[],[f1797,f1196]) ).
fof(f21143,plain,
( spl0_740
| ~ spl0_81
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2010,f1784,f1199,f21141]) ).
fof(f21141,plain,
( spl0_740
<=> ! [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_740])]) ).
fof(f2010,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_81
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1998]) ).
fof(f1998,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_81
| ~ spl0_160 ),
inference(resolution,[],[f1785,f1200]) ).
fof(f21136,plain,
( spl0_739
| ~ spl0_80
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2009,f1784,f1195,f21134]) ).
fof(f21134,plain,
( spl0_739
<=> ! [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_739])]) ).
fof(f2009,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_80
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f2000]) ).
fof(f2000,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_80
| ~ spl0_160 ),
inference(resolution,[],[f1785,f1196]) ).
fof(f21132,plain,
( spl0_738
| ~ spl0_35
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1665,f1589,f997,f21130]) ).
fof(f21130,plain,
( spl0_738
<=> ! [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_738])]) ).
fof(f1665,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_35
| ~ spl0_142 ),
inference(resolution,[],[f1590,f998]) ).
fof(f21128,plain,
( spl0_737
| ~ spl0_35
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1638,f1581,f997,f21126]) ).
fof(f21126,plain,
( spl0_737
<=> ! [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_737])]) ).
fof(f1638,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_35
| ~ spl0_140 ),
inference(resolution,[],[f1582,f998]) ).
fof(f21124,plain,
( spl0_736
| ~ spl0_61
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1544,f1450,f1104,f21122]) ).
fof(f21122,plain,
( spl0_736
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(X3)
| c_in(c_Pair(X2,X3,X0,X1),c_snd(X0,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f1544,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X3)
| c_in(c_Pair(X2,X3,X0,X1),c_snd(X0,X1),X4) )
| ~ spl0_61
| ~ spl0_124 ),
inference(superposition,[],[f1105,f1451]) ).
fof(f21120,plain,
( spl0_735
| ~ spl0_61
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1543,f1446,f1104,f21118]) ).
fof(f21118,plain,
( spl0_735
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X2)
| c_in(c_Pair(X2,X3,X0,X1),c_fst(X0,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f1543,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X2)
| c_in(c_Pair(X2,X3,X0,X1),c_fst(X0,X1),X4) )
| ~ spl0_61
| ~ spl0_123 ),
inference(superposition,[],[f1105,f1447]) ).
fof(f21116,plain,
( spl0_734
| ~ spl0_98
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1368,f1340,f1320,f21113]) ).
fof(f21113,plain,
( spl0_734
<=> v_Lab____ = c_Set_Oinsert(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f1368,plain,
( v_Lab____ = c_Set_Oinsert(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_98
| ~ spl0_103 ),
inference(resolution,[],[f1342,f1321]) ).
fof(f20995,plain,
( spl0_733
| ~ spl0_104
| ~ spl0_703 ),
inference(avatar_split_clause,[],[f20355,f20296,f1351,f20993]) ).
fof(f20296,plain,
( spl0_703
<=> ! [X2,X0,X1,X3] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f20355,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_Lab____,X0),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_104
| ~ spl0_703 ),
inference(superposition,[],[f20297,f1352]) ).
fof(f20297,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0))
| ~ spl0_703 ),
inference(avatar_component_clause,[],[f20296]) ).
fof(f20589,plain,
( spl0_732
| ~ spl0_244
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5463,f5098,f2913,f20587]) ).
fof(f20587,plain,
( spl0_732
<=> ! [X0,X1] : ~ c_Wellfounded_Oacyclic(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f5463,plain,
( ! [X0,X1] : ~ c_Wellfounded_Oacyclic(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ spl0_244
| ~ spl0_376 ),
inference(resolution,[],[f5099,f2914]) ).
fof(f20585,plain,
( spl0_731
| ~ spl0_148
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4986,f4541,f1618,f20583]) ).
fof(f20583,plain,
( spl0_731
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f4986,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1))
| ~ spl0_148
| ~ spl0_354 ),
inference(resolution,[],[f4542,f1619]) ).
fof(f20581,plain,
( spl0_730
| ~ spl0_147
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4985,f4541,f1614,f20579]) ).
fof(f4985,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2))
| ~ spl0_147
| ~ spl0_354 ),
inference(resolution,[],[f4542,f1615]) ).
fof(f20577,plain,
( spl0_729
| ~ spl0_38
| ~ spl0_156
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4932,f4529,f1768,f1009,f20575]) ).
fof(f20575,plain,
( spl0_729
<=> ! [X0,X1] : c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f4932,plain,
( ! [X0,X1] : c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1)
| ~ spl0_38
| ~ spl0_156
| ~ spl0_351 ),
inference(forward_demodulation,[],[f4917,f1769]) ).
fof(f4917,plain,
( ! [X0,X1] : c_in(X0,c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ spl0_38
| ~ spl0_351 ),
inference(resolution,[],[f4530,f1010]) ).
fof(f20573,plain,
( spl0_728
| ~ spl0_61
| ~ spl0_711 ),
inference(avatar_split_clause,[],[f20527,f20468,f1104,f20571]) ).
fof(f20571,plain,
( spl0_728
<=> ! [X2,X0,X1] : c_in(v_a____,c_Set_Oinsert(X0,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f20468,plain,
( spl0_711
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f20527,plain,
( ! [X2,X0,X1] : c_in(v_a____,c_Set_Oinsert(X0,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)
| ~ spl0_61
| ~ spl0_711 ),
inference(resolution,[],[f20469,f1105]) ).
fof(f20469,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_a____))
| ~ spl0_711 ),
inference(avatar_component_clause,[],[f20468]) ).
fof(f20569,plain,
( spl0_727
| ~ spl0_187
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4435,f4039,f1897,f20567]) ).
fof(f20567,plain,
( spl0_727
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,X3,X2)
| ~ c_Nitpick_Orefl_H(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f4435,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,X3,X2)
| ~ c_Nitpick_Orefl_H(X3,X2) )
| ~ spl0_187
| ~ spl0_333 ),
inference(resolution,[],[f4040,f1898]) ).
fof(f20565,plain,
( spl0_726
| ~ spl0_187
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4430,f4035,f1897,f20563]) ).
fof(f20563,plain,
( spl0_726
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_Nitpick_Orefl_H(c_Product__Type_OSigma(X1,X3,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f4430,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Nitpick_Orefl_H(c_Product__Type_OSigma(X1,X3,X2,X2),X2) )
| ~ spl0_187
| ~ spl0_332 ),
inference(resolution,[],[f4036,f1898]) ).
fof(f20561,plain,
( spl0_725
| ~ spl0_187
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4394,f4027,f1897,f20559]) ).
fof(f20559,plain,
( spl0_725
<=> ! [X0,X3,X2,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,X3,X2)
| ~ c_Nitpick_Orefl_H(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f4394,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,X3,X2)
| ~ c_Nitpick_Orefl_H(X3,X2) )
| ~ spl0_187
| ~ spl0_330 ),
inference(resolution,[],[f4028,f1898]) ).
fof(f20557,plain,
( spl0_724
| ~ spl0_72
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2800,f2377,f1163,f20555]) ).
fof(f20555,plain,
( spl0_724
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f2800,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) )
| ~ spl0_72
| ~ spl0_217 ),
inference(resolution,[],[f2378,f1164]) ).
fof(f20553,plain,
( spl0_723
| ~ spl0_72
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2775,f2373,f1163,f20551]) ).
fof(f20551,plain,
( spl0_723
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f2775,plain,
( ! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) )
| ~ spl0_72
| ~ spl0_216 ),
inference(resolution,[],[f2374,f1164]) ).
fof(f20549,plain,
( spl0_722
| ~ spl0_72
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2750,f2369,f1163,f20547]) ).
fof(f20547,plain,
( spl0_722
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f2750,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) )
| ~ spl0_72
| ~ spl0_215 ),
inference(resolution,[],[f2370,f1164]) ).
fof(f20545,plain,
( spl0_721
| ~ spl0_72
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2490,f2279,f1163,f20543]) ).
fof(f20543,plain,
( spl0_721
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f2490,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool)) = X1
| ~ spl0_72
| ~ spl0_195 ),
inference(resolution,[],[f2280,f1164]) ).
fof(f20541,plain,
( spl0_720
| ~ spl0_72
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2467,f2275,f1163,f20539]) ).
fof(f20539,plain,
( spl0_720
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f2467,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)) = X0
| ~ spl0_72
| ~ spl0_194 ),
inference(resolution,[],[f2276,f1164]) ).
fof(f20537,plain,
( spl0_719
| ~ spl0_62
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2246,f1897,f1108,f20535]) ).
fof(f20535,plain,
( spl0_719
<=> ! [X2,X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f2246,plain,
( ! [X2,X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))) )
| ~ spl0_62
| ~ spl0_187 ),
inference(resolution,[],[f1898,f1109]) ).
fof(f20533,plain,
( spl0_718
| ~ spl0_38
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1950,f1768,f1009,f20531]) ).
fof(f20531,plain,
( spl0_718
<=> ! [X0,X1] : ~ c_in(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1950,plain,
( ! [X0,X1] : ~ c_in(X1,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0))
| ~ spl0_38
| ~ spl0_156 ),
inference(superposition,[],[f1010,f1769]) ).
fof(f20526,plain,
( spl0_717
| ~ spl0_37
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1949,f1768,f1005,f20524]) ).
fof(f20524,plain,
( spl0_717
<=> ! [X0,X1] : c_Relation_Ototal__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1,tc_prod(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1949,plain,
( ! [X0,X1] : c_Relation_Ototal__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1,tc_prod(X0,X0))
| ~ spl0_37
| ~ spl0_156 ),
inference(superposition,[],[f1006,f1769]) ).
fof(f20522,plain,
( spl0_716
| ~ spl0_35
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1724,f1605,f997,f20520]) ).
fof(f20520,plain,
( spl0_716
<=> ! [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_716])]) ).
fof(f1724,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_35
| ~ spl0_145 ),
inference(resolution,[],[f1606,f998]) ).
fof(f20518,plain,
( spl0_715
| ~ spl0_35
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1694,f1597,f997,f20516]) ).
fof(f20516,plain,
( spl0_715
<=> ! [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_715])]) ).
fof(f1694,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_35
| ~ spl0_143 ),
inference(resolution,[],[f1598,f998]) ).
fof(f20514,plain,
( spl0_714
| ~ spl0_20
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1560,f1474,f937,f20512]) ).
fof(f20512,plain,
( spl0_714
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f1560,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1) )
| ~ spl0_20
| ~ spl0_130 ),
inference(resolution,[],[f1475,f938]) ).
fof(f20510,plain,
( spl0_713
| ~ spl0_62
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1541,f1442,f1108,f20508]) ).
fof(f20508,plain,
( spl0_713
<=> ! [X2,X0,X1,X3] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1541,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X2),X0)) )
| ~ spl0_62
| ~ spl0_122 ),
inference(resolution,[],[f1443,f1109]) ).
fof(f20506,plain,
( spl0_712
| ~ spl0_61
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1532,f1426,f1104,f20504]) ).
fof(f20504,plain,
( spl0_712
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| c_in(X1,c_Set_Oinsert(X2,X0,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f1532,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| c_in(X1,c_Set_Oinsert(X2,X0,X3),X4) )
| ~ spl0_61
| ~ spl0_118 ),
inference(resolution,[],[f1427,f1105]) ).
fof(f20470,plain,
( spl0_711
| ~ spl0_521
| ~ spl0_703 ),
inference(avatar_split_clause,[],[f20359,f20296,f12233,f20468]) ).
fof(f12233,plain,
( spl0_521
<=> ! [X0] : c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Set_Oinsert(v_a____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f20359,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_a____))
| ~ spl0_521
| ~ spl0_703 ),
inference(superposition,[],[f20297,f12234]) ).
fof(f12234,plain,
( ! [X0] : c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Set_Oinsert(v_a____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)
| ~ spl0_521 ),
inference(avatar_component_clause,[],[f12233]) ).
fof(f20344,plain,
( spl0_710
| ~ spl0_148
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f7529,f6614,f1618,f20342]) ).
fof(f20342,plain,
( spl0_710
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f7529,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_148
| ~ spl0_418 ),
inference(resolution,[],[f6615,f1619]) ).
fof(f20340,plain,
( spl0_709
| ~ spl0_103
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5496,f5102,f1340,f20337]) ).
fof(f20337,plain,
( spl0_709
<=> c_in(v_a____,c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f5496,plain,
( c_in(v_a____,c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_103
| ~ spl0_377 ),
inference(resolution,[],[f5103,f1342]) ).
fof(f20335,plain,
( spl0_708
| ~ spl0_135
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4971,f4537,f1494,f20333]) ).
fof(f20333,plain,
( spl0_708
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId(X0),X0,X0),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f4971,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(c_Relation_OId(X0),X0,X0),X1),X1))
| ~ spl0_135
| ~ spl0_353 ),
inference(resolution,[],[f4538,f1495]) ).
fof(f20314,plain,
( spl0_707
| ~ spl0_154
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4843,f4513,f1756,f20312]) ).
fof(f20312,plain,
( spl0_707
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X1),X2))
| ~ hBOOL(hAPP(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f4843,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X1),X2))
| ~ hBOOL(hAPP(X0,X2)) )
| ~ spl0_154
| ~ spl0_347 ),
inference(superposition,[],[f1757,f4514]) ).
fof(f20310,plain,
( spl0_706
| ~ spl0_106
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4841,f4513,f1375,f20308]) ).
fof(f20308,plain,
( spl0_706
<=> ! [X0,X1] : c_lessequals(X0,c_Transitive__Closure_Otrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f4841,plain,
( ! [X0,X1] : c_lessequals(X0,c_Transitive__Closure_Otrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool))
| ~ spl0_106
| ~ spl0_347 ),
inference(superposition,[],[f1376,f4514]) ).
fof(f20306,plain,
( spl0_705
| ~ spl0_53
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4733,f4493,f1072,f20304]) ).
fof(f20304,plain,
( spl0_705
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| ~ c_in(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f4493,plain,
( spl0_342
<=> ! [X5,X9,X6,X2] :
( ~ c_in(X6,X9,X2)
| ~ c_in(X6,X5,X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f4733,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| ~ c_in(X2,X0,X1) )
| ~ spl0_53
| ~ spl0_342 ),
inference(duplicate_literal_removal,[],[f4723]) ).
fof(f4723,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| ~ c_in(X2,X0,X1)
| ~ c_in(X2,X0,X1) )
| ~ spl0_53
| ~ spl0_342 ),
inference(superposition,[],[f4494,f1073]) ).
fof(f4494,plain,
( ! [X2,X6,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool))
| ~ c_in(X6,X5,X2)
| ~ c_in(X6,X9,X2) )
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f4493]) ).
fof(f20302,plain,
( spl0_704
| ~ spl0_187
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3930,f3501,f1897,f20300]) ).
fof(f20300,plain,
( spl0_704
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(X1,X2,X2),X2)
| ~ c_Nitpick_Orefl_H(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f3930,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(X1,X2,X2),X2)
| ~ c_Nitpick_Orefl_H(X1,X2) )
| ~ spl0_187
| ~ spl0_307 ),
inference(resolution,[],[f3502,f1898]) ).
fof(f20298,plain,
( spl0_703
| ~ spl0_41
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f3010,f2889,f1021,f20296]) ).
fof(f3010,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0))
| ~ spl0_41
| ~ spl0_238 ),
inference(superposition,[],[f1022,f2890]) ).
fof(f20294,plain,
( spl0_702
| ~ spl0_20
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1354,f1324,f937,f20292]) ).
fof(f20292,plain,
( spl0_702
<=> ! [X0,X3,X2,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X2,X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f1354,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X2,X1,X3),X3) )
| ~ spl0_20
| ~ spl0_99 ),
inference(resolution,[],[f1325,f938]) ).
fof(f20290,plain,
( spl0_701
| ~ spl0_27
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f1127,f1068,f965,f20288]) ).
fof(f20288,plain,
( spl0_701
<=> ! [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_701])]) ).
fof(f1068,plain,
( spl0_52
<=> ! [X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1127,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_27
| ~ spl0_52 ),
inference(resolution,[],[f1069,f966]) ).
fof(f1069,plain,
( ! [X2,X6] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X2) = X6 )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f20286,plain,
( spl0_700
| ~ spl0_26
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f1117,f1046,f961,f20284]) ).
fof(f20284,plain,
( spl0_700
<=> ! [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_700])]) ).
fof(f1046,plain,
( spl0_47
<=> ! [X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1117,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_26
| ~ spl0_47 ),
inference(resolution,[],[f1047,f962]) ).
fof(f1047,plain,
( ! [X2,X6] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X2) = X6 )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1046]) ).
fof(f20269,plain,
( spl0_699
| ~ spl0_157
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f12907,f12233,f1772,f20267]) ).
fof(f20267,plain,
( spl0_699
<=> ! [X0,X1] :
( ~ c_lessequals(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_fun(X0,tc_bool))
| c_in(v_a____,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f12907,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_fun(X0,tc_bool))
| c_in(v_a____,X1,X0) )
| ~ spl0_157
| ~ spl0_521 ),
inference(superposition,[],[f1773,f12234]) ).
fof(f19944,plain,
( spl0_698
| ~ spl0_57
| ~ spl0_86
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6152,f5563,f1220,f1088,f19942]) ).
fof(f19942,plain,
( spl0_698
<=> ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1220,plain,
( spl0_86
<=> ! [X2,X8,X3] : c_Relation_Orel__comp(X8,c_Relation_OId(X3),X2,X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f6152,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0)
| ~ spl0_57
| ~ spl0_86
| ~ spl0_390 ),
inference(trivial_inequality_removal,[],[f6151]) ).
fof(f6151,plain,
( ! [X0] :
( c_Relation_OId(X0) != c_Relation_OId(X0)
| c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
| ~ spl0_57
| ~ spl0_86
| ~ spl0_390 ),
inference(forward_demodulation,[],[f6145,f1221]) ).
fof(f1221,plain,
( ! [X2,X3,X8] : c_Relation_Orel__comp(X8,c_Relation_OId(X3),X2,X3,X3) = X8
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1220]) ).
fof(f6145,plain,
( ! [X0] :
( c_Relation_OId(X0) != c_Relation_Orel__comp(c_Relation_OId(X0),c_Relation_OId(X0),X0,X0,X0)
| c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
| ~ spl0_57
| ~ spl0_390 ),
inference(superposition,[],[f5564,f1089]) ).
fof(f19940,plain,
( spl0_697
| ~ spl0_148
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6061,f5555,f1618,f19938]) ).
fof(f19938,plain,
( spl0_697
<=> ! [X0,X1] : ~ c_in(X0,c_Relation_ORange(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f6061,plain,
( ! [X0,X1] : ~ c_in(X0,c_Relation_ORange(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_148
| ~ spl0_388 ),
inference(resolution,[],[f5556,f1619]) ).
fof(f19936,plain,
( spl0_696
| ~ spl0_103
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4975,f4537,f1340,f19933]) ).
fof(f19933,plain,
( spl0_696
<=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f4975,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))
| ~ spl0_103
| ~ spl0_353 ),
inference(resolution,[],[f4538,f1342]) ).
fof(f19898,plain,
( spl0_695
| ~ spl0_135
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4437,f4039,f1494,f19896]) ).
fof(f19896,plain,
( spl0_695
<=> ! [X2,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,c_Relation_OId(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f4437,plain,
( ! [X2,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Relation_Orefl__on(X1,c_Relation_OId(X2),X2) )
| ~ spl0_135
| ~ spl0_333 ),
inference(resolution,[],[f4040,f1495]) ).
fof(f19894,plain,
( spl0_694
| ~ spl0_135
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4396,f4027,f1494,f19892]) ).
fof(f19892,plain,
( spl0_694
<=> ! [X2,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_OId(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f4396,plain,
( ! [X2,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_OId(X2),X2) )
| ~ spl0_135
| ~ spl0_330 ),
inference(resolution,[],[f4028,f1495]) ).
fof(f19890,plain,
( spl0_693
| ~ spl0_185
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3343,f3179,f1889,f19888]) ).
fof(f19888,plain,
( spl0_693
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_Relation_Oirrefl(c_Relation_OId__on(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f3343,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_Relation_Oirrefl(c_Relation_OId__on(X1,X2),X2) )
| ~ spl0_185
| ~ spl0_268 ),
inference(resolution,[],[f3180,f1890]) ).
fof(f19886,plain,
( spl0_692
| ~ spl0_188
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3342,f3179,f1901,f19884]) ).
fof(f19884,plain,
( spl0_692
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_Wellfounded_Owf(c_Relation_OId__on(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f3342,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_Wellfounded_Owf(c_Relation_OId__on(X1,X2),X2) )
| ~ spl0_188
| ~ spl0_268 ),
inference(resolution,[],[f3180,f1902]) ).
fof(f19882,plain,
( spl0_691
| ~ spl0_187
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3338,f3175,f1897,f19880]) ).
fof(f19880,plain,
( spl0_691
<=> ! [X2,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Nitpick_Orefl_H(c_Relation_OId__on(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f3338,plain,
( ! [X2,X0,X1] :
( c_in(X0,X1,X2)
| ~ c_Nitpick_Orefl_H(c_Relation_OId__on(X1,X2),X2) )
| ~ spl0_187
| ~ spl0_267 ),
inference(resolution,[],[f3176,f1898]) ).
fof(f19878,plain,
( spl0_690
| ~ spl0_62
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f2236,f1885,f1108,f19876]) ).
fof(f19876,plain,
( spl0_690
<=> ! [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_690])]) ).
fof(f2236,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1))) )
| ~ spl0_62
| ~ spl0_184 ),
inference(resolution,[],[f1886,f1109]) ).
fof(f19874,plain,
( spl0_689
| ~ spl0_36
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1948,f1768,f1001,f19872]) ).
fof(f19872,plain,
( spl0_689
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1001,plain,
( spl0_36
<=> ! [X6,X2] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1948,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1))
| ~ spl0_36
| ~ spl0_156 ),
inference(superposition,[],[f1002,f1769]) ).
fof(f1002,plain,
( ! [X2,X6] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f19870,plain,
( spl0_688
| ~ spl0_62
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1575,f1494,f1108,f19868]) ).
fof(f19868,plain,
( spl0_688
<=> ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Pair(X1,X1,X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f1575,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Pair(X1,X1,X0,X0)))
| ~ spl0_62
| ~ spl0_135 ),
inference(resolution,[],[f1495,f1109]) ).
fof(f19866,plain,
( spl0_687
| ~ spl0_1
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1536,f1430,f851,f19864]) ).
fof(f19864,plain,
( spl0_687
<=> ! [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_687])]) ).
fof(f1536,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool)
| ~ spl0_1
| ~ spl0_119 ),
inference(resolution,[],[f1431,f853]) ).
fof(f19862,plain,
( spl0_686
| ~ spl0_6
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1526,f1410,f876,f19860]) ).
fof(f19860,plain,
( spl0_686
<=> ! [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_686])]) ).
fof(f1526,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0
| ~ spl0_6
| ~ spl0_114 ),
inference(resolution,[],[f1411,f878]) ).
fof(f19857,plain,
( spl0_685
| ~ spl0_6
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1524,f1406,f876,f19855]) ).
fof(f19855,plain,
( spl0_685
<=> ! [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_685])]) ).
fof(f1524,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = X0
| ~ spl0_6
| ~ spl0_113 ),
inference(resolution,[],[f1407,f878]) ).
fof(f19853,plain,
( spl0_684
| ~ spl0_2
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1504,f1379,f856,f19851]) ).
fof(f19851,plain,
( spl0_684
<=> ! [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_684])]) ).
fof(f856,plain,
( spl0_2
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1504,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool)
| ~ spl0_2
| ~ spl0_107 ),
inference(resolution,[],[f1380,f858]) ).
fof(f858,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f19849,plain,
( spl0_683
| ~ spl0_62
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f1275,f1204,f1108,f19847]) ).
fof(f19847,plain,
( spl0_683
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f1275,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) )
| ~ spl0_62
| ~ spl0_82 ),
inference(resolution,[],[f1205,f1109]) ).
fof(f19845,plain,
( spl0_682
| ~ spl0_48
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f1133,f1104,f1050,f19843]) ).
fof(f19843,plain,
( spl0_682
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X0)
| c_in(X3,c_COMBK(X0,X1,X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1133,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X0)
| c_in(X3,c_COMBK(X0,X1,X2),X4) )
| ~ spl0_48
| ~ spl0_61 ),
inference(superposition,[],[f1105,f1051]) ).
fof(f19841,plain,
( spl0_681
| ~ spl0_18
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f1130,f1080,f929,f19839]) ).
fof(f19839,plain,
( spl0_681
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f19837,plain,
( spl0_680
| ~ spl0_15
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f1129,f1080,f917,f19835]) ).
fof(f19835,plain,
( spl0_680
<=> ! [X0,X1] : c_Relation_OId__on(X0,X1) = c_Transitive__Closure_Otrancl(c_Relation_OId__on(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f917,plain,
( spl0_15
<=> ! [X2,X5] : c_Relation_Otrans(c_Relation_OId__on(X5,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1129,plain,
( ! [X0,X1] : c_Relation_OId__on(X0,X1) = c_Transitive__Closure_Otrancl(c_Relation_OId__on(X0,X1),X1)
| ~ spl0_15
| ~ spl0_55 ),
inference(resolution,[],[f1081,f918]) ).
fof(f918,plain,
( ! [X2,X5] : c_Relation_Otrans(c_Relation_OId__on(X5,X2),X2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f917]) ).
fof(f19774,plain,
( spl0_679
| ~ spl0_61
| ~ spl0_616 ),
inference(avatar_split_clause,[],[f19479,f17078,f1104,f19772]) ).
fof(f19772,plain,
( spl0_679
<=> ! [X0,X1] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f17078,plain,
( spl0_616
<=> ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f19479,plain,
( ! [X0,X1] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1) )
| ~ spl0_61
| ~ spl0_616 ),
inference(resolution,[],[f17079,f1105]) ).
fof(f17079,plain,
( ! [X0] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_616 ),
inference(avatar_component_clause,[],[f17078]) ).
fof(f19696,plain,
( spl0_678
| ~ spl0_61
| ~ spl0_611 ),
inference(avatar_split_clause,[],[f17310,f16740,f1104,f19694]) ).
fof(f19694,plain,
( spl0_678
<=> ! [X0,X1] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f17310,plain,
( ! [X0,X1] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1) )
| ~ spl0_61
| ~ spl0_611 ),
inference(resolution,[],[f16741,f1105]) ).
fof(f19692,plain,
( spl0_677
| ~ spl0_148
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4901,f4529,f1618,f19690]) ).
fof(f19690,plain,
( spl0_677
<=> ! [X0,X1] : c_in(X0,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f4901,plain,
( ! [X0,X1] : c_in(X0,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_148
| ~ spl0_351 ),
inference(resolution,[],[f4530,f1619]) ).
fof(f19688,plain,
( spl0_676
| ~ spl0_103
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4441,f4039,f1340,f19686]) ).
fof(f19686,plain,
( spl0_676
<=> ! [X0] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f4441,plain,
( ! [X0] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_103
| ~ spl0_333 ),
inference(resolution,[],[f4040,f1342]) ).
fof(f19684,plain,
( spl0_675
| ~ spl0_103
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4400,f4027,f1340,f19682]) ).
fof(f19682,plain,
( spl0_675
<=> ! [X0] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f4400,plain,
( ! [X0] :
( c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_103
| ~ spl0_330 ),
inference(resolution,[],[f4028,f1342]) ).
fof(f19680,plain,
( spl0_674
| ~ spl0_135
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3932,f3501,f1494,f19678]) ).
fof(f19678,plain,
( spl0_674
<=> ! [X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f3932,plain,
( ! [X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_OId(X1),X1,X1),X1)
| ~ spl0_135
| ~ spl0_307 ),
inference(resolution,[],[f3502,f1495]) ).
fof(f19676,plain,
( spl0_673
| ~ spl0_244
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3847,f3469,f2913,f19674]) ).
fof(f19674,plain,
( spl0_673
<=> ! [X0,X1] :
( c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(X0,X1),X1)
| ~ c_Wellfounded_Oacyclic(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f3847,plain,
( ! [X0,X1] :
( c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(X0,X1),X1)
| ~ c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl0_244
| ~ spl0_299 ),
inference(resolution,[],[f3470,f2914]) ).
fof(f19672,plain,
( spl0_672
| ~ spl0_187
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f3087,f2913,f1897,f19670]) ).
fof(f19670,plain,
( spl0_672
<=> ! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f3087,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_187
| ~ spl0_244 ),
inference(resolution,[],[f2914,f1898]) ).
fof(f19668,plain,
( spl0_671
| ~ spl0_38
| ~ spl0_156
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2254,f1897,f1768,f1009,f19666]) ).
fof(f19666,plain,
( spl0_671
<=> ! [X0] : ~ c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f2254,plain,
( ! [X0] : ~ c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| ~ spl0_38
| ~ spl0_156
| ~ spl0_187 ),
inference(forward_demodulation,[],[f2248,f1769]) ).
fof(f2248,plain,
( ! [X0] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_38
| ~ spl0_187 ),
inference(resolution,[],[f1898,f1010]) ).
fof(f19664,plain,
( spl0_670
| ~ spl0_18
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2231,f1881,f929,f19662]) ).
fof(f19662,plain,
( spl0_670
<=> ! [X0,X1] : c_Relation_Otrans(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f2231,plain,
( ! [X0,X1] : c_Relation_Otrans(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1)
| ~ spl0_18
| ~ spl0_183 ),
inference(superposition,[],[f930,f1882]) ).
fof(f19660,plain,
( spl0_669
| ~ spl0_110
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1548,f1462,f1394,f19658]) ).
fof(f19658,plain,
( spl0_669
<=> ! [X0] : c_Relation_Oirrefl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1548,plain,
( ! [X0] : c_Relation_Oirrefl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| ~ spl0_110
| ~ spl0_127 ),
inference(forward_demodulation,[],[f1547,f196]) ).
fof(f196,axiom,
! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).
fof(f1547,plain,
( ! [X0] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_110
| ~ spl0_127 ),
inference(superposition,[],[f1463,f1395]) ).
fof(f19656,plain,
( spl0_668
| ~ spl0_62
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1369,f1340,f1108,f19653]) ).
fof(f19653,plain,
( spl0_668
<=> hBOOL(hAPP(v_Lab____,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1369,plain,
( hBOOL(hAPP(v_Lab____,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_62
| ~ spl0_103 ),
inference(resolution,[],[f1342,f1109]) ).
fof(f19651,plain,
( spl0_667
| ~ spl0_156
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2445,f2401,f1768,f19649]) ).
fof(f19649,plain,
( spl0_667
<=> ! [X0] : ~ c_lessequals(v_Lab____,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f2401,plain,
( spl0_223
<=> ! [X0] : ~ c_lessequals(v_Lab____,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2445,plain,
( ! [X0] : ~ c_lessequals(v_Lab____,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_156
| ~ spl0_223 ),
inference(superposition,[],[f2402,f1769]) ).
fof(f2402,plain,
( ! [X0] : ~ c_lessequals(v_Lab____,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2401]) ).
fof(f19647,plain,
( spl0_666
| ~ spl0_4
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1346,f1316,f866,f19645]) ).
fof(f19645,plain,
( spl0_666
<=> ! [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_666])]) ).
fof(f866,plain,
( spl0_4
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1346,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_4
| ~ spl0_97 ),
inference(resolution,[],[f1317,f868]) ).
fof(f868,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f866]) ).
fof(f19643,plain,
( spl0_665
| ~ spl0_4
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1344,f1311,f866,f19641]) ).
fof(f19641,plain,
( spl0_665
<=> ! [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_665])]) ).
fof(f1344,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_4
| ~ spl0_96 ),
inference(resolution,[],[f1312,f868]) ).
fof(f19639,plain,
( spl0_664
| ~ spl0_20
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f1136,f1123,f937,f19637]) ).
fof(f19637,plain,
( spl0_664
<=> ! [X0] : c_Wellfounded_Oacyclic(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f1136,plain,
( ! [X0] : c_Wellfounded_Oacyclic(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
| ~ spl0_20
| ~ spl0_65 ),
inference(resolution,[],[f1124,f938]) ).
fof(f19635,plain,
( spl0_663
| ~ spl0_20
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f1131,f1092,f937,f19633]) ).
fof(f19633,plain,
( spl0_663
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f1092,plain,
( spl0_58
<=> ! [X2,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1131,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_20
| ~ spl0_58 ),
inference(resolution,[],[f1093,f938]) ).
fof(f1093,plain,
( ! [X2,X4] :
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X4,X2),X2)
| ~ c_Wellfounded_Owf(X4,X2) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f19528,plain,
( spl0_662
| ~ spl0_103
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3936,f3501,f1340,f19525]) ).
fof(f19525,plain,
( spl0_662
<=> c_in(v_b____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f3936,plain,
( c_in(v_b____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_103
| ~ spl0_307 ),
inference(resolution,[],[f3502,f1342]) ).
fof(f19477,plain,
( spl0_661
| ~ spl0_4
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1265,f1171,f866,f19475]) ).
fof(f19475,plain,
( spl0_661
<=> ! [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_661])]) ).
fof(f1265,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_4
| ~ spl0_74 ),
inference(resolution,[],[f1172,f868]) ).
fof(f19473,plain,
( spl0_660
| ~ spl0_4
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f1263,f1167,f866,f19471]) ).
fof(f19471,plain,
( spl0_660
<=> ! [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_660])]) ).
fof(f1263,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_4
| ~ spl0_73 ),
inference(resolution,[],[f1168,f868]) ).
fof(f19469,plain,
( spl0_659
| ~ spl0_41
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f1132,f1104,f1021,f19467]) ).
fof(f19467,plain,
( spl0_659
<=> ! [X0,X3,X2,X1] : c_in(X0,c_Set_Oinsert(X0,X1,X2),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f1132,plain,
( ! [X2,X3,X0,X1] : c_in(X0,c_Set_Oinsert(X0,X1,X2),X3)
| ~ spl0_41
| ~ spl0_61 ),
inference(resolution,[],[f1105,f1022]) ).
fof(f19455,plain,
( spl0_658
| ~ spl0_188
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3845,f3469,f1901,f19453]) ).
fof(f19453,plain,
( spl0_658
<=> ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| ~ c_Wellfounded_Owf(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f3845,plain,
( ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_188
| ~ spl0_299 ),
inference(resolution,[],[f3470,f1902]) ).
fof(f19451,plain,
( spl0_657
| ~ spl0_187
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2256,f1901,f1897,f19449]) ).
fof(f19449,plain,
( spl0_657
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| ~ c_Nitpick_Orefl_H(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f2256,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| ~ c_Nitpick_Orefl_H(X0,X1) )
| ~ spl0_187
| ~ spl0_188 ),
inference(resolution,[],[f1902,f1898]) ).
fof(f19447,plain,
( spl0_656
| ~ spl0_185
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2244,f1897,f1889,f19445]) ).
fof(f19445,plain,
( spl0_656
<=> ! [X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2244,plain,
( ! [X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1) )
| ~ spl0_185
| ~ spl0_187 ),
inference(resolution,[],[f1898,f1890]) ).
fof(f19438,plain,
( spl0_655
| ~ spl0_148
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2243,f1897,f1618,f19436]) ).
fof(f19436,plain,
( spl0_655
<=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2243,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_148
| ~ spl0_187 ),
inference(resolution,[],[f1898,f1619]) ).
fof(f19434,plain,
( spl0_654
| ~ spl0_147
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2242,f1897,f1614,f19432]) ).
fof(f19432,plain,
( spl0_654
<=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2242,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_147
| ~ spl0_187 ),
inference(resolution,[],[f1898,f1615]) ).
fof(f19430,plain,
( spl0_653
| ~ spl0_135
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3830,f3457,f1494,f19428]) ).
fof(f19428,plain,
( spl0_653
<=> ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f3830,plain,
( ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0)
| ~ spl0_135
| ~ spl0_296 ),
inference(resolution,[],[f3458,f1495]) ).
fof(f19426,plain,
( spl0_652
| ~ spl0_135
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2255,f1901,f1494,f19424]) ).
fof(f19424,plain,
( spl0_652
<=> ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2255,plain,
( ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0)
| ~ spl0_135
| ~ spl0_188 ),
inference(resolution,[],[f1902,f1495]) ).
fof(f19422,plain,
( spl0_651
| ~ spl0_135
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2237,f1889,f1494,f19420]) ).
fof(f19420,plain,
( spl0_651
<=> ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2237,plain,
( ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0)
| ~ spl0_135
| ~ spl0_185 ),
inference(resolution,[],[f1890,f1495]) ).
fof(f19341,plain,
( spl0_650
| ~ spl0_156
| ~ spl0_627 ),
inference(avatar_split_clause,[],[f17943,f17648,f1768,f19339]) ).
fof(f19339,plain,
( spl0_650
<=> ! [X0] : ~ c_in(v_b____,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f17648,plain,
( spl0_627
<=> ! [X0] : ~ c_in(v_b____,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f17943,plain,
( ! [X0] : ~ c_in(v_b____,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_156
| ~ spl0_627 ),
inference(superposition,[],[f17649,f1769]) ).
fof(f17649,plain,
( ! [X0] : ~ c_in(v_b____,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_627 ),
inference(avatar_component_clause,[],[f17648]) ).
fof(f19337,plain,
spl0_649,
inference(avatar_split_clause,[],[f797,f19335]) ).
fof(f19335,plain,
( spl0_649
<=> ! [X4,X7,X22,X6,X2] :
( ~ c_Relation_Osingle__valued(X4,X2,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X7,X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X22,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f797,plain,
! [X2,X6,X7,X4,X22] :
( ~ c_Relation_Osingle__valued(X4,X2,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X7,X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X22,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f493,f440,f440,f440,f440]) ).
fof(f440,axiom,
! [X2,X4] : c_Transitive__Closure_Ortrancl(X4,X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
fof(f493,axiom,
! [X2,X6,X7,X4,X22] :
( ~ c_Relation_Osingle__valued(X4,X2,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X7,X22,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X22,X7,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
fof(f19267,plain,
spl0_648,
inference(avatar_split_clause,[],[f124,f19265]) ).
fof(f19265,plain,
( spl0_648
<=> ! [X3,X9,X0,X5,X2,X1] : c_Product__Type_OSigma(c_Set_Oinsert(X0,X5,X2),c_COMBK(c_Set_Oinsert(X1,X9,X3),tc_fun(X3,tc_bool),X2),X2,X3) = c_Set_Oinsert(c_Pair(X0,X1,X2,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X5,c_COMBK(c_Set_Oinsert(X1,X9,X3),tc_fun(X3,tc_bool),X2),X2,X3),c_Product__Type_OSigma(c_Set_Oinsert(X0,X5,X2),c_COMBK(X9,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),tc_prod(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f124,axiom,
! [X2,X3,X0,X1,X9,X5] : c_Product__Type_OSigma(c_Set_Oinsert(X0,X5,X2),c_COMBK(c_Set_Oinsert(X1,X9,X3),tc_fun(X3,tc_bool),X2),X2,X3) = c_Set_Oinsert(c_Pair(X0,X1,X2,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X5,c_COMBK(c_Set_Oinsert(X1,X9,X3),tc_fun(X3,tc_bool),X2),X2,X3),c_Product__Type_OSigma(c_Set_Oinsert(X0,X5,X2),c_COMBK(X9,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),tc_prod(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).
fof(f19015,plain,
( spl0_647
| ~ spl0_322
| ~ spl0_406
| ~ spl0_407
| ~ spl0_425
| ~ spl0_426
| ~ spl0_646 ),
inference(avatar_split_clause,[],[f19011,f19005,f6647,f6643,f6563,f6559,f3994,f19013]) ).
fof(f19013,plain,
( spl0_647
<=> ! [X13,X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X8,X2),c_Transitive__Closure_Otrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f6647,plain,
( spl0_426
<=> ! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Transitive__Closure_Otrancl(X4,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f19005,plain,
( spl0_646
<=> ! [X13,X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f19011,plain,
( ! [X2,X8,X13] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X8,X2),c_Transitive__Closure_Otrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_322
| ~ spl0_406
| ~ spl0_407
| ~ spl0_425
| ~ spl0_426
| ~ spl0_646 ),
inference(forward_demodulation,[],[f19010,f3995]) ).
fof(f19010,plain,
( ! [X2,X8,X13] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X8,X2),c_Transitive__Closure_Otrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_322
| ~ spl0_406
| ~ spl0_407
| ~ spl0_425
| ~ spl0_426
| ~ spl0_646 ),
inference(forward_demodulation,[],[f19009,f7805]) ).
fof(f7805,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool))
| ~ spl0_406
| ~ spl0_407
| ~ spl0_425 ),
inference(forward_demodulation,[],[f7774,f6560]) ).
fof(f7774,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ spl0_407
| ~ spl0_425 ),
inference(superposition,[],[f6564,f6644]) ).
fof(f19009,plain,
( ! [X2,X8,X13] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_322
| ~ spl0_406
| ~ spl0_426
| ~ spl0_646 ),
inference(forward_demodulation,[],[f19008,f3995]) ).
fof(f19008,plain,
( ! [X2,X8,X13] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_406
| ~ spl0_426
| ~ spl0_646 ),
inference(forward_demodulation,[],[f19006,f7830]) ).
fof(f7830,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Transitive__Closure_Otrancl(X1,X0),tc_fun(tc_prod(X0,X0),tc_bool)),tc_fun(tc_prod(X0,X0),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_406
| ~ spl0_426 ),
inference(superposition,[],[f6560,f6648]) ).
fof(f6648,plain,
( ! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Transitive__Closure_Otrancl(X4,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ spl0_426 ),
inference(avatar_component_clause,[],[f6647]) ).
fof(f19006,plain,
( ! [X2,X8,X13] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_646 ),
inference(avatar_component_clause,[],[f19005]) ).
fof(f19007,plain,
spl0_646,
inference(avatar_split_clause,[],[f818,f19005]) ).
fof(f818,plain,
! [X2,X8,X13] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(forward_demodulation,[],[f817,f228]) ).
fof(f228,axiom,
! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f817,plain,
! [X2,X8,X13] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(forward_demodulation,[],[f737,f228]) ).
fof(f737,plain,
! [X2,X8,X13] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(definition_unfolding,[],[f243,f440,f440,f440,f440]) ).
fof(f243,axiom,
! [X2,X8,X13] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X8,X2),c_Transitive__Closure_Ortrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
fof(f19003,plain,
spl0_645,
inference(avatar_split_clause,[],[f779,f19001]) ).
fof(f19001,plain,
( spl0_645
<=> ! [X2,X4,X14] :
( ~ c_lessequals(c_Relation_OId(X2),X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X14,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)),X4,X2,X2,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f779,plain,
! [X2,X14,X4] :
( ~ c_lessequals(c_Relation_OId(X2),X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X14,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)),X4,X2,X2,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(definition_unfolding,[],[f356,f440,f440]) ).
fof(f356,axiom,
! [X2,X14,X4] :
( ~ c_lessequals(c_Relation_OId(X2),X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X4,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X4,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)),X4,X2,X2,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).
fof(f18995,plain,
spl0_644,
inference(avatar_split_clause,[],[f423,f18993]) ).
fof(f18993,plain,
( spl0_644
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f423,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_14) ).
fof(f18991,plain,
spl0_643,
inference(avatar_split_clause,[],[f408,f18989]) ).
fof(f18989,plain,
( spl0_643
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X0,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f408,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X0,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_14) ).
fof(f18958,plain,
spl0_642,
inference(avatar_split_clause,[],[f105,f18956]) ).
fof(f18956,plain,
( spl0_642
<=> ! [X3,X4,X11,X9,X10,X14,X5,X2] :
( ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X9,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool))
| ~ c_lessequals(X14,c_Product__Type_OSigma(X9,c_COMBK(X11,tc_fun(X10,tc_bool),X3),X3,X10),tc_fun(tc_prod(X3,X10),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X4,X14,X2,X3,X10),c_Product__Type_OSigma(X5,c_COMBK(X11,tc_fun(X10,tc_bool),X2),X2,X10),tc_fun(tc_prod(X2,X10),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f105,axiom,
! [X2,X3,X10,X11,X9,X14,X4,X5] :
( ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X9,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool))
| ~ c_lessequals(X14,c_Product__Type_OSigma(X9,c_COMBK(X11,tc_fun(X10,tc_bool),X3),X3,X10),tc_fun(tc_prod(X3,X10),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X4,X14,X2,X3,X10),c_Product__Type_OSigma(X5,c_COMBK(X11,tc_fun(X10,tc_bool),X2),X2,X10),tc_fun(tc_prod(X2,X10),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
fof(f18596,plain,
( spl0_641
| ~ spl0_152
| ~ spl0_164
| ~ spl0_484
| ~ spl0_495
| ~ spl0_640 ),
inference(avatar_split_clause,[],[f18592,f18588,f10105,f9953,f1800,f1748,f18594]) ).
fof(f18594,plain,
( spl0_641
<=> ! [X9,X11,X5,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X5,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f9953,plain,
( spl0_484
<=> ! [X9,X11,X5,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f10105,plain,
( spl0_495
<=> ! [X9,X11,X5,X2] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f18588,plain,
( spl0_640
<=> ! [X9,X11,X5,X2] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f18592,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X5,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_152
| ~ spl0_164
| ~ spl0_484
| ~ spl0_495
| ~ spl0_640 ),
inference(forward_demodulation,[],[f18591,f10198]) ).
fof(f10198,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_152
| ~ spl0_484 ),
inference(superposition,[],[f9954,f1749]) ).
fof(f9954,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_484 ),
inference(avatar_component_clause,[],[f9953]) ).
fof(f18591,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X5,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_164
| ~ spl0_495
| ~ spl0_640 ),
inference(forward_demodulation,[],[f18589,f10830]) ).
fof(f10830,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_164
| ~ spl0_495 ),
inference(superposition,[],[f10106,f1801]) ).
fof(f10106,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f10105]) ).
fof(f18589,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_640 ),
inference(avatar_component_clause,[],[f18588]) ).
fof(f18590,plain,
spl0_640,
inference(avatar_split_clause,[],[f821,f18588]) ).
fof(f821,plain,
! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(forward_demodulation,[],[f195,f84]) ).
fof(f84,axiom,
! [X2,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X9,X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f195,axiom,
! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
fof(f18310,plain,
( spl0_639
| ~ spl0_48
| ~ spl0_611 ),
inference(avatar_split_clause,[],[f17315,f16740,f1050,f18308]) ).
fof(f18308,plain,
( spl0_639
<=> ! [X2,X0,X1] :
( hBOOL(X0)
| ~ c_in(v_b____,c_COMBK(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f17315,plain,
( ! [X2,X0,X1] :
( hBOOL(X0)
| ~ c_in(v_b____,c_COMBK(X0,X1,X2),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_48
| ~ spl0_611 ),
inference(superposition,[],[f16741,f1051]) ).
fof(f18306,plain,
( spl0_638
| ~ spl0_322
| ~ spl0_406
| ~ spl0_407
| ~ spl0_425
| ~ spl0_426
| ~ spl0_637 ),
inference(avatar_split_clause,[],[f18302,f18297,f6647,f6643,f6563,f6559,f3994,f18304]) ).
fof(f18304,plain,
( spl0_638
<=> ! [X13,X2,X8] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X8,X2),c_Transitive__Closure_Otrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f18297,plain,
( spl0_637
<=> ! [X13,X2,X8] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f18302,plain,
( ! [X2,X8,X13] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X8,X2),c_Transitive__Closure_Otrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ spl0_322
| ~ spl0_406
| ~ spl0_407
| ~ spl0_425
| ~ spl0_426
| ~ spl0_637 ),
inference(forward_demodulation,[],[f18301,f3995]) ).
fof(f18301,plain,
( ! [X2,X8,X13] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X8,X2),c_Transitive__Closure_Otrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ spl0_406
| ~ spl0_407
| ~ spl0_425
| ~ spl0_426
| ~ spl0_637 ),
inference(forward_demodulation,[],[f18300,f7805]) ).
fof(f18300,plain,
( ! [X2,X8,X13] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ spl0_406
| ~ spl0_426
| ~ spl0_637 ),
inference(forward_demodulation,[],[f18298,f7830]) ).
fof(f18298,plain,
( ! [X2,X8,X13] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ spl0_637 ),
inference(avatar_component_clause,[],[f18297]) ).
fof(f18299,plain,
spl0_637,
inference(avatar_split_clause,[],[f820,f18297]) ).
fof(f820,plain,
! [X2,X8,X13] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(forward_demodulation,[],[f740,f228]) ).
fof(f740,plain,
! [X2,X8,X13] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(definition_unfolding,[],[f17,f440,f440,f440]) ).
fof(f17,axiom,
! [X2,X8,X13] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X8,X2),c_Transitive__Closure_Ortrancl(X13,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
fof(f18295,plain,
spl0_636,
inference(avatar_split_clause,[],[f794,f18293]) ).
fof(f18293,plain,
( spl0_636
<=> ! [X2,X18,X4,X0,X1] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X18,X1,X4,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f794,plain,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X18,X1,X4,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f468,f440,f440]) ).
fof(f468,axiom,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X18,X1,X4,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).
fof(f18291,plain,
spl0_635,
inference(avatar_split_clause,[],[f793,f18289]) ).
fof(f18289,plain,
( spl0_635
<=> ! [X2,X18,X4,X0,X1] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X18,X0,X4,X2),X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f793,plain,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X18,X0,X4,X2),X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f469,f440,f440]) ).
fof(f469,axiom,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X18,X0,X4,X2),X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
fof(f17938,plain,
spl0_634,
inference(avatar_split_clause,[],[f783,f17936]) ).
fof(f17936,plain,
( spl0_634
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f783,plain,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f626,f440,f440]) ).
fof(f626,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
fof(f17934,plain,
spl0_633,
inference(avatar_split_clause,[],[f782,f17932]) ).
fof(f17932,plain,
( spl0_633
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f782,plain,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f625,f440,f440]) ).
fof(f625,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
fof(f17930,plain,
spl0_632,
inference(avatar_split_clause,[],[f421,f17928]) ).
fof(f17928,plain,
( spl0_632
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X6 = X7
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f421,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X6 = X7
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_8) ).
fof(f17926,plain,
spl0_631,
inference(avatar_split_clause,[],[f420,f17924]) ).
fof(f17924,plain,
( spl0_631
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X1 = X7
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X0,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f420,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X1 = X7
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X0,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_10) ).
fof(f17922,plain,
spl0_630,
inference(avatar_split_clause,[],[f406,f17920]) ).
fof(f17920,plain,
( spl0_630
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X6 = X7
| X0 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f406,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X6 = X7
| X0 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_8) ).
fof(f17918,plain,
spl0_629,
inference(avatar_split_clause,[],[f405,f17916]) ).
fof(f17916,plain,
( spl0_629
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X0 = X6
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f405,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X0 = X6
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_10) ).
fof(f17822,plain,
spl0_628,
inference(avatar_split_clause,[],[f778,f17820]) ).
fof(f17820,plain,
( spl0_628
<=> ! [X13,X2,X8] :
( c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_lessequals(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X13,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f778,plain,
! [X2,X8,X13] :
( c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_lessequals(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X13,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(definition_unfolding,[],[f191,f440,f440,f440]) ).
fof(f191,axiom,
! [X2,X8,X13] :
( c_Transitive__Closure_Ortrancl(X8,X2) = c_Transitive__Closure_Ortrancl(X13,X2)
| ~ c_lessequals(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X13,c_Transitive__Closure_Ortrancl(X8,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
fof(f17650,plain,
( spl0_627
| ~ spl0_36
| ~ spl0_611 ),
inference(avatar_split_clause,[],[f17309,f16740,f1001,f17648]) ).
fof(f17309,plain,
( ! [X0] : ~ c_in(v_b____,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_36
| ~ spl0_611 ),
inference(resolution,[],[f16741,f1002]) ).
fof(f17646,plain,
spl0_626,
inference(avatar_split_clause,[],[f775,f17644]) ).
fof(f17644,plain,
( spl0_626
<=> ! [X2,X4,X6,X22] :
( X6 = X22
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X6,X22,X2),X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f775,plain,
! [X2,X6,X4,X22] :
( X6 = X22
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X6,X22,X2),X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f465,f440,f440]) ).
fof(f465,axiom,
! [X2,X6,X4,X22] :
( X6 = X22
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X6,X22,X2),X22,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).
fof(f17642,plain,
spl0_625,
inference(avatar_split_clause,[],[f774,f17640]) ).
fof(f17640,plain,
( spl0_625
<=> ! [X4,X0,X2,X1] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X4,X2),X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f774,plain,
! [X2,X0,X1,X4] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X4,X2),X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f475,f440,f440]) ).
fof(f475,axiom,
! [X2,X0,X1,X4] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X4,X2),X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).
fof(f17323,plain,
spl0_624,
inference(avatar_split_clause,[],[f849,f17321]) ).
fof(f17321,plain,
( spl0_624
<=> ! [X9,X11,X5,X2] :
( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X2,X2),tc_bool)),X11,X2,X2,X2) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X5,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X9,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f849,plain,
! [X2,X11,X9,X5] :
( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X2,X2),tc_bool)),X11,X2,X2,X2) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X5,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X9,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(forward_demodulation,[],[f848,f196]) ).
fof(f848,plain,
! [X2,X11,X9,X5] :
( c_Relation_Orel__comp(X5,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X9,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X2,X2),tc_bool)),X11,X2,X2,X2) ),
inference(forward_demodulation,[],[f847,f196]) ).
fof(f847,plain,
! [X2,X11,X9,X5] :
( c_Relation_Orel__comp(X9,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X5,X11,X2,X2,X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X2,X2),tc_bool)),X11,X2,X2,X2) ),
inference(forward_demodulation,[],[f137,f196]) ).
fof(f137,axiom,
! [X2,X11,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X9,X11,X2,X2,X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X5,X11,X2,X2,X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X2,X2),tc_bool)),X11,X2,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyL_0) ).
fof(f17319,plain,
spl0_623,
inference(avatar_split_clause,[],[f846,f17317]) ).
fof(f17317,plain,
( spl0_623
<=> ! [X9,X11,X5,X2] :
( c_Relation_Orel__comp(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X5,X9,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X5,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f846,plain,
! [X2,X11,X9,X5] :
( c_Relation_Orel__comp(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X5,X9,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X5,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(forward_demodulation,[],[f845,f196]) ).
fof(f845,plain,
! [X2,X11,X9,X5] :
( c_Relation_Orel__comp(X5,X9,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Relation_Orel__comp(X5,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) ),
inference(forward_demodulation,[],[f844,f196]) ).
fof(f844,plain,
! [X2,X11,X9,X5] :
( c_Relation_Orel__comp(X5,X11,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X5,X9,X2,X2,X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) ),
inference(forward_demodulation,[],[f138,f196]) ).
fof(f138,axiom,
! [X2,X11,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X5,X11,X2,X2,X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X5,X9,X2,X2,X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyR_0) ).
fof(f17308,plain,
spl0_622,
inference(avatar_split_clause,[],[f796,f17306]) ).
fof(f17306,plain,
( spl0_622
<=> ! [X2,X18,X4,X0,X1] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X18,X0,X4,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X18,X0,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f796,plain,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X18,X0,X4,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X18,X0,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f354,f440]) ).
fof(f354,axiom,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X18,X0,X4,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X18,X0,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
fof(f17304,plain,
spl0_621,
inference(avatar_split_clause,[],[f795,f17302]) ).
fof(f17302,plain,
( spl0_621
<=> ! [X2,X18,X4,X0,X1] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X18,X1,X4,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X18,X1,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f795,plain,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X18,X1,X4,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X18,X1,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f353,f440]) ).
fof(f353,axiom,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X18,X1,X4,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X18,X1,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).
fof(f17300,plain,
spl0_620,
inference(avatar_split_clause,[],[f768,f17298]) ).
fof(f17298,plain,
( spl0_620
<=> ! [X41,X4,X42] :
( X41 = X42
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X41,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X41,X42,X4),t_a,t_a),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a),tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f768,plain,
! [X41,X4,X42] :
( X41 = X42
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X41,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X41,X42,X4),t_a,t_a),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a),tc_prod(t_a,t_a)) ),
inference(definition_unfolding,[],[f471,f440,f440]) ).
fof(f471,axiom,
! [X41,X4,X42] :
( X41 = X42
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Ortrancl(X4,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X41,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X41,X42,X4),t_a,t_a),c_Transitive__Closure_Ortrancl(X4,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).
fof(f17296,plain,
spl0_619,
inference(avatar_split_clause,[],[f755,f17294]) ).
fof(f17294,plain,
( spl0_619
<=> ! [X2,X4,X14] :
( ~ c_lessequals(X4,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f755,plain,
! [X2,X14,X4] :
( ~ c_lessequals(X4,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(definition_unfolding,[],[f164,f440,f440,f440]) ).
fof(f164,axiom,
! [X2,X14,X4] :
( ~ c_lessequals(X4,c_Transitive__Closure_Ortrancl(X14,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X4,X2),c_Transitive__Closure_Ortrancl(X14,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
fof(f17088,plain,
spl0_618,
inference(avatar_split_clause,[],[f788,f17086]) ).
fof(f17086,plain,
( spl0_618
<=> ! [X4,X0,X5,X2,X1] :
( X0 = X1
| c_in(X0,X5,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f788,plain,
! [X2,X0,X1,X4,X5] :
( X0 = X1
| c_in(X0,X5,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(definition_unfolding,[],[f485,f440]) ).
fof(f485,axiom,
! [X2,X0,X1,X4,X5] :
( X0 = X1
| c_in(X0,X5,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
fof(f17084,plain,
spl0_617,
inference(avatar_split_clause,[],[f785,f17082]) ).
fof(f17082,plain,
( spl0_617
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f785,plain,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f495,f440]) ).
fof(f495,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
fof(f17080,plain,
( spl0_616
| ~ spl0_62
| ~ spl0_580 ),
inference(avatar_split_clause,[],[f15879,f14919,f1108,f17078]) ).
fof(f14919,plain,
( spl0_580
<=> ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f15879,plain,
( ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_62
| ~ spl0_580 ),
inference(resolution,[],[f14920,f1109]) ).
fof(f14920,plain,
( ! [X0] :
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_580 ),
inference(avatar_component_clause,[],[f14919]) ).
fof(f17076,plain,
spl0_615,
inference(avatar_split_clause,[],[f784,f17074]) ).
fof(f17074,plain,
( spl0_615
<=> ! [X2,X4,X7,X6,X22] :
( ~ c_in(c_Pair(X7,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f784,plain,
! [X2,X6,X7,X4,X22] :
( ~ c_in(c_Pair(X7,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f496,f440]) ).
fof(f496,axiom,
! [X2,X6,X7,X4,X22] :
( ~ c_in(c_Pair(X7,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
fof(f17072,plain,
spl0_614,
inference(avatar_split_clause,[],[f358,f17070]) ).
fof(f17070,plain,
( spl0_614
<=> ! [X4,X0,X5,X2,X1] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X1,X5,X2)
| c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_lessequals(c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f358,axiom,
! [X2,X0,X1,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X1,X5,X2)
| c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_lessequals(c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
fof(f16750,plain,
spl0_613,
inference(avatar_split_clause,[],[f426,f16748]) ).
fof(f16748,plain,
( spl0_613
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X0 = X6
| X6 = X7
| X0 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f426,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X0 = X6
| X6 = X7
| X0 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_4) ).
fof(f16746,plain,
spl0_612,
inference(avatar_split_clause,[],[f411,f16744]) ).
fof(f16744,plain,
( spl0_612
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X1 = X7
| X6 = X7
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f411,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X1 = X7
| X6 = X7
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_4) ).
fof(f16742,plain,
( spl0_611
| ~ spl0_62
| ~ spl0_579 ),
inference(avatar_split_clause,[],[f15486,f14297,f1108,f16740]) ).
fof(f14297,plain,
( spl0_579
<=> ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f15486,plain,
( ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_62
| ~ spl0_579 ),
inference(resolution,[],[f14298,f1109]) ).
fof(f14298,plain,
( ! [X0] :
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_579 ),
inference(avatar_component_clause,[],[f14297]) ).
fof(f16738,plain,
spl0_610,
inference(avatar_split_clause,[],[f394,f16736]) ).
fof(f16736,plain,
( spl0_610
<=> ! [X38,X4,X7,X6,X5,X2,X37] :
( X37 = X38
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X7,X38,X2)
| ~ c_in(X6,X37,X2)
| ~ c_in(X37,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| ~ c_in(X38,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f394,axiom,
! [X2,X38,X37,X6,X7,X4,X5] :
( X37 = X38
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X7,X38,X2)
| ~ c_in(X6,X37,X2)
| ~ c_in(X37,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| ~ c_in(X38,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eqI_0) ).
fof(f16734,plain,
spl0_609,
inference(avatar_split_clause,[],[f357,f16732]) ).
fof(f16732,plain,
( spl0_609
<=> ! [X6,X4,X0,X5,X2,X1] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f357,axiom,
! [X2,X0,X1,X6,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
fof(f16730,plain,
spl0_608,
inference(avatar_split_clause,[],[f55,f16728]) ).
fof(f16728,plain,
( spl0_608
<=> ! [X6,X4,X7,X5,X2] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X7,X5,X2)
| ~ c_in(X6,X5,X2)
| c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X4,X2) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f55,axiom,
! [X2,X6,X7,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X7,X5,X2)
| ~ c_in(X6,X5,X2)
| c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X4,X2) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).
fof(f16726,plain,
spl0_607,
inference(avatar_split_clause,[],[f54,f16724]) ).
fof(f16724,plain,
( spl0_607
<=> ! [X5,X4,X7,X6,X2] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X6,X5,X2)
| ~ c_in(X7,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X4,X2) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f54,axiom,
! [X2,X6,X7,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X6,X5,X2)
| ~ c_in(X7,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X4,X2) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).
fof(f16602,plain,
spl0_606,
inference(avatar_split_clause,[],[f781,f16600]) ).
fof(f16600,plain,
( spl0_606
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f781,plain,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f390,f440]) ).
fof(f390,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
fof(f16598,plain,
spl0_605,
inference(avatar_split_clause,[],[f780,f16596]) ).
fof(f16596,plain,
( spl0_605
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f780,plain,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f487,f440]) ).
fof(f487,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
fof(f16584,plain,
spl0_604,
inference(avatar_split_clause,[],[f480,f16582]) ).
fof(f16582,plain,
( spl0_604
<=> ! [X4,X0,X5,X2,X1] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X1,X5,X2)
| c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f480,axiom,
! [X2,X0,X1,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X1,X5,X2)
| c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
fof(f16302,plain,
spl0_603,
inference(avatar_split_clause,[],[f835,f16300]) ).
fof(f16300,plain,
( spl0_603
<=> ! [X6,X2,X4] :
( c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X4,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f835,plain,
! [X2,X6,X4] :
( c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X4,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
inference(forward_demodulation,[],[f761,f196]) ).
fof(f761,plain,
! [X2,X6,X4] :
( ~ c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X4,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(definition_unfolding,[],[f479,f440]) ).
fof(f479,axiom,
! [X2,X6,X4] :
( ~ c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X4,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).
fof(f16298,plain,
spl0_602,
inference(avatar_split_clause,[],[f416,f16296]) ).
fof(f16296,plain,
( spl0_602
<=> ! [X40,X7,X6,X1] :
( X1 = X7
| X6 = X7
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X1,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f416,axiom,
! [X40,X1,X6,X7] :
( X1 = X7
| X6 = X7
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X1,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_2) ).
fof(f16294,plain,
spl0_601,
inference(avatar_split_clause,[],[f415,f16292]) ).
fof(f16292,plain,
( spl0_601
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X0 = X7
| X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f415,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X0 = X7
| X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_3) ).
fof(f16290,plain,
( spl0_600
| spl0_313
| ~ spl0_202
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3092,f2933,f2307,f3878,f16288]) ).
fof(f16288,plain,
( spl0_600
<=> ! [X0] : ~ c_lessequals(v_Lab____,c_Relation_OId__on(X0,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f3092,plain,
( ! [X0] :
( v_a____ = v_b____
| ~ c_lessequals(v_Lab____,c_Relation_OId__on(X0,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_202
| ~ spl0_249 ),
inference(resolution,[],[f2934,f2308]) ).
fof(f16286,plain,
spl0_599,
inference(avatar_split_clause,[],[f401,f16284]) ).
fof(f16284,plain,
( spl0_599
<=> ! [X40,X0,X6,X27] :
( X0 = X27
| X6 = X27
| X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X27,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f401,axiom,
! [X40,X0,X6,X27] :
( X0 = X27
| X6 = X27
| X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X27,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_2) ).
fof(f16282,plain,
spl0_598,
inference(avatar_split_clause,[],[f400,f16280]) ).
fof(f16280,plain,
( spl0_598
<=> ! [X40,X0,X6,X1,X7] :
( X0 = X1
| X1 = X6
| X1 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f400,axiom,
! [X40,X0,X1,X6,X7] :
( X0 = X1
| X1 = X6
| X1 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_3) ).
fof(f16278,plain,
spl0_597,
inference(avatar_split_clause,[],[f89,f16276]) ).
fof(f16276,plain,
( spl0_597
<=> ! [X4,X0,X5,X2,X1] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| c_lessequals(c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f89,axiom,
! [X2,X0,X1,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| c_lessequals(c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
fof(f16274,plain,
spl0_596,
inference(avatar_split_clause,[],[f31,f16272]) ).
fof(f16272,plain,
( spl0_596
<=> ! [X2,X4,X14] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(X4,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X4,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)),X4,X2,X2,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f31,axiom,
! [X2,X14,X4] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(X4,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X4,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)),X4,X2,X2,X2),X14,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).
fof(f16001,plain,
spl0_595,
inference(avatar_split_clause,[],[f828,f15999]) ).
fof(f15999,plain,
( spl0_595
<=> ! [X13,X8,X6,X2] :
( c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f828,plain,
! [X2,X8,X6,X13] :
( c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(forward_demodulation,[],[f753,f228]) ).
fof(f753,plain,
! [X2,X8,X6,X13] :
( ~ c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f366,f440,f440]) ).
fof(f366,axiom,
! [X2,X8,X6,X13] :
( ~ c_in(X6,c_Transitive__Closure_Ortrancl(X13,X2),tc_prod(X2,X2))
| c_in(X6,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
fof(f15997,plain,
spl0_594,
inference(avatar_split_clause,[],[f827,f15995]) ).
fof(f15995,plain,
( spl0_594
<=> ! [X13,X8,X6,X2] :
( c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f827,plain,
! [X2,X8,X6,X13] :
( c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| ~ c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(forward_demodulation,[],[f752,f228]) ).
fof(f752,plain,
! [X2,X8,X6,X13] :
( ~ c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(X6,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f365,f440,f440]) ).
fof(f365,axiom,
! [X2,X8,X6,X13] :
( ~ c_in(X6,c_Transitive__Closure_Ortrancl(X8,X2),tc_prod(X2,X2))
| c_in(X6,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
fof(f15815,plain,
spl0_593,
inference(avatar_split_clause,[],[f725,f15813]) ).
fof(f15813,plain,
( spl0_593
<=> ! [X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f725,plain,
! [X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2),
inference(definition_unfolding,[],[f564,f440,f440,f440]) ).
fof(f564,axiom,
! [X2,X8] : c_Transitive__Closure_Ortrancl(X8,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X8,X2),c_Transitive__Closure_Ortrancl(X8,X2),X2,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
fof(f15811,plain,
spl0_592,
inference(avatar_split_clause,[],[f456,f15809]) ).
fof(f15809,plain,
( spl0_592
<=> ! [X4,X0,X2,X1] :
( c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X0,X1,X4,X2),X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f456,axiom,
! [X2,X0,X1,X4] :
( c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X0,X1,X4,X2),X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).
fof(f15807,plain,
spl0_591,
inference(avatar_split_clause,[],[f451,f15805]) ).
fof(f15805,plain,
( spl0_591
<=> ! [X2,X4,X6,X22] :
( c_in(c_Pair(X6,X22,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X6,X22,X2),X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f451,axiom,
! [X2,X6,X4,X22] :
( c_in(c_Pair(X6,X22,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X6,X22,X2),X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
fof(f15295,plain,
spl0_590,
inference(avatar_split_clause,[],[f804,f15293]) ).
fof(f15293,plain,
( spl0_590
<=> ! [X40,X0,X6,X27] :
( X6 = X27
| X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X27,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f804,plain,
! [X40,X0,X6,X27] :
( X6 = X27
| X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X27,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f398]) ).
fof(f398,axiom,
! [X40,X0,X6,X27] :
( X6 = X27
| X0 = X6
| X6 = X27
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X27,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_7) ).
fof(f15291,plain,
spl0_589,
inference(avatar_split_clause,[],[f803,f15289]) ).
fof(f15289,plain,
( spl0_589
<=> ! [X40,X7,X6,X1] :
( X6 = X7
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f803,plain,
! [X40,X1,X6,X7] :
( X6 = X7
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f413]) ).
fof(f413,axiom,
! [X40,X1,X6,X7] :
( X6 = X7
| X1 = X6
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_7) ).
fof(f15287,plain,
spl0_588,
inference(avatar_split_clause,[],[f802,f15285]) ).
fof(f15285,plain,
( spl0_588
<=> ! [X40,X7,X6,X1] :
( X1 = X6
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f802,plain,
! [X40,X1,X6,X7] :
( X1 = X6
| X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f399]) ).
fof(f399,axiom,
! [X40,X1,X6,X7] :
( X1 = X6
| X6 = X7
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_6) ).
fof(f15283,plain,
spl0_587,
inference(avatar_split_clause,[],[f801,f15281]) ).
fof(f15281,plain,
( spl0_587
<=> ! [X40,X0,X6,X27] :
( X0 = X6
| X6 = X27
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f801,plain,
! [X40,X0,X6,X27] :
( X0 = X6
| X6 = X27
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f414]) ).
fof(f414,axiom,
! [X40,X0,X6,X27] :
( X0 = X6
| X6 = X27
| X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_6) ).
fof(f15279,plain,
spl0_586,
inference(avatar_split_clause,[],[f773,f15277]) ).
fof(f15277,plain,
( spl0_586
<=> ! [X4,X0,X2,X1] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X4,X2),X1,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f773,plain,
! [X2,X0,X1,X4] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X4,X2),X1,X2,X2),X4,tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f464,f440]) ).
fof(f464,axiom,
! [X2,X0,X1,X4] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X4,X2),X1,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).
fof(f15275,plain,
spl0_585,
inference(avatar_split_clause,[],[f772,f15273]) ).
fof(f15273,plain,
( spl0_585
<=> ! [X2,X4,X6,X22] :
( X6 = X22
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X6,X22,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f772,plain,
! [X2,X6,X4,X22] :
( X6 = X22
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X6,X22,X2),X2,X2),X4,tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f466,f440]) ).
fof(f466,axiom,
! [X2,X6,X4,X22] :
( X6 = X22
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X6,X22,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).
fof(f15261,plain,
spl0_584,
inference(avatar_split_clause,[],[f453,f15259]) ).
fof(f15259,plain,
( spl0_584
<=> ! [X41,X4,X42] :
( c_in(c_Pair(X41,X42,t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Otrancl(X4,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X41,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X41,X42,X4),t_a,t_a),c_Transitive__Closure_Otrancl(X4,t_a),tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f453,axiom,
! [X41,X4,X42] :
( c_in(c_Pair(X41,X42,t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Otrancl(X4,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X41,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X41,X42,X4),t_a,t_a),c_Transitive__Closure_Otrancl(X4,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
fof(f15257,plain,
spl0_583,
inference(avatar_split_clause,[],[f425,f15255]) ).
fof(f15255,plain,
( spl0_583
<=> ! [X40,X6,X27,X1] :
( X6 = X27
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X27,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f425,axiom,
! [X40,X1,X6,X27] :
( X6 = X27
| X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X27,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_9) ).
fof(f15253,plain,
spl0_582,
inference(avatar_split_clause,[],[f410,f15251]) ).
fof(f15251,plain,
( spl0_582
<=> ! [X40,X0,X6,X7] :
( X6 = X7
| X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X0,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f410,axiom,
! [X40,X0,X6,X7] :
( X6 = X7
| X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X0,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_9) ).
fof(f15249,plain,
spl0_581,
inference(avatar_split_clause,[],[f368,f15247]) ).
fof(f15247,plain,
( spl0_581
<=> ! [X4,X0,X5,X2,X1] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) = c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f368,axiom,
! [X2,X0,X1,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) = c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
fof(f14921,plain,
( spl0_580
| ~ spl0_301
| ~ spl0_472 ),
inference(avatar_split_clause,[],[f9660,f9294,f3477,f14919]) ).
fof(f9294,plain,
( spl0_472
<=> ! [X0] :
( c_in(v_a____,c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f9660,plain,
( ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_301
| ~ spl0_472 ),
inference(resolution,[],[f9295,f3478]) ).
fof(f9295,plain,
( ! [X0] :
( c_in(v_a____,c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_472 ),
inference(avatar_component_clause,[],[f9294]) ).
fof(f14299,plain,
( spl0_579
| ~ spl0_303
| ~ spl0_472 ),
inference(avatar_split_clause,[],[f9659,f9294,f3485,f14297]) ).
fof(f9659,plain,
( ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_a____,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_303
| ~ spl0_472 ),
inference(resolution,[],[f9295,f3486]) ).
fof(f14232,plain,
spl0_578,
inference(avatar_split_clause,[],[f792,f14230]) ).
fof(f14230,plain,
( spl0_578
<=> ! [X2,X18,X4,X0,X1] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X18,X1,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f792,plain,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X18,X1,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f467,f440]) ).
fof(f467,axiom,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X18,X1,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).
fof(f14228,plain,
spl0_577,
inference(avatar_split_clause,[],[f791,f14226]) ).
fof(f14226,plain,
( spl0_577
<=> ! [X2,X18,X4,X0,X1] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X18,X0,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f791,plain,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X18,X0,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f472,f440]) ).
fof(f472,axiom,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X18,X0,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).
fof(f14224,plain,
spl0_576,
inference(avatar_split_clause,[],[f790,f14222]) ).
fof(f14222,plain,
( spl0_576
<=> ! [X2,X18,X4,X0,X1] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X18,X1,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f790,plain,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X18,X1,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f474,f440]) ).
fof(f474,axiom,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X1))
| hBOOL(hAPP(X18,X0))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X18,X1,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
fof(f14220,plain,
spl0_575,
inference(avatar_split_clause,[],[f789,f14218]) ).
fof(f14218,plain,
( spl0_575
<=> ! [X2,X18,X4,X0,X1] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X18,X0,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f789,plain,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X18,X0,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f470,f440]) ).
fof(f470,axiom,
! [X2,X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X1))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X18,X0,X4,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).
fof(f14216,plain,
spl0_574,
inference(avatar_split_clause,[],[f787,f14214]) ).
fof(f14214,plain,
( spl0_574
<=> ! [X2,X4,X14] :
( ~ c_Wellfounded_Owf(X14,X2)
| ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X4,X2,X2),X2,X2),c_Relation_ORange(X14,X2,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f787,plain,
! [X2,X14,X4] :
( ~ c_Wellfounded_Owf(X14,X2)
| ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X4,X2,X2),X2,X2),c_Relation_ORange(X14,X2,X2),tc_fun(X2,tc_bool)) ),
inference(definition_unfolding,[],[f110,f557]) ).
fof(f557,axiom,
! [X2,X3,X4] : c_Relation_ODomain(X4,X2,X3) = c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
fof(f110,axiom,
! [X2,X14,X4] :
( ~ c_Wellfounded_Owf(X14,X2)
| ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X4,X2,X2),c_Relation_ORange(X14,X2,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).
fof(f14212,plain,
spl0_573,
inference(avatar_split_clause,[],[f767,f14210]) ).
fof(f14210,plain,
( spl0_573
<=> ! [X41,X4,X42] :
( X41 = X42
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X41,X42,X4),X42,t_a,t_a),X4,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f767,plain,
! [X41,X4,X42] :
( X41 = X42
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X41,X42,X4),X42,t_a,t_a),X4,tc_prod(t_a,t_a)) ),
inference(definition_unfolding,[],[f473,f440]) ).
fof(f473,axiom,
! [X41,X4,X42] :
( X41 = X42
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Ortrancl(X4,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X41,X42,X4),X42,t_a,t_a),X4,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
fof(f14208,plain,
spl0_572,
inference(avatar_split_clause,[],[f760,f14206]) ).
fof(f14206,plain,
( spl0_572
<=> ! [X7,X8,X6,X2] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X8,X6,X7,X2),X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f760,plain,
! [X2,X8,X6,X7] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X8,X6,X7,X2),X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f428,f440]) ).
fof(f428,axiom,
! [X2,X8,X6,X7] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X8,X6,X7,X2),X7,X2,X2),c_Transitive__Closure_Ortrancl(X8,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).
fof(f14204,plain,
spl0_571,
inference(avatar_split_clause,[],[f759,f14202]) ).
fof(f14202,plain,
( spl0_571
<=> ! [X7,X8,X6,X2] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X8,X6,X7,X2),X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f759,plain,
! [X2,X8,X6,X7] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X8,X6,X7,X2),X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f427,f440]) ).
fof(f427,axiom,
! [X2,X8,X6,X7] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X8,X6,X7,X2),X2,X2),c_Transitive__Closure_Ortrancl(X8,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).
fof(f14200,plain,
( spl0_570
| ~ spl0_61
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f9339,f7927,f1104,f14198]) ).
fof(f14198,plain,
( spl0_570
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,v_b____))
| c_in(v_b____,c_Recdef_Ocut(X0,v_Lab____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f7927,plain,
( spl0_442
<=> ! [X0,X1] : hAPP(X0,v_b____) = hAPP(c_Recdef_Ocut(X0,v_Lab____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,X1),v_b____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f9339,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,v_b____))
| c_in(v_b____,c_Recdef_Ocut(X0,v_Lab____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,X1),X2) )
| ~ spl0_61
| ~ spl0_442 ),
inference(superposition,[],[f1105,f7928]) ).
fof(f7928,plain,
( ! [X0,X1] : hAPP(X0,v_b____) = hAPP(c_Recdef_Ocut(X0,v_Lab____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,X1),v_b____)
| ~ spl0_442 ),
inference(avatar_component_clause,[],[f7927]) ).
fof(f14196,plain,
spl0_569,
inference(avatar_split_clause,[],[f750,f14194]) ).
fof(f14194,plain,
( spl0_569
<=> ! [X2,X4,X14] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f750,plain,
! [X2,X14,X4] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(definition_unfolding,[],[f91,f440,f440]) ).
fof(f91,axiom,
! [X2,X14,X4] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X4,X2),c_Transitive__Closure_Ortrancl(X14,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
fof(f14192,plain,
spl0_568,
inference(avatar_split_clause,[],[f739,f14190]) ).
fof(f14190,plain,
( spl0_568
<=> ! [X3,X9,X5,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(c_Relation_Oconverse(X5,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X9,X2,X3),X3,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f739,plain,
! [X2,X3,X9,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(c_Relation_Oconverse(X5,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X9,X2,X3),X3,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),tc_fun(X2,tc_bool)),
inference(definition_unfolding,[],[f35,f557,f557,f557]) ).
fof(f35,axiom,
! [X2,X3,X9,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X5,X2,X3),c_Relation_ODomain(X9,X2,X3),tc_fun(X2,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).
fof(f14188,plain,
spl0_567,
inference(avatar_split_clause,[],[f738,f14186]) ).
fof(f14186,plain,
( spl0_567
<=> ! [X3,X9,X5,X2] : c_lessequals(c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X5,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X9,X2,X3),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f738,plain,
! [X2,X3,X9,X5] : c_lessequals(c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X5,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X9,X2,X3),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(definition_unfolding,[],[f92,f557,f557,f557]) ).
fof(f92,axiom,
! [X2,X3,X9,X5] : c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X5,X2,X3),c_Relation_ODomain(X9,X2,X3),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).
fof(f14184,plain,
spl0_566,
inference(avatar_split_clause,[],[f646,f14182]) ).
fof(f14182,plain,
( spl0_566
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f646,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
fof(f14180,plain,
spl0_565,
inference(avatar_split_clause,[],[f458,f14178]) ).
fof(f14178,plain,
( spl0_565
<=> ! [X2,X4,X6,X22] :
( c_in(c_Pair(X6,X22,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X6,X22,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f458,axiom,
! [X2,X6,X4,X22] :
( c_in(c_Pair(X6,X22,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X22,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X6,X22,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
fof(f14176,plain,
spl0_564,
inference(avatar_split_clause,[],[f455,f14174]) ).
fof(f14174,plain,
( spl0_564
<=> ! [X4,X0,X2,X1] :
( c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X0,X1,X4,X2),X1,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f455,axiom,
! [X2,X0,X1,X4] :
( c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X0,X1,X4,X2),X1,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).
fof(f14172,plain,
spl0_563,
inference(avatar_split_clause,[],[f334,f14170]) ).
fof(f14170,plain,
( spl0_563
<=> ! [X38,X4,X5,X2,X37] :
( X37 = X38
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X37,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| ~ c_in(X38,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X37,X38,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f334,axiom,
! [X2,X38,X37,X4,X5] :
( X37 = X38
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X37,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| ~ c_in(X38,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X37,X38,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__disj_0) ).
fof(f14168,plain,
spl0_562,
inference(avatar_split_clause,[],[f163,f14166]) ).
fof(f14166,plain,
( spl0_562
<=> ! [X2,X5,X4] :
( ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(X4,X2),c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f163,axiom,
! [X2,X4,X5] :
( ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(X4,X2),c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
fof(f14164,plain,
spl0_561,
inference(avatar_split_clause,[],[f26,f14162]) ).
fof(f14162,plain,
( spl0_561
<=> ! [X5,X3,X9,X11,X6,X2] :
( ~ c_in(X6,X11,X2)
| c_lessequals(X5,X9,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X5,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X9,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f26,axiom,
! [X2,X3,X11,X6,X9,X5] :
( ~ c_in(X6,X11,X2)
| c_lessequals(X5,X9,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X5,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X9,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
fof(f14160,plain,
spl0_560,
inference(avatar_split_clause,[],[f25,f14158]) ).
fof(f14158,plain,
( spl0_560
<=> ! [X5,X3,X9,X11,X6,X2] :
( ~ c_in(X6,X11,X2)
| ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
| c_lessequals(c_Product__Type_OSigma(X5,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X9,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f25,axiom,
! [X2,X3,X11,X6,X9,X5] :
( ~ c_in(X6,X11,X2)
| ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
| c_lessequals(c_Product__Type_OSigma(X5,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X9,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
fof(f13809,plain,
spl0_559,
inference(avatar_split_clause,[],[f770,f13807]) ).
fof(f13807,plain,
( spl0_559
<=> ! [X7,X8,X6,X2] :
( X6 = X7
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f770,plain,
! [X2,X8,X6,X7] :
( X6 = X7
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f489,f440]) ).
fof(f489,axiom,
! [X2,X8,X6,X7] :
( X6 = X7
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Ortrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
fof(f13805,plain,
spl0_558,
inference(avatar_split_clause,[],[f765,f13803]) ).
fof(f13803,plain,
( spl0_558
<=> ! [X4,X7,X6,X2] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f765,plain,
! [X2,X6,X7,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f430,f440]) ).
fof(f430,axiom,
! [X2,X6,X7,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).
fof(f13801,plain,
spl0_557,
inference(avatar_split_clause,[],[f764,f13799]) ).
fof(f13799,plain,
( spl0_557
<=> ! [X4,X7,X6,X2] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f764,plain,
! [X2,X6,X7,X4] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f351,f440]) ).
fof(f351,axiom,
! [X2,X6,X7,X4] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
fof(f13797,plain,
spl0_556,
inference(avatar_split_clause,[],[f678,f13795]) ).
fof(f13795,plain,
( spl0_556
<=> ! [X5,X4,X6,X27,X2] :
( X6 = X27
| ~ c_Relation_Ototal__on(X5,X4,X2)
| ~ c_in(X6,X5,X2)
| ~ c_in(X27,X5,X2)
| c_in(c_Pair(X6,X27,X2,X2),X4,tc_prod(X2,X2))
| c_in(c_Pair(X27,X6,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f678,axiom,
! [X2,X6,X27,X4,X5] :
( X6 = X27
| ~ c_Relation_Ototal__on(X5,X4,X2)
| ~ c_in(X6,X5,X2)
| ~ c_in(X27,X5,X2)
| c_in(c_Pair(X6,X27,X2,X2),X4,tc_prod(X2,X2))
| c_in(c_Pair(X27,X6,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
fof(f13793,plain,
( spl0_555
| ~ spl0_156
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f13619,f13347,f1768,f13791]) ).
fof(f13791,plain,
( spl0_555
<=> ! [X0] : c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f13347,plain,
( spl0_543
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f13619,plain,
( ! [X0] : c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_156
| ~ spl0_543 ),
inference(superposition,[],[f13348,f1769]) ).
fof(f13348,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_543 ),
inference(avatar_component_clause,[],[f13347]) ).
fof(f13789,plain,
spl0_554,
inference(avatar_split_clause,[],[f644,f13787]) ).
fof(f13787,plain,
( spl0_554
<=> ! [X4,X19,X0,X14,X3,X10,X2,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))
| ~ c_in(c_Pair(X1,X19,X3,X10),X14,tc_prod(X3,X10))
| c_in(c_Pair(X0,X19,X2,X10),c_Relation_Orel__comp(X4,X14,X2,X3,X10),tc_prod(X2,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f644,axiom,
! [X2,X3,X10,X0,X1,X19,X14,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))
| ~ c_in(c_Pair(X1,X19,X3,X10),X14,tc_prod(X3,X10))
| c_in(c_Pair(X0,X19,X2,X10),c_Relation_Orel__comp(X4,X14,X2,X3,X10),tc_prod(X2,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
fof(f13785,plain,
spl0_553,
inference(avatar_split_clause,[],[f459,f13783]) ).
fof(f13783,plain,
( spl0_553
<=> ! [X41,X4,X42] :
( c_in(c_Pair(X41,X42,t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Otrancl(X4,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X41,X42,X4),X42,t_a,t_a),X4,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f459,axiom,
! [X41,X4,X42] :
( c_in(c_Pair(X41,X42,t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X41,X42,t_a,t_a),c_Transitive__Closure_Otrancl(X4,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X41,X42,X4),X42,t_a,t_a),X4,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
fof(f13631,plain,
spl0_552,
inference(avatar_split_clause,[],[f624,f13629]) ).
fof(f13629,plain,
( spl0_552
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f624,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
fof(f13627,plain,
spl0_551,
inference(avatar_split_clause,[],[f623,f13625]) ).
fof(f13625,plain,
( spl0_551
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f623,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
fof(f13623,plain,
spl0_550,
inference(avatar_split_clause,[],[f417,f13621]) ).
fof(f13621,plain,
( spl0_550
<=> ! [X40,X6,X27,X1] :
( X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X27,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f417,axiom,
! [X40,X1,X6,X27] :
( X1 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X27,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_1) ).
fof(f13618,plain,
spl0_549,
inference(avatar_split_clause,[],[f402,f13616]) ).
fof(f13616,plain,
( spl0_549
<=> ! [X40,X0,X6,X7] :
( X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X0,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f402,axiom,
! [X40,X0,X6,X7] :
( X0 = X6
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X0,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_1) ).
fof(f13614,plain,
spl0_548,
inference(avatar_split_clause,[],[f44,f13612]) ).
fof(f13612,plain,
( spl0_548
<=> ! [X3,X4,X10,X14,X23,X2,X24] :
( ~ c_lessequals(X23,X4,tc_fun(tc_prod(X2,X3),tc_bool))
| ~ c_lessequals(X24,X14,tc_fun(tc_prod(X3,X10),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X23,X24,X2,X3,X10),c_Relation_Orel__comp(X4,X14,X2,X3,X10),tc_fun(tc_prod(X2,X10),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f44,axiom,
! [X2,X3,X10,X14,X4,X24,X23] :
( ~ c_lessequals(X23,X4,tc_fun(tc_prod(X2,X3),tc_bool))
| ~ c_lessequals(X24,X14,tc_fun(tc_prod(X3,X10),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X23,X24,X2,X3,X10),c_Relation_Orel__comp(X4,X14,X2,X3,X10),tc_fun(tc_prod(X2,X10),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
fof(f13429,plain,
spl0_547,
inference(avatar_split_clause,[],[f766,f13427]) ).
fof(f13427,plain,
( spl0_547
<=> ! [X7,X8,X6,X2] :
( X6 = X7
| c_in(X6,c_Relation_ORange(c_Relation_Oconverse(X8,X2,X2),X2,X2),X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f766,plain,
! [X2,X8,X6,X7] :
( X6 = X7
| c_in(X6,c_Relation_ORange(c_Relation_Oconverse(X8,X2,X2),X2,X2),X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f608,f557,f440]) ).
fof(f608,axiom,
! [X2,X8,X6,X7] :
( X6 = X7
| c_in(X6,c_Relation_ODomain(X8,X2,X2),X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Ortrancl(X8,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
fof(f13425,plain,
spl0_546,
inference(avatar_split_clause,[],[f736,f13423]) ).
fof(f13423,plain,
( spl0_546
<=> ! [X3,X9,X5,X2] : c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X5,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X9,X2,X3),X3,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f736,plain,
! [X2,X3,X9,X5] : c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X5,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X9,X2,X3),X3,X2),tc_fun(X2,tc_bool)),
inference(definition_unfolding,[],[f231,f557,f557,f557]) ).
fof(f231,axiom,
! [X2,X3,X9,X5] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X5,X2,X3),c_Relation_ODomain(X9,X2,X3),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
fof(f13417,plain,
spl0_545,
inference(avatar_split_clause,[],[f717,f13415]) ).
fof(f13415,plain,
( spl0_545
<=> ! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f717,plain,
! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(definition_unfolding,[],[f586,f440,f440,f440]) ).
fof(f586,axiom,
! [X2,X4] : c_Transitive__Closure_Ortrancl(X4,X2) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
fof(f13413,plain,
spl0_544,
inference(avatar_split_clause,[],[f618,f13411]) ).
fof(f13411,plain,
( spl0_544
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_Relation_Otrans(X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f618,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_Relation_Otrans(X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),X4,tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).
fof(f13349,plain,
( spl0_543
| ~ spl0_77
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f12903,f12233,f1183,f13347]) ).
fof(f12903,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_77
| ~ spl0_521 ),
inference(superposition,[],[f1184,f12234]) ).
fof(f12819,plain,
spl0_542,
inference(avatar_split_clause,[],[f834,f12817]) ).
fof(f834,plain,
! [X2,X8,X13] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(forward_demodulation,[],[f833,f217]) ).
fof(f217,axiom,
! [X2,X3,X10,X8,X13,X33] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X13,X33,tc_fun(tc_prod(X2,X10),tc_bool)),X8,X2,X10,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X13,X8,X2,X10,X3),c_Relation_Orel__comp(X33,X8,X2,X10,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
fof(f833,plain,
! [X2,X8,X13] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X8,X8,X2,X2,X2),c_Relation_Orel__comp(X13,X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(forward_demodulation,[],[f371,f228]) ).
fof(f371,axiom,
! [X2,X8,X13] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X8,X8,X2,X2,X2),c_Relation_Orel__comp(X13,X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
fof(f12815,plain,
spl0_541,
inference(avatar_split_clause,[],[f832,f12813]) ).
fof(f832,plain,
! [X2,X8,X13] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(forward_demodulation,[],[f831,f217]) ).
fof(f831,plain,
! [X2,X8,X13] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X8,X8,X2,X2,X2),c_Relation_Orel__comp(X13,X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(forward_demodulation,[],[f370,f228]) ).
fof(f370,axiom,
! [X2,X8,X13] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X8,X8,X2,X2,X2),c_Relation_Orel__comp(X13,X8,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
fof(f12811,plain,
spl0_540,
inference(avatar_split_clause,[],[f776,f12809]) ).
fof(f12809,plain,
( spl0_540
<=> ! [X4,X0,X2,X1] :
( ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(X1,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f776,plain,
! [X2,X0,X1,X4] :
( ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(X1,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f597,f440]) ).
fof(f597,axiom,
! [X2,X0,X1,X4] :
( ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(X1,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
fof(f12807,plain,
spl0_539,
inference(avatar_split_clause,[],[f757,f12805]) ).
fof(f12805,plain,
( spl0_539
<=> ! [X4,X7,X6,X2] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f757,plain,
! [X2,X6,X7,X4] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f429,f440]) ).
fof(f429,axiom,
! [X2,X6,X7,X4] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
fof(f12803,plain,
spl0_538,
inference(avatar_split_clause,[],[f756,f12801]) ).
fof(f756,plain,
! [X2,X6,X7,X4] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f352,f440]) ).
fof(f352,axiom,
! [X2,X6,X7,X4] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
fof(f12799,plain,
spl0_537,
inference(avatar_split_clause,[],[f645,f12797]) ).
fof(f12797,plain,
( spl0_537
<=> ! [X19,X0,X8,X2,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X8,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),X8,tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f645,axiom,
! [X2,X0,X1,X8,X19] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X8,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X19,X2,X2),X8,tc_prod(X2,X2))
| c_in(c_Pair(X0,X19,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
fof(f12795,plain,
spl0_536,
inference(avatar_split_clause,[],[f449,f12793]) ).
fof(f12793,plain,
( spl0_536
<=> ! [X10,X19,X14,X4,X0,X3,X2] :
( ~ c_in(c_Pair(X0,X19,X2,X3),c_Relation_Orel__comp(X4,X14,X2,X10,X3),tc_prod(X2,X3))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X0,X19,X4,X14,X2,X3,X10),X2,X10),X4,tc_prod(X2,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f449,axiom,
! [X2,X3,X10,X0,X19,X14,X4] :
( ~ c_in(c_Pair(X0,X19,X2,X3),c_Relation_Orel__comp(X4,X14,X2,X10,X3),tc_prod(X2,X3))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X0,X19,X4,X14,X2,X3,X10),X2,X10),X4,tc_prod(X2,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
fof(f12791,plain,
spl0_535,
inference(avatar_split_clause,[],[f448,f12789]) ).
fof(f12789,plain,
( spl0_535
<=> ! [X10,X19,X14,X4,X0,X3,X2] :
( ~ c_in(c_Pair(X0,X19,X2,X3),c_Relation_Orel__comp(X4,X14,X2,X10,X3),tc_prod(X2,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X0,X19,X4,X14,X2,X3,X10),X19,X10,X3),X14,tc_prod(X10,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f448,axiom,
! [X2,X3,X10,X0,X19,X14,X4] :
( ~ c_in(c_Pair(X0,X19,X2,X3),c_Relation_Orel__comp(X4,X14,X2,X10,X3),tc_prod(X2,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X0,X19,X4,X14,X2,X3,X10),X19,X10,X3),X14,tc_prod(X10,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
fof(f12787,plain,
spl0_534,
inference(avatar_split_clause,[],[f434,f12785]) ).
fof(f12785,plain,
( spl0_534
<=> ! [X5,X3,X8,X9,X2] :
( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X8,X3,X2),X2,X3)
| c_Relation_OImage(X8,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X8,X5,X3,X2),c_Relation_OImage(X8,X9,X3,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f434,axiom,
! [X2,X3,X8,X9,X5] :
( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X8,X3,X2),X2,X3)
| c_Relation_OImage(X8,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X8,X5,X3,X2),c_Relation_OImage(X8,X9,X3,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
fof(f12776,plain,
spl0_533,
inference(avatar_split_clause,[],[f253,f12774]) ).
fof(f12774,plain,
( spl0_533
<=> ! [X3,X4,X36,X12,X6,X2] :
( c_Recdef_Ocut(X12,X4,X6,X2,X3) = c_Recdef_Ocut(X36,X4,X6,X2,X3)
| hAPP(X12,c_List_Osko__Recdef__Xcuts__eq__1__1(X12,X36,X4,X6,X2,X3)) != hAPP(X36,c_List_Osko__Recdef__Xcuts__eq__1__1(X12,X36,X4,X6,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f253,axiom,
! [X2,X3,X36,X6,X4,X12] :
( c_Recdef_Ocut(X12,X4,X6,X2,X3) = c_Recdef_Ocut(X36,X4,X6,X2,X3)
| hAPP(X12,c_List_Osko__Recdef__Xcuts__eq__1__1(X12,X36,X4,X6,X2,X3)) != hAPP(X36,c_List_Osko__Recdef__Xcuts__eq__1__1(X12,X36,X4,X6,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
fof(f12772,plain,
spl0_532,
inference(avatar_split_clause,[],[f218,f12770]) ).
fof(f12770,plain,
( spl0_532
<=> ! [X3,X10,X8,X13,X33,X2] : c_Relation_Orel__comp(X8,c_Lattices_Oupper__semilattice__class_Osup(X13,X33,tc_fun(tc_prod(X10,X3),tc_bool)),X2,X10,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X8,X13,X2,X10,X3),c_Relation_Orel__comp(X8,X33,X2,X10,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f218,axiom,
! [X2,X3,X10,X8,X13,X33] : c_Relation_Orel__comp(X8,c_Lattices_Oupper__semilattice__class_Osup(X13,X33,tc_fun(tc_prod(X10,X3),tc_bool)),X2,X10,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X8,X13,X2,X10,X3),c_Relation_Orel__comp(X8,X33,X2,X10,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
fof(f12768,plain,
spl0_531,
inference(avatar_split_clause,[],[f217,f12766]) ).
fof(f12766,plain,
( spl0_531
<=> ! [X33,X10,X8,X13,X3,X2] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X13,X33,tc_fun(tc_prod(X2,X10),tc_bool)),X8,X2,X10,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X13,X8,X2,X10,X3),c_Relation_Orel__comp(X33,X8,X2,X10,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f12495,plain,
spl0_530,
inference(avatar_split_clause,[],[f813,f12493]) ).
fof(f12493,plain,
( spl0_530
<=> ! [X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f813,plain,
! [X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(forward_demodulation,[],[f729,f228]) ).
fof(f729,plain,
! [X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(definition_unfolding,[],[f375,f440,f440]) ).
fof(f375,axiom,
! [X2,X8] : c_Transitive__Closure_Ortrancl(X8,X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
fof(f12445,plain,
( spl0_529
| ~ spl0_320
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f12441,f12438,f3986,f12443]) ).
fof(f12443,plain,
( spl0_529
<=> ! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f12438,plain,
( spl0_528
<=> ! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f12441,plain,
( ! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_320
| ~ spl0_528 ),
inference(forward_demodulation,[],[f12439,f3987]) ).
fof(f12439,plain,
( ! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_528 ),
inference(avatar_component_clause,[],[f12438]) ).
fof(f12440,plain,
spl0_528,
inference(avatar_split_clause,[],[f812,f12438]) ).
fof(f812,plain,
! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(forward_demodulation,[],[f728,f228]) ).
fof(f728,plain,
! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(definition_unfolding,[],[f377,f440,f440]) ).
fof(f377,axiom,
! [X2,X4] : c_Transitive__Closure_Ortrancl(X4,X2) = c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).
fof(f12429,plain,
spl0_527,
inference(avatar_split_clause,[],[f798,f12427]) ).
fof(f12427,plain,
( spl0_527
<=> ! [X5,X4,X7,X6,X27,X2] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X27,X6,X2)
| ~ c_in(X7,X6,X2)
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| c_in(c_Pair(X27,X7,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f798,plain,
! [X2,X6,X7,X27,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X27,X6,X2)
| ~ c_in(X7,X6,X2)
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| c_in(c_Pair(X27,X7,X2,X2),X4,tc_prod(X2,X2)) ),
inference(duplicate_literal_removal,[],[f395]) ).
fof(f395,axiom,
! [X2,X6,X7,X27,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X27,X6,X2)
| ~ c_in(X7,X6,X2)
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool))
| c_in(c_Pair(X27,X7,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).
fof(f12425,plain,
spl0_526,
inference(avatar_split_clause,[],[f732,f12423]) ).
fof(f12423,plain,
( spl0_526
<=> ! [X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f732,plain,
! [X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(definition_unfolding,[],[f374,f440,f440]) ).
fof(f374,axiom,
! [X2,X8] : c_Transitive__Closure_Ortrancl(X8,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X8,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
fof(f12421,plain,
spl0_525,
inference(avatar_split_clause,[],[f587,f12419]) ).
fof(f12419,plain,
( spl0_525
<=> ! [X6,X40,X7] :
( X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f587,axiom,
! [X40,X6,X7] :
( X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
fof(f12379,plain,
spl0_524,
inference(avatar_split_clause,[],[f636,f12377]) ).
fof(f12377,plain,
( spl0_524
<=> ! [X6,X4,X3,X7,X12,X36,X2] :
( hAPP(X12,X7) = hAPP(X36,X7)
| ~ c_in(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2))
| c_Recdef_Ocut(X12,X4,X6,X2,X3) != c_Recdef_Ocut(X36,X4,X6,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f636,axiom,
! [X2,X3,X36,X6,X7,X4,X12] :
( hAPP(X12,X7) = hAPP(X36,X7)
| ~ c_in(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2))
| c_Recdef_Ocut(X12,X4,X6,X2,X3) != c_Recdef_Ocut(X36,X4,X6,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
fof(f12375,plain,
spl0_523,
inference(avatar_split_clause,[],[f27,f12373]) ).
fof(f12373,plain,
( spl0_523
<=> ! [X5,X9,X6,X2] :
( ~ c_in(X6,X5,X2)
| c_lessequals(X5,c_Set_Oinsert(X6,X9,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f27,axiom,
! [X2,X6,X9,X5] :
( ~ c_in(X6,X5,X2)
| c_lessequals(X5,c_Set_Oinsert(X6,X9,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
fof(f12306,plain,
( spl0_522
| ~ spl0_57
| ~ spl0_458
| ~ spl0_520 ),
inference(avatar_split_clause,[],[f12050,f12047,f8819,f1088,f12304]) ).
fof(f12304,plain,
( spl0_522
<=> ! [X2,X4] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f8819,plain,
( spl0_458
<=> ! [X4,X14,X3,X2] : c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X4,X3,X2),c_Relation_Oconverse(X14,X3,X2),tc_fun(tc_prod(X2,X3),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f12047,plain,
( spl0_520
<=> ! [X2,X4] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Oconverse(X4,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f12050,plain,
( ! [X2,X4] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2)
| ~ spl0_57
| ~ spl0_458
| ~ spl0_520 ),
inference(forward_demodulation,[],[f12048,f8856]) ).
fof(f8856,plain,
( ! [X0,X1] : c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),X1,tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Relation_Oconverse(X1,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_57
| ~ spl0_458 ),
inference(superposition,[],[f8820,f1089]) ).
fof(f8820,plain,
( ! [X2,X3,X14,X4] : c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X4,X3,X2),c_Relation_Oconverse(X14,X3,X2),tc_fun(tc_prod(X2,X3),tc_bool))
| ~ spl0_458 ),
inference(avatar_component_clause,[],[f8819]) ).
fof(f12048,plain,
( ! [X2,X4] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Oconverse(X4,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_520 ),
inference(avatar_component_clause,[],[f12047]) ).
fof(f12235,plain,
( spl0_521
| ~ spl0_98
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4611,f4509,f1320,f12233]) ).
fof(f4611,plain,
( ! [X0] : c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Set_Oinsert(v_a____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)
| ~ spl0_98
| ~ spl0_346 ),
inference(resolution,[],[f4510,f1321]) ).
fof(f12049,plain,
spl0_520,
inference(avatar_split_clause,[],[f811,f12047]) ).
fof(f811,plain,
! [X2,X4] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Oconverse(X4,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(forward_demodulation,[],[f724,f228]) ).
fof(f724,plain,
! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X4,X2,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2),
inference(definition_unfolding,[],[f569,f440,f440]) ).
fof(f569,axiom,
! [X2,X4] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X4,X2),X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
fof(f12045,plain,
spl0_519,
inference(avatar_split_clause,[],[f442,f12043]) ).
fof(f442,axiom,
! [X2,X3,X36,X6,X4,X12] :
( c_Recdef_Ocut(X12,X4,X6,X2,X3) = c_Recdef_Ocut(X36,X4,X6,X2,X3)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X12,X36,X4,X6,X2,X3),X6,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
fof(f12041,plain,
spl0_518,
inference(avatar_split_clause,[],[f106,f12039]) ).
fof(f12039,plain,
( spl0_518
<=> ! [X13,X2,X8] :
( ~ c_Wellfounded_Owf(X8,X2)
| ~ c_Wellfounded_Owf(X13,X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_lessequals(c_Relation_Orel__comp(X8,X13,X2,X2,X2),X8,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f106,axiom,
! [X2,X8,X13] :
( ~ c_Wellfounded_Owf(X8,X2)
| ~ c_Wellfounded_Owf(X13,X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_lessequals(c_Relation_Orel__comp(X8,X13,X2,X2,X2),X8,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
fof(f12037,plain,
spl0_517,
inference(avatar_split_clause,[],[f101,f12035]) ).
fof(f12035,plain,
( spl0_517
<=> ! [X9,X11,X5,X2] :
( ~ c_lessequals(X11,X5,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f101,axiom,
! [X2,X11,X9,X5] :
( ~ c_lessequals(X11,X5,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
fof(f12033,plain,
spl0_516,
inference(avatar_split_clause,[],[f100,f12031]) ).
fof(f100,axiom,
! [X2,X11,X9,X5] :
( c_lessequals(X11,X5,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
fof(f11890,plain,
( spl0_515
| ~ spl0_98
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3751,f3509,f1320,f11888]) ).
fof(f11888,plain,
( spl0_515
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| v_Lab____ = c_Set_Oinsert(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1),v_Lab____,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f3751,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| v_Lab____ = c_Set_Oinsert(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1),v_Lab____,X2) )
| ~ spl0_98
| ~ spl0_309 ),
inference(resolution,[],[f3510,f1321]) ).
fof(f11561,plain,
( spl0_514
| ~ spl0_98
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3578,f3465,f1320,f11559]) ).
fof(f11559,plain,
( spl0_514
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| v_Lab____ = c_Set_Oinsert(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1),v_Lab____,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f3578,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| v_Lab____ = c_Set_Oinsert(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1),v_Lab____,X2) )
| ~ spl0_98
| ~ spl0_298 ),
inference(resolution,[],[f3466,f1321]) ).
fof(f10181,plain,
spl0_513,
inference(avatar_split_clause,[],[f819,f10179]) ).
fof(f10179,plain,
( spl0_513
<=> ! [X9,X11,X5,X2] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f819,plain,
! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)),
inference(forward_demodulation,[],[f127,f328]) ).
fof(f328,axiom,
! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
fof(f127,axiom,
! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(X11,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
fof(f10177,plain,
spl0_512,
inference(avatar_split_clause,[],[f658,f10175]) ).
fof(f10175,plain,
( spl0_512
<=> ! [X40,X7,X6,X22] :
( X7 = X22
| X6 = X22
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f658,axiom,
! [X40,X6,X7,X22] :
( X7 = X22
| X6 = X22
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
fof(f10173,plain,
spl0_511,
inference(avatar_split_clause,[],[f657,f10171]) ).
fof(f10171,plain,
( spl0_511
<=> ! [X40,X7,X6,X22] :
( X7 = X22
| X6 = X7
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f657,axiom,
! [X40,X6,X7,X22] :
( X7 = X22
| X6 = X7
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
fof(f10169,plain,
spl0_510,
inference(avatar_split_clause,[],[f650,f10167]) ).
fof(f10167,plain,
( spl0_510
<=> ! [X40,X7,X6,X22] :
( X6 = X22
| X7 = X22
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f650,axiom,
! [X40,X6,X7,X22] :
( X6 = X22
| X7 = X22
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
fof(f10165,plain,
spl0_509,
inference(avatar_split_clause,[],[f649,f10163]) ).
fof(f10163,plain,
( spl0_509
<=> ! [X40,X7,X6,X22] :
( X6 = X22
| X6 = X7
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f649,axiom,
! [X40,X6,X7,X22] :
( X6 = X22
| X6 = X7
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
fof(f10161,plain,
spl0_508,
inference(avatar_split_clause,[],[f641,f10159]) ).
fof(f10159,plain,
( spl0_508
<=> ! [X3,X4,X7,X6,X12,X2] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Relation_Oinv__image(X4,X12,X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(hAPP(X12,X6),hAPP(X12,X7),X3,X3),X4,tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f641,axiom,
! [X2,X3,X6,X7,X4,X12] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Relation_Oinv__image(X4,X12,X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(hAPP(X12,X6),hAPP(X12,X7),X3,X3),X4,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
fof(f10157,plain,
( spl0_507
| ~ spl0_61
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f10112,f9965,f1104,f10155]) ).
fof(f10155,plain,
( spl0_507
<=> ! [X0,X1] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a____,c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f9965,plain,
( spl0_487
<=> ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(hAPP(c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f10112,plain,
( ! [X0,X1] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a____,c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) )
| ~ spl0_61
| ~ spl0_487 ),
inference(resolution,[],[f9966,f1105]) ).
fof(f9966,plain,
( ! [X0] :
( hBOOL(hAPP(c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____))
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f9965]) ).
fof(f10153,plain,
spl0_506,
inference(avatar_split_clause,[],[f640,f10151]) ).
fof(f640,axiom,
! [X2,X3,X6,X7,X4,X12] :
( ~ c_in(c_Pair(hAPP(X12,X6),hAPP(X12,X7),X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X6,X7,X2,X2),c_Relation_Oinv__image(X4,X12,X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
fof(f10149,plain,
spl0_505,
inference(avatar_split_clause,[],[f603,f10147]) ).
fof(f10147,plain,
( spl0_505
<=> ! [X18,X4,X6,X48] :
( hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| c_in(X48,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X48,v_sko__Wellfounded__Xacc__Xinduct__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f603,axiom,
! [X48,X18,X6,X4] :
( hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| c_in(X48,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X48,v_sko__Wellfounded__Xacc__Xinduct__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
fof(f10145,plain,
spl0_504,
inference(avatar_split_clause,[],[f598,f10143]) ).
fof(f10143,plain,
( spl0_504
<=> ! [X18,X4,X6,X48] :
( hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| c_in(X48,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X48,v_sko__Wellfounded__Xacc__Xinducts__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f598,axiom,
! [X48,X18,X6,X4] :
( hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| c_in(X48,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X48,v_sko__Wellfounded__Xacc__Xinducts__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
fof(f10141,plain,
spl0_503,
inference(avatar_split_clause,[],[f588,f10139]) ).
fof(f588,axiom,
! [X40,X0,X1] :
( ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
fof(f10137,plain,
spl0_502,
inference(avatar_split_clause,[],[f363,f10135]) ).
fof(f10135,plain,
( spl0_502
<=> ! [X5,X6,X3,X11,X9,X2] :
( X5 = X9
| ~ c_in(X6,X11,X2)
| c_Product__Type_OSigma(X5,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2) != c_Product__Type_OSigma(X9,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f363,axiom,
! [X2,X3,X11,X6,X9,X5] :
( X5 = X9
| ~ c_in(X6,X11,X2)
| c_Product__Type_OSigma(X5,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2) != c_Product__Type_OSigma(X9,c_COMBK(X11,tc_fun(X2,tc_bool),X3),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
fof(f10133,plain,
spl0_501,
inference(avatar_split_clause,[],[f347,f10131]) ).
fof(f10131,plain,
( spl0_501
<=> ! [X3,X4,X23,X5,X2,X39] :
( ~ c_lessequals(X39,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(X23,X4,tc_fun(tc_prod(X2,X3),tc_bool))
| c_lessequals(c_Relation_OImage(X23,X39,X2,X3),c_Relation_OImage(X4,X5,X2,X3),tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f347,axiom,
! [X2,X3,X39,X4,X5,X23] :
( ~ c_lessequals(X39,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(X23,X4,tc_fun(tc_prod(X2,X3),tc_bool))
| c_lessequals(c_Relation_OImage(X23,X39,X2,X3),c_Relation_OImage(X4,X5,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).
fof(f10129,plain,
spl0_500,
inference(avatar_split_clause,[],[f332,f10127]) ).
fof(f332,axiom,
! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
fof(f10125,plain,
spl0_499,
inference(avatar_split_clause,[],[f327,f10123]) ).
fof(f327,axiom,
! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
fof(f10121,plain,
spl0_498,
inference(avatar_split_clause,[],[f326,f10119]) ).
fof(f10119,plain,
( spl0_498
<=> ! [X9,X11,X5,X2,X30] :
( ~ c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X30,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X30,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f326,axiom,
! [X2,X11,X9,X5,X30] :
( ~ c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X30,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X30,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
fof(f10117,plain,
spl0_497,
inference(avatar_split_clause,[],[f290,f10115]) ).
fof(f10115,plain,
( spl0_497
<=> ! [X9,X11,X5,X2] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f290,axiom,
! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
fof(f10111,plain,
spl0_496,
inference(avatar_split_clause,[],[f227,f10109]) ).
fof(f227,axiom,
! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
fof(f10107,plain,
spl0_495,
inference(avatar_split_clause,[],[f189,f10105]) ).
fof(f189,axiom,
! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
fof(f10103,plain,
spl0_494,
inference(avatar_split_clause,[],[f173,f10101]) ).
fof(f10101,plain,
( spl0_494
<=> ! [X9,X11,X5,X2,X30] :
( ~ c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X30,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X11,X30,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f173,axiom,
! [X2,X11,X9,X5,X30] :
( ~ c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X30,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X11,X30,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
fof(f10099,plain,
spl0_493,
inference(avatar_split_clause,[],[f134,f10097]) ).
fof(f134,axiom,
! [X2,X11,X9,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
fof(f10095,plain,
spl0_492,
inference(avatar_split_clause,[],[f130,f10093]) ).
fof(f10093,plain,
( spl0_492
<=> ! [X9,X11,X5,X2,X30] :
( ~ c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(X30,X9,tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X11,X30,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f130,axiom,
! [X2,X11,X9,X5,X30] :
( ~ c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(X30,X9,tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X11,X30,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
fof(f9984,plain,
( spl0_491
| ~ spl0_490 ),
inference(avatar_split_clause,[],[f9980,f9977,f9982]) ).
fof(f9977,plain,
( spl0_490
<=> ! [X9,X11,X5,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f9980,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool))
| ~ spl0_490 ),
inference(forward_demodulation,[],[f9978,f134]) ).
fof(f9978,plain,
( ! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_490 ),
inference(avatar_component_clause,[],[f9977]) ).
fof(f9979,plain,
spl0_490,
inference(avatar_split_clause,[],[f128,f9977]) ).
fof(f128,axiom,
! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
fof(f9975,plain,
spl0_489,
inference(avatar_split_clause,[],[f99,f9973]) ).
fof(f9973,plain,
( spl0_489
<=> ! [X5,X3,X8,X9,X2] : c_lessequals(c_Relation_OImage(X8,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X3,tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X8,X5,X3,X2),c_Relation_OImage(X8,X9,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f99,axiom,
! [X2,X3,X8,X9,X5] : c_lessequals(c_Relation_OImage(X8,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X3,tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X8,X5,X3,X2),c_Relation_OImage(X8,X9,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
fof(f9971,plain,
spl0_488,
inference(avatar_split_clause,[],[f98,f9969]) ).
fof(f9969,plain,
( spl0_488
<=> ! [X5,X3,X12,X9,X2] : c_lessequals(c_Set_Oimage(X12,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X3,tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X12,X5,X3,X2),c_Set_Oimage(X12,X9,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f98,axiom,
! [X2,X3,X9,X5,X12] : c_lessequals(c_Set_Oimage(X12,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X3,tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X12,X5,X3,X2),c_Set_Oimage(X12,X9,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
fof(f9967,plain,
( spl0_487
| ~ spl0_62
| ~ spl0_472 ),
inference(avatar_split_clause,[],[f9662,f9294,f1108,f9965]) ).
fof(f9662,plain,
( ! [X0] :
( ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(hAPP(c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____)) )
| ~ spl0_62
| ~ spl0_472 ),
inference(resolution,[],[f9295,f1109]) ).
fof(f9963,plain,
spl0_486,
inference(avatar_split_clause,[],[f61,f9961]) ).
fof(f9961,plain,
( spl0_486
<=> ! [X3,X9,X12,X5,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X12,X5,X3,X2),c_Set_Oimage(X12,X9,X3,X2),tc_fun(X2,tc_bool)),c_Set_Oimage(X12,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f61,axiom,
! [X2,X3,X9,X5,X12] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X12,X5,X3,X2),c_Set_Oimage(X12,X9,X3,X2),tc_fun(X2,tc_bool)),c_Set_Oimage(X12,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
fof(f9959,plain,
spl0_485,
inference(avatar_split_clause,[],[f37,f9957]) ).
fof(f9957,plain,
( spl0_485
<=> ! [X9,X11,X5,X2] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f37,axiom,
! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
fof(f9955,plain,
spl0_484,
inference(avatar_split_clause,[],[f36,f9953]) ).
fof(f36,axiom,
! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
fof(f9343,plain,
spl0_483,
inference(avatar_split_clause,[],[f735,f9341]) ).
fof(f9341,plain,
( spl0_483
<=> ! [X4,X0,X3,X2,X1] : c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X3,X2) = c_Set_Oinsert(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f735,plain,
! [X2,X3,X0,X1,X4] : c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X3,X2) = c_Set_Oinsert(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2),
inference(definition_unfolding,[],[f1,f557,f557]) ).
fof(f1,axiom,
! [X2,X3,X0,X1,X4] : c_Relation_ODomain(c_Set_Oinsert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3) = c_Set_Oinsert(X0,c_Relation_ODomain(X4,X2,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
fof(f9336,plain,
spl0_482,
inference(avatar_split_clause,[],[f612,f9334]) ).
fof(f612,axiom,
! [X2,X3,X6,X7,X4,X22] :
( X7 = X22
| ~ c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_in(c_Pair(X6,X7,X2,X3),X4,tc_prod(X2,X3))
| ~ c_in(c_Pair(X6,X22,X2,X3),X4,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
fof(f9332,plain,
spl0_481,
inference(avatar_split_clause,[],[f604,f9330]) ).
fof(f9330,plain,
( spl0_481
<=> ! [X18,X4,X0,X2,X7] :
( hBOOL(hAPP(X18,X7))
| hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f604,axiom,
! [X2,X0,X18,X7,X4] :
( hBOOL(hAPP(X18,X7))
| hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).
fof(f9328,plain,
spl0_480,
inference(avatar_split_clause,[],[f591,f9326]) ).
fof(f9326,plain,
( spl0_480
<=> ! [X18,X4,X0,X2,X7] :
( hBOOL(hAPP(X18,X7))
| hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f591,axiom,
! [X2,X0,X18,X7,X4] :
( hBOOL(hAPP(X18,X7))
| hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
fof(f9324,plain,
spl0_479,
inference(avatar_split_clause,[],[f331,f9322]) ).
fof(f9322,plain,
( spl0_479
<=> ! [X6,X2,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
| c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = X5
| ~ c_lessequals(X5,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f331,axiom,
! [X2,X6,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
| c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = X5
| ~ c_lessequals(X5,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f9320,plain,
spl0_478,
inference(avatar_split_clause,[],[f241,f9318]) ).
fof(f9318,plain,
( spl0_478
<=> ! [X3,X9,X5,X2] : c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X5,X3,X2),c_Relation_ORange(X9,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f241,axiom,
! [X2,X3,X9,X5] : c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X5,X3,X2),c_Relation_ORange(X9,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).
fof(f9316,plain,
spl0_477,
inference(avatar_split_clause,[],[f201,f9314]) ).
fof(f9314,plain,
( spl0_477
<=> ! [X11,X21,X3,X2,X20] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X20,X21,tc_fun(X2,tc_bool)),X11,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X20,X11,X2,X3),c_Product__Type_OSigma(X21,X11,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f201,axiom,
! [X2,X21,X3,X11,X20] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X20,X21,tc_fun(X2,tc_bool)),X11,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X20,X11,X2,X3),c_Product__Type_OSigma(X21,X11,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
fof(f9312,plain,
spl0_476,
inference(avatar_split_clause,[],[f161,f9310]) ).
fof(f9310,plain,
( spl0_476
<=> ! [X32,X0,X19,X2,X1] :
( X1 = X32
| X0 = X32
| c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X19,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f161,axiom,
! [X2,X0,X1,X19,X32] :
( X1 = X32
| X0 = X32
| c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X19,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
fof(f9308,plain,
spl0_475,
inference(avatar_split_clause,[],[f160,f9306]) ).
fof(f9306,plain,
( spl0_475
<=> ! [X19,X0,X32,X2,X1] :
( X0 = X19
| X1 = X19
| c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X19,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f160,axiom,
! [X2,X0,X1,X19,X32] :
( X0 = X19
| X1 = X19
| c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X19,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
fof(f9304,plain,
spl0_474,
inference(avatar_split_clause,[],[f102,f9302]) ).
fof(f9302,plain,
( spl0_474
<=> ! [X11,X21,X3,X2,X20] : c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X20,X21,tc_fun(X2,tc_bool)),X11,X2,X3) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X20,X11,X2,X3),c_Product__Type_OSigma(X21,X11,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f102,axiom,
! [X2,X21,X3,X11,X20] : c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X20,X21,tc_fun(X2,tc_bool)),X11,X2,X3) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X20,X11,X2,X3),c_Product__Type_OSigma(X21,X11,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).
fof(f9300,plain,
spl0_473,
inference(avatar_split_clause,[],[f57,f9298]) ).
fof(f57,axiom,
! [X2,X3,X11,X9,X4,X5] :
( c_lessequals(c_Relation_OImage(X4,X11,X2,X3),X9,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X9,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).
fof(f9296,plain,
( spl0_472
| ~ spl0_92
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f6513,f6211,f1244,f9294]) ).
fof(f6513,plain,
( ! [X0] :
( c_in(v_a____,c_Relation_OImage(v_Lab____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_92
| ~ spl0_403 ),
inference(resolution,[],[f6212,f1245]) ).
fof(f9292,plain,
spl0_471,
inference(avatar_split_clause,[],[f45,f9290]) ).
fof(f9290,plain,
( spl0_471
<=> ! [X3,X13,X8,X5,X2] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X3,X2),tc_bool)),X5,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X8,X5,X3,X2),c_Relation_OImage(X13,X5,X3,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f45,axiom,
! [X2,X3,X8,X5,X13] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X8,X13,tc_fun(tc_prod(X3,X2),tc_bool)),X5,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X8,X5,X3,X2),c_Relation_OImage(X13,X5,X3,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).
fof(f9288,plain,
spl0_470,
inference(avatar_split_clause,[],[f32,f9286]) ).
fof(f9286,plain,
( spl0_470
<=> ! [X11,X21,X3,X2,X20] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X2,tc_bool)),X11,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X20,X11,X2,X3),c_Product__Type_OSigma(X21,X11,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f32,axiom,
! [X2,X21,X3,X11,X20] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X2,tc_bool)),X11,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X20,X11,X2,X3),c_Product__Type_OSigma(X21,X11,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
fof(f9284,plain,
spl0_469,
inference(avatar_split_clause,[],[f21,f9282]) ).
fof(f9282,plain,
( spl0_469
<=> ! [X3,X9,X5,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X5,X3,X2),c_Relation_ORange(X9,X3,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f21,axiom,
! [X2,X3,X9,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X5,X3,X2),c_Relation_ORange(X9,X3,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).
fof(f9280,plain,
spl0_468,
inference(avatar_split_clause,[],[f8,f9278]) ).
fof(f9278,plain,
( spl0_468
<=> ! [X9,X0,X5,X2] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f8,axiom,
! [X2,X0,X9,X5] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
fof(f9276,plain,
spl0_467,
inference(avatar_split_clause,[],[f7,f9274]) ).
fof(f7,axiom,
! [X2,X0,X9,X5] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
fof(f8853,plain,
spl0_466,
inference(avatar_split_clause,[],[f751,f8851]) ).
fof(f8851,plain,
( spl0_466
<=> ! [X4,X14,X3,X2] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X3),tc_bool))
| c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X14,X2,X3),X3,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f751,plain,
! [X2,X3,X14,X4] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X3),tc_bool))
| c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X14,X2,X3),X3,X2),tc_fun(X2,tc_bool)) ),
inference(definition_unfolding,[],[f330,f557,f557]) ).
fof(f330,axiom,
! [X2,X3,X14,X4] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X3),tc_bool))
| c_lessequals(c_Relation_ODomain(X4,X2,X3),c_Relation_ODomain(X14,X2,X3),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
fof(f8849,plain,
spl0_465,
inference(avatar_split_clause,[],[f632,f8847]) ).
fof(f632,axiom,
! [X2,X6,X7,X4] :
( ~ c_Relation_Oantisym(X4,X2)
| X6 = X7
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X7,X6,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).
fof(f8845,plain,
spl0_464,
inference(avatar_split_clause,[],[f600,f8843]) ).
fof(f600,axiom,
! [X18,X6,X7,X4] :
( hBOOL(hAPP(X18,X7))
| hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X7,v_sko__Wellfounded__Xacc__Xinducts__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
fof(f8841,plain,
spl0_463,
inference(avatar_split_clause,[],[f592,f8839]) ).
fof(f592,axiom,
! [X18,X6,X7,X4] :
( hBOOL(hAPP(X18,X7))
| hBOOL(hAPP(X18,X6))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X7,v_sko__Wellfounded__Xacc__Xinduct__1(X18,X4),t_a,t_a),X4,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
fof(f8837,plain,
spl0_462,
inference(avatar_split_clause,[],[f457,f8835]) ).
fof(f457,axiom,
! [X2,X8,X6,X7] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X8,X6,X7,X2),X7,X2,X2),X8,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).
fof(f8833,plain,
spl0_461,
inference(avatar_split_clause,[],[f452,f8831]) ).
fof(f452,axiom,
! [X2,X8,X6,X7] :
( ~ c_in(c_Pair(X6,X7,X2,X2),c_Transitive__Closure_Otrancl(X8,X2),tc_prod(X2,X2))
| c_in(c_Pair(X6,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X8,X6,X7,X2),X2,X2),X8,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).
fof(f8829,plain,
spl0_460,
inference(avatar_split_clause,[],[f450,f8827]) ).
fof(f8827,plain,
( spl0_460
<=> ! [X6,X2,X4] :
( ~ c_in(c_Pair(X6,X6,X2,X2),X4,tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X4,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X4,X2),X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f450,axiom,
! [X2,X6,X4] :
( ~ c_in(c_Pair(X6,X6,X2,X2),X4,tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X4,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X4,X2),X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
fof(f8825,plain,
spl0_459,
inference(avatar_split_clause,[],[f207,f8823]) ).
fof(f8823,plain,
( spl0_459
<=> ! [X4,X14,X3,X2] : c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X4,X14,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X4,X3,X2),c_Relation_Oconverse(X14,X3,X2),tc_fun(tc_prod(X2,X3),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f207,axiom,
! [X2,X3,X14,X4] : c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X4,X14,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X4,X3,X2),c_Relation_Oconverse(X14,X3,X2),tc_fun(tc_prod(X2,X3),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).
fof(f8821,plain,
spl0_458,
inference(avatar_split_clause,[],[f174,f8819]) ).
fof(f174,axiom,
! [X2,X3,X14,X4] : c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X4,X3,X2),c_Relation_Oconverse(X14,X3,X2),tc_fun(tc_prod(X2,X3),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).
fof(f8604,plain,
spl0_457,
inference(avatar_split_clause,[],[f716,f8602]) ).
fof(f8602,plain,
( spl0_457
<=> ! [X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X8,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f716,plain,
! [X2,X8] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X8,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(definition_unfolding,[],[f585,f440,f440]) ).
fof(f585,axiom,
! [X2,X8] : c_Transitive__Closure_Ortrancl(X8,X2) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X8,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
fof(f8600,plain,
( ~ spl0_456
| ~ spl0_82
| spl0_448 ),
inference(avatar_split_clause,[],[f8393,f8143,f1204,f8597]) ).
fof(f8597,plain,
( spl0_456
<=> c_Wellfounded_Owf(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f8143,plain,
( spl0_448
<=> c_in(v_a____,c_Wellfounded_Oacc(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f8393,plain,
( ~ c_Wellfounded_Owf(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_82
| spl0_448 ),
inference(resolution,[],[f8145,f1205]) ).
fof(f8145,plain,
( ~ c_in(v_a____,c_Wellfounded_Oacc(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_448 ),
inference(avatar_component_clause,[],[f8143]) ).
fof(f8595,plain,
spl0_455,
inference(avatar_split_clause,[],[f660,f8593]) ).
fof(f8593,plain,
( spl0_455
<=> ! [X40,X7,X6,X22] :
( X6 = X22
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f660,axiom,
! [X40,X6,X7,X22] :
( X6 = X22
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
fof(f8591,plain,
spl0_454,
inference(avatar_split_clause,[],[f653,f8589]) ).
fof(f8589,plain,
( spl0_454
<=> ! [X40,X7,X6,X22] :
( X7 = X22
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f653,axiom,
! [X40,X6,X7,X22] :
( X7 = X22
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
fof(f8587,plain,
spl0_453,
inference(avatar_split_clause,[],[f343,f8585]) ).
fof(f8585,plain,
( spl0_453
<=> ! [X5,X3,X12,X9,X2] : c_Set_Oimage(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X12,X5,X3,X2),c_Set_Oimage(X12,X9,X3,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f343,axiom,
! [X2,X3,X9,X5,X12] : c_Set_Oimage(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X12,X5,X3,X2),c_Set_Oimage(X12,X9,X3,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
fof(f8583,plain,
spl0_452,
inference(avatar_split_clause,[],[f336,f8581]) ).
fof(f8581,plain,
( spl0_452
<=> ! [X9,X11,X5,X2] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X11,tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f336,axiom,
! [X2,X11,X9,X5] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X11,tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X11,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
fof(f8579,plain,
spl0_451,
inference(avatar_split_clause,[],[f46,f8577]) ).
fof(f8577,plain,
( spl0_451
<=> ! [X5,X3,X8,X9,X2] : c_Relation_OImage(X8,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X8,X5,X3,X2),c_Relation_OImage(X8,X9,X3,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f46,axiom,
! [X2,X3,X8,X9,X5] : c_Relation_OImage(X8,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X8,X5,X3,X2),c_Relation_OImage(X8,X9,X3,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
fof(f8575,plain,
spl0_450,
inference(avatar_split_clause,[],[f19,f8573]) ).
fof(f8573,plain,
( spl0_450
<=> ! [X17,X3,X16,X2] :
( X16 = X17
| hAPP(c_fst(X2,X3),X16) != hAPP(c_fst(X2,X3),X17)
| hAPP(c_snd(X2,X3),X16) != hAPP(c_snd(X2,X3),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f19,axiom,
! [X2,X3,X16,X17] :
( X16 = X17
| hAPP(c_fst(X2,X3),X16) != hAPP(c_fst(X2,X3),X17)
| hAPP(c_snd(X2,X3),X16) != hAPP(c_snd(X2,X3),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod__eqI_0) ).
fof(f8150,plain,
( ~ spl0_448
| spl0_449
| ~ spl0_92
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f6485,f6207,f1244,f8147,f8143]) ).
fof(f8147,plain,
( spl0_449
<=> c_in(v_b____,c_Wellfounded_Oacc(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f6207,plain,
( spl0_402
<=> ! [X4,X0,X2,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f6485,plain,
( c_in(v_b____,c_Wellfounded_Oacc(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,c_Wellfounded_Oacc(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_92
| ~ spl0_402 ),
inference(resolution,[],[f6208,f1245]) ).
fof(f6208,plain,
( ! [X2,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(X1,c_Wellfounded_Oacc(X4,X2),X2) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f6207]) ).
fof(f7949,plain,
spl0_447,
inference(avatar_split_clause,[],[f808,f7947]) ).
fof(f7947,plain,
( spl0_447
<=> ! [X6,X27,X40] :
( X6 = X27
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X6,X27,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X27),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f808,plain,
! [X40,X6,X27] :
( X6 = X27
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X6,X27,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X27),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f407]) ).
fof(f407,axiom,
! [X40,X6,X27] :
( X6 = X27
| X6 = X27
| X6 = X27
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X6,X27,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X6,X27),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_5) ).
fof(f7945,plain,
spl0_446,
inference(avatar_split_clause,[],[f807,f7943]) ).
fof(f7943,plain,
( spl0_446
<=> ! [X6,X27,X40] :
( X6 = X27
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X27,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f807,plain,
! [X40,X6,X27] :
( X6 = X27
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X27,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f422]) ).
fof(f422,axiom,
! [X40,X6,X27] :
( X6 = X27
| X6 = X27
| X6 = X27
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X27,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_5) ).
fof(f7941,plain,
spl0_445,
inference(avatar_split_clause,[],[f745,f7939]) ).
fof(f745,plain,
! [X2,X3,X0,X4] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,X4,X2,X3),X2,X3),X4,tc_prod(X2,X3)) ),
inference(definition_unfolding,[],[f606,f557]) ).
fof(f606,axiom,
! [X2,X3,X0,X4] :
( ~ c_in(X0,c_Relation_ODomain(X4,X2,X3),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,X4,X2,X3),X2,X3),X4,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
fof(f7937,plain,
spl0_444,
inference(avatar_split_clause,[],[f744,f7935]) ).
fof(f744,plain,
! [X2,X3,X0,X4] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,X4,X2,X3),X2,X3),X4,tc_prod(X2,X3)) ),
inference(definition_unfolding,[],[f602,f557]) ).
fof(f602,axiom,
! [X2,X3,X0,X4] :
( ~ c_in(X0,c_Relation_ODomain(X4,X2,X3),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,X4,X2,X3),X2,X3),X4,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).
fof(f7933,plain,
spl0_443,
inference(avatar_split_clause,[],[f662,f7931]) ).
fof(f662,axiom,
! [X2,X3,X0,X1,X9,X5] :
( ~ c_in(X0,X5,X2)
| ~ c_in(X1,hAPP(X9,X0),X3)
| c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
fof(f7929,plain,
( spl0_442
| ~ spl0_92
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f6457,f6203,f1244,f7927]) ).
fof(f6457,plain,
( ! [X0,X1] : hAPP(X0,v_b____) = hAPP(c_Recdef_Ocut(X0,v_Lab____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,X1),v_b____)
| ~ spl0_92
| ~ spl0_401 ),
inference(resolution,[],[f6204,f1245]) ).
fof(f7925,plain,
spl0_441,
inference(avatar_split_clause,[],[f605,f7923]) ).
fof(f7923,plain,
( spl0_441
<=> ! [X4,X7,X27,X2,X26] :
( ~ c_Wellfounded_Owf(X4,X2)
| ~ c_in(X27,X26,X2)
| ~ c_in(X7,X26,X2)
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X26,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f605,axiom,
! [X2,X26,X7,X27,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| ~ c_in(X27,X26,X2)
| ~ c_in(X7,X26,X2)
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X26,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
fof(f7921,plain,
spl0_440,
inference(avatar_split_clause,[],[f593,f7919]) ).
fof(f7919,plain,
( spl0_440
<=> ! [X7,X8,X6,X2,X26] :
( ~ c_Wellfounded_Owf(X8,X2)
| ~ c_in(X6,X26,X2)
| ~ c_in(X7,X26,X2)
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X26,X8,X2),X2,X2),X8,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f593,axiom,
! [X2,X8,X6,X26,X7] :
( ~ c_Wellfounded_Owf(X8,X2)
| ~ c_in(X6,X26,X2)
| ~ c_in(X7,X26,X2)
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X26,X8,X2),X2,X2),X8,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
fof(f7917,plain,
spl0_439,
inference(avatar_split_clause,[],[f463,f7915]) ).
fof(f7915,plain,
( spl0_439
<=> ! [X18,X4,X0,X2,X7] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X7))
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f463,axiom,
! [X2,X0,X18,X7,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X7))
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).
fof(f7913,plain,
spl0_438,
inference(avatar_split_clause,[],[f462,f7911]) ).
fof(f7911,plain,
( spl0_438
<=> ! [X18,X43,X7,X8,X2] :
( ~ c_Wellfounded_Owf(X8,X2)
| hBOOL(hAPP(X18,X43))
| hBOOL(hAPP(X18,X7))
| ~ c_in(c_Pair(X7,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X18,X8,X2),X2,X2),X8,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f462,axiom,
! [X2,X18,X8,X7,X43] :
( ~ c_Wellfounded_Owf(X8,X2)
| hBOOL(hAPP(X18,X43))
| hBOOL(hAPP(X18,X7))
| ~ c_in(c_Pair(X7,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X18,X8,X2),X2,X2),X8,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
fof(f7909,plain,
spl0_437,
inference(avatar_split_clause,[],[f461,f7907]) ).
fof(f7907,plain,
( spl0_437
<=> ! [X18,X4,X7,X27,X2] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X27))
| hBOOL(hAPP(X18,X7))
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f461,axiom,
! [X2,X18,X7,X27,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X27))
| hBOOL(hAPP(X18,X7))
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).
fof(f7905,plain,
spl0_436,
inference(avatar_split_clause,[],[f460,f7903]) ).
fof(f7903,plain,
( spl0_436
<=> ! [X18,X4,X0,X2,X7] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X7))
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f460,axiom,
! [X2,X0,X18,X7,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X0))
| hBOOL(hAPP(X18,X7))
| ~ c_in(c_Pair(X7,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X18,X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
fof(f7901,plain,
spl0_435,
inference(avatar_split_clause,[],[f412,f7899]) ).
fof(f412,axiom,
! [X40,X0,X1,X6] :
( X0 = X1
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_0) ).
fof(f7897,plain,
spl0_434,
inference(avatar_split_clause,[],[f397,f7895]) ).
fof(f397,axiom,
! [X40,X0,X1,X6] :
( X0 = X1
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X40,X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_0) ).
fof(f7893,plain,
spl0_433,
inference(avatar_split_clause,[],[f367,f7891]) ).
fof(f7891,plain,
( spl0_433
<=> ! [X4,X14,X16,X2] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(X16,c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(X16,c_Transitive__Closure_Otrancl(X14,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f367,axiom,
! [X2,X16,X14,X4] :
( ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(X16,c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2))
| c_in(X16,c_Transitive__Closure_Otrancl(X14,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
fof(f7889,plain,
spl0_432,
inference(avatar_split_clause,[],[f362,f7887]) ).
fof(f7887,plain,
( spl0_432
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Pair(X0,X1,X3,X2),X4,tc_prod(X3,X2))
| c_in(X1,c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f362,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X1,X3,X2),X4,tc_prod(X3,X2))
| c_in(X1,c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
fof(f7876,plain,
spl0_431,
inference(avatar_split_clause,[],[f361,f7874]) ).
fof(f7874,plain,
( spl0_431
<=> ! [X4,X0,X3,X2,X1] :
( c_in(c_Pair(X0,X1,X3,X2),X4,tc_prod(X3,X2))
| ~ c_in(X1,c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f361,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X0,X1,X3,X2),X4,tc_prod(X3,X2))
| ~ c_in(X1,c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
fof(f7872,plain,
spl0_430,
inference(avatar_split_clause,[],[f298,f7870]) ).
fof(f7870,plain,
( spl0_430
<=> ! [X3,X9,X5,X2] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X5,X3,X2),c_Relation_ORange(X9,X3,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f298,axiom,
! [X2,X3,X9,X5] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X5,X3,X2),c_Relation_ORange(X9,X3,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
fof(f7868,plain,
spl0_429,
inference(avatar_split_clause,[],[f156,f7866]) ).
fof(f156,axiom,
! [X2,X9,X14,X4,X5] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| ~ c_Relation_Orefl__on(X9,X14,X2)
| c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).
fof(f7864,plain,
spl0_428,
inference(avatar_split_clause,[],[f112,f7862]) ).
fof(f112,axiom,
! [X2,X9,X14,X4,X5] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| ~ c_Relation_Orefl__on(X9,X14,X2)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
fof(f7628,plain,
( spl0_427
| ~ spl0_61
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f7056,f6622,f1104,f7626]) ).
fof(f6622,plain,
( spl0_420
<=> hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f7056,plain,
( ! [X0] : c_in(v_b____,c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)
| ~ spl0_61
| ~ spl0_420 ),
inference(resolution,[],[f6624,f1105]) ).
fof(f6624,plain,
( hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____))
| ~ spl0_420 ),
inference(avatar_component_clause,[],[f6622]) ).
fof(f6649,plain,
spl0_426,
inference(avatar_split_clause,[],[f816,f6647]) ).
fof(f816,plain,
! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Transitive__Closure_Otrancl(X4,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(forward_demodulation,[],[f734,f719]) ).
fof(f719,plain,
! [X2,X4] : c_Transitive__Closure_Otrancl(X4,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X4,X2,X2,X2),
inference(definition_unfolding,[],[f578,f440]) ).
fof(f578,axiom,
! [X2,X4] : c_Transitive__Closure_Otrancl(X4,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X2),X4,X2,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
fof(f734,plain,
! [X2,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X4,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(definition_unfolding,[],[f438,f440,f440]) ).
fof(f438,axiom,
! [X2,X4] : c_Transitive__Closure_Ortrancl(X4,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X2),X4,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
fof(f6645,plain,
spl0_425,
inference(avatar_split_clause,[],[f730,f6643]) ).
fof(f730,plain,
! [X2,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X4,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(definition_unfolding,[],[f439,f440]) ).
fof(f439,axiom,
! [X2,X4] : c_Transitive__Closure_Ortrancl(X4,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X4,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
fof(f6641,plain,
spl0_424,
inference(avatar_split_clause,[],[f643,f6639]) ).
fof(f6639,plain,
( spl0_424
<=> ! [X4,X0,X2,X1] :
( ~ c_Relation_Osym(X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| c_in(c_Pair(X1,X0,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f643,axiom,
! [X2,X0,X1,X4] :
( ~ c_Relation_Osym(X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2))
| c_in(c_Pair(X1,X0,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).
fof(f6637,plain,
spl0_423,
inference(avatar_split_clause,[],[f631,f6635]) ).
fof(f6635,plain,
( spl0_423
<=> ! [X4,X0,X6,X2] :
( ~ c_Wellfounded_Owf(X4,X2)
| ~ c_in(c_Pair(X0,X6,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X0,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f631,axiom,
! [X2,X0,X6,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| ~ c_in(c_Pair(X0,X6,X2,X2),X4,tc_prod(X2,X2))
| ~ c_in(c_Pair(X6,X0,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
fof(f6633,plain,
spl0_422,
inference(avatar_split_clause,[],[f621,f6631]) ).
fof(f621,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
fof(f6629,plain,
spl0_421,
inference(avatar_split_clause,[],[f619,f6627]) ).
fof(f619,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
| c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
fof(f6625,plain,
( spl0_420
| ~ spl0_62
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6574,f6380,f1108,f6622]) ).
fof(f6380,plain,
( spl0_405
<=> c_in(v_b____,c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f6574,plain,
( hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____))
| ~ spl0_62
| ~ spl0_405 ),
inference(resolution,[],[f6382,f1109]) ).
fof(f6382,plain,
( c_in(v_b____,c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_405 ),
inference(avatar_component_clause,[],[f6380]) ).
fof(f6620,plain,
spl0_419,
inference(avatar_split_clause,[],[f607,f6618]) ).
fof(f607,axiom,
! [X2,X3,X1,X4,X5] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X5,X1,X4,X3,X2),X1,X3,X2),X4,tc_prod(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).
fof(f6616,plain,
spl0_418,
inference(avatar_split_clause,[],[f589,f6614]) ).
fof(f589,axiom,
! [X2,X3,X1,X4,X5] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X5,X1,X4,X3,X2),X1,X3,X2),X4,tc_prod(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).
fof(f6612,plain,
spl0_417,
inference(avatar_split_clause,[],[f550,f6610]) ).
fof(f6610,plain,
( spl0_417
<=> ! [X2,X8,X33,X10,X13,X3,X45] : c_Relation_Orel__comp(c_Relation_Orel__comp(X8,X13,X2,X45,X10),X33,X2,X10,X3) = c_Relation_Orel__comp(X8,c_Relation_Orel__comp(X13,X33,X45,X10,X3),X2,X45,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f550,axiom,
! [X2,X3,X10,X8,X45,X13,X33] : c_Relation_Orel__comp(c_Relation_Orel__comp(X8,X13,X2,X45,X10),X33,X2,X10,X3) = c_Relation_Orel__comp(X8,c_Relation_Orel__comp(X13,X33,X45,X10,X3),X2,X45,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
fof(f6608,plain,
spl0_416,
inference(avatar_split_clause,[],[f328,f6606]) ).
fof(f6604,plain,
spl0_415,
inference(avatar_split_clause,[],[f244,f6602]) ).
fof(f6602,plain,
( spl0_415
<=> ! [X5,X9,X6,X2] :
( c_in(X6,X9,X2)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X6,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f244,axiom,
! [X2,X6,X9,X5] :
( c_in(X6,X9,X2)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X6,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
fof(f6600,plain,
spl0_414,
inference(avatar_split_clause,[],[f184,f6598]) ).
fof(f6598,plain,
( spl0_414
<=> ! [X9,X11,X5,X2] :
( ~ c_lessequals(X11,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(X11,X9,tc_fun(X2,tc_bool))
| c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f184,axiom,
! [X2,X11,X9,X5] :
( ~ c_lessequals(X11,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(X11,X9,tc_fun(X2,tc_bool))
| c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
fof(f6596,plain,
spl0_413,
inference(avatar_split_clause,[],[f170,f6594]) ).
fof(f6594,plain,
( spl0_413
<=> ! [X9,X0,X5,X2] :
( ~ c_in(X0,X5,X2)
| c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f170,axiom,
! [X2,X0,X9,X5] :
( ~ c_in(X0,X5,X2)
| c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
fof(f6592,plain,
spl0_412,
inference(avatar_split_clause,[],[f169,f6590]) ).
fof(f6590,plain,
( spl0_412
<=> ! [X11,X0,X9,X2] :
( ~ c_in(X0,X11,X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X9,X2),X11,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f169,axiom,
! [X2,X0,X11,X9] :
( ~ c_in(X0,X11,X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X9,X2),X11,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
fof(f6588,plain,
spl0_411,
inference(avatar_split_clause,[],[f135,f6586]) ).
fof(f6586,plain,
( spl0_411
<=> ! [X5,X4,X6,X2] :
( ~ c_in(X6,X5,X2)
| c_in(c_Relation_OImage(X4,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f135,axiom,
! [X2,X6,X4,X5] :
( ~ c_in(X6,X5,X2)
| c_in(c_Relation_OImage(X4,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Equiv__Relations_Oquotient(X5,X4,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientI_0) ).
fof(f6584,plain,
spl0_410,
inference(avatar_split_clause,[],[f118,f6582]) ).
fof(f118,axiom,
! [X2,X11,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
fof(f6573,plain,
spl0_409,
inference(avatar_split_clause,[],[f117,f6571]) ).
fof(f6569,plain,
spl0_408,
inference(avatar_split_clause,[],[f73,f6567]) ).
fof(f6567,plain,
( spl0_408
<=> ! [X9,X11,X5,X2] :
( ~ c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X11,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f73,axiom,
! [X2,X11,X9,X5] :
( ~ c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X11,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
fof(f6565,plain,
spl0_407,
inference(avatar_split_clause,[],[f63,f6563]) ).
fof(f63,axiom,
! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
fof(f6561,plain,
spl0_406,
inference(avatar_split_clause,[],[f62,f6559]) ).
fof(f62,axiom,
! [X2,X11,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
fof(f6383,plain,
( spl0_405
| ~ spl0_92
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5497,f5102,f1244,f6380]) ).
fof(f5497,plain,
( c_in(v_b____,c_Relation_ORange(c_Relation_Oconverse(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_92
| ~ spl0_377 ),
inference(resolution,[],[f5103,f1245]) ).
fof(f6217,plain,
spl0_404,
inference(avatar_split_clause,[],[f743,f6215]) ).
fof(f6215,plain,
( spl0_404
<=> ! [X2,X16,X4] :
( ~ c_in(X16,X4,tc_prod(X2,X2))
| c_in(X16,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f743,plain,
! [X2,X16,X4] :
( ~ c_in(X16,X4,tc_prod(X2,X2))
| c_in(X16,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f392,f440]) ).
fof(f392,axiom,
! [X2,X16,X4] :
( ~ c_in(X16,X4,tc_prod(X2,X2))
| c_in(X16,c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
fof(f6213,plain,
spl0_403,
inference(avatar_split_clause,[],[f666,f6211]) ).
fof(f666,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X0,X5,X2)
| c_in(X1,c_Relation_OImage(X4,X5,X2,X3),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
fof(f6209,plain,
spl0_402,
inference(avatar_split_clause,[],[f664,f6207]) ).
fof(f664,axiom,
! [X2,X0,X1,X4] :
( ~ c_in(X1,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).
fof(f6205,plain,
spl0_401,
inference(avatar_split_clause,[],[f614,f6203]) ).
fof(f614,axiom,
! [X2,X3,X0,X6,X4,X12] :
( ~ c_in(c_Pair(X6,X0,X2,X2),X4,tc_prod(X2,X2))
| hAPP(X12,X6) = hAPP(c_Recdef_Ocut(X12,X4,X0,X2,X3),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).
fof(f6201,plain,
spl0_400,
inference(avatar_split_clause,[],[f538,f6199]) ).
fof(f538,axiom,
! [X2,X3,X10,X14,X4] : c_Relation_Oconverse(c_Relation_Orel__comp(X4,X14,X3,X10,X2),X3,X2) = c_Relation_Orel__comp(c_Relation_Oconverse(X14,X10,X2),c_Relation_Oconverse(X4,X3,X10),X2,X10,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
fof(f6197,plain,
spl0_399,
inference(avatar_split_clause,[],[f396,f6195]) ).
fof(f6195,plain,
( spl0_399
<=> ! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| ~ c_Relation_Osym(X4,X2)
| c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2),X4,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f396,axiom,
! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| ~ c_Relation_Osym(X4,X2)
| c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2),X4,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
fof(f6193,plain,
spl0_398,
inference(avatar_split_clause,[],[f383,f6191]) ).
fof(f383,axiom,
! [X40,X6,X7] :
( X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Obelow(X40,X6,X7),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__Lin_0) ).
fof(f6189,plain,
spl0_397,
inference(avatar_split_clause,[],[f382,f6187]) ).
fof(f382,axiom,
! [X40,X6,X7] :
( X6 = X7
| ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Oabove(X40,X6,X7),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_above__Lin_0) ).
fof(f6185,plain,
spl0_396,
inference(avatar_split_clause,[],[f355,f6183]) ).
fof(f6183,plain,
( spl0_396
<=> ! [X4,X0,X5,X2] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X0,X5,X2)
| c_in(X0,c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f355,axiom,
! [X2,X0,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| ~ c_in(X0,X5,X2)
| c_in(X0,c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
fof(f6181,plain,
spl0_395,
inference(avatar_split_clause,[],[f252,f6179]) ).
fof(f6179,plain,
( spl0_395
<=> ! [X9,X11,X5,X2] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool))
| c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f252,axiom,
! [X2,X11,X9,X5] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool))
| c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
fof(f6177,plain,
spl0_394,
inference(avatar_split_clause,[],[f251,f6175]) ).
fof(f251,axiom,
! [X2,X11,X9,X5] :
( ~ c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
fof(f6173,plain,
spl0_393,
inference(avatar_split_clause,[],[f129,f6171]) ).
fof(f6171,plain,
( spl0_393
<=> ! [X3,X19,X5,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
| c_Set_Oimage(c_COMBK(X19,X2,X3),X5,X3,X2) = c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f129,axiom,
! [X2,X3,X19,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
| c_Set_Oimage(c_COMBK(X19,X2,X3),X5,X3,X2) = c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
fof(f6169,plain,
spl0_392,
inference(avatar_split_clause,[],[f5,f6167]) ).
fof(f5,axiom,
! [X2,X0,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X5,X2),c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
fof(f5600,plain,
( spl0_391
| ~ spl0_61
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5529,f5385,f1104,f5598]) ).
fof(f5385,plain,
( spl0_379
<=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f5529,plain,
( ! [X0] : c_in(v_a____,hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),X0)
| ~ spl0_61
| ~ spl0_379 ),
inference(resolution,[],[f5387,f1105]) ).
fof(f5387,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____))
| ~ spl0_379 ),
inference(avatar_component_clause,[],[f5385]) ).
fof(f5565,plain,
spl0_390,
inference(avatar_split_clause,[],[f746,f5563]) ).
fof(f746,plain,
! [X2,X4] :
( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X4,X2,X2),X2,X2),X4,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2) != X4 ),
inference(definition_unfolding,[],[f555,f557]) ).
fof(f555,axiom,
! [X2,X4] :
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X4,X2,X2),X4,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
fof(f5561,plain,
spl0_389,
inference(avatar_split_clause,[],[f609,f5559]) ).
fof(f609,axiom,
! [X2,X3,X0,X4] :
( ~ c_in(X0,c_Relation_ORange(X4,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X4,X2,X3),X0,X3,X2),X4,tc_prod(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).
fof(f5557,plain,
spl0_388,
inference(avatar_split_clause,[],[f594,f5555]) ).
fof(f594,axiom,
! [X2,X3,X1,X4] :
( ~ c_in(X1,c_Relation_ORange(X4,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X4,X2,X3),X1,X3,X2),X4,tc_prod(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).
fof(f5553,plain,
spl0_387,
inference(avatar_split_clause,[],[f443,f5551]) ).
fof(f5551,plain,
( spl0_387
<=> ! [X2,X5,X19] :
( ~ c_in(X19,c_Relation_OId__on(X5,X2),tc_prod(X2,X2))
| c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X5,X19,X2),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X5,X19,X2),X2,X2) = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f443,axiom,
! [X2,X19,X5] :
( ~ c_in(X19,c_Relation_OId__on(X5,X2),tc_prod(X2,X2))
| c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X5,X19,X2),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X5,X19,X2),X2,X2) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).
fof(f5549,plain,
spl0_386,
inference(avatar_split_clause,[],[f348,f5547]) ).
fof(f348,axiom,
! [X2,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).
fof(f5545,plain,
spl0_385,
inference(avatar_split_clause,[],[f250,f5543]) ).
fof(f5543,plain,
( spl0_385
<=> ! [X6,X2,X5] :
( c_in(X6,X5,X2)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X5,X2),c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f250,axiom,
! [X2,X6,X5] :
( c_in(X6,X5,X2)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X5,X2),c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
fof(f5541,plain,
spl0_384,
inference(avatar_split_clause,[],[f248,f5539]) ).
fof(f5539,plain,
( spl0_384
<=> ! [X4,X0,X3,X2,X1] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X0,X1,X3,X2),X4,tc_prod(X3,X2)),X3,X2) = c_Set_Oinsert(X1,c_Relation_ORange(X4,X3,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f248,axiom,
! [X2,X3,X0,X1,X4] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X0,X1,X3,X2),X4,tc_prod(X3,X2)),X3,X2) = c_Set_Oinsert(X1,c_Relation_ORange(X4,X3,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).
fof(f5537,plain,
spl0_383,
inference(avatar_split_clause,[],[f190,f5535]) ).
fof(f190,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
fof(f5533,plain,
spl0_382,
inference(avatar_split_clause,[],[f146,f5531]) ).
fof(f146,axiom,
! [X2,X3,X10,X18,X22] : hAPP(c_split(X18,X3,X10,X2),X22) = hAPP(hAPP(X18,hAPP(c_fst(X3,X10),X22)),hAPP(c_snd(X3,X10),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__beta_0) ).
fof(f5528,plain,
spl0_381,
inference(avatar_split_clause,[],[f133,f5526]) ).
fof(f133,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
fof(f5524,plain,
spl0_380,
inference(avatar_split_clause,[],[f41,f5522]) ).
fof(f41,axiom,
! [X2,X4,X5] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
fof(f5388,plain,
( spl0_379
| ~ spl0_92
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4976,f4537,f1244,f5385]) ).
fof(f4976,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____))
| ~ spl0_92
| ~ spl0_353 ),
inference(resolution,[],[f4538,f1245]) ).
fof(f5108,plain,
spl0_378,
inference(avatar_split_clause,[],[f754,f5106]) ).
fof(f5106,plain,
( spl0_378
<=> ! [X4,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = X4
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f754,plain,
! [X2,X3,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = X4
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2) ),
inference(definition_unfolding,[],[f238,f557]) ).
fof(f238,axiom,
! [X2,X3,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = X4
| c_Relation_ODomain(X4,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).
fof(f5104,plain,
spl0_377,
inference(avatar_split_clause,[],[f747,f5102]) ).
fof(f747,plain,
! [X2,X3,X0,X6,X4] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2)
| ~ c_in(c_Pair(X0,X6,X2,X3),X4,tc_prod(X2,X3)) ),
inference(definition_unfolding,[],[f674,f557]) ).
fof(f674,axiom,
! [X2,X3,X0,X6,X4] :
( c_in(X0,c_Relation_ODomain(X4,X2,X3),X2)
| ~ c_in(c_Pair(X0,X6,X2,X3),X4,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
fof(f5100,plain,
spl0_376,
inference(avatar_split_clause,[],[f722,f5098]) ).
fof(f722,plain,
! [X2,X8,X6] : c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)),
inference(definition_unfolding,[],[f630,f440]) ).
fof(f630,axiom,
! [X2,X8,X6] : c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Ortrancl(X8,X2),tc_prod(X2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
fof(f5096,plain,
spl0_375,
inference(avatar_split_clause,[],[f719,f5094]) ).
fof(f5094,plain,
( spl0_375
<=> ! [X2,X4] : c_Transitive__Closure_Otrancl(X4,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X4,X2,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f5092,plain,
spl0_374,
inference(avatar_split_clause,[],[f710,f5090]) ).
fof(f5090,plain,
( spl0_374
<=> ! [X2,X4] : c_Transitive__Closure_Otrancl(X4,X2) = c_Relation_Orel__comp(X4,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f710,plain,
! [X2,X4] : c_Transitive__Closure_Otrancl(X4,X2) = c_Relation_Orel__comp(X4,c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2),
inference(definition_unfolding,[],[f579,f440]) ).
fof(f579,axiom,
! [X2,X4] : c_Transitive__Closure_Otrancl(X4,X2) = c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X2),X2,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
fof(f5088,plain,
spl0_373,
inference(avatar_split_clause,[],[f676,f5086]) ).
fof(f676,axiom,
! [X2,X3,X0,X1,X9,X5] :
( c_in(X1,hAPP(X9,X0),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
fof(f5084,plain,
spl0_372,
inference(avatar_split_clause,[],[f437,f5082]) ).
fof(f5082,plain,
( spl0_372
<=> ! [X2,X5,X4] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_lessequals(X4,c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f437,axiom,
! [X2,X4,X5] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_lessequals(X4,c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
fof(f5080,plain,
spl0_371,
inference(avatar_split_clause,[],[f360,f5078]) ).
fof(f360,axiom,
! [X2,X3,X6,X9,X5,X12] :
( ~ c_in(X6,X5,X3)
| c_in(hAPP(X12,X6),X9,X2)
| ~ c_lessequals(c_Set_Oimage(X12,X5,X3,X2),X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f5076,plain,
spl0_370,
inference(avatar_split_clause,[],[f359,f5074]) ).
fof(f5074,plain,
( spl0_370
<=> ! [X5,X3,X12,X6,X2] :
( ~ c_in(X6,X5,X2)
| c_Set_Oimage(X12,X5,X2,X3) = c_Set_Oinsert(hAPP(X12,X6),c_Set_Oimage(X12,X5,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f359,axiom,
! [X2,X3,X6,X5,X12] :
( ~ c_in(X6,X5,X2)
| c_Set_Oimage(X12,X5,X2,X3) = c_Set_Oinsert(hAPP(X12,X6),c_Set_Oimage(X12,X5,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
fof(f5072,plain,
spl0_369,
inference(avatar_split_clause,[],[f339,f5070]) ).
fof(f5070,plain,
( spl0_369
<=> ! [X3,X9,X12,X5,X2] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_lessequals(c_Set_Oimage(X12,X5,X2,X3),c_Set_Oimage(X12,X9,X2,X3),tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f339,axiom,
! [X2,X3,X9,X5,X12] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_lessequals(c_Set_Oimage(X12,X5,X2,X3),c_Set_Oimage(X12,X9,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
fof(f5068,plain,
spl0_368,
inference(avatar_split_clause,[],[f333,f5066]) ).
fof(f5066,plain,
( spl0_368
<=> ! [X2,X5,X3] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Product__Type_OSigma(X5,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool),X2),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f333,axiom,
! [X2,X3,X5] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Product__Type_OSigma(X5,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool),X2),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).
fof(f5064,plain,
spl0_367,
inference(avatar_split_clause,[],[f282,f5062]) ).
fof(f5062,plain,
( spl0_367
<=> ! [X5,X9,X6,X2] :
( X5 = X9
| c_in(X6,X5,X2)
| c_in(X6,X9,X2)
| c_Set_Oinsert(X6,X5,X2) != c_Set_Oinsert(X6,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f282,axiom,
! [X2,X6,X9,X5] :
( X5 = X9
| c_in(X6,X5,X2)
| c_in(X6,X9,X2)
| c_Set_Oinsert(X6,X5,X2) != c_Set_Oinsert(X6,X9,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f5060,plain,
spl0_366,
inference(avatar_split_clause,[],[f209,f5058]) ).
fof(f5058,plain,
( spl0_366
<=> ! [X11,X0,X9,X2] :
( c_in(X0,X11,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X9,X2),X11,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f209,axiom,
! [X2,X0,X11,X9] :
( c_in(X0,X11,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X11,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X9,X2),X11,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
fof(f5056,plain,
spl0_365,
inference(avatar_split_clause,[],[f208,f5054]) ).
fof(f5054,plain,
( spl0_365
<=> ! [X9,X0,X5,X2] :
( c_in(X0,X5,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f208,axiom,
! [X2,X0,X9,X5] :
( c_in(X0,X5,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
fof(f5052,plain,
spl0_364,
inference(avatar_split_clause,[],[f193,f5050]) ).
fof(f193,axiom,
! [X2,X0,X5] : c_Set_Oinsert(X0,X5,X2) = c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
fof(f5048,plain,
spl0_363,
inference(avatar_split_clause,[],[f188,f5046]) ).
fof(f188,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f5044,plain,
spl0_362,
inference(avatar_split_clause,[],[f187,f5042]) ).
fof(f187,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X6,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2),c_Lattices_Oupper__semilattice__class_Osup(X22,X6,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f5040,plain,
( spl0_361
| ~ spl0_92
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4442,f4039,f1244,f5038]) ).
fof(f5038,plain,
( spl0_361
<=> ! [X0] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f4442,plain,
( ! [X0] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Orefl__on(X0,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_92
| ~ spl0_333 ),
inference(resolution,[],[f4040,f1245]) ).
fof(f5036,plain,
spl0_360,
inference(avatar_split_clause,[],[f39,f5034]) ).
fof(f39,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2),c_Lattices_Olower__semilattice__class_Oinf(X22,X6,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f5032,plain,
spl0_359,
inference(avatar_split_clause,[],[f38,f5030]) ).
fof(f38,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Odistrib__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f5028,plain,
spl0_358,
inference(avatar_split_clause,[],[f30,f5026]) ).
fof(f5026,plain,
( spl0_358
<=> ! [X5,X3,X19,X6,X2] :
( ~ c_in(X6,X5,X2)
| c_Set_Oimage(c_COMBK(X19,X3,X2),X5,X2,X3) = c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f30,axiom,
! [X2,X3,X6,X19,X5] :
( ~ c_in(X6,X5,X2)
| c_Set_Oimage(c_COMBK(X19,X3,X2),X5,X2,X3) = c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
fof(f5024,plain,
spl0_357,
inference(avatar_split_clause,[],[f24,f5022]) ).
fof(f5022,plain,
( spl0_357
<=> ! [X5,X9,X6,X2] :
( ~ c_in(X6,X9,X2)
| c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f24,axiom,
! [X2,X6,X9,X5] :
( ~ c_in(X6,X9,X2)
| c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
fof(f4892,plain,
( spl0_356
| ~ spl0_92
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4401,f4027,f1244,f4890]) ).
fof(f4890,plain,
( spl0_356
<=> ! [X0] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f4401,plain,
( ! [X0] :
( c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X0,v_Lab____,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_92
| ~ spl0_330 ),
inference(resolution,[],[f4028,f1245]) ).
fof(f4547,plain,
spl0_355,
inference(avatar_split_clause,[],[f711,f4545]) ).
fof(f4545,plain,
( spl0_355
<=> ! [X2] : c_Relation_OId(X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f711,plain,
! [X2] : c_Relation_OId(X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(definition_unfolding,[],[f376,f440]) ).
fof(f376,axiom,
! [X2] : c_Relation_OId(X2) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).
fof(f4543,plain,
spl0_354,
inference(avatar_split_clause,[],[f616,f4541]) ).
fof(f616,axiom,
! [X2,X3,X8,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X8,X2,X3),X6),X7))
| c_in(c_Pair(X6,X7,X2,X3),X8,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).
fof(f4539,plain,
spl0_353,
inference(avatar_split_clause,[],[f615,f4537]) ).
fof(f615,axiom,
! [X2,X3,X8,X6,X7] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X8,X2,X3),X6),X7))
| ~ c_in(c_Pair(X6,X7,X2,X3),X8,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).
fof(f4535,plain,
spl0_352,
inference(avatar_split_clause,[],[f595,f4533]) ).
fof(f595,axiom,
! [X2,X6,X4] :
( c_in(X6,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X4,X6,X2),X6,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
fof(f4531,plain,
spl0_351,
inference(avatar_split_clause,[],[f590,f4529]) ).
fof(f590,axiom,
! [X2,X8,X6] :
( c_in(X6,c_Wellfounded_Oacc(X8,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X8,X6,X2),X6,X2,X2),X8,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
fof(f4527,plain,
spl0_350,
inference(avatar_split_clause,[],[f584,f4525]) ).
fof(f4525,plain,
( spl0_350
<=> ! [X18,X4,X0,X2] :
( hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X18,X4,X2),c_Wellfounded_Oacc(X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f584,axiom,
! [X2,X0,X18,X4] :
( hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X18,X4,X2),c_Wellfounded_Oacc(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).
fof(f4523,plain,
spl0_349,
inference(avatar_split_clause,[],[f513,f4521]) ).
fof(f4521,plain,
( spl0_349
<=> ! [X18,X4,X0,X2] :
( hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X18,X4,X2),c_Wellfounded_Oacc(X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f513,axiom,
! [X2,X0,X18,X4] :
( hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X18,X4,X2),c_Wellfounded_Oacc(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
fof(f4519,plain,
spl0_348,
inference(avatar_split_clause,[],[f476,f4517]) ).
fof(f4517,plain,
( spl0_348
<=> ! [X9,X3,X19,X5,X2] :
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X5,X9,X19,X2,X3),X5,X2)
| ~ c_in(X19,c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f476,axiom,
! [X2,X3,X19,X9,X5] :
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X5,X9,X19,X2,X3),X5,X2)
| ~ c_in(X19,c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaE_0) ).
fof(f4515,plain,
spl0_347,
inference(avatar_split_clause,[],[f373,f4513]) ).
fof(f373,axiom,
! [X2,X4] : c_Transitive__Closure_Otrancl(X4,X2) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X4,X2),X4,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
fof(f4511,plain,
( spl0_346
| ~ spl0_61
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f4469,f4300,f1104,f4509]) ).
fof(f4300,plain,
( spl0_336
<=> hBOOL(hAPP(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f4469,plain,
( ! [X0] : c_in(v_a____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)
| ~ spl0_61
| ~ spl0_336 ),
inference(resolution,[],[f4302,f1105]) ).
fof(f4302,plain,
( hBOOL(hAPP(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____))
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f4300]) ).
fof(f4507,plain,
spl0_345,
inference(avatar_split_clause,[],[f293,f4505]) ).
fof(f4505,plain,
( spl0_345
<=> ! [X5,X9,X6,X2] :
( ~ c_in(X6,X9,X2)
| ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_lessequals(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f293,axiom,
! [X2,X6,X9,X5] :
( ~ c_in(X6,X9,X2)
| ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_lessequals(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f4503,plain,
spl0_344,
inference(avatar_split_clause,[],[f204,f4501]) ).
fof(f4501,plain,
( spl0_344
<=> ! [X5,X9,X6,X2] :
( c_in(X6,X5,X2)
| c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X5,c_Set_Oinsert(X6,X9,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f204,axiom,
! [X2,X6,X9,X5] :
( c_in(X6,X5,X2)
| c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X5,c_Set_Oinsert(X6,X9,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
fof(f4499,plain,
spl0_343,
inference(avatar_split_clause,[],[f171,f4497]) ).
fof(f171,axiom,
! [X2,X3,X0,X9,X12] : c_Set_Oimage(X12,c_Set_Oinsert(X0,X9,X3),X3,X2) = c_Set_Oinsert(hAPP(X12,X0),c_Set_Oimage(X12,X9,X3,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f4495,plain,
spl0_342,
inference(avatar_split_clause,[],[f131,f4493]) ).
fof(f131,axiom,
! [X2,X6,X9,X5] :
( ~ c_in(X6,X9,X2)
| ~ c_in(X6,X5,X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f4491,plain,
spl0_341,
inference(avatar_split_clause,[],[f125,f4489]) ).
fof(f4489,plain,
( spl0_341
<=> ! [X2,X5,X8] :
( ~ c_Wellfounded_Owf(X8,X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
| ~ c_lessequals(X5,c_Relation_OImage(X8,X5,X2,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f125,axiom,
! [X2,X8,X5] :
( ~ c_Wellfounded_Owf(X8,X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
| ~ c_lessequals(X5,c_Relation_OImage(X8,X5,X2,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
fof(f4487,plain,
spl0_340,
inference(avatar_split_clause,[],[f40,f4485]) ).
fof(f40,axiom,
! [X2,X5] : c_lessequals(c_Relation_OId__on(X5,X2),c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
fof(f4483,plain,
spl0_339,
inference(avatar_split_clause,[],[f34,f4481]) ).
fof(f34,axiom,
! [X2,X9,X5] :
( c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
fof(f4479,plain,
spl0_338,
inference(avatar_split_clause,[],[f15,f4477]) ).
fof(f4475,plain,
spl0_337,
inference(avatar_split_clause,[],[f14,f4473]) ).
fof(f4303,plain,
( spl0_336
| ~ spl0_62
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f4053,f4006,f1108,f4300]) ).
fof(f4006,plain,
( spl0_325
<=> c_in(v_a____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f4053,plain,
( hBOOL(hAPP(c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____))
| ~ spl0_62
| ~ spl0_325 ),
inference(resolution,[],[f4008,f1109]) ).
fof(f4008,plain,
( c_in(v_a____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f4006]) ).
fof(f4049,plain,
spl0_335,
inference(avatar_split_clause,[],[f682,f4047]) ).
fof(f4047,plain,
( spl0_335
<=> ! [X4,X0,X5,X2] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| ~ c_in(X0,X5,X2)
| c_in(c_Pair(X0,X0,X2,X2),X4,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f682,axiom,
! [X2,X0,X4,X5] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| ~ c_in(X0,X5,X2)
| c_in(c_Pair(X0,X0,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
fof(f4045,plain,
spl0_334,
inference(avatar_split_clause,[],[f681,f4043]) ).
fof(f681,axiom,
! [X2,X6,X7,X4,X5] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_in(X6,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
fof(f4041,plain,
spl0_333,
inference(avatar_split_clause,[],[f680,f4039]) ).
fof(f680,axiom,
! [X2,X6,X7,X4,X5] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_in(X7,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
fof(f4037,plain,
spl0_332,
inference(avatar_split_clause,[],[f677,f4035]) ).
fof(f677,axiom,
! [X2,X3,X0,X1,X9,X5] :
( c_in(X0,X5,X2)
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X5,X9,X2,X3),tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
fof(f4033,plain,
spl0_331,
inference(avatar_split_clause,[],[f671,f4031]) ).
fof(f671,axiom,
! [X2,X6,X7,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_in(X6,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
fof(f4029,plain,
spl0_330,
inference(avatar_split_clause,[],[f670,f4027]) ).
fof(f670,axiom,
! [X2,X6,X7,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_in(X7,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
fof(f4025,plain,
spl0_329,
inference(avatar_split_clause,[],[f575,f4023]) ).
fof(f575,axiom,
! [X40,X6] :
( ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(X40,X6),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).
fof(f4021,plain,
spl0_328,
inference(avatar_split_clause,[],[f574,f4019]) ).
fof(f574,axiom,
! [X40,X6] :
( ~ c_in(X40,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omkbot(X40,X6),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).
fof(f4017,plain,
spl0_327,
inference(avatar_split_clause,[],[f447,f4015]) ).
fof(f4015,plain,
( spl0_327
<=> ! [X2,X16] :
( ~ c_in(X16,c_Relation_OId(X2),tc_prod(X2,X2))
| c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X16,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X16,X2),X2,X2) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f447,axiom,
! [X2,X16] :
( ~ c_in(X16,c_Relation_OId(X2),tc_prod(X2,X2))
| c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X16,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X16,X2),X2,X2) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).
fof(f4013,plain,
spl0_326,
inference(avatar_split_clause,[],[f341,f4011]) ).
fof(f4011,plain,
( spl0_326
<=> ! [X11,X0,X30,X2] :
( ~ c_lessequals(X11,X30,tc_fun(X2,tc_bool))
| c_lessequals(c_Set_Oinsert(X0,X11,X2),c_Set_Oinsert(X0,X30,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f341,axiom,
! [X2,X0,X11,X30] :
( ~ c_lessequals(X11,X30,tc_fun(X2,tc_bool))
| c_lessequals(c_Set_Oinsert(X0,X11,X2),c_Set_Oinsert(X0,X30,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f4009,plain,
( spl0_325
| ~ spl0_92
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3937,f3501,f1244,f4006]) ).
fof(f3937,plain,
( c_in(v_a____,c_Relation_ORange(v_Lab____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_92
| ~ spl0_307 ),
inference(resolution,[],[f3502,f1245]) ).
fof(f4004,plain,
spl0_324,
inference(avatar_split_clause,[],[f316,f4002]) ).
fof(f316,axiom,
! [X2,X11,X9,X5] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X11,tc_fun(X2,tc_bool))
| c_lessequals(X5,X11,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f4000,plain,
spl0_323,
inference(avatar_split_clause,[],[f297,f3998]) ).
fof(f3998,plain,
( spl0_323
<=> ! [X2,X5,X9] : c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f297,axiom,
! [X2,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f3996,plain,
spl0_322,
inference(avatar_split_clause,[],[f235,f3994]) ).
fof(f235,axiom,
! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f3992,plain,
spl0_321,
inference(avatar_split_clause,[],[f234,f3990]) ).
fof(f3990,plain,
( spl0_321
<=> ! [X34,X2,X35] :
( ~ c_lessequals(X35,X34,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X34,X2),c_Wellfounded_Oacc(X35,X2),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f234,axiom,
! [X2,X34,X35] :
( ~ c_lessequals(X35,X34,tc_fun(tc_prod(X2,X2),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X34,X2),c_Wellfounded_Oacc(X35,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).
fof(f3988,plain,
spl0_320,
inference(avatar_split_clause,[],[f216,f3986]) ).
fof(f216,axiom,
! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
fof(f3984,plain,
spl0_319,
inference(avatar_split_clause,[],[f215,f3982]) ).
fof(f215,axiom,
! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
fof(f3980,plain,
spl0_318,
inference(avatar_split_clause,[],[f194,f3978]) ).
fof(f3978,plain,
( spl0_318
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f194,axiom,
! [X2,X0,X1] :
( X0 = X1
| c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f3976,plain,
spl0_317,
inference(avatar_split_clause,[],[f149,f3974]) ).
fof(f149,axiom,
! [X2,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
fof(f3972,plain,
spl0_316,
inference(avatar_split_clause,[],[f53,f3970]) ).
fof(f3970,plain,
( spl0_316
<=> ! [X2,X5,X9] : c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f53,axiom,
! [X2,X9,X5] : c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f3968,plain,
spl0_315,
inference(avatar_split_clause,[],[f13,f3966]) ).
fof(f13,axiom,
! [X2,X3,X10,X8] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X10),tc_bool)),X8,X2,X10,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).
fof(f3964,plain,
spl0_314,
inference(avatar_split_clause,[],[f12,f3962]) ).
fof(f12,axiom,
! [X2,X3,X10,X8] : c_Relation_Orel__comp(X8,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X3),tc_bool)),X2,X10,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).
fof(f3881,plain,
( ~ spl0_312
| spl0_313
| ~ spl0_202
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2872,f2429,f2307,f3878,f3874]) ).
fof(f3874,plain,
( spl0_312
<=> c_lessequals(v_Lab____,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2872,plain,
( v_a____ = v_b____
| ~ c_lessequals(v_Lab____,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_202
| ~ spl0_230 ),
inference(resolution,[],[f2430,f2308]) ).
fof(f3519,plain,
spl0_311,
inference(avatar_split_clause,[],[f727,f3517]) ).
fof(f727,plain,
! [X2,X3,X8] : c_Set_Oimage(c_fst(X2,X3),X8,tc_prod(X2,X3),X2) = c_Relation_ORange(c_Relation_Oconverse(X8,X2,X3),X3,X2),
inference(definition_unfolding,[],[f486,f557]) ).
fof(f486,axiom,
! [X2,X3,X8] : c_Set_Oimage(c_fst(X2,X3),X8,tc_prod(X2,X3),X2) = c_Relation_ODomain(X8,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__eq__Domain_0) ).
fof(f3515,plain,
spl0_310,
inference(avatar_split_clause,[],[f726,f3513]) ).
fof(f726,plain,
! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),
inference(definition_unfolding,[],[f48,f557]) ).
fof(f48,axiom,
! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty_0) ).
fof(f3511,plain,
( spl0_309
| ~ spl0_61
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3383,f3204,f1104,f3509]) ).
fof(f3204,plain,
( spl0_272
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(v_Lab____,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f3383,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1),v_Lab____,X2) )
| ~ spl0_61
| ~ spl0_272 ),
inference(resolution,[],[f3205,f1105]) ).
fof(f3205,plain,
( ! [X0,X1] :
( hBOOL(hAPP(v_Lab____,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1)))
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f3204]) ).
fof(f3507,plain,
spl0_308,
inference(avatar_split_clause,[],[f718,f3505]) ).
fof(f718,plain,
! [X2,X4] : c_Relation_ORange(c_Relation_Oconverse(X4,X2,X2),X2,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X2),X2,X2),X2,X2),
inference(definition_unfolding,[],[f516,f557,f557]) ).
fof(f516,axiom,
! [X2,X4] : c_Relation_ODomain(X4,X2,X2) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X4,X2),X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
fof(f3503,plain,
spl0_307,
inference(avatar_split_clause,[],[f672,f3501]) ).
fof(f672,axiom,
! [X2,X3,X0,X6,X4] :
( c_in(X0,c_Relation_ORange(X4,X3,X2),X2)
| ~ c_in(c_Pair(X6,X0,X3,X2),X4,tc_prod(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).
fof(f3499,plain,
spl0_306,
inference(avatar_split_clause,[],[f560,f3497]) ).
fof(f3497,plain,
( spl0_306
<=> ! [X4,X10,X14,X3,X2] :
( ~ c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_Relation_Osingle__valued(X14,X3,X10)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X4,X14,X2,X3,X10),X2,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f560,axiom,
! [X2,X3,X10,X14,X4] :
( ~ c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_Relation_Osingle__valued(X14,X3,X10)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X4,X14,X2,X3,X10),X2,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
fof(f3495,plain,
spl0_305,
inference(avatar_split_clause,[],[f551,f3493]) ).
fof(f551,axiom,
! [X2,X3,X8,X12] : c_Relation_Oconverse(c_Relation_Oinv__image(X8,X12,X3,X2),X2,X2) = c_Relation_Oinv__image(c_Relation_Oconverse(X8,X3,X3),X12,X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
fof(f3491,plain,
spl0_304,
inference(avatar_split_clause,[],[f525,f3489]) ).
fof(f3489,plain,
( spl0_304
<=> ! [X18,X4,X0,X2] :
( hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X18,X4,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f525,axiom,
! [X2,X0,X18,X4] :
( hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X18,X4,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
fof(f3487,plain,
spl0_303,
inference(avatar_split_clause,[],[f517,f3485]) ).
fof(f517,axiom,
! [X2,X3,X1,X4,X5] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X5,X1,X4,X3,X2),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).
fof(f3483,plain,
spl0_302,
inference(avatar_split_clause,[],[f510,f3481]) ).
fof(f3481,plain,
( spl0_302
<=> ! [X18,X4,X0,X2] :
( hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X18,X4,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f510,axiom,
! [X2,X0,X18,X4] :
( hBOOL(hAPP(X18,X0))
| ~ c_in(X0,c_Wellfounded_Oacc(X4,X2),X2)
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X18,X4,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).
fof(f3479,plain,
spl0_301,
inference(avatar_split_clause,[],[f508,f3477]) ).
fof(f508,axiom,
! [X2,X3,X1,X4,X5] :
( ~ c_in(X1,c_Relation_OImage(X4,X5,X3,X2),X2)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X5,X1,X4,X3,X2),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).
fof(f3475,plain,
spl0_300,
inference(avatar_split_clause,[],[f500,f3473]) ).
fof(f500,axiom,
! [X2,X3,X10,X0,X1,X12] : hAPP(hAPP(X12,X0),X1) = hAPP(c_split(X12,X2,X3,X10),c_Pair(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__case__cert_0) ).
fof(f3471,plain,
spl0_299,
inference(avatar_split_clause,[],[f435,f3469]) ).
fof(f435,axiom,
! [X2,X4] :
( c_Relation_Oirrefl(X4,X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X4,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
fof(f3467,plain,
( spl0_298
| ~ spl0_61
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3336,f3159,f1104,f3465]) ).
fof(f3159,plain,
( spl0_263
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(v_Lab____,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f3336,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1),v_Lab____,X2) )
| ~ spl0_61
| ~ spl0_263 ),
inference(resolution,[],[f3160,f1105]) ).
fof(f3160,plain,
( ! [X0,X1] :
( hBOOL(hAPP(v_Lab____,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1)))
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f3159]) ).
fof(f3463,plain,
spl0_297,
inference(avatar_split_clause,[],[f433,f3461]) ).
fof(f3461,plain,
( spl0_297
<=> ! [X2,X4] :
( ~ c_Relation_Oantisym(X4,X2)
| ~ c_Relation_Otrans(X4,X2)
| c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f433,axiom,
! [X2,X4] :
( ~ c_Relation_Oantisym(X4,X2)
| ~ c_Relation_Otrans(X4,X2)
| c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).
fof(f3459,plain,
spl0_296,
inference(avatar_split_clause,[],[f432,f3457]) ).
fof(f432,axiom,
! [X2,X4] :
( c_Nitpick_Orefl_H(X4,X2)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X4,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X4,X2),X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
fof(f3455,plain,
spl0_295,
inference(avatar_split_clause,[],[f346,f3453]) ).
fof(f346,axiom,
! [X2,X3,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)) = X4
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ORange(X4,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).
fof(f3451,plain,
spl0_294,
inference(avatar_split_clause,[],[f335,f3449]) ).
fof(f335,axiom,
! [X2,X6,X9,X5] :
( ~ hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(X9,X6))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f3447,plain,
spl0_293,
inference(avatar_split_clause,[],[f311,f3445]) ).
fof(f311,axiom,
! [X2,X11,X9,X5] :
( c_lessequals(X9,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f3443,plain,
spl0_292,
inference(avatar_split_clause,[],[f310,f3441]) ).
fof(f310,axiom,
! [X2,X11,X9,X5] :
( c_lessequals(X5,X11,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X11,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f3439,plain,
spl0_291,
inference(avatar_split_clause,[],[f281,f3437]) ).
fof(f281,axiom,
! [X2,X19,X9,X5] :
( ~ c_in(X19,X5,X2)
| c_in(X19,X9,X2)
| c_in(X19,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
fof(f3435,plain,
spl0_290,
inference(avatar_split_clause,[],[f271,f3433]) ).
fof(f3433,plain,
( spl0_290
<=> ! [X9,X5,X19,X2] :
( c_in(X19,X9,X2)
| c_in(X19,X5,X2)
| ~ c_in(X19,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f271,axiom,
! [X2,X19,X9,X5] :
( c_in(X19,X9,X2)
| c_in(X19,X5,X2)
| ~ c_in(X19,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f3431,plain,
spl0_289,
inference(avatar_split_clause,[],[f257,f3429]) ).
fof(f257,axiom,
! [X2,X19,X9,X5] :
( ~ c_in(X19,X5,X2)
| ~ c_in(X19,X9,X2)
| c_in(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
fof(f3427,plain,
spl0_288,
inference(avatar_split_clause,[],[f232,f3425]) ).
fof(f232,axiom,
! [X2,X0,X5] : c_Set_Oinsert(X0,X5,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
fof(f3423,plain,
spl0_287,
inference(avatar_split_clause,[],[f220,f3421]) ).
fof(f220,axiom,
! [X2,X11,X9,X5] :
( c_lessequals(X11,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f3419,plain,
spl0_286,
inference(avatar_split_clause,[],[f219,f3417]) ).
fof(f219,axiom,
! [X2,X11,X9,X5] :
( c_lessequals(X11,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f3415,plain,
spl0_285,
inference(avatar_split_clause,[],[f212,f3413]) ).
fof(f212,axiom,
! [X2,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f3411,plain,
spl0_284,
inference(avatar_split_clause,[],[f211,f3409]) ).
fof(f211,axiom,
! [X2,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X9
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f3407,plain,
spl0_283,
inference(avatar_split_clause,[],[f177,f3405]) ).
fof(f3405,plain,
( spl0_283
<=> ! [X7,X22,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| ~ c_lessequals(X6,X22,X2)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f177,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| ~ c_lessequals(X6,X22,X2)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
fof(f3403,plain,
spl0_282,
inference(avatar_split_clause,[],[f116,f3401]) ).
fof(f3401,plain,
( spl0_282
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X22,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f116,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X22,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f3399,plain,
spl0_281,
inference(avatar_split_clause,[],[f115,f3397]) ).
fof(f3397,plain,
( spl0_281
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f115,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f3395,plain,
spl0_280,
inference(avatar_split_clause,[],[f114,f3393]) ).
fof(f114,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f3391,plain,
spl0_279,
inference(avatar_split_clause,[],[f113,f3389]) ).
fof(f113,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X22,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f3387,plain,
spl0_278,
inference(avatar_split_clause,[],[f107,f3385]) ).
fof(f3385,plain,
( spl0_278
<=> ! [X5,X9,X6,X2] :
( hBOOL(hAPP(X9,X6))
| hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f107,axiom,
! [X2,X6,X9,X5] :
( hBOOL(hAPP(X9,X6))
| hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f3382,plain,
spl0_277,
inference(avatar_split_clause,[],[f80,f3380]) ).
fof(f3380,plain,
( spl0_277
<=> ! [X7,X22,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| ~ c_lessequals(X22,X6,X2)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f80,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| ~ c_lessequals(X22,X6,X2)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
fof(f3378,plain,
spl0_276,
inference(avatar_split_clause,[],[f67,f3376]) ).
fof(f3376,plain,
( spl0_276
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X22,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f67,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X22,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f3374,plain,
spl0_275,
inference(avatar_split_clause,[],[f66,f3372]) ).
fof(f3372,plain,
( spl0_275
<=> ! [X2,X7,X6,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f66,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f3370,plain,
spl0_274,
inference(avatar_split_clause,[],[f65,f3368]) ).
fof(f65,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f3366,plain,
spl0_273,
inference(avatar_split_clause,[],[f64,f3364]) ).
fof(f64,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X22,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f3206,plain,
( spl0_272
| ~ spl0_62
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3113,f2929,f1108,f3204]) ).
fof(f2929,plain,
( spl0_248
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1),v_Lab____,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3113,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(v_Lab____,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1))) )
| ~ spl0_62
| ~ spl0_248 ),
inference(resolution,[],[f2930,f1109]) ).
fof(f2930,plain,
( ! [X0,X1] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1),v_Lab____,X1)
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2929]) ).
fof(f3193,plain,
spl0_271,
inference(avatar_split_clause,[],[f822,f3191]) ).
fof(f822,plain,
! [X2,X8] :
( c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Relation_Orel__comp(X8,X8,X2,X2,X2)
| c_Wellfounded_Owf(X8,X2) ),
inference(forward_demodulation,[],[f372,f196]) ).
fof(f372,axiom,
! [X2,X8] :
( c_Wellfounded_Owf(X8,X2)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X8,X8,X2,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).
fof(f3189,plain,
spl0_270,
inference(avatar_split_clause,[],[f742,f3187]) ).
fof(f742,plain,
! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ),
inference(definition_unfolding,[],[f528,f440]) ).
fof(f528,axiom,
! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
fof(f3185,plain,
spl0_269,
inference(avatar_split_clause,[],[f741,f3183]) ).
fof(f741,plain,
! [X2,X4] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ),
inference(definition_unfolding,[],[f378,f440]) ).
fof(f378,axiom,
! [X2,X4] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
fof(f3181,plain,
spl0_268,
inference(avatar_split_clause,[],[f669,f3179]) ).
fof(f669,axiom,
! [X2,X6,X5] :
( ~ c_in(X6,X5,X2)
| c_in(c_Pair(X6,X6,X2,X2),c_Relation_OId__on(X5,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
fof(f3177,plain,
spl0_267,
inference(avatar_split_clause,[],[f668,f3175]) ).
fof(f668,axiom,
! [X2,X6,X7,X5] :
( c_in(X6,X5,X2)
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Relation_OId__on(X5,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
fof(f3173,plain,
spl0_266,
inference(avatar_split_clause,[],[f567,f3171]) ).
fof(f567,axiom,
! [X18,X6,X4] :
( hBOOL(hAPP(X18,X6))
| ~ hBOOL(hAPP(X18,v_sko__Wellfounded__Xacc__Xinduct__1(X18,X4)))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
fof(f3169,plain,
spl0_265,
inference(avatar_split_clause,[],[f512,f3167]) ).
fof(f512,axiom,
! [X18,X6,X4] :
( hBOOL(hAPP(X18,X6))
| ~ hBOOL(hAPP(X18,v_sko__Wellfounded__Xacc__Xinducts__1(X18,X4)))
| ~ c_in(X6,c_Wellfounded_Oacc(X4,t_a),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
fof(f3165,plain,
spl0_264,
inference(avatar_split_clause,[],[f389,f3163]) ).
fof(f389,axiom,
! [X2,X4,X5] :
( ~ c_Relation_Ototal__on(X5,X4,X2)
| c_Relation_Ototal__on(X5,c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).
fof(f3161,plain,
( spl0_263
| ~ spl0_62
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f3068,f2885,f1108,f3159]) ).
fof(f2885,plain,
( spl0_237
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1),v_Lab____,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f3068,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(v_Lab____,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1))) )
| ~ spl0_62
| ~ spl0_237 ),
inference(resolution,[],[f2886,f1109]) ).
fof(f2886,plain,
( ! [X0,X1] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1),v_Lab____,X1)
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2885]) ).
fof(f3157,plain,
spl0_262,
inference(avatar_split_clause,[],[f388,f3155]) ).
fof(f388,axiom,
! [X2,X4,X5] :
( c_Relation_Ototal__on(X5,X4,X2)
| ~ c_Relation_Ototal__on(X5,c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).
fof(f3153,plain,
spl0_261,
inference(avatar_split_clause,[],[f379,f3151]) ).
fof(f379,axiom,
! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| c_lessequals(c_Relation_Orel__comp(X4,X4,X2,X2,X2),X4,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
fof(f3149,plain,
spl0_260,
inference(avatar_split_clause,[],[f324,f3147]) ).
fof(f324,axiom,
! [X2,X3,X14,X4] :
( ~ c_Relation_Osingle__valued(X14,X2,X3)
| c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X3),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
fof(f3145,plain,
spl0_259,
inference(avatar_split_clause,[],[f255,f3143]) ).
fof(f255,axiom,
! [X2,X3,X36,X6,X12] :
( ~ class_HOL_Oord(X3)
| ~ c_lessequals(X12,X36,tc_fun(X2,X3))
| c_lessequals(hAPP(X12,X6),hAPP(X36,X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f3141,plain,
spl0_258,
inference(avatar_split_clause,[],[f249,f3139]) ).
fof(f3139,plain,
( spl0_258
<=> ! [X2,X4,X14] :
( ~ c_Relation_Osym(X4,X2)
| ~ c_Relation_Osym(X14,X2)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f249,axiom,
! [X2,X14,X4] :
( ~ c_Relation_Osym(X4,X2)
| ~ c_Relation_Osym(X14,X2)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).
fof(f3137,plain,
spl0_257,
inference(avatar_split_clause,[],[f240,f3135]) ).
fof(f240,axiom,
! [X2,X9,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
fof(f3133,plain,
spl0_256,
inference(avatar_split_clause,[],[f132,f3131]) ).
fof(f3131,plain,
( spl0_256
<=> ! [X2,X4,X14] :
( ~ c_Relation_Otrans(X4,X2)
| ~ c_Relation_Otrans(X14,X2)
| c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f132,axiom,
! [X2,X14,X4] :
( ~ c_Relation_Otrans(X4,X2)
| ~ c_Relation_Otrans(X14,X2)
| c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Int_0) ).
fof(f3129,plain,
spl0_255,
inference(avatar_split_clause,[],[f90,f3127]) ).
fof(f3127,plain,
( spl0_255
<=> ! [X2,X4,X14] :
( ~ c_Relation_Osym(X4,X2)
| ~ c_Relation_Osym(X14,X2)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f90,axiom,
! [X2,X14,X4] :
( ~ c_Relation_Osym(X4,X2)
| ~ c_Relation_Osym(X14,X2)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).
fof(f3125,plain,
spl0_254,
inference(avatar_split_clause,[],[f16,f3123]) ).
fof(f3123,plain,
( spl0_254
<=> ! [X3,X12,X5,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X12,X5,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f16,axiom,
! [X2,X3,X5,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X12,X5,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
fof(f2951,plain,
spl0_253,
inference(avatar_split_clause,[],[f810,f2949]) ).
fof(f810,plain,
! [X40,X6,X27] :
( X6 = X27
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f659]) ).
fof(f659,axiom,
! [X40,X6,X27] :
( X6 = X27
| X6 = X27
| c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).
fof(f2947,plain,
spl0_252,
inference(avatar_split_clause,[],[f809,f2945]) ).
fof(f809,plain,
! [X40,X6,X7] :
( X6 = X7
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f654]) ).
fof(f654,axiom,
! [X40,X6,X7] :
( X6 = X7
| X6 = X7
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
fof(f2943,plain,
spl0_251,
inference(avatar_split_clause,[],[f712,f2941]) ).
fof(f2941,plain,
( spl0_251
<=> ! [X2,X4,X3] : c_Relation_ORange(X4,X3,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X4,X3,X2),X2,X3),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f712,plain,
! [X2,X3,X4] : c_Relation_ORange(X4,X3,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X4,X3,X2),X2,X3),X3,X2),
inference(definition_unfolding,[],[f577,f557]) ).
fof(f577,axiom,
! [X2,X3,X4] : c_Relation_ORange(X4,X3,X2) = c_Relation_ODomain(c_Relation_Oconverse(X4,X3,X2),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
fof(f2939,plain,
spl0_250,
inference(avatar_split_clause,[],[f661,f2937]) ).
fof(f661,axiom,
! [X0,X1] :
( X0 = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
fof(f2935,plain,
spl0_249,
inference(avatar_split_clause,[],[f635,f2933]) ).
fof(f635,axiom,
! [X2,X6,X7,X5] :
( X6 = X7
| ~ c_in(c_Pair(X6,X7,X2,X2),c_Relation_OId__on(X5,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
fof(f2931,plain,
( spl0_248
| ~ spl0_92
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2866,f2425,f1244,f2929]) ).
fof(f2866,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(v_Lab____,X0,X1),v_Lab____,X1) )
| ~ spl0_92
| ~ spl0_229 ),
inference(resolution,[],[f2426,f1245]) ).
fof(f2927,plain,
spl0_247,
inference(avatar_split_clause,[],[f572,f2925]) ).
fof(f2925,plain,
( spl0_247
<=> ! [X6,X2,X4] :
( c_in(X6,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X4,X6,X2),c_Wellfounded_Oacc(X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f572,axiom,
! [X2,X6,X4] :
( c_in(X6,c_Wellfounded_Oacc(X4,X2),X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X4,X6,X2),c_Wellfounded_Oacc(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
fof(f2923,plain,
spl0_246,
inference(avatar_split_clause,[],[f563,f2921]) ).
fof(f2921,plain,
( spl0_246
<=> ! [X2,X5,X4] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f563,axiom,
! [X2,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X4,X2,X2),X4,X2,X2,X2) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
fof(f2919,plain,
spl0_245,
inference(avatar_split_clause,[],[f518,f2917]) ).
fof(f2917,plain,
( spl0_245
<=> ! [X6,X2,X8] :
( c_in(X6,c_Wellfounded_Oacc(X8,X2),X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X8,X6,X2),c_Wellfounded_Oacc(X8,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f518,axiom,
! [X2,X8,X6] :
( c_in(X6,c_Wellfounded_Oacc(X8,X2),X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X8,X6,X2),c_Wellfounded_Oacc(X8,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
fof(f2915,plain,
spl0_244,
inference(avatar_split_clause,[],[f454,f2913]) ).
fof(f454,axiom,
! [X2,X6,X4] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| ~ c_in(c_Pair(X6,X6,X2,X2),c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
fof(f2911,plain,
spl0_243,
inference(avatar_split_clause,[],[f444,f2909]) ).
fof(f444,axiom,
! [X2,X19,X5] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X5,X19,X2),X5,X2)
| ~ c_in(X19,c_Relation_OId__on(X5,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).
fof(f2907,plain,
spl0_242,
inference(avatar_split_clause,[],[f233,f2905]) ).
fof(f2905,plain,
( spl0_242
<=> ! [X2,X9,X3] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X9,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f233,axiom,
! [X2,X3,X9] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X9,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).
fof(f2903,plain,
spl0_241,
inference(avatar_split_clause,[],[f165,f2901]) ).
fof(f2901,plain,
( spl0_241
<=> ! [X2,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
| ~ c_lessequals(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f165,axiom,
! [X2,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
| ~ c_lessequals(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f2899,plain,
spl0_240,
inference(avatar_split_clause,[],[f142,f2897]) ).
fof(f142,axiom,
! [X2,X9,X5] :
( X5 = X9
| ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X5,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
fof(f2895,plain,
spl0_239,
inference(avatar_split_clause,[],[f50,f2893]) ).
fof(f50,axiom,
! [X2,X3,X15] : c_Pair(hAPP(c_fst(X2,X3),X15),hAPP(c_snd(X2,X3),X15),X2,X3) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surjective__pairing_0) ).
fof(f2891,plain,
spl0_238,
inference(avatar_split_clause,[],[f49,f2889]) ).
fof(f49,axiom,
! [X2,X6,X7,X5] : c_Set_Oinsert(X6,c_Set_Oinsert(X7,X5,X2),X2) = c_Set_Oinsert(X7,c_Set_Oinsert(X6,X5,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f2887,plain,
( spl0_237
| ~ spl0_92
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2853,f2421,f1244,f2885]) ).
fof(f2853,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_Lab____,X0,X1),v_Lab____,X1) )
| ~ spl0_92
| ~ spl0_228 ),
inference(resolution,[],[f2422,f1245]) ).
fof(f2883,plain,
spl0_236,
inference(avatar_split_clause,[],[f23,f2881]) ).
fof(f23,axiom,
! [X2,X6,X9,X5] :
( c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
fof(f2879,plain,
spl0_235,
inference(avatar_split_clause,[],[f22,f2877]) ).
fof(f22,axiom,
! [X2,X1,X9,X5] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_lessequals(X5,c_Set_Oinsert(X1,X9,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
fof(f2690,plain,
( spl0_234
| ~ spl0_148
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2351,f2307,f1618,f2688]) ).
fof(f2688,plain,
( spl0_234
<=> ! [X0] : ~ c_lessequals(v_Lab____,c_Arrow__Order__Mirabelle_Omkbot(X0,v_a____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2351,plain,
( ! [X0] : ~ c_lessequals(v_Lab____,c_Arrow__Order__Mirabelle_Omkbot(X0,v_a____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_148
| ~ spl0_202 ),
inference(resolution,[],[f2308,f1619]) ).
fof(f2611,plain,
( spl0_233
| ~ spl0_147
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2350,f2307,f1614,f2609]) ).
fof(f2609,plain,
( spl0_233
<=> ! [X0] : ~ c_lessequals(v_Lab____,c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2350,plain,
( ! [X0] : ~ c_lessequals(v_Lab____,c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_147
| ~ spl0_202 ),
inference(resolution,[],[f2308,f1615]) ).
fof(f2439,plain,
spl0_232,
inference(avatar_split_clause,[],[f684,f2437]) ).
fof(f684,axiom,
! [X2,X3,X0,X1,X54,X53] :
( X0 = X53
| c_Pair(X0,X1,X2,X3) != c_Pair(X53,X54,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
fof(f2435,plain,
spl0_231,
inference(avatar_split_clause,[],[f683,f2433]) ).
fof(f683,axiom,
! [X2,X3,X0,X1,X54,X53] :
( X1 = X54
| c_Pair(X0,X1,X2,X3) != c_Pair(X53,X54,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
fof(f2431,plain,
spl0_230,
inference(avatar_split_clause,[],[f637,f2429]) ).
fof(f637,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
fof(f2427,plain,
spl0_229,
inference(avatar_split_clause,[],[f570,f2425]) ).
fof(f570,axiom,
! [X2,X8,X6,X26] :
( ~ c_Wellfounded_Owf(X8,X2)
| ~ c_in(X6,X26,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X26,X8,X2),X26,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).
fof(f2423,plain,
spl0_228,
inference(avatar_split_clause,[],[f558,f2421]) ).
fof(f558,axiom,
! [X2,X26,X27,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| ~ c_in(X27,X26,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X26,X4,X2),X26,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
fof(f2419,plain,
spl0_227,
inference(avatar_split_clause,[],[f524,f2417]) ).
fof(f524,axiom,
! [X2,X4] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X4,X2,X2),X2)
| c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X2),X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
fof(f2415,plain,
spl0_226,
inference(avatar_split_clause,[],[f505,f2413]) ).
fof(f505,axiom,
! [X2,X6,X44,X5,X12] :
( ~ c_in(X6,X5,X44)
| c_in(hAPP(X12,X6),c_Set_Oimage(X12,X5,X44,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
fof(f2411,plain,
spl0_225,
inference(avatar_split_clause,[],[f484,f2409]) ).
fof(f484,axiom,
! [X2,X3,X8] : c_Set_Oimage(c_snd(X3,X2),X8,tc_prod(X3,X2),X2) = c_Relation_ORange(X8,X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eq__Range_0) ).
fof(f2407,plain,
spl0_224,
inference(avatar_split_clause,[],[f431,f2405]) ).
fof(f431,axiom,
! [X2,X4,X5] :
( ~ c_Relation_Oirrefl(X4,X2)
| ~ c_Relation_Otrans(X4,X2)
| ~ c_Relation_Ototal__on(X5,X4,X2)
| c_Order__Relation_Ostrict__linear__order__on(X5,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).
fof(f2403,plain,
( spl0_223
| ~ spl0_38
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2355,f2307,f1009,f2401]) ).
fof(f2355,plain,
( ! [X0] : ~ c_lessequals(v_Lab____,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_38
| ~ spl0_202 ),
inference(resolution,[],[f2308,f1010]) ).
fof(f2399,plain,
spl0_222,
inference(avatar_split_clause,[],[f391,f2397]) ).
fof(f391,axiom,
! [X2,X16,X4] :
( ~ c_in(X16,X4,tc_prod(X2,X2))
| c_in(X16,c_Transitive__Closure_Otrancl(X4,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
fof(f2395,plain,
spl0_221,
inference(avatar_split_clause,[],[f387,f2393]) ).
fof(f387,axiom,
! [X2,X4] :
( ~ c_Relation_Oantisym(X4,X2)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
fof(f2391,plain,
spl0_220,
inference(avatar_split_clause,[],[f386,f2389]) ).
fof(f2389,plain,
( spl0_220
<=> ! [X2,X4] :
( c_Relation_Oantisym(X4,X2)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f386,axiom,
! [X2,X4] :
( c_Relation_Oantisym(X4,X2)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
fof(f2387,plain,
spl0_219,
inference(avatar_split_clause,[],[f385,f2385]) ).
fof(f2385,plain,
( spl0_219
<=> ! [X2,X5,X9] : c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X5,X2),X9,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f385,axiom,
! [X2,X9,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X5,X2),X9,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
fof(f2383,plain,
spl0_218,
inference(avatar_split_clause,[],[f384,f2381]) ).
fof(f384,axiom,
! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
fof(f2379,plain,
spl0_217,
inference(avatar_split_clause,[],[f323,f2377]) ).
fof(f323,axiom,
! [X2,X14,X4] :
( ~ c_Wellfounded_Oacyclic(X14,X2)
| c_Wellfounded_Oacyclic(X4,X2)
| ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
fof(f2375,plain,
spl0_216,
inference(avatar_split_clause,[],[f321,f2373]) ).
fof(f321,axiom,
! [X2,X14,X4] :
( ~ c_Relation_Oantisym(X14,X2)
| c_Relation_Oantisym(X4,X2)
| ~ c_lessequals(X4,X14,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
fof(f2371,plain,
spl0_215,
inference(avatar_split_clause,[],[f318,f2369]) ).
fof(f318,axiom,
! [X2,X16,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(X16,X2)
| ~ c_lessequals(X16,X4,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
fof(f2367,plain,
spl0_214,
inference(avatar_split_clause,[],[f317,f2365]) ).
fof(f317,axiom,
! [X2,X18,X6,X26] :
( ~ hBOOL(hAPP(X18,X6))
| hBOOL(hAPP(X26,X6))
| ~ c_lessequals(X18,X26,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
fof(f2363,plain,
spl0_213,
inference(avatar_split_clause,[],[f313,f2361]) ).
fof(f313,axiom,
! [X2,X6,X7,X22] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X6,X7,X2)
| ~ c_lessequals(X7,X22,X2)
| c_lessequals(X6,X22,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f2349,plain,
spl0_212,
inference(avatar_split_clause,[],[f312,f2347]) ).
fof(f312,axiom,
! [X2,X6,X7,X22] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X7,X6,X2)
| ~ c_lessequals(X22,X7,X2)
| c_lessequals(X22,X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f2345,plain,
spl0_211,
inference(avatar_split_clause,[],[f296,f2343]) ).
fof(f2343,plain,
( spl0_211
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f296,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f2341,plain,
spl0_210,
inference(avatar_split_clause,[],[f295,f2339]) ).
fof(f295,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f2337,plain,
spl0_209,
inference(avatar_split_clause,[],[f270,f2335]) ).
fof(f2335,plain,
( spl0_209
<=> ! [X0,X5,X2,X1] :
( X0 = X1
| c_in(X0,X5,X2)
| ~ c_in(X0,c_Set_Oinsert(X1,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f270,axiom,
! [X2,X0,X1,X5] :
( X0 = X1
| c_in(X0,X5,X2)
| ~ c_in(X0,c_Set_Oinsert(X1,X5,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f2333,plain,
spl0_208,
inference(avatar_split_clause,[],[f263,f2331]) ).
fof(f263,axiom,
! [X2,X6,X9,X5] :
( ~ c_in(X6,X5,X2)
| c_in(X6,X9,X2)
| ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
fof(f2329,plain,
spl0_207,
inference(avatar_split_clause,[],[f242,f2327]) ).
fof(f2327,plain,
( spl0_207
<=> ! [X18,X4,X0,X2] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X0))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X18,X4,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f242,axiom,
! [X2,X0,X18,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X0))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X18,X4,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
fof(f2325,plain,
spl0_206,
inference(avatar_split_clause,[],[f237,f2323]) ).
fof(f2323,plain,
( spl0_206
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f237,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f2321,plain,
spl0_205,
inference(avatar_split_clause,[],[f236,f2319]) ).
fof(f236,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f2317,plain,
spl0_204,
inference(avatar_split_clause,[],[f158,f2315]) ).
fof(f2315,plain,
( spl0_204
<=> ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f158,axiom,
! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty_0) ).
fof(f2313,plain,
spl0_203,
inference(avatar_split_clause,[],[f155,f2311]) ).
fof(f155,axiom,
! [X2,X9,X5] :
( c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) != X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f2309,plain,
( spl0_202
| ~ spl0_104
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1971,f1772,f1351,f2307]) ).
fof(f1971,plain,
( ! [X0,X1] :
( ~ c_lessequals(v_Lab____,X1,tc_fun(X0,tc_bool))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,X0) )
| ~ spl0_104
| ~ spl0_157 ),
inference(superposition,[],[f1773,f1352]) ).
fof(f2305,plain,
spl0_201,
inference(avatar_split_clause,[],[f154,f2303]) ).
fof(f154,axiom,
! [X2,X9,X5] :
( ~ c_lessequals(X9,X5,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f2301,plain,
spl0_200,
inference(avatar_split_clause,[],[f153,f2299]) ).
fof(f153,axiom,
! [X2,X9,X5] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f2297,plain,
spl0_199,
inference(avatar_split_clause,[],[f139,f2295]) ).
fof(f2295,plain,
( spl0_199
<=> ! [X18,X4,X31,X2] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X31))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X18,X4,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f139,axiom,
! [X2,X31,X18,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X31))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X18,X4,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).
fof(f2293,plain,
spl0_198,
inference(avatar_split_clause,[],[f123,f2291]) ).
fof(f2291,plain,
( spl0_198
<=> ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f123,axiom,
! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f2289,plain,
spl0_197,
inference(avatar_split_clause,[],[f96,f2287]) ).
fof(f96,axiom,
! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f2285,plain,
spl0_196,
inference(avatar_split_clause,[],[f95,f2283]) ).
fof(f95,axiom,
! [X2,X9] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f2281,plain,
spl0_195,
inference(avatar_split_clause,[],[f69,f2279]) ).
fof(f69,axiom,
! [X2,X9,X5] :
( ~ c_lessequals(X9,X5,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f2277,plain,
spl0_194,
inference(avatar_split_clause,[],[f68,f2275]) ).
fof(f68,axiom,
! [X2,X9,X5] :
( ~ c_lessequals(X5,X9,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f2273,plain,
spl0_193,
inference(avatar_split_clause,[],[f47,f2271]) ).
fof(f2271,plain,
( spl0_193
<=> ! [X18,X8,X25,X2] :
( ~ c_Wellfounded_Owf(X8,X2)
| hBOOL(hAPP(X18,X25))
| ~ hBOOL(hAPP(X18,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X18,X8,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f47,axiom,
! [X2,X18,X8,X25] :
( ~ c_Wellfounded_Owf(X8,X2)
| hBOOL(hAPP(X18,X25))
| ~ hBOOL(hAPP(X18,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X18,X8,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
fof(f2269,plain,
spl0_192,
inference(avatar_split_clause,[],[f20,f2267]) ).
fof(f2267,plain,
( spl0_192
<=> ! [X18,X4,X0,X2] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X0))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X18,X4,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f20,axiom,
! [X2,X0,X18,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| hBOOL(hAPP(X18,X0))
| ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X18,X4,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).
fof(f2264,plain,
spl0_191,
inference(avatar_split_clause,[],[f2,f2262]) ).
fof(f2262,plain,
( spl0_191
<=> ! [X5,X7,X6,X2] :
( X6 = X7
| hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(c_Set_Oinsert(X7,X5,X2),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2,axiom,
! [X2,X6,X7,X5] :
( X6 = X7
| hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(c_Set_Oinsert(X7,X5,X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f2161,plain,
( spl0_190
| ~ spl0_156
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2097,f1981,f1768,f2159]) ).
fof(f2159,plain,
( spl0_190
<=> ! [X0] : v_Lab____ != c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1981,plain,
( spl0_189
<=> ! [X0] : v_Lab____ != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f2097,plain,
( ! [X0] : v_Lab____ != c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_prod(X0,X0))
| ~ spl0_156
| ~ spl0_189 ),
inference(superposition,[],[f1982,f1769]) ).
fof(f1982,plain,
( ! [X0] : v_Lab____ != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1981]) ).
fof(f1983,plain,
( spl0_189
| ~ spl0_120
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1957,f1768,f1434,f1981]) ).
fof(f1434,plain,
( spl0_120
<=> ! [X0] : v_Lab____ != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1957,plain,
( ! [X0] : v_Lab____ != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
| ~ spl0_120
| ~ spl0_156 ),
inference(superposition,[],[f1435,f1769]) ).
fof(f1435,plain,
( ! [X0] : v_Lab____ != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f1903,plain,
spl0_188,
inference(avatar_split_clause,[],[f639,f1901]) ).
fof(f639,axiom,
! [X2,X0,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| ~ c_in(c_Pair(X0,X0,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
fof(f1899,plain,
spl0_187,
inference(avatar_split_clause,[],[f638,f1897]) ).
fof(f638,axiom,
! [X2,X6,X4] :
( ~ c_Nitpick_Orefl_H(X4,X2)
| c_in(c_Pair(X6,X6,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
fof(f1895,plain,
( spl0_186
| ~ spl0_13
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f1128,f1080,f909,f1893]) ).
fof(f1893,plain,
( spl0_186
<=> ! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Otrancl(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f909,plain,
( spl0_13
<=> ! [X2] : c_Relation_Otrans(c_Relation_OId(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1128,plain,
( ! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Otrancl(c_Relation_OId(X0),X0)
| ~ spl0_13
| ~ spl0_55 ),
inference(resolution,[],[f1081,f910]) ).
fof(f910,plain,
( ! [X2] : c_Relation_Otrans(c_Relation_OId(X2),X2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f909]) ).
fof(f1891,plain,
spl0_185,
inference(avatar_split_clause,[],[f622,f1889]) ).
fof(f622,axiom,
! [X2,X6,X4] :
( ~ c_Relation_Oirrefl(X4,X2)
| ~ c_in(c_Pair(X6,X6,X2,X2),X4,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
fof(f1887,plain,
spl0_184,
inference(avatar_split_clause,[],[f576,f1885]) ).
fof(f576,axiom,
! [X0,X1] :
( X0 = X1
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_0) ).
fof(f1883,plain,
spl0_183,
inference(avatar_split_clause,[],[f552,f1881]) ).
fof(f1879,plain,
spl0_182,
inference(avatar_split_clause,[],[f381,f1877]) ).
fof(f1877,plain,
( spl0_182
<=> ! [X2,X4] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X4,c_Relation_Oconverse(X4,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f381,axiom,
! [X2,X4] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X4,c_Relation_Oconverse(X4,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
fof(f1875,plain,
spl0_181,
inference(avatar_split_clause,[],[f380,f1873]) ).
fof(f1873,plain,
( spl0_181
<=> ! [X2,X4] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_Oconverse(X4,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f380,axiom,
! [X2,X4] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Relation_Oconverse(X4,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
fof(f1871,plain,
spl0_180,
inference(avatar_split_clause,[],[f309,f1869]) ).
fof(f309,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X0,X6,X2)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
fof(f1867,plain,
spl0_179,
inference(avatar_split_clause,[],[f308,f1865]) ).
fof(f308,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X1,X6,X2)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
fof(f1863,plain,
spl0_178,
inference(avatar_split_clause,[],[f307,f1861]) ).
fof(f307,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X6,X0,X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f1859,plain,
spl0_177,
inference(avatar_split_clause,[],[f306,f1857]) ).
fof(f306,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X6,X1,X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f1855,plain,
spl0_176,
inference(avatar_split_clause,[],[f300,f1853]) ).
fof(f300,axiom,
! [X2,X4,X23] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X23,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
fof(f1846,plain,
spl0_175,
inference(avatar_split_clause,[],[f299,f1844]) ).
fof(f299,axiom,
! [X2,X4,X23] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X4,X23,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
fof(f1842,plain,
spl0_174,
inference(avatar_split_clause,[],[f278,f1840]) ).
fof(f278,axiom,
! [X2,X19,X9,X5] :
( c_in(X19,X5,X2)
| ~ c_in(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f1838,plain,
spl0_173,
inference(avatar_split_clause,[],[f277,f1836]) ).
fof(f277,axiom,
! [X2,X19,X9,X5] :
( c_in(X19,X9,X2)
| ~ c_in(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f1834,plain,
spl0_172,
inference(avatar_split_clause,[],[f273,f1832]) ).
fof(f1832,plain,
( spl0_172
<=> ! [X9,X5,X19,X2] :
( c_in(X19,X5,X2)
| ~ c_in(X19,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f273,axiom,
! [X2,X19,X9,X5] :
( c_in(X19,X5,X2)
| ~ c_in(X19,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f1830,plain,
spl0_171,
inference(avatar_split_clause,[],[f272,f1828]) ).
fof(f272,axiom,
! [X2,X19,X9,X5] :
( ~ c_in(X19,X9,X2)
| ~ c_in(X19,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f1826,plain,
spl0_170,
inference(avatar_split_clause,[],[f265,f1824]) ).
fof(f265,axiom,
! [X2,X19,X9,X5] :
( ~ c_in(X19,X9,X2)
| c_in(X19,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f1822,plain,
spl0_169,
inference(avatar_split_clause,[],[f264,f1820]) ).
fof(f264,axiom,
! [X2,X19,X9,X5] :
( ~ c_in(X19,X5,X2)
| c_in(X19,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f1818,plain,
spl0_168,
inference(avatar_split_clause,[],[f247,f1816]) ).
fof(f247,axiom,
! [X2,X6,X9,X5] :
( hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f1814,plain,
spl0_167,
inference(avatar_split_clause,[],[f246,f1812]) ).
fof(f246,axiom,
! [X2,X6,X9,X5] :
( hBOOL(hAPP(X9,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f1810,plain,
spl0_166,
inference(avatar_split_clause,[],[f239,f1808]) ).
fof(f239,axiom,
! [X2,X3,X12] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Set_Oimage(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
fof(f1806,plain,
( spl0_165
| ~ spl0_98
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1534,f1509,f1320,f1804]) ).
fof(f1804,plain,
( spl0_165
<=> ! [X0] : c_Arrow__Order__Mirabelle_OLin = c_Set_Oinsert(v_Lab____,c_Arrow__Order__Mirabelle_OLin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1509,plain,
( spl0_137
<=> ! [X0] : c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1534,plain,
( ! [X0] : c_Arrow__Order__Mirabelle_OLin = c_Set_Oinsert(v_Lab____,c_Arrow__Order__Mirabelle_OLin,X0)
| ~ spl0_98
| ~ spl0_137 ),
inference(resolution,[],[f1510,f1321]) ).
fof(f1510,plain,
( ! [X0] : c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,X0)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1509]) ).
fof(f1802,plain,
spl0_164,
inference(avatar_split_clause,[],[f228,f1800]) ).
fof(f1798,plain,
spl0_163,
inference(avatar_split_clause,[],[f225,f1796]) ).
fof(f225,axiom,
! [X2,X6,X7,X22] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X7,X2)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X22,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f1794,plain,
spl0_162,
inference(avatar_split_clause,[],[f224,f1792]) ).
fof(f224,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,X6,X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f1790,plain,
spl0_161,
inference(avatar_split_clause,[],[f223,f1788]) ).
fof(f223,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,X6,X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f1786,plain,
spl0_160,
inference(avatar_split_clause,[],[f222,f1784]) ).
fof(f222,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X1,X2)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
fof(f1782,plain,
spl0_159,
inference(avatar_split_clause,[],[f214,f1780]) ).
fof(f1780,plain,
( spl0_159
<=> ! [X2,X5,X9] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = X9
| c_Orderings_Obot__class_Obot(X2) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f214,axiom,
! [X2,X9,X5] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = X9
| c_Orderings_Obot__class_Obot(X2) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f1778,plain,
spl0_158,
inference(avatar_split_clause,[],[f213,f1776]) ).
fof(f1776,plain,
( spl0_158
<=> ! [X2,X5,X9] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = X5
| c_Orderings_Obot__class_Obot(X2) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f213,axiom,
! [X2,X9,X5] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = X5
| c_Orderings_Obot__class_Obot(X2) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f1774,plain,
spl0_157,
inference(avatar_split_clause,[],[f200,f1772]) ).
fof(f200,axiom,
! [X2,X6,X9,X5] :
( c_in(X6,X9,X2)
| ~ c_lessequals(c_Set_Oinsert(X6,X5,X2),X9,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f1770,plain,
spl0_156,
inference(avatar_split_clause,[],[f196,f1768]) ).
fof(f1766,plain,
spl0_155,
inference(avatar_split_clause,[],[f144,f1764]) ).
fof(f144,axiom,
! [X2,X6,X7] :
( ~ class_Orderings_Oorder(X2)
| X6 = X7
| ~ c_lessequals(X6,X7,X2)
| ~ c_lessequals(X7,X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f1758,plain,
spl0_154,
inference(avatar_split_clause,[],[f109,f1756]) ).
fof(f109,axiom,
! [X2,X6,X9,X5] :
( ~ hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f1754,plain,
spl0_153,
inference(avatar_split_clause,[],[f108,f1752]) ).
fof(f108,axiom,
! [X2,X6,X9,X5] :
( ~ hBOOL(hAPP(X9,X6))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f1750,plain,
spl0_152,
inference(avatar_split_clause,[],[f84,f1748]) ).
fof(f1746,plain,
spl0_151,
inference(avatar_split_clause,[],[f33,f1744]) ).
fof(f1744,plain,
( spl0_151
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_in(X1,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f33,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ c_in(X1,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f1742,plain,
spl0_150,
inference(avatar_split_clause,[],[f4,f1740]) ).
fof(f4,axiom,
! [X2,X3,X8] : c_Relation_OImage(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
fof(f1683,plain,
( ~ spl0_1
| spl0_149
| ~ spl0_64
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1256,f1142,f1119,f1681,f851]) ).
fof(f1681,plain,
( spl0_149
<=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1119,plain,
( spl0_64
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1256,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_64
| ~ spl0_67 ),
inference(superposition,[],[f1143,f1120]) ).
fof(f1120,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1119]) ).
fof(f1620,plain,
spl0_148,
inference(avatar_split_clause,[],[f656,f1618]) ).
fof(f656,axiom,
! [X40,X6,X27] : ~ c_in(c_Pair(X27,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
fof(f1616,plain,
spl0_147,
inference(avatar_split_clause,[],[f652,f1614]) ).
fof(f652,axiom,
! [X40,X6,X7] : ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X40,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
fof(f1611,plain,
spl0_146,
inference(avatar_split_clause,[],[f168,f1609]) ).
fof(f1609,plain,
( spl0_146
<=> ! [X2] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f168,axiom,
! [X2] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).
fof(f1607,plain,
spl0_145,
inference(avatar_split_clause,[],[f152,f1605]) ).
fof(f152,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f1603,plain,
spl0_144,
inference(avatar_split_clause,[],[f151,f1601]) ).
fof(f1601,plain,
( spl0_144
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,X7,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) != X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f151,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,X7,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f1599,plain,
spl0_143,
inference(avatar_split_clause,[],[f150,f1597]) ).
fof(f150,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f1591,plain,
spl0_142,
inference(avatar_split_clause,[],[f72,f1589]) ).
fof(f72,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f1587,plain,
spl0_141,
inference(avatar_split_clause,[],[f71,f1585]) ).
fof(f1585,plain,
( spl0_141
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X7,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) != X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f71,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X7,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) != X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f1583,plain,
spl0_140,
inference(avatar_split_clause,[],[f70,f1581]) ).
fof(f70,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f1579,plain,
spl0_139,
inference(avatar_split_clause,[],[f3,f1577]) ).
fof(f1577,plain,
( spl0_139
<=> ! [X6,X2,X5] : c_Set_Oinsert(X6,X5,X2) = c_Set_Oinsert(X6,c_Set_Oinsert(X6,X5,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f3,axiom,
! [X2,X6,X5] : c_Set_Oinsert(X6,X5,X2) = c_Set_Oinsert(X6,c_Set_Oinsert(X6,X5,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f1559,plain,
( spl0_138
| ~ spl0_2
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f1126,f1068,f856,f1557]) ).
fof(f1557,plain,
( spl0_138
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1126,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
| ~ spl0_2
| ~ spl0_52 ),
inference(resolution,[],[f1069,f858]) ).
fof(f1511,plain,
( spl0_137
| ~ spl0_61
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1314,f1280,f1104,f1509]) ).
fof(f1280,plain,
( spl0_95
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1314,plain,
( ! [X0] : c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,X0)
| ~ spl0_61
| ~ spl0_95 ),
inference(resolution,[],[f1282,f1105]) ).
fof(f1282,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____))
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1280]) ).
fof(f1500,plain,
spl0_136,
inference(avatar_split_clause,[],[f714,f1498]) ).
fof(f1498,plain,
( spl0_136
<=> ! [X2,X5] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X5,X2),X2,X2),X2,X2) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f714,plain,
! [X2,X5] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X5,X2),X2,X2),X2,X2) = X5,
inference(definition_unfolding,[],[f533,f557]) ).
fof(f533,axiom,
! [X2,X5] : c_Relation_ODomain(c_Relation_OId__on(X5,X2),X2,X2) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
fof(f1496,plain,
spl0_135,
inference(avatar_split_clause,[],[f648,f1494]) ).
fof(f648,axiom,
! [X2,X0] : c_in(c_Pair(X0,X0,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).
fof(f1492,plain,
spl0_134,
inference(avatar_split_clause,[],[f582,f1490]) ).
fof(f1490,plain,
( spl0_134
<=> ! [X2,X5,X4] :
( ~ c_Relation_Ototal__on(X5,X4,X2)
| c_Relation_Ototal__on(X5,c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f582,axiom,
! [X2,X4,X5] :
( ~ c_Relation_Ototal__on(X5,X4,X2)
| c_Relation_Ototal__on(X5,c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
fof(f1488,plain,
spl0_133,
inference(avatar_split_clause,[],[f581,f1486]) ).
fof(f1486,plain,
( spl0_133
<=> ! [X2,X5,X4] :
( c_Relation_Ototal__on(X5,X4,X2)
| ~ c_Relation_Ototal__on(X5,c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f581,axiom,
! [X2,X4,X5] :
( c_Relation_Ototal__on(X5,X4,X2)
| ~ c_Relation_Ototal__on(X5,c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
fof(f1484,plain,
spl0_132,
inference(avatar_split_clause,[],[f536,f1482]) ).
fof(f536,axiom,
! [X2,X4] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X4,X2),X2,X2) = c_Relation_ORange(X4,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
fof(f1480,plain,
spl0_131,
inference(avatar_split_clause,[],[f530,f1478]) ).
fof(f530,axiom,
! [X2,X8] :
( c_Wellfounded_Owf(X8,X2)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X2,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
fof(f1476,plain,
spl0_130,
inference(avatar_split_clause,[],[f529,f1474]) ).
fof(f529,axiom,
! [X2,X8] :
( ~ c_Wellfounded_Owf(X8,X2)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X2,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
fof(f1472,plain,
spl0_129,
inference(avatar_split_clause,[],[f527,f1470]) ).
fof(f1470,plain,
( spl0_129
<=> ! [X2,X5,X4] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_Relation_Orefl__on(X5,c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f527,axiom,
! [X2,X4,X5] :
( ~ c_Relation_Orefl__on(X5,X4,X2)
| c_Relation_Orefl__on(X5,c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
fof(f1468,plain,
spl0_128,
inference(avatar_split_clause,[],[f526,f1466]) ).
fof(f1466,plain,
( spl0_128
<=> ! [X2,X5,X4] :
( c_Relation_Orefl__on(X5,X4,X2)
| ~ c_Relation_Orefl__on(X5,c_Relation_Oconverse(X4,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f526,axiom,
! [X2,X4,X5] :
( c_Relation_Orefl__on(X5,X4,X2)
| ~ c_Relation_Orefl__on(X5,c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
fof(f1464,plain,
spl0_127,
inference(avatar_split_clause,[],[f478,f1462]) ).
fof(f478,axiom,
! [X2,X4] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X4,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).
fof(f1460,plain,
spl0_126,
inference(avatar_split_clause,[],[f446,f1458]) ).
fof(f1458,plain,
( spl0_126
<=> ! [X2,X4] :
( c_Wellfounded_Owf(X4,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X4,X2),c_Wellfounded_Oacc(X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f446,axiom,
! [X2,X4] :
( c_Wellfounded_Owf(X4,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X4,X2),c_Wellfounded_Oacc(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
fof(f1456,plain,
spl0_125,
inference(avatar_split_clause,[],[f445,f1454]) ).
fof(f1454,plain,
( spl0_125
<=> ! [X2,X4] :
( c_Wellfounded_Owf(X4,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X4,X2),c_Wellfounded_Oacc(X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f445,axiom,
! [X2,X4] :
( c_Wellfounded_Owf(X4,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X4,X2),c_Wellfounded_Oacc(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
fof(f1452,plain,
spl0_124,
inference(avatar_split_clause,[],[f287,f1450]) ).
fof(f287,axiom,
! [X2,X3,X6,X7] : hAPP(c_snd(X3,X2),c_Pair(X6,X7,X3,X2)) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eqD_0) ).
fof(f1448,plain,
spl0_123,
inference(avatar_split_clause,[],[f284,f1446]) ).
fof(f284,axiom,
! [X2,X3,X0,X1] : hAPP(c_fst(X2,X3),c_Pair(X0,X1,X2,X3)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__conv_0) ).
fof(f1444,plain,
spl0_122,
inference(avatar_split_clause,[],[f259,f1442]) ).
fof(f259,axiom,
! [X2,X0,X1,X9] :
( ~ c_in(X0,X9,X2)
| c_in(X0,c_Set_Oinsert(X1,X9,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
fof(f1440,plain,
spl0_121,
inference(avatar_split_clause,[],[f230,f1438]) ).
fof(f1438,plain,
( spl0_121
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f230,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f1436,plain,
( spl0_120
| ~ spl0_77
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1390,f1351,f1183,f1434]) ).
fof(f1390,plain,
( ! [X0] : v_Lab____ != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| ~ spl0_77
| ~ spl0_104 ),
inference(superposition,[],[f1184,f1352]) ).
fof(f1432,plain,
spl0_119,
inference(avatar_split_clause,[],[f229,f1430]) ).
fof(f229,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f1428,plain,
spl0_118,
inference(avatar_split_clause,[],[f202,f1426]) ).
fof(f202,axiom,
! [X2,X6,X7,X5] :
( ~ hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(c_Set_Oinsert(X7,X5,X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f1424,plain,
spl0_117,
inference(avatar_split_clause,[],[f192,f1422]) ).
fof(f192,axiom,
! [X2,X9,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f1420,plain,
spl0_116,
inference(avatar_split_clause,[],[f183,f1418]) ).
fof(f183,axiom,
! [X2,X9,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f1416,plain,
spl0_115,
inference(avatar_split_clause,[],[f182,f1414]) ).
fof(f182,axiom,
! [X2,X9,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X9,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f1412,plain,
spl0_114,
inference(avatar_split_clause,[],[f148,f1410]) ).
fof(f148,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f1408,plain,
spl0_113,
inference(avatar_split_clause,[],[f136,f1406]) ).
fof(f136,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f1404,plain,
spl0_112,
inference(avatar_split_clause,[],[f122,f1402]) ).
fof(f122,axiom,
! [X2,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f1400,plain,
spl0_111,
inference(avatar_split_clause,[],[f121,f1398]) ).
fof(f121,axiom,
! [X2,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X9,tc_fun(X2,tc_bool)) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f1396,plain,
spl0_110,
inference(avatar_split_clause,[],[f104,f1394]) ).
fof(f104,axiom,
! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f1389,plain,
spl0_109,
inference(avatar_split_clause,[],[f103,f1387]) ).
fof(f103,axiom,
! [X2,X5] : c_HOL_Ominus__class_Ominus(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f1385,plain,
spl0_108,
inference(avatar_split_clause,[],[f86,f1383]) ).
fof(f1383,plain,
( spl0_108
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f86,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f1381,plain,
spl0_107,
inference(avatar_split_clause,[],[f85,f1379]) ).
fof(f85,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f1377,plain,
spl0_106,
inference(avatar_split_clause,[],[f75,f1375]) ).
fof(f75,axiom,
! [X2,X9,X5] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f1373,plain,
spl0_105,
inference(avatar_split_clause,[],[f74,f1371]) ).
fof(f74,axiom,
! [X2,X9,X5] : c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f1353,plain,
( spl0_104
| ~ spl0_92
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1349,f1320,f1244,f1351]) ).
fof(f1349,plain,
( ! [X0] : v_Lab____ = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,X0)
| ~ spl0_92
| ~ spl0_98 ),
inference(resolution,[],[f1321,f1245]) ).
fof(f1343,plain,
spl0_103,
inference(avatar_split_clause,[],[f688,f1340]) ).
fof(f688,axiom,
c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f1338,plain,
spl0_102,
inference(avatar_split_clause,[],[f554,f1336]) ).
fof(f554,axiom,
! [X2,X5] : c_Relation_OId__on(X5,X2) = c_Relation_Oconverse(c_Relation_OId__on(X5,X2),X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
fof(f1334,plain,
spl0_101,
inference(avatar_split_clause,[],[f553,f1332]) ).
fof(f553,axiom,
! [X2,X3,X4,X12] :
( ~ c_Relation_Otrans(X4,X2)
| c_Relation_Otrans(c_Relation_Oinv__image(X4,X12,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
fof(f1330,plain,
spl0_100,
inference(avatar_split_clause,[],[f543,f1328]) ).
fof(f543,axiom,
! [X2,X3,X4,X12] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Osym(c_Relation_Oinv__image(X4,X12,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
fof(f1326,plain,
spl0_99,
inference(avatar_split_clause,[],[f541,f1324]) ).
fof(f541,axiom,
! [X2,X3,X4,X12] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X4,X12,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
fof(f1322,plain,
spl0_98,
inference(avatar_split_clause,[],[f283,f1320]) ).
fof(f283,axiom,
! [X2,X0,X5] :
( ~ c_in(X0,X5,X2)
| c_Set_Oinsert(X0,X5,X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f1318,plain,
spl0_97,
inference(avatar_split_clause,[],[f94,f1316]) ).
fof(f94,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f1313,plain,
spl0_96,
inference(avatar_split_clause,[],[f93,f1311]) ).
fof(f93,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f1283,plain,
( spl0_95
| ~ spl0_62
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f1135,f1112,f1108,f1280]) ).
fof(f1135,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____))
| ~ spl0_62
| ~ spl0_63 ),
inference(resolution,[],[f1114,f1109]) ).
fof(f1114,plain,
( c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1112]) ).
fof(f1254,plain,
spl0_94,
inference(avatar_split_clause,[],[f566,f1252]) ).
fof(f566,axiom,
! [X2,X4] :
( ~ c_Relation_Oantisym(X4,X2)
| c_Relation_Oantisym(c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
fof(f1250,plain,
spl0_93,
inference(avatar_split_clause,[],[f565,f1248]) ).
fof(f565,axiom,
! [X2,X4] :
( c_Relation_Oantisym(X4,X2)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
fof(f1246,plain,
( spl0_92
| ~ spl0_61
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f1202,f1158,f1104,f1244]) ).
fof(f1158,plain,
( spl0_71
<=> hBOOL(hAPP(v_Lab____,c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1202,plain,
( ! [X0] : c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,X0)
| ~ spl0_61
| ~ spl0_71 ),
inference(resolution,[],[f1160,f1105]) ).
fof(f1160,plain,
( hBOOL(hAPP(v_Lab____,c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f1242,plain,
spl0_91,
inference(avatar_split_clause,[],[f561,f1240]) ).
fof(f561,axiom,
! [X2,X3,X4] : c_Relation_Oconverse(c_Relation_Oconverse(X4,X2,X3),X3,X2) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
fof(f1238,plain,
spl0_90,
inference(avatar_split_clause,[],[f547,f1236]) ).
fof(f547,axiom,
! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| c_Relation_Otrans(c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).
fof(f1234,plain,
spl0_89,
inference(avatar_split_clause,[],[f546,f1232]) ).
fof(f546,axiom,
! [X2,X4] :
( c_Relation_Otrans(X4,X2)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).
fof(f1230,plain,
spl0_88,
inference(avatar_split_clause,[],[f535,f1228]) ).
fof(f1228,plain,
( spl0_88
<=> ! [X2,X4] :
( c_Relation_Osym(X4,X2)
| c_Relation_Oconverse(X4,X2,X2) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f535,axiom,
! [X2,X4] :
( c_Relation_Osym(X4,X2)
| c_Relation_Oconverse(X4,X2,X2) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
fof(f1226,plain,
spl0_87,
inference(avatar_split_clause,[],[f534,f1224]) ).
fof(f534,axiom,
! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Oconverse(X4,X2,X2) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
fof(f1222,plain,
spl0_86,
inference(avatar_split_clause,[],[f522,f1220]) ).
fof(f522,axiom,
! [X2,X3,X8] : c_Relation_Orel__comp(X8,c_Relation_OId(X3),X2,X3,X3) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
fof(f1218,plain,
spl0_85,
inference(avatar_split_clause,[],[f521,f1216]) ).
fof(f521,axiom,
! [X2,X3,X8] : c_Relation_Orel__comp(c_Relation_OId(X2),X8,X2,X2,X3) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
fof(f1214,plain,
spl0_84,
inference(avatar_split_clause,[],[f515,f1212]) ).
fof(f515,axiom,
! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Osym(c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
fof(f1210,plain,
spl0_83,
inference(avatar_split_clause,[],[f514,f1208]) ).
fof(f514,axiom,
! [X2,X4] :
( c_Relation_Osym(X4,X2)
| ~ c_Relation_Osym(c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
fof(f1206,plain,
spl0_82,
inference(avatar_split_clause,[],[f506,f1204]) ).
fof(f506,axiom,
! [X2,X6,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_in(X6,c_Wellfounded_Oacc(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
fof(f1201,plain,
spl0_81,
inference(avatar_split_clause,[],[f181,f1199]) ).
fof(f181,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f1197,plain,
spl0_80,
inference(avatar_split_clause,[],[f180,f1195]) ).
fof(f180,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f1193,plain,
spl0_79,
inference(avatar_split_clause,[],[f176,f1191]) ).
fof(f176,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f1189,plain,
spl0_78,
inference(avatar_split_clause,[],[f175,f1187]) ).
fof(f175,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f1185,plain,
spl0_77,
inference(avatar_split_clause,[],[f167,f1183]) ).
fof(f167,axiom,
! [X2,X0,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X0,X5,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
fof(f1181,plain,
spl0_76,
inference(avatar_split_clause,[],[f141,f1179]) ).
fof(f141,axiom,
! [X2,X4] :
( ~ c_Wellfounded_Oacyclic(X4,X2)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
fof(f1177,plain,
spl0_75,
inference(avatar_split_clause,[],[f140,f1175]) ).
fof(f140,axiom,
! [X2,X4] :
( c_Wellfounded_Oacyclic(X4,X2)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X4,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
fof(f1173,plain,
spl0_74,
inference(avatar_split_clause,[],[f120,f1171]) ).
fof(f120,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X6,X2) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1169,plain,
spl0_73,
inference(avatar_split_clause,[],[f119,f1167]) ).
fof(f119,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X2),X2) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1165,plain,
spl0_72,
inference(avatar_split_clause,[],[f97,f1163]) ).
fof(f97,axiom,
! [X2,X0,X9] : c_lessequals(X9,c_Set_Oinsert(X0,X9,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f1161,plain,
( spl0_71
| ~ spl0_10
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f1134,f1108,f896,f1158]) ).
fof(f1134,plain,
( hBOOL(hAPP(v_Lab____,c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_10
| ~ spl0_62 ),
inference(resolution,[],[f1109,f898]) ).
fof(f898,plain,
( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f896]) ).
fof(f1156,plain,
spl0_70,
inference(avatar_split_clause,[],[f83,f1154]) ).
fof(f83,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f1152,plain,
spl0_69,
inference(avatar_split_clause,[],[f82,f1150]) ).
fof(f82,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f1148,plain,
spl0_68,
inference(avatar_split_clause,[],[f79,f1146]) ).
fof(f79,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1144,plain,
spl0_67,
inference(avatar_split_clause,[],[f78,f1142]) ).
fof(f78,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1140,plain,
spl0_66,
inference(avatar_split_clause,[],[f11,f1138]) ).
fof(f11,axiom,
! [X2,X5] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f1125,plain,
( spl0_65
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1062,f1059,f1123]) ).
fof(f1059,plain,
( spl0_50
<=> ! [X2] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1062,plain,
( ! [X2] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
| ~ spl0_50 ),
inference(forward_demodulation,[],[f1060,f196]) ).
fof(f1060,plain,
( ! [X2] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1059]) ).
fof(f1121,plain,
( spl0_64
| ~ spl0_1
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f1116,f1046,f851,f1119]) ).
fof(f1116,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_1
| ~ spl0_47 ),
inference(resolution,[],[f1047,f853]) ).
fof(f1115,plain,
spl0_63,
inference(avatar_split_clause,[],[f687,f1112]) ).
fof(f687,axiom,
c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,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) ).
fof(f1110,plain,
spl0_62,
inference(avatar_split_clause,[],[f686,f1108]) ).
fof(f686,axiom,
! [X2,X6,X13] :
( ~ c_in(X6,X13,X2)
| hBOOL(hAPP(X13,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1106,plain,
spl0_61,
inference(avatar_split_clause,[],[f685,f1104]) ).
fof(f685,axiom,
! [X2,X6,X13] :
( ~ hBOOL(hAPP(X13,X6))
| c_in(X6,X13,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1102,plain,
spl0_60,
inference(avatar_split_clause,[],[f568,f1100]) ).
fof(f1100,plain,
( spl0_60
<=> ! [X2,X5,X4] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_Relation_Orefl__on(X5,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f568,axiom,
! [X2,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X4,X2)
| c_Relation_Orefl__on(X5,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
fof(f1098,plain,
spl0_59,
inference(avatar_split_clause,[],[f559,f1096]) ).
fof(f559,axiom,
! [X2,X5] : c_Relation_ORange(c_Relation_OId__on(X5,X2),X2,X2) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
fof(f1094,plain,
spl0_58,
inference(avatar_split_clause,[],[f549,f1092]) ).
fof(f549,axiom,
! [X2,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
fof(f1090,plain,
spl0_57,
inference(avatar_split_clause,[],[f548,f1088]) ).
fof(f548,axiom,
! [X2] : c_Relation_OId(X2) = c_Relation_Oconverse(c_Relation_OId(X2),X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
fof(f1086,plain,
spl0_56,
inference(avatar_split_clause,[],[f531,f1084]) ).
fof(f531,axiom,
! [X2,X5] : c_Relation_OImage(c_Relation_OId(X2),X5,X2,X2) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
fof(f1082,plain,
spl0_55,
inference(avatar_split_clause,[],[f511,f1080]) ).
fof(f511,axiom,
! [X2,X4] :
( ~ c_Relation_Otrans(X4,X2)
| c_Transitive__Closure_Otrancl(X4,X2) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).
fof(f1078,plain,
spl0_54,
inference(avatar_split_clause,[],[f509,f1076]) ).
fof(f509,axiom,
! [X2,X4] :
( ~ c_Relation_Osym(X4,X2)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
fof(f1074,plain,
spl0_53,
inference(avatar_split_clause,[],[f303,f1072]) ).
fof(f303,axiom,
! [X2,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X5,tc_fun(X2,tc_bool)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f1070,plain,
spl0_52,
inference(avatar_split_clause,[],[f302,f1068]) ).
fof(f302,axiom,
! [X2,X6] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X2) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f1066,plain,
spl0_51,
inference(avatar_split_clause,[],[f210,f1064]) ).
fof(f1064,plain,
( spl0_51
<=> ! [X2,X5,X4] :
( ~ c_Order__Relation_Ostrict__linear__order__on(X5,X4,X2)
| c_Relation_Ototal__on(X5,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f210,axiom,
! [X2,X4,X5] :
( ~ c_Order__Relation_Ostrict__linear__order__on(X5,X4,X2)
| c_Relation_Ototal__on(X5,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).
fof(f1061,plain,
spl0_50,
inference(avatar_split_clause,[],[f199,f1059]) ).
fof(f199,axiom,
! [X2] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).
fof(f1056,plain,
spl0_49,
inference(avatar_split_clause,[],[f157,f1054]) ).
fof(f1054,plain,
( spl0_49
<=> ! [X2] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f157,axiom,
! [X2] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).
fof(f1052,plain,
spl0_48,
inference(avatar_split_clause,[],[f52,f1050]) ).
fof(f52,axiom,
! [X2,X3,X18,X26] : hAPP(c_COMBK(X18,X2,X3),X26) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f1048,plain,
spl0_47,
inference(avatar_split_clause,[],[f43,f1046]) ).
fof(f43,axiom,
! [X2,X6] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X2) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f1044,plain,
spl0_46,
inference(avatar_split_clause,[],[f42,f1042]) ).
fof(f42,axiom,
! [X2,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_fun(X2,tc_bool)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f1039,plain,
spl0_45,
inference(avatar_split_clause,[],[f709,f1037]) ).
fof(f1037,plain,
( spl0_45
<=> ! [X38,X2,X37] :
( X37 = X38
| ~ c_fequal(X37,X38,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f709,axiom,
! [X2,X38,X37] :
( X37 = X38
| ~ c_fequal(X37,X38,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1035,plain,
spl0_44,
inference(avatar_split_clause,[],[f583,f1033]) ).
fof(f1033,plain,
( spl0_44
<=> ! [X2,X5,X4] :
( c_Relation_Otrans(X4,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f583,axiom,
! [X2,X4,X5] :
( c_Relation_Otrans(X4,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
fof(f1031,plain,
spl0_43,
inference(avatar_split_clause,[],[f571,f1029]) ).
fof(f1029,plain,
( spl0_43
<=> ! [X2,X5,X4] :
( c_Relation_Osym(X4,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f571,axiom,
! [X2,X4,X5] :
( c_Relation_Osym(X4,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
fof(f1027,plain,
spl0_42,
inference(avatar_split_clause,[],[f350,f1025]) ).
fof(f1025,plain,
( spl0_42
<=> ! [X2,X5,X4] :
( c_Relation_Oirrefl(X4,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X5,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f350,axiom,
! [X2,X4,X5] :
( c_Relation_Oirrefl(X4,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X5,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).
fof(f1023,plain,
spl0_41,
inference(avatar_split_clause,[],[f292,f1021]) ).
fof(f292,axiom,
! [X2,X6,X5] : hBOOL(hAPP(c_Set_Oinsert(X6,X5,X2),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f1019,plain,
spl0_40,
inference(avatar_split_clause,[],[f291,f1017]) ).
fof(f1017,plain,
( spl0_40
<=> ! [X2,X5,X4] :
( c_Relation_Otrans(X4,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X5,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f291,axiom,
! [X2,X4,X5] :
( c_Relation_Otrans(X4,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X5,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).
fof(f1015,plain,
spl0_39,
inference(avatar_split_clause,[],[f276,f1013]) ).
fof(f1013,plain,
( spl0_39
<=> ! [X6,X2,X9] : c_in(X6,c_Set_Oinsert(X6,X9,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f276,axiom,
! [X2,X6,X9] : c_in(X6,c_Set_Oinsert(X6,X9,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f1011,plain,
spl0_38,
inference(avatar_split_clause,[],[f266,f1009]) ).
fof(f266,axiom,
! [X2,X6] : ~ c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
fof(f1007,plain,
spl0_37,
inference(avatar_split_clause,[],[f172,f1005]) ).
fof(f172,axiom,
! [X2,X4] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
fof(f1003,plain,
spl0_36,
inference(avatar_split_clause,[],[f126,f1001]) ).
fof(f126,axiom,
! [X2,X6] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f999,plain,
spl0_35,
inference(avatar_split_clause,[],[f9,f997]) ).
fof(f9,axiom,
! [X2,X6] :
( ~ class_Orderings_Obot(X2)
| c_lessequals(c_Orderings_Obot__class_Obot(X2),X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f995,plain,
spl0_34,
inference(avatar_split_clause,[],[f698,f993]) ).
fof(f993,plain,
( spl0_34
<=> ! [X55,X56] :
( ~ class_HOL_Oord(X56)
| class_HOL_Oord(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f698,axiom,
! [X56,X55] :
( ~ class_HOL_Oord(X56)
| class_HOL_Oord(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f991,plain,
spl0_33,
inference(avatar_split_clause,[],[f697,f989]) ).
fof(f989,plain,
( spl0_33
<=> ! [X55,X56] :
( ~ class_Orderings_Obot(X56)
| class_Orderings_Obot(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f697,axiom,
! [X56,X55] :
( ~ class_Orderings_Obot(X56)
| class_Orderings_Obot(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f987,plain,
spl0_32,
inference(avatar_split_clause,[],[f696,f985]) ).
fof(f985,plain,
( spl0_32
<=> ! [X55,X56] :
( ~ class_Orderings_Oorder(X56)
| class_Orderings_Oorder(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f696,axiom,
! [X56,X55] :
( ~ class_Orderings_Oorder(X56)
| class_Orderings_Oorder(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f983,plain,
spl0_31,
inference(avatar_split_clause,[],[f695,f981]) ).
fof(f695,axiom,
! [X56,X55] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Olattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f979,plain,
spl0_30,
inference(avatar_split_clause,[],[f694,f977]) ).
fof(f977,plain,
( spl0_30
<=> ! [X55,X56] :
( ~ class_Orderings_Opreorder(X56)
| class_Orderings_Opreorder(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f694,axiom,
! [X56,X55] :
( ~ class_Orderings_Opreorder(X56)
| class_Orderings_Opreorder(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f975,plain,
spl0_29,
inference(avatar_split_clause,[],[f693,f973]) ).
fof(f693,axiom,
! [X56,X55] :
( ~ class_Lattices_Obounded__lattice(X56)
| class_Lattices_Obounded__lattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f971,plain,
spl0_28,
inference(avatar_split_clause,[],[f692,f969]) ).
fof(f969,plain,
( spl0_28
<=> ! [X55,X56] :
( ~ class_Lattices_Odistrib__lattice(X56)
| class_Lattices_Odistrib__lattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f692,axiom,
! [X56,X55] :
( ~ class_Lattices_Odistrib__lattice(X56)
| class_Lattices_Odistrib__lattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f967,plain,
spl0_27,
inference(avatar_split_clause,[],[f691,f965]) ).
fof(f691,axiom,
! [X56,X55] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Olower__semilattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f963,plain,
spl0_26,
inference(avatar_split_clause,[],[f690,f961]) ).
fof(f690,axiom,
! [X56,X55] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Oupper__semilattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f959,plain,
spl0_25,
inference(avatar_split_clause,[],[f540,f957]) ).
fof(f957,plain,
( spl0_25
<=> ! [X2,X5] : c_Relation_Orefl__on(X5,c_Relation_OId__on(X5,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f540,axiom,
! [X2,X5] : c_Relation_Orefl__on(X5,c_Relation_OId__on(X5,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
fof(f955,plain,
spl0_24,
inference(avatar_split_clause,[],[f507,f953]) ).
fof(f953,plain,
( spl0_24
<=> ! [X2,X5] : c_Relation_Osingle__valued(c_Relation_OId__on(X5,X2),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f507,axiom,
! [X2,X5] : c_Relation_Osingle__valued(c_Relation_OId__on(X5,X2),X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
fof(f951,plain,
spl0_23,
inference(avatar_split_clause,[],[f320,f949]) ).
fof(f320,axiom,
! [X2,X6] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X6,X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f947,plain,
spl0_22,
inference(avatar_split_clause,[],[f319,f945]) ).
fof(f319,axiom,
! [X2,X6] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X6,X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f943,plain,
spl0_21,
inference(avatar_split_clause,[],[f315,f941]) ).
fof(f315,axiom,
! [X2,X5] : c_lessequals(X5,X5,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
fof(f939,plain,
spl0_20,
inference(avatar_split_clause,[],[f87,f937]) ).
fof(f87,axiom,
! [X2,X4] :
( ~ c_Wellfounded_Owf(X4,X2)
| c_Wellfounded_Oacyclic(X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
fof(f935,plain,
spl0_19,
inference(avatar_split_clause,[],[f539,f933]) ).
fof(f933,plain,
( spl0_19
<=> ! [X2,X5] : c_Relation_Osym(c_Relation_OId__on(X5,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f539,axiom,
! [X2,X5] : c_Relation_Osym(c_Relation_OId__on(X5,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
fof(f931,plain,
spl0_18,
inference(avatar_split_clause,[],[f537,f929]) ).
fof(f537,axiom,
! [X2,X4] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X4,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
fof(f927,plain,
spl0_17,
inference(avatar_split_clause,[],[f532,f925]) ).
fof(f925,plain,
( spl0_17
<=> ! [X2] : c_Relation_Osingle__valued(c_Relation_OId(X2),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f532,axiom,
! [X2] : c_Relation_Osingle__valued(c_Relation_OId(X2),X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
fof(f923,plain,
spl0_16,
inference(avatar_split_clause,[],[f523,f921]) ).
fof(f921,plain,
( spl0_16
<=> ! [X2,X5] : c_Relation_Oantisym(c_Relation_OId__on(X5,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f523,axiom,
! [X2,X5] : c_Relation_Oantisym(c_Relation_OId__on(X5,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
fof(f919,plain,
spl0_15,
inference(avatar_split_clause,[],[f520,f917]) ).
fof(f520,axiom,
! [X2,X5] : c_Relation_Otrans(c_Relation_OId__on(X5,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
fof(f915,plain,
spl0_14,
inference(avatar_split_clause,[],[f708,f913]) ).
fof(f913,plain,
( spl0_14
<=> ! [X6,X2] : c_fequal(X6,X6,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f708,axiom,
! [X2,X6] : c_fequal(X6,X6,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f911,plain,
spl0_13,
inference(avatar_split_clause,[],[f562,f909]) ).
fof(f562,axiom,
! [X2] : c_Relation_Otrans(c_Relation_OId(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).
fof(f907,plain,
spl0_12,
inference(avatar_split_clause,[],[f556,f905]) ).
fof(f905,plain,
( spl0_12
<=> ! [X2] : c_Relation_Oantisym(c_Relation_OId(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f556,axiom,
! [X2] : c_Relation_Oantisym(c_Relation_OId(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
fof(f903,plain,
spl0_11,
inference(avatar_split_clause,[],[f519,f901]) ).
fof(f901,plain,
( spl0_11
<=> ! [X2] : c_Relation_Osym(c_Relation_OId(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f519,axiom,
! [X2] : c_Relation_Osym(c_Relation_OId(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
fof(f899,plain,
spl0_10,
inference(avatar_split_clause,[],[f689,f896]) ).
fof(f689,axiom,
c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f894,plain,
spl0_9,
inference(avatar_split_clause,[],[f707,f891]) ).
fof(f707,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f889,plain,
spl0_8,
inference(avatar_split_clause,[],[f706,f886]) ).
fof(f886,plain,
( spl0_8
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f706,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f884,plain,
spl0_7,
inference(avatar_split_clause,[],[f705,f881]) ).
fof(f881,plain,
( spl0_7
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f705,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f879,plain,
spl0_6,
inference(avatar_split_clause,[],[f704,f876]) ).
fof(f704,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f874,plain,
spl0_5,
inference(avatar_split_clause,[],[f703,f871]) ).
fof(f871,plain,
( spl0_5
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f703,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f869,plain,
spl0_4,
inference(avatar_split_clause,[],[f702,f866]) ).
fof(f702,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f864,plain,
spl0_3,
inference(avatar_split_clause,[],[f701,f861]) ).
fof(f701,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f859,plain,
spl0_2,
inference(avatar_split_clause,[],[f700,f856]) ).
fof(f700,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f854,plain,
spl0_1,
inference(avatar_split_clause,[],[f699,f851]) ).
fof(f699,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT074-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Apr 29 22:24:02 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (5035)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.41 % (5039)WARNING: value z3 for option sas not known
% 0.22/0.41 % (5039)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.41 % (5037)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.41 % (5040)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.41 % (5042)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)
% 0.22/0.41 % (5038)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.41 % (5043)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)
% 0.22/0.41 % (5041)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)
% 1.87/0.66 TRYING [1]
% 2.12/0.70 TRYING [2]
% 6.20/1.30 TRYING [1]
% 6.91/1.43 TRYING [3]
% 6.91/1.43 TRYING [2]
% 8.80/1.66 TRYING [1]
% 9.14/1.69 TRYING [2]
% 12.23/2.14 TRYING [3]
% 19.81/3.25 % (5041)First to succeed.
% 20.22/3.31 % (5041)Refutation found. Thanks to Tanya!
% 20.22/3.31 % SZS status Unsatisfiable for theBenchmark
% 20.22/3.31 % SZS output start Proof for theBenchmark
% See solution above
% 20.22/3.35 % (5041)------------------------------
% 20.22/3.35 % (5041)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 20.22/3.35 % (5041)Termination reason: Refutation
% 20.22/3.35
% 20.22/3.36 % (5041)Memory used [KB]: 27437
% 20.22/3.36 % (5041)Time elapsed: 2.885 s
% 20.22/3.36 % (5041)Instructions burned: 6625 (million)
% 20.22/3.36 % (5041)------------------------------
% 20.22/3.36 % (5041)------------------------------
% 20.22/3.36 % (5035)Success in time 2.978 s
%------------------------------------------------------------------------------