TSTP Solution File: SWV909-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV909-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:07:55 EDT 2024
% Result : Unsatisfiable 74.15s 10.94s
% Output : Refutation 74.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2305
% Syntax : Number of formulae : 6179 ( 696 unt; 0 def)
% Number of atoms : 20029 (2189 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 25610 (11760 ~;12057 |; 0 &)
% (1793 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 1818 (1816 usr;1794 prp; 0-9 aty)
% Number of functors : 80 ( 80 usr; 12 con; 0-6 aty)
% Number of variables : 16131 (16131 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f121205,plain,
$false,
inference(avatar_sat_refutation,[],[f965,f970,f975,f980,f985,f990,f995,f1000,f1005,f1010,f1015,f1020,f1025,f1030,f1035,f1040,f1045,f1050,f1055,f1060,f1065,f1070,f1075,f1080,f1084,f1088,f1092,f1096,f1100,f1104,f1108,f1113,f1117,f1121,f1125,f1129,f1133,f1137,f1141,f1145,f1149,f1153,f1157,f1161,f1165,f1169,f1173,f1178,f1185,f1189,f1193,f1197,f1201,f1205,f1209,f1216,f1220,f1224,f1229,f1233,f1237,f1241,f1246,f1250,f1254,f1258,f1262,f1267,f1271,f1275,f1279,f1284,f1288,f1293,f1297,f1301,f1305,f1309,f1313,f1317,f1321,f1326,f1330,f1334,f1338,f1342,f1346,f1350,f1355,f1363,f1377,f1381,f1385,f1389,f1393,f1398,f1403,f1407,f1411,f1415,f1419,f1423,f1427,f1431,f1435,f1439,f1444,f1448,f1452,f1457,f1461,f1465,f1469,f1478,f1482,f1486,f1499,f1506,f1512,f1525,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1557,f1561,f1565,f1569,f1581,f1600,f1604,f1608,f1612,f1617,f1621,f1625,f1629,f1633,f1637,f1641,f1645,f1649,f1653,f1657,f1662,f1666,f1670,f1674,f1678,f1683,f1687,f1692,f1696,f1701,f1705,f1709,f1724,f1743,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1837,f1841,f1846,f1850,f1854,f1858,f1862,f1866,f1870,f1874,f1878,f1882,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f1915,f1924,f1991,f1995,f1999,f2003,f2007,f2011,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2058,f2062,f2066,f2070,f2074,f2078,f2083,f2087,f2091,f2095,f2099,f2103,f2107,f2111,f2249,f2253,f2257,f2261,f2265,f2269,f2273,f2277,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2313,f2317,f2321,f2330,f2489,f2493,f2497,f2501,f2505,f2518,f2522,f2526,f2530,f2534,f2538,f2542,f2546,f2550,f2554,f2558,f2562,f2566,f2570,f2574,f2578,f2582,f2914,f2918,f2922,f2930,f2934,f2938,f2942,f2946,f2950,f2954,f2958,f2962,f2966,f2970,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3002,f3006,f3010,f3014,f3018,f3022,f3026,f3139,f3231,f3349,f3362,f3366,f3370,f3374,f3378,f3382,f3386,f3390,f3394,f3398,f3402,f3406,f3410,f3414,f3418,f3422,f3426,f3431,f3436,f3441,f3464,f3468,f3669,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3943,f3947,f3951,f3955,f3959,f3963,f3967,f3971,f3975,f3979,f3983,f3987,f3991,f4281,f4317,f4321,f4325,f4329,f4333,f4337,f4342,f4346,f4350,f4354,f4358,f4362,f4366,f4370,f4374,f4378,f4382,f4386,f4390,f4394,f4398,f4402,f4407,f4411,f4517,f4834,f5020,f5024,f5028,f5032,f5036,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5068,f5078,f5419,f5465,f5469,f5473,f5477,f5481,f5485,f5489,f5493,f5497,f5501,f5505,f5509,f5513,f5517,f5521,f5525,f5529,f5533,f5537,f5541,f5545,f5549,f5553,f5557,f5561,f5565,f5569,f5744,f5986,f6410,f6414,f6418,f6422,f6426,f6430,f6434,f6438,f6442,f6670,f6689,f6693,f6697,f6701,f6705,f6709,f6713,f6717,f6721,f6725,f6730,f6734,f6738,f6742,f6746,f6750,f6754,f6758,f6762,f6766,f6770,f6774,f7482,f7486,f7490,f7494,f7498,f7502,f7506,f7529,f7864,f7911,f7915,f7919,f7923,f7927,f7931,f7935,f7939,f7943,f7947,f7951,f7955,f8408,f8412,f8416,f8420,f8424,f8428,f8432,f8436,f8440,f8444,f8448,f8452,f8456,f8460,f8638,f9224,f9228,f9232,f9236,f9313,f9317,f9321,f9325,f9329,f9333,f9337,f9341,f9478,f9482,f9486,f9490,f9494,f9498,f9502,f9506,f9510,f9514,f9518,f9522,f9526,f9530,f9534,f9538,f9542,f9546,f10318,f10322,f10326,f10330,f10334,f10338,f10512,f10571,f10575,f10579,f10583,f10587,f10591,f10602,f10606,f11031,f11035,f11039,f11043,f11047,f11051,f11055,f11059,f11642,f11646,f11650,f11654,f11725,f11729,f11934,f11938,f11942,f11952,f11956,f11960,f11964,f11968,f11972,f12037,f12104,f12108,f12112,f12134,f12202,f12206,f12210,f12359,f12380,f12384,f12388,f12463,f12471,f12475,f12479,f12512,f12563,f12567,f12579,f12587,f12592,f12596,f12619,f12839,f12844,f12849,f12854,f12858,f13038,f13043,f13047,f13051,f13055,f13331,f13335,f13339,f13343,f13347,f13351,f13355,f13359,f13363,f13367,f13371,f13375,f13410,f13526,f13600,f13604,f13608,f13612,f13616,f13620,f13627,f13631,f13635,f13639,f13643,f13647,f13651,f13655,f13659,f13663,f13667,f13671,f13675,f13679,f14155,f14631,f14635,f14639,f14643,f14647,f14651,f14655,f14659,f14666,f17424,f17432,f17436,f17446,f17466,f17584,f26987,f27533,f28396,f28401,f28405,f28409,f28413,f28417,f28430,f28611,f28615,f28619,f28623,f28627,f28631,f28635,f28639,f28643,f28647,f28651,f28655,f28662,f28666,f28670,f28674,f28678,f28696,f28700,f28704,f28708,f28713,f28755,f28987,f28992,f28996,f29000,f29004,f29008,f29012,f29016,f29020,f29024,f29028,f29033,f29037,f29041,f29045,f29049,f29053,f29057,f29061,f29065,f29069,f29073,f29077,f29081,f29085,f29089,f29093,f29097,f29101,f29105,f29109,f29113,f29117,f29121,f29125,f29129,f29133,f29137,f29141,f29145,f29149,f29153,f29157,f29161,f29165,f29169,f29173,f29177,f29181,f29185,f29189,f29306,f29310,f29314,f29318,f29322,f29489,f29835,f30223,f30646,f31069,f31348,f31352,f31356,f31360,f31364,f31368,f31372,f31407,f31411,f31415,f31419,f31423,f31427,f31431,f31435,f31439,f31443,f31478,f31482,f31486,f31490,f31494,f31498,f31502,f31506,f31510,f31514,f31519,f31523,f31527,f31531,f31535,f31539,f31543,f31571,f31575,f31580,f31584,f31588,f31722,f31726,f31730,f31734,f31738,f31926,f32868,f32899,f32903,f32907,f32911,f32915,f32919,f32923,f32927,f32931,f32935,f32939,f32943,f32947,f32951,f32955,f32959,f32963,f32967,f32971,f32975,f32979,f32983,f32987,f32991,f32996,f33000,f33004,f33008,f33012,f33016,f33026,f33030,f33034,f33038,f33042,f33046,f33050,f33054,f33058,f33062,f33078,f33082,f33086,f33090,f33094,f33098,f33102,f33106,f33110,f33114,f33166,f33170,f33174,f33178,f33182,f33186,f33190,f33230,f33234,f33284,f33288,f33292,f33296,f33300,f33304,f33308,f33312,f33316,f33320,f33324,f33328,f33332,f33336,f33340,f33344,f33348,f33978,f34292,f34326,f34864,f36338,f36342,f36346,f36350,f36355,f36359,f36363,f36367,f36371,f36375,f36379,f36383,f36387,f36391,f36460,f36464,f36468,f36472,f36476,f36480,f36484,f36488,f36492,f36496,f36552,f36556,f36560,f36564,f36568,f36572,f36579,f36587,f36591,f36595,f36599,f36603,f36607,f36611,f36615,f36619,f36623,f36627,f36631,f36636,f36640,f36644,f36648,f36652,f36656,f36660,f36664,f36668,f36672,f36676,f36680,f36684,f36839,f36843,f36847,f36851,f36855,f36859,f36863,f36867,f36871,f36875,f36879,f36883,f36887,f36891,f36895,f36899,f36903,f36907,f36911,f36915,f40035,f40828,f40832,f40836,f40840,f40844,f40848,f40852,f40856,f40860,f40864,f40868,f40872,f40876,f40880,f40884,f40888,f40892,f40896,f40900,f40904,f40908,f40912,f40916,f40920,f40924,f40928,f40932,f40936,f40940,f40944,f40948,f40952,f40956,f40960,f40964,f40968,f40972,f40976,f40980,f40984,f40988,f40992,f40996,f41000,f41011,f41302,f41306,f41479,f41483,f41487,f41491,f41495,f41511,f41515,f41519,f41523,f41527,f41531,f41535,f41539,f41543,f41547,f42039,f42852,f44024,f44028,f44032,f44036,f44040,f44048,f44052,f44056,f44060,f44064,f44069,f44074,f44078,f44082,f44086,f44090,f44094,f44098,f44102,f44106,f44110,f44114,f44118,f44122,f44126,f44130,f44131,f44135,f44139,f44143,f44147,f44151,f44155,f44159,f44163,f44167,f44171,f44190,f44194,f44198,f44202,f44206,f44210,f44214,f44218,f44222,f44226,f44230,f44234,f44238,f44245,f44252,f44364,f44368,f44372,f44376,f44380,f44384,f44388,f44392,f44396,f44400,f44404,f44408,f44412,f44417,f44421,f44425,f44429,f44433,f44437,f44441,f44445,f44449,f44453,f44457,f44461,f44465,f44469,f44473,f44477,f44481,f44485,f44489,f44493,f44497,f44501,f44532,f44536,f44540,f44544,f44607,f44784,f44963,f47482,f47486,f47490,f47494,f47498,f47502,f47534,f47538,f47542,f47546,f47550,f47554,f47558,f47562,f47566,f47570,f47605,f47609,f47613,f47617,f47621,f47625,f47629,f47633,f47637,f47641,f47693,f47697,f47701,f47705,f47709,f47713,f47717,f47721,f47725,f47729,f47733,f47737,f47741,f47745,f47749,f47753,f47757,f47761,f47765,f47769,f47773,f47812,f47816,f47820,f47824,f47828,f47832,f47836,f47840,f47844,f47848,f47852,f47856,f47860,f47864,f47868,f47872,f47876,f47880,f47884,f47888,f47892,f47896,f47900,f47904,f47908,f47912,f47916,f47920,f47924,f47928,f47932,f47936,f47940,f47944,f47948,f47952,f47957,f47961,f47965,f47969,f47973,f47977,f48205,f49240,f49622,f49992,f50314,f51779,f52622,f55150,f55154,f55158,f55162,f55166,f55170,f55174,f55187,f55191,f55195,f55199,f55203,f55207,f55211,f55215,f55219,f55223,f55230,f55234,f55238,f55242,f55246,f55250,f55254,f55258,f55262,f55266,f55385,f55389,f55393,f55397,f55401,f55405,f55409,f55413,f55417,f55421,f55572,f55576,f55580,f55584,f55588,f55592,f55596,f55600,f55604,f55608,f55728,f55732,f55736,f55740,f55744,f55748,f55752,f55756,f55760,f55764,f55849,f55853,f55857,f55861,f55865,f55869,f55873,f55877,f55881,f55885,f56008,f56012,f56016,f56020,f56024,f56028,f56032,f56036,f56040,f56044,f56048,f56052,f56056,f56060,f56064,f56068,f56072,f56076,f56080,f56084,f56088,f56145,f56149,f56153,f56157,f56161,f56165,f56169,f56173,f56177,f56181,f56188,f56192,f56196,f56200,f56204,f56208,f56212,f56216,f56220,f56224,f56228,f56232,f56236,f56240,f56244,f56248,f56252,f56256,f56260,f56264,f56268,f56272,f56276,f56280,f56284,f56288,f56292,f56296,f56300,f56304,f56308,f56312,f56316,f56320,f56324,f56328,f56332,f56336,f56340,f56344,f56348,f56352,f56356,f56360,f56364,f56368,f56372,f56376,f56380,f56384,f56388,f56392,f56396,f56400,f56404,f56408,f56412,f56416,f56420,f56424,f56428,f56432,f56436,f56440,f56444,f56448,f56452,f56456,f56460,f56464,f56468,f56472,f56476,f56480,f56839,f57649,f57850,f58400,f59167,f59849,f60639,f61671,f62430,f63275,f64222,f65119,f66125,f68320,f70479,f72362,f72366,f72370,f72374,f72378,f72382,f72386,f72397,f72401,f72405,f72409,f72413,f72417,f72421,f72425,f72429,f72433,f72441,f72445,f72449,f72453,f72457,f72461,f72465,f72469,f72473,f72477,f72492,f72496,f72500,f72504,f72508,f72512,f72516,f72520,f72524,f72528,f72601,f72605,f72609,f72613,f72617,f72621,f72625,f72629,f72633,f72637,f72647,f72651,f72655,f72659,f72663,f72667,f72671,f72675,f72679,f72683,f72694,f72698,f72702,f72706,f72713,f72750,f72754,f72758,f72762,f72766,f73461,f73465,f73469,f73473,f73481,f73485,f73489,f73493,f73497,f73501,f73505,f73509,f73513,f73517,f73532,f73536,f73737,f73741,f73745,f73749,f73753,f73757,f73761,f73771,f73775,f73831,f74020,f74024,f74028,f74032,f74036,f74047,f74051,f74055,f74059,f74063,f74067,f74071,f74075,f74079,f74083,f74091,f74095,f74099,f74103,f74107,f74111,f74115,f74119,f74123,f74127,f74142,f74146,f74150,f74154,f74158,f74162,f74166,f74170,f74174,f74178,f81452,f82793,f85196,f85849,f87173,f87882,f88193,f88197,f88201,f88205,f88209,f88213,f88217,f88221,f88225,f88229,f88233,f88237,f88241,f88245,f88249,f88253,f88257,f88261,f88455,f88459,f88463,f88467,f88471,f88475,f88479,f88483,f88487,f88491,f88495,f88499,f88503,f88507,f88511,f88515,f88519,f88523,f88527,f88531,f88535,f88794,f88798,f88802,f88806,f88810,f88814,f88818,f88822,f88826,f88830,f88835,f88839,f88843,f88847,f88851,f88855,f88859,f88863,f88867,f88871,f88875,f88879,f88883,f88887,f88891,f88895,f88899,f88903,f88907,f88911,f88915,f88919,f88923,f88927,f88931,f88935,f88939,f88943,f88947,f88951,f88955,f88959,f89026,f89030,f89034,f89038,f89042,f89046,f89050,f89054,f89058,f89062,f89066,f89070,f89074,f89078,f89082,f89086,f89090,f89094,f89098,f89102,f89106,f89110,f89114,f89118,f89122,f89126,f89130,f89134,f89138,f89142,f89146,f89150,f89189,f89193,f89197,f89201,f89205,f89209,f89213,f89217,f89221,f89225,f89492,f89496,f89500,f89504,f89508,f89512,f89516,f89520,f89524,f89528,f89532,f89536,f89540,f89544,f89548,f89552,f89556,f89560,f89564,f91181,f91798,f101277,f105495,f106069,f106074,f106078,f106082,f106086,f106090,f106094,f106179,f106183,f106187,f106191,f106195,f106199,f106203,f106207,f106211,f106215,f106219,f106223,f106227,f106231,f106235,f106239,f106243,f106247,f106251,f106255,f106259,f106344,f106348,f106352,f106356,f106360,f106364,f106368,f106372,f106376,f106380,f106384,f106388,f106392,f106396,f106400,f106404,f106408,f106412,f106416,f106420,f106424,f106431,f106435,f106439,f106443,f106447,f106451,f106455,f106459,f106463,f106467,f106471,f106475,f106479,f106483,f106487,f106491,f106495,f106499,f106503,f106507,f106853,f106857,f107097,f107101,f107105,f107109,f107444,f107448,f107452,f107457,f107461,f107465,f107469,f107473,f107477,f107481,f107485,f107489,f107493,f107497,f107501,f107505,f107509,f107513,f107517,f107521,f107525,f107529,f107533,f107537,f107541,f107558,f107562,f107566,f107570,f107574,f107578,f107582,f107586,f107590,f107594,f107612,f107616,f107620,f107624,f107628,f107632,f107636,f107640,f107905,f108169,f108173,f108177,f108181,f108185,f108189,f108193,f108197,f108201,f108341,f108345,f108349,f108353,f108357,f108599,f109513,f110190,f111233,f118454,f119667,f121204]) ).
fof(f121204,plain,
( spl0_56
| spl0_49
| ~ spl0_70
| ~ spl0_1761 ),
inference(avatar_split_clause,[],[f119970,f107580,f1273,f1182,f1213]) ).
fof(f1213,plain,
( spl0_56
<=> hBOOL(c_False) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1182,plain,
( spl0_49
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1273,plain,
( spl0_70
<=> ! [X30,X0,X29,X7] : hAPP(c_COMBK(X29,X0,X7),X30) = X29 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f107580,plain,
( spl0_1761
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).
fof(f119970,plain,
( hBOOL(c_False)
| spl0_49
| ~ spl0_70
| ~ spl0_1761 ),
inference(forward_demodulation,[],[f119913,f1274]) ).
fof(f1274,plain,
( ! [X29,X0,X7,X30] : hAPP(c_COMBK(X29,X0,X7),X30) = X29
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f119913,plain,
( hBOOL(hAPP(c_COMBK(c_False,tc_bool,tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_Q,v_c)))
| spl0_49
| ~ spl0_1761 ),
inference(resolution,[],[f107581,f1184]) ).
fof(f1184,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a)),t_a)
| spl0_49 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f107581,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) )
| ~ spl0_1761 ),
inference(avatar_component_clause,[],[f107580]) ).
fof(f119667,plain,
( spl0_1793
| ~ spl0_113
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106270,f106217,f1467,f119665]) ).
fof(f119665,plain,
( spl0_1793
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool) != X1
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).
fof(f1467,plain,
( spl0_113
<=> ! [X29,X0,X3] :
( c_COMBK(c_False,tc_bool,X0) != X29
| ~ hBOOL(hAPP(X29,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f106217,plain,
( spl0_1672
<=> ! [X0] : c_COMBK(c_False,tc_bool,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f106270,plain,
( ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool) != X1
| ~ hBOOL(hAPP(X1,X2)) )
| ~ spl0_113
| ~ spl0_1672 ),
inference(superposition,[],[f1468,f106218]) ).
fof(f106218,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool)
| ~ spl0_1672 ),
inference(avatar_component_clause,[],[f106217]) ).
fof(f1468,plain,
( ! [X3,X0,X29] :
( c_COMBK(c_False,tc_bool,X0) != X29
| ~ hBOOL(hAPP(X29,X3)) )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1467]) ).
fof(f118454,plain,
( spl0_1792
| ~ spl0_579
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106265,f106217,f12851,f118452]) ).
fof(f118452,plain,
( spl0_1792
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).
fof(f12851,plain,
( spl0_579
<=> c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(c_False,tc_bool,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f106265,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool))
| ~ spl0_579
| ~ spl0_1672 ),
inference(superposition,[],[f12853,f106218]) ).
fof(f12853,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(c_False,tc_bool,tc_bool))
| ~ spl0_579 ),
inference(avatar_component_clause,[],[f12851]) ).
fof(f111233,plain,
( spl0_1791
| ~ spl0_386
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106266,f106217,f5416,f111231]) ).
fof(f111231,plain,
( spl0_1791
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).
fof(f5416,plain,
( spl0_386
<=> c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_COMBK(c_False,tc_bool,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f106266,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool))
| ~ spl0_386
| ~ spl0_1672 ),
inference(superposition,[],[f5418,f106218]) ).
fof(f5418,plain,
( c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_COMBK(c_False,tc_bool,tc_bool))
| ~ spl0_386 ),
inference(avatar_component_clause,[],[f5416]) ).
fof(f110190,plain,
( spl0_1790
| ~ spl0_726
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106262,f106217,f30221,f110188]) ).
fof(f110188,plain,
( spl0_1790
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_False,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).
fof(f30221,plain,
( spl0_726
<=> ! [X0] : c_COMBK(c_False,tc_bool,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f106262,plain,
( ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_False,tc_bool)
| ~ spl0_726
| ~ spl0_1672 ),
inference(superposition,[],[f106218,f30222]) ).
fof(f30222,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool)
| ~ spl0_726 ),
inference(avatar_component_clause,[],[f30221]) ).
fof(f109513,plain,
( spl0_1789
| ~ spl0_728
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106261,f106217,f31067,f109511]) ).
fof(f109511,plain,
( spl0_1789
<=> ! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_False,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).
fof(f31067,plain,
( spl0_728
<=> ! [X0] : c_COMBK(c_False,tc_bool,tc_bool) = c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f106261,plain,
( ! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_False,tc_bool)
| ~ spl0_728
| ~ spl0_1672 ),
inference(superposition,[],[f106218,f31068]) ).
fof(f31068,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,tc_bool) = c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool)
| ~ spl0_728 ),
inference(avatar_component_clause,[],[f31067]) ).
fof(f108599,plain,
( spl0_1788
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106260,f106217,f108597]) ).
fof(f108597,plain,
( spl0_1788
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_False,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f106260,plain,
( ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_False,tc_bool)
| ~ spl0_1672 ),
inference(superposition,[],[f106218,f106218]) ).
fof(f108357,plain,
( spl0_1787
| ~ spl0_156
| ~ spl0_551 ),
inference(avatar_split_clause,[],[f12030,f11970,f1694,f108355]) ).
fof(f108355,plain,
( spl0_1787
<=> ! [X4,X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSemi(X3,c_Com_Ocom_OSKIP),X4,X1)),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f1694,plain,
( spl0_156
<=> ! [X29,X0,X13] : c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSKIP,X29,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f11970,plain,
( spl0_551
<=> ! [X5,X31,X0,X13,X6,X29,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X5,X6),X31,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X30,X6,X31,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f12030,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSemi(X3,c_Com_Ocom_OSKIP),X4,X1)),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X1)),X1) )
| ~ spl0_156
| ~ spl0_551 ),
inference(resolution,[],[f11971,f1695]) ).
fof(f1695,plain,
( ! [X0,X29,X13] : c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSKIP,X29,X0)),X0)
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1694]) ).
fof(f11971,plain,
( ! [X31,X0,X29,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X30,X6,X31,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X5,X6),X31,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,X0)),X0) )
| ~ spl0_551 ),
inference(avatar_component_clause,[],[f11970]) ).
fof(f108353,plain,
( spl0_1786
| ~ spl0_156
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f12026,f11966,f1694,f108351]) ).
fof(f108351,plain,
( spl0_1786
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq12__1(X1,X3,X2,X3)),v_sko__Hoare__Mirabelle__Xconseq12__2(X1,X3,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f11966,plain,
( spl0_550
<=> ! [X5,X13,X75,X29,X76,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f12026,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq12__1(X1,X3,X2,X3)),v_sko__Hoare__Mirabelle__Xconseq12__2(X1,X3,X2,X3))) )
| ~ spl0_156
| ~ spl0_550 ),
inference(resolution,[],[f11967,f1695]) ).
fof(f11967,plain,
( ! [X29,X76,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75))) )
| ~ spl0_550 ),
inference(avatar_component_clause,[],[f11966]) ).
fof(f108349,plain,
( spl0_1785
| ~ spl0_171
| ~ spl0_191
| ~ spl0_221
| ~ spl0_536 ),
inference(avatar_split_clause,[],[f11634,f11057,f2097,f1904,f1792,f108347]) ).
fof(f108347,plain,
( spl0_1785
<=> ! [X0,X3,X2,X1] :
( c_Fun_Oinj__on(X2,hAPP(c_fequal(X0),X1),X0,X3)
| hBOOL(c_in(hAPP(X2,X1),c_COMBK(c_False,tc_bool,X3),X3))
| ~ c_Fun_Oinj__on(X2,c_COMBK(c_False,tc_bool,X0),X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f1792,plain,
( spl0_171
<=> ! [X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1904,plain,
( spl0_191
<=> ! [X0,X7,X8] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_Set_Oimage(X8,X7,X0),c_COMBK(c_False,tc_bool,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2097,plain,
( spl0_221
<=> ! [X0,X11] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f11057,plain,
( spl0_536
<=> ! [X8,X11,X0,X1,X7] :
( hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))),X7))
| ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f11634,plain,
( ! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X2,hAPP(c_fequal(X0),X1),X0,X3)
| hBOOL(c_in(hAPP(X2,X1),c_COMBK(c_False,tc_bool,X3),X3))
| ~ c_Fun_Oinj__on(X2,c_COMBK(c_False,tc_bool,X0),X0,X3) )
| ~ spl0_171
| ~ spl0_191
| ~ spl0_221
| ~ spl0_536 ),
inference(forward_demodulation,[],[f11633,f1793]) ).
fof(f1793,plain,
( ! [X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f11633,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(hAPP(X2,X1),c_COMBK(c_False,tc_bool,X3),X3))
| ~ c_Fun_Oinj__on(X2,c_COMBK(c_False,tc_bool,X0),X0,X3)
| c_Fun_Oinj__on(X2,hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),X0,X3) )
| ~ spl0_191
| ~ spl0_221
| ~ spl0_536 ),
inference(forward_demodulation,[],[f11620,f1905]) ).
fof(f1905,plain,
( ! [X0,X8,X7] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_Set_Oimage(X8,X7,X0),c_COMBK(c_False,tc_bool,X7))
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1904]) ).
fof(f11620,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(hAPP(X2,X1),hAPP(c_Set_Oimage(X2,X0,X3),c_COMBK(c_False,tc_bool,X0)),X3))
| ~ c_Fun_Oinj__on(X2,c_COMBK(c_False,tc_bool,X0),X0,X3)
| c_Fun_Oinj__on(X2,hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),X0,X3) )
| ~ spl0_221
| ~ spl0_536 ),
inference(superposition,[],[f11058,f2098]) ).
fof(f2098,plain,
( ! [X0,X11] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X11)
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2097]) ).
fof(f11058,plain,
( ! [X0,X11,X1,X8,X7] :
( hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))),X7))
| ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) )
| ~ spl0_536 ),
inference(avatar_component_clause,[],[f11057]) ).
fof(f108345,plain,
( spl0_1784
| ~ spl0_351
| ~ spl0_522 ),
inference(avatar_split_clause,[],[f10749,f10573,f4335,f108343]) ).
fof(f108343,plain,
( spl0_1784
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f4335,plain,
( spl0_351
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f10573,plain,
( spl0_522
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f10749,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_351
| ~ spl0_522 ),
inference(resolution,[],[f10574,f4336]) ).
fof(f4336,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f4335]) ).
fof(f10574,plain,
( ! [X3,X10,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10))))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_522 ),
inference(avatar_component_clause,[],[f10573]) ).
fof(f108341,plain,
( spl0_1783
| ~ spl0_353
| ~ spl0_522 ),
inference(avatar_split_clause,[],[f10748,f10573,f4344,f108339]) ).
fof(f108339,plain,
( spl0_1783
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3)))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f4344,plain,
( spl0_353
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f10748,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_353
| ~ spl0_522 ),
inference(resolution,[],[f10574,f4345]) ).
fof(f4345,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f4344]) ).
fof(f108201,plain,
( spl0_1782
| ~ spl0_365
| ~ spl0_522 ),
inference(avatar_split_clause,[],[f10744,f10573,f4392,f108199]) ).
fof(f108199,plain,
( spl0_1782
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f4392,plain,
( spl0_365
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f10744,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_365
| ~ spl0_522 ),
inference(resolution,[],[f10574,f4393]) ).
fof(f4393,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_365 ),
inference(avatar_component_clause,[],[f4392]) ).
fof(f108197,plain,
( spl0_1781
| ~ spl0_351
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f10612,f10569,f4335,f108195]) ).
fof(f108195,plain,
( spl0_1781
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f10569,plain,
( spl0_521
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f10612,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_351
| ~ spl0_521 ),
inference(resolution,[],[f10570,f4336]) ).
fof(f10570,plain,
( ! [X3,X10,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10))))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_521 ),
inference(avatar_component_clause,[],[f10569]) ).
fof(f108193,plain,
( spl0_1780
| ~ spl0_361
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f10608,f10569,f4376,f108191]) ).
fof(f108191,plain,
( spl0_1780
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f4376,plain,
( spl0_361
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f10608,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_361
| ~ spl0_521 ),
inference(resolution,[],[f10570,f4377]) ).
fof(f4377,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f4376]) ).
fof(f108189,plain,
( spl0_1779
| ~ spl0_365
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f10607,f10569,f4392,f108187]) ).
fof(f108187,plain,
( spl0_1779
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f10607,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_365
| ~ spl0_521 ),
inference(resolution,[],[f10570,f4393]) ).
fof(f108185,plain,
( spl0_1778
| ~ spl0_238
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f10421,f10328,f2299,f108183]) ).
fof(f108183,plain,
( spl0_1778
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X0),X4)),hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f2299,plain,
( spl0_238
<=> ! [X11,X0,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f10328,plain,
( spl0_517
<=> ! [X11,X0,X12,X8,X7] : hAPP(c_Set_Oimage(X8,X7,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X7,tc_bool)),X11),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X11)),hAPP(c_Set_Oimage(X8,X7,X0),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f10421,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X0),X4)),hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))))
| ~ spl0_238
| ~ spl0_517 ),
inference(superposition,[],[f2300,f10329]) ).
fof(f10329,plain,
( ! [X0,X11,X8,X7,X12] : hAPP(c_Set_Oimage(X8,X7,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X7,tc_bool)),X11),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X11)),hAPP(c_Set_Oimage(X8,X7,X0),X12))
| ~ spl0_517 ),
inference(avatar_component_clause,[],[f10328]) ).
fof(f2300,plain,
( ! [X0,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)))
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2299]) ).
fof(f108181,plain,
( spl0_1777
| ~ spl0_237
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f10420,f10328,f2295,f108179]) ).
fof(f108179,plain,
( spl0_1777
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X0),X3)),hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f2295,plain,
( spl0_237
<=> ! [X11,X0,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f10420,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X0),X3)),hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))))
| ~ spl0_237
| ~ spl0_517 ),
inference(superposition,[],[f2296,f10329]) ).
fof(f2296,plain,
( ! [X0,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)))
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2295]) ).
fof(f108177,plain,
( spl0_1776
| ~ spl0_167
| ~ spl0_505 ),
inference(avatar_split_clause,[],[f10005,f9512,f1776,f108175]) ).
fof(f108175,plain,
( spl0_1776
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X1,X2)),hAPP(c_Set_Oinsert(X3,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1,X5,tc_fun(X0,tc_bool)))))
| ~ hBOOL(c_in(X2,X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f1776,plain,
( spl0_167
<=> ! [X0,X12,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(c_Set_Oinsert(X1,X0),X12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f9512,plain,
( spl0_505
<=> ! [X3,X11,X7,X0,X12,X28] :
( ~ hBOOL(c_in(X3,X28,X7))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X11,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28,X11,X7,tc_fun(X0,tc_bool))),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f10005,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X1,X2)),hAPP(c_Set_Oinsert(X3,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1,X5,tc_fun(X0,tc_bool)))))
| ~ hBOOL(c_in(X2,X4,X5)) )
| ~ spl0_167
| ~ spl0_505 ),
inference(resolution,[],[f9513,f1777]) ).
fof(f1777,plain,
( ! [X0,X1,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(c_Set_Oinsert(X1,X0),X12)))
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f9513,plain,
( ! [X28,X3,X0,X11,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28,X11,X7,tc_fun(X0,tc_bool))),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X11,X3)),X12))
| ~ hBOOL(c_in(X3,X28,X7)) )
| ~ spl0_505 ),
inference(avatar_component_clause,[],[f9512]) ).
fof(f108173,plain,
( spl0_1775
| ~ spl0_319
| ~ spl0_503 ),
inference(avatar_split_clause,[],[f9802,f9504,f3466,f108171]) ).
fof(f108171,plain,
( spl0_1775
<=> ! [X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))
| c_COMBK(c_False,tc_bool,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f3466,plain,
( spl0_319
<=> ! [X11,X0,X12] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f9504,plain,
( spl0_503
<=> ! [X18,X11,X0,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f9802,plain,
( ! [X2,X3,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))
| c_COMBK(c_False,tc_bool,X0) = X1 )
| ~ spl0_319
| ~ spl0_503 ),
inference(superposition,[],[f3467,f9505]) ).
fof(f9505,plain,
( ! [X0,X11,X18,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X18))
| ~ spl0_503 ),
inference(avatar_component_clause,[],[f9504]) ).
fof(f3467,plain,
( ! [X0,X11,X12] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X11 )
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f3466]) ).
fof(f108169,plain,
( spl0_1774
| ~ spl0_318
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f9640,f9500,f3462,f108167]) ).
fof(f108167,plain,
( spl0_1774
<=> ! [X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))
| c_COMBK(c_False,tc_bool,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f3462,plain,
( spl0_318
<=> ! [X11,X0,X12] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f9500,plain,
( spl0_502
<=> ! [X18,X11,X0,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f9640,plain,
( ! [X2,X3,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))
| c_COMBK(c_False,tc_bool,X0) = X3 )
| ~ spl0_318
| ~ spl0_502 ),
inference(superposition,[],[f3463,f9501]) ).
fof(f9501,plain,
( ! [X0,X11,X18,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18))
| ~ spl0_502 ),
inference(avatar_component_clause,[],[f9500]) ).
fof(f3463,plain,
( ! [X0,X11,X12] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X12 )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3462]) ).
fof(f107905,plain,
( spl0_1773
| ~ spl0_24
| ~ spl0_146
| ~ spl0_484 ),
inference(avatar_split_clause,[],[f9276,f9222,f1651,f1077,f107903]) ).
fof(f107903,plain,
( spl0_1773
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f1077,plain,
( spl0_24
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1651,plain,
( spl0_146
<=> ! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f9222,plain,
( spl0_484
<=> ! [X0,X9,X8,X7] :
( ~ class_HOL_Oord(X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X8),X9))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X7)),X8),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X9),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f9276,plain,
( ! [X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1)) )
| ~ spl0_146
| ~ spl0_484 ),
inference(resolution,[],[f9223,f1652]) ).
fof(f1652,plain,
( ! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1651]) ).
fof(f9223,plain,
( ! [X0,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X8),X9))
| ~ class_HOL_Oord(X7)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X7)),X8),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X9),X8)) )
| ~ spl0_484 ),
inference(avatar_component_clause,[],[f9222]) ).
fof(f107640,plain,
( spl0_1772
| ~ spl0_24
| ~ spl0_155
| ~ spl0_484 ),
inference(avatar_split_clause,[],[f9244,f9222,f1690,f1077,f107638]) ).
fof(f107638,plain,
( spl0_1772
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f1690,plain,
( spl0_155
<=> ! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f9244,plain,
( ! [X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0))) )
| ~ spl0_155
| ~ spl0_484 ),
inference(resolution,[],[f9223,f1691]) ).
fof(f1691,plain,
( ! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X11))
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1690]) ).
fof(f107636,plain,
( spl0_1771
| ~ spl0_241
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f9100,f8450,f2311,f107634]) ).
fof(f107634,plain,
( spl0_1771
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X3,X1),X2)),X1))
| hBOOL(c_in(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f2311,plain,
( spl0_241
<=> ! [X11,X0,X12,X5] :
( hBOOL(c_in(X5,X11,X0))
| ~ hBOOL(c_in(X5,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f8450,plain,
( spl0_480
<=> ! [X11,X0,X12,X1] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f9100,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X3,X1),X2)),X1))
| hBOOL(c_in(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X1)) )
| ~ spl0_241
| ~ spl0_480 ),
inference(superposition,[],[f2312,f8451]) ).
fof(f8451,plain,
( ! [X0,X11,X1,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))
| ~ spl0_480 ),
inference(avatar_component_clause,[],[f8450]) ).
fof(f2312,plain,
( ! [X0,X11,X5,X12] :
( ~ hBOOL(c_in(X5,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0))
| hBOOL(c_in(X5,X11,X0)) )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2311]) ).
fof(f107632,plain,
( spl0_1770
| ~ spl0_233
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f9099,f8450,f2279,f107630]) ).
fof(f107630,plain,
( spl0_1770
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Fun_Oinj__on(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X3,X1),X2)),X1,X5)
| ~ c_Fun_Oinj__on(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f2279,plain,
( spl0_233
<=> ! [X11,X0,X12,X8,X7] :
( ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| c_Fun_Oinj__on(X8,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f9099,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Fun_Oinj__on(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X3,X1),X2)),X1,X5)
| ~ c_Fun_Oinj__on(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X1,X5) )
| ~ spl0_233
| ~ spl0_480 ),
inference(superposition,[],[f2280,f8451]) ).
fof(f2280,plain,
( ! [X0,X11,X8,X7,X12] :
( c_Fun_Oinj__on(X8,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0,X7)
| ~ c_Fun_Oinj__on(X8,X11,X0,X7) )
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2279]) ).
fof(f107628,plain,
( spl0_1769
| ~ spl0_449
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f9022,f8446,f7484,f107626]) ).
fof(f107626,plain,
( spl0_1769
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(c_in(hAPP(X3,X4),hAPP(c_Set_Oimage(X3,X0,X5),X2),X5))
| ~ hBOOL(c_in(X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f7484,plain,
( spl0_449
<=> ! [X11,X0,X12,X3,X8,X7] :
( ~ hBOOL(c_in(X3,X11,X7))
| hBOOL(c_in(hAPP(X8,X3),X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X11)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f8446,plain,
( spl0_479
<=> ! [X11,X0,X3,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X3),X11))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X3)),hAPP(c_Set_Oimage(X8,X7,X0),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f9022,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(c_in(hAPP(X3,X4),hAPP(c_Set_Oimage(X3,X0,X5),X2),X5))
| ~ hBOOL(c_in(X4,X1,X0)) )
| ~ spl0_449
| ~ spl0_479 ),
inference(resolution,[],[f8447,f7485]) ).
fof(f7485,plain,
( ! [X3,X0,X11,X8,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X11)),X12))
| hBOOL(c_in(hAPP(X8,X3),X12,X0))
| ~ hBOOL(c_in(X3,X11,X7)) )
| ~ spl0_449 ),
inference(avatar_component_clause,[],[f7484]) ).
fof(f8447,plain,
( ! [X3,X0,X11,X8,X7] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X3)),hAPP(c_Set_Oimage(X8,X7,X0),X11)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X3),X11)) )
| ~ spl0_479 ),
inference(avatar_component_clause,[],[f8446]) ).
fof(f107624,plain,
( spl0_1768
| ~ spl0_257
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8761,f8434,f2544,f107622]) ).
fof(f107622,plain,
( spl0_1768
<=> ! [X2,X4,X0,X3,X5,X1] :
( hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f2544,plain,
( spl0_257
<=> ! [X11,X0,X12,X5] :
( ~ hBOOL(c_in(X5,X12,X0))
| hBOOL(c_in(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f8434,plain,
( spl0_476
<=> ! [X11,X0,X12,X1,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X1,X7),X11),X12,X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X12,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f8761,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X0)) )
| ~ spl0_257
| ~ spl0_476 ),
inference(superposition,[],[f2545,f8435]) ).
fof(f8435,plain,
( ! [X0,X11,X1,X7,X12] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X1,X7),X11),X12,X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X12,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool)))
| ~ spl0_476 ),
inference(avatar_component_clause,[],[f8434]) ).
fof(f2545,plain,
( ! [X0,X11,X5,X12] :
( hBOOL(c_in(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0))
| ~ hBOOL(c_in(X5,X12,X0)) )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2544]) ).
fof(f107620,plain,
( spl0_1767
| ~ spl0_248
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8757,f8434,f2499,f107618]) ).
fof(f107618,plain,
( spl0_1767
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( ~ c_Fun_Oinj__on(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0,X6)
| c_Fun_Oinj__on(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(f2499,plain,
( spl0_248
<=> ! [X11,X0,X12,X8,X7] :
( c_Fun_Oinj__on(X8,X12,X0,X7)
| ~ c_Fun_Oinj__on(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f8757,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Fun_Oinj__on(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0,X6)
| c_Fun_Oinj__on(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X0,X6) )
| ~ spl0_248
| ~ spl0_476 ),
inference(superposition,[],[f2500,f8435]) ).
fof(f2500,plain,
( ! [X0,X11,X8,X7,X12] :
( ~ c_Fun_Oinj__on(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0,X7)
| c_Fun_Oinj__on(X8,X12,X0,X7) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2499]) ).
fof(f107616,plain,
( spl0_1766
| ~ spl0_259
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f8310,f7945,f2552,f107614]) ).
fof(f107614,plain,
( spl0_1766
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(c_in(X3,X2,X0))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f2552,plain,
( spl0_259
<=> ! [X29,X30,X0,X3] :
( ~ hBOOL(hAPP(X29,X3))
| hBOOL(hAPP(X30,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X29),X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f7945,plain,
( spl0_466
<=> ! [X11,X0,X12,X3] :
( ~ hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X11)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f8310,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(c_in(X3,X2,X0))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X1),X4)) )
| ~ spl0_259
| ~ spl0_466 ),
inference(resolution,[],[f7946,f2553]) ).
fof(f2553,plain,
( ! [X3,X0,X29,X30] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X29),X30))
| hBOOL(hAPP(X30,X3))
| ~ hBOOL(hAPP(X29,X3)) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f2552]) ).
fof(f7946,plain,
( ! [X3,X0,X11,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X11)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(c_in(X3,X12,X0)) )
| ~ spl0_466 ),
inference(avatar_component_clause,[],[f7945]) ).
fof(f107612,plain,
( spl0_1765
| ~ spl0_70
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f7855,f7527,f1273,f107610]) ).
fof(f107610,plain,
( spl0_1765
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xescape__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f7527,plain,
( spl0_455
<=> ! [X5,X13,X29,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f7855,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xescape__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) )
| ~ spl0_70
| ~ spl0_455 ),
inference(superposition,[],[f7528,f1274]) ).
fof(f7528,plain,
( ! [X29,X5,X13,X30] :
( hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a) )
| ~ spl0_455 ),
inference(avatar_component_clause,[],[f7527]) ).
fof(f107594,plain,
( spl0_1764
| ~ spl0_110
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f7834,f7527,f1455,f107592]) ).
fof(f107592,plain,
( spl0_1764
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xescape__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xescape__2(X0,c_fequal(X1),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).
fof(f1455,plain,
( spl0_110
<=> ! [X82,X0,X81] :
( X81 = X82
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X81),X82)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f7834,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xescape__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xescape__2(X0,c_fequal(X1),X3,X2) )
| ~ spl0_110
| ~ spl0_455 ),
inference(resolution,[],[f7528,f1456]) ).
fof(f1456,plain,
( ! [X82,X0,X81] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X0),X81),X82))
| X81 = X82 )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1455]) ).
fof(f107590,plain,
( spl0_1763
| ~ spl0_70
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f7786,f7504,f1273,f107588]) ).
fof(f107588,plain,
( spl0_1763
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).
fof(f7504,plain,
( spl0_454
<=> ! [X5,X13,X29,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f7786,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) )
| ~ spl0_70
| ~ spl0_454 ),
inference(superposition,[],[f7505,f1274]) ).
fof(f7505,plain,
( ! [X29,X5,X13,X30] :
( hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a) )
| ~ spl0_454 ),
inference(avatar_component_clause,[],[f7504]) ).
fof(f107586,plain,
( spl0_1762
| ~ spl0_110
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f7765,f7504,f1455,f107584]) ).
fof(f107584,plain,
( spl0_1762
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,c_fequal(X1),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).
fof(f7765,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,c_fequal(X1),X3,X2) )
| ~ spl0_110
| ~ spl0_454 ),
inference(resolution,[],[f7505,f1456]) ).
fof(f107582,plain,
( spl0_1761
| ~ spl0_70
| ~ spl0_453 ),
inference(avatar_split_clause,[],[f7717,f7500,f1273,f107580]) ).
fof(f7500,plain,
( spl0_453
<=> ! [X5,X13,X29,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f7717,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) )
| ~ spl0_70
| ~ spl0_453 ),
inference(superposition,[],[f7501,f1274]) ).
fof(f7501,plain,
( ! [X29,X5,X13,X30] :
( hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a) )
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f7500]) ).
fof(f107578,plain,
( spl0_1760
| ~ spl0_110
| ~ spl0_453 ),
inference(avatar_split_clause,[],[f7696,f7500,f1455,f107576]) ).
fof(f107576,plain,
( spl0_1760
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,c_fequal(X1),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).
fof(f7696,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,c_fequal(X1),X3,X2) )
| ~ spl0_110
| ~ spl0_453 ),
inference(resolution,[],[f7501,f1456]) ).
fof(f107574,plain,
( spl0_1759
| ~ spl0_205
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7227,f6752,f2029,f107572]) ).
fof(f107572,plain,
( spl0_1759
<=> ! [X2,X3,X4,X0,X5,X1] : hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).
fof(f2029,plain,
( spl0_205
<=> ! [X0,X3,X8,X7] : hBOOL(c_in(hAPP(X8,X3),hAPP(c_Set_Oimage(X8,X7,X0),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f6752,plain,
( spl0_442
<=> ! [X11,X0,X12,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f7227,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))),X5))
| ~ spl0_205
| ~ spl0_442 ),
inference(superposition,[],[f2030,f6753]) ).
fof(f6753,plain,
( ! [X0,X11,X1,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12))
| ~ spl0_442 ),
inference(avatar_component_clause,[],[f6752]) ).
fof(f2030,plain,
( ! [X3,X0,X8,X7] : hBOOL(c_in(hAPP(X8,X3),hAPP(c_Set_Oimage(X8,X7,X0),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool))),X0))
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2029]) ).
fof(f107570,plain,
( spl0_1758
| ~ spl0_148
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7205,f6752,f1660,f107568]) ).
fof(f107568,plain,
( spl0_1758
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).
fof(f1660,plain,
( spl0_148
<=> ! [X4,X0,X11,X3] :
( ~ hBOOL(hAPP(X11,X3))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X4,X0),X11),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f7205,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) )
| ~ spl0_148
| ~ spl0_442 ),
inference(superposition,[],[f1661,f6753]) ).
fof(f1661,plain,
( ! [X3,X0,X11,X4] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X4,X0),X11),X3))
| ~ hBOOL(hAPP(X11,X3)) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1660]) ).
fof(f107566,plain,
( spl0_1757
| ~ spl0_70
| ~ spl0_165
| ~ spl0_185
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f7002,f6711,f1880,f1768,f1273,f107564]) ).
fof(f107564,plain,
( spl0_1757
<=> ! [X5,X3,X4,X2,X7,X0,X6,X1] :
( ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f1768,plain,
( spl0_165
<=> ! [X17,X7,X5,X8] : hAPP(c_Fun_Ocomp(c_COMBK(X5,X7,X17),X8,X17,X7,t_a),v_x) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1880,plain,
( spl0_185
<=> ! [X1,X17,X54,X0,X2,X7] : hAPP(X1,hAPP(X2,X54)) = hAPP(c_Fun_Ocomp(X1,X2,X17,X7,X0),X54) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f6711,plain,
( spl0_432
<=> ! [X4,X11,X0,X3,X8,X7] :
( X3 = X4
| ~ hBOOL(c_in(X4,X11,X0))
| ~ hBOOL(c_in(X3,X11,X0))
| ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| hAPP(X8,X3) != hAPP(X8,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f7002,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 )
| ~ spl0_70
| ~ spl0_165
| ~ spl0_185
| ~ spl0_432 ),
inference(trivial_inequality_removal,[],[f7001]) ).
fof(f7001,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X0 != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 )
| ~ spl0_70
| ~ spl0_165
| ~ spl0_185
| ~ spl0_432 ),
inference(forward_demodulation,[],[f7000,f1274]) ).
fof(f7000,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(c_COMBK(X0,X1,X2),hAPP(X3,X4)) != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 )
| ~ spl0_165
| ~ spl0_185
| ~ spl0_432 ),
inference(forward_demodulation,[],[f6931,f1881]) ).
fof(f1881,plain,
( ! [X2,X0,X1,X54,X7,X17] : hAPP(X1,hAPP(X2,X54)) = hAPP(c_Fun_Ocomp(X1,X2,X17,X7,X0),X54)
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1880]) ).
fof(f6931,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4) != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 )
| ~ spl0_165
| ~ spl0_432 ),
inference(superposition,[],[f6712,f1769]) ).
fof(f1769,plain,
( ! [X8,X7,X17,X5] : hAPP(c_Fun_Ocomp(c_COMBK(X5,X7,X17),X8,X17,X7,t_a),v_x) = X5
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1768]) ).
fof(f6712,plain,
( ! [X3,X0,X11,X8,X7,X4] :
( hAPP(X8,X3) != hAPP(X8,X4)
| ~ hBOOL(c_in(X4,X11,X0))
| ~ hBOOL(c_in(X3,X11,X0))
| ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| X3 = X4 )
| ~ spl0_432 ),
inference(avatar_component_clause,[],[f6711]) ).
fof(f107562,plain,
( spl0_1756
| ~ spl0_239
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f6990,f6711,f2303,f107560]) ).
fof(f107560,plain,
( spl0_1756
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X3,X4,X5)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f2303,plain,
( spl0_239
<=> ! [X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f6990,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X3,X4,X5)
| X1 = X2 )
| ~ spl0_239
| ~ spl0_432 ),
inference(trivial_inequality_removal,[],[f6989]) ).
fof(f6989,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X3,X4,X5)
| X1 = X2 )
| ~ spl0_239
| ~ spl0_432 ),
inference(forward_demodulation,[],[f6895,f2304]) ).
fof(f2304,plain,
( ! [X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X12)
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2303]) ).
fof(f6895,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2)
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X3,X4,X5)
| X1 = X2 )
| ~ spl0_239
| ~ spl0_432 ),
inference(superposition,[],[f6712,f2304]) ).
fof(f107558,plain,
( spl0_1755
| ~ spl0_185
| ~ spl0_431 ),
inference(avatar_split_clause,[],[f6869,f6707,f1880,f107556]) ).
fof(f107556,plain,
( spl0_1755
<=> ! [X2,X4,X7,X0,X6,X5,X3,X1] : hAPP(X0,hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X7)) = hAPP(c_Fun_Ofun__upd(c_Fun_Ocomp(X0,X1,X5,X6,X4),X2,hAPP(X0,X3),X4,X6),X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f6707,plain,
( spl0_431
<=> ! [X17,X4,X9,X0,X3,X8,X7] : c_Fun_Ocomp(X8,c_Fun_Ofun__upd(X9,X3,X4,X0,X17),X17,X7,X0) = c_Fun_Ofun__upd(c_Fun_Ocomp(X8,X9,X17,X7,X0),X3,hAPP(X8,X4),X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f6869,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X0,hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X7)) = hAPP(c_Fun_Ofun__upd(c_Fun_Ocomp(X0,X1,X5,X6,X4),X2,hAPP(X0,X3),X4,X6),X7)
| ~ spl0_185
| ~ spl0_431 ),
inference(superposition,[],[f1881,f6708]) ).
fof(f6708,plain,
( ! [X3,X0,X8,X9,X7,X4,X17] : c_Fun_Ocomp(X8,c_Fun_Ofun__upd(X9,X3,X4,X0,X17),X17,X7,X0) = c_Fun_Ofun__upd(c_Fun_Ocomp(X8,X9,X17,X7,X0),X3,hAPP(X8,X4),X0,X7)
| ~ spl0_431 ),
inference(avatar_component_clause,[],[f6707]) ).
fof(f107541,plain,
( spl0_1754
| ~ spl0_255
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f6342,f5559,f2536,f107539]) ).
fof(f107539,plain,
( spl0_1754
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f2536,plain,
( spl0_255
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f5559,plain,
( spl0_411
<=> ! [X0,X11,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X1,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X11,X0),X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f6342,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)),X2) = X2 )
| ~ spl0_255
| ~ spl0_411 ),
inference(resolution,[],[f5560,f2537]) ).
fof(f2537,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = X4 )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f2536]) ).
fof(f5560,plain,
( ! [X0,X11,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X11,X0),X0)),X1))
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X1,X11,X0))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f5559]) ).
fof(f107537,plain,
( spl0_1753
| ~ spl0_253
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f6341,f5559,f2528,f107535]) ).
fof(f107535,plain,
( spl0_1753
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f2528,plain,
( spl0_253
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f6341,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)) = X2 )
| ~ spl0_253
| ~ spl0_411 ),
inference(resolution,[],[f5560,f2529]) ).
fof(f2529,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = X3 )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2528]) ).
fof(f107533,plain,
( spl0_1752
| ~ spl0_261
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6316,f5555,f2560,f107531]) ).
fof(f107531,plain,
( spl0_1752
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f2560,plain,
( spl0_261
<=> ! [X0,X11,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f5555,plain,
( spl0_410
<=> ! [X4,X0,X3,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f6316,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_410 ),
inference(resolution,[],[f5556,f2561]) ).
fof(f2561,plain,
( ! [X3,X0,X11] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X11)))
| ~ hBOOL(c_in(X3,X11,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f2560]) ).
fof(f5556,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10)) )
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f5555]) ).
fof(f107529,plain,
( spl0_1751
| ~ spl0_256
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6298,f5555,f2540,f107527]) ).
fof(f107527,plain,
( spl0_1751
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f2540,plain,
( spl0_256
<=> ! [X0,X11,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X11)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f6298,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_410 ),
inference(resolution,[],[f5556,f2541]) ).
fof(f2541,plain,
( ! [X3,X0,X11] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X11)),X3))
| ~ hBOOL(c_in(X3,X11,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2540]) ).
fof(f107525,plain,
( spl0_1750
| ~ spl0_261
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6277,f5551,f2560,f107523]) ).
fof(f107523,plain,
( spl0_1750
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f5551,plain,
( spl0_409
<=> ! [X4,X0,X3,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X10),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X10),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f6277,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_409 ),
inference(resolution,[],[f5552,f2561]) ).
fof(f5552,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X10),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X10),X3)) )
| ~ spl0_409 ),
inference(avatar_component_clause,[],[f5551]) ).
fof(f107521,plain,
( spl0_1749
| ~ spl0_256
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6259,f5551,f2540,f107519]) ).
fof(f107519,plain,
( spl0_1749
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f6259,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_409 ),
inference(resolution,[],[f5552,f2541]) ).
fof(f107517,plain,
( spl0_1748
| ~ spl0_205
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f6229,f5547,f2029,f107515]) ).
fof(f107515,plain,
( spl0_1748
<=> ! [X5,X3,X4,X7,X0,X6,X2,X1] : hBOOL(c_in(hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X3,X1,X2,X4),X4,X2),X5),hAPP(c_Set_Oimage(c_Set_Oimage(X0,X1,X2),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f5547,plain,
( spl0_408
<=> ! [X59,X7,X0,X9,X17,X8] : hAPP(c_Set_Oimage(c_Fun_Ocomp(X8,X9,X17,X0,X7),X7,X0),X59) = hAPP(c_Set_Oimage(X8,X17,X0),hAPP(c_Set_Oimage(X9,X7,X17),X59)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f6229,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hBOOL(c_in(hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X3,X1,X2,X4),X4,X2),X5),hAPP(c_Set_Oimage(c_Set_Oimage(X0,X1,X2),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7))
| ~ spl0_205
| ~ spl0_408 ),
inference(superposition,[],[f2030,f5548]) ).
fof(f5548,plain,
( ! [X0,X59,X8,X9,X7,X17] : hAPP(c_Set_Oimage(c_Fun_Ocomp(X8,X9,X17,X0,X7),X7,X0),X59) = hAPP(c_Set_Oimage(X8,X17,X0),hAPP(c_Set_Oimage(X9,X7,X17),X59))
| ~ spl0_408 ),
inference(avatar_component_clause,[],[f5547]) ).
fof(f107513,plain,
( spl0_1747
| ~ spl0_228
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f6192,f5547,f2259,f107511]) ).
fof(f107511,plain,
( spl0_1747
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)),X3)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X0,X1,X2,X3,X4),X5,X4,X3)
| c_Finite__Set_Ofinite(X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f2259,plain,
( spl0_228
<=> ! [X11,X0,X8,X7] :
( c_Finite__Set_Ofinite(X11,X7)
| ~ c_Fun_Oinj__on(X8,X11,X7,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X8,X7,X0),X11),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f6192,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)),X3)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X0,X1,X2,X3,X4),X5,X4,X3)
| c_Finite__Set_Ofinite(X5,X4) )
| ~ spl0_228
| ~ spl0_408 ),
inference(superposition,[],[f2260,f5548]) ).
fof(f2260,plain,
( ! [X0,X11,X8,X7] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X8,X7,X0),X11),X0)
| ~ c_Fun_Oinj__on(X8,X11,X7,X0)
| c_Finite__Set_Ofinite(X11,X7) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2259]) ).
fof(f107509,plain,
( spl0_1746
| ~ spl0_205
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6142,f5535,f2029,f107507]) ).
fof(f107507,plain,
( spl0_1746
<=> ! [X5,X3,X4,X0,X6,X2,X1] : hBOOL(c_in(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(X0,X1),X2),X5,X6),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool))),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f5535,plain,
( spl0_405
<=> ! [X1,X0,X12,X8,X7] : hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_Set_Oinsert(X1,X7),X12)) = hAPP(c_Set_Oinsert(hAPP(X8,X1),X0),hAPP(c_Set_Oimage(X8,X7,X0),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f6142,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(c_in(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(X0,X1),X2),X5,X6),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool))),X6))
| ~ spl0_205
| ~ spl0_405 ),
inference(superposition,[],[f2030,f5536]) ).
fof(f5536,plain,
( ! [X0,X1,X8,X7,X12] : hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_Set_Oinsert(X1,X7),X12)) = hAPP(c_Set_Oinsert(hAPP(X8,X1),X0),hAPP(c_Set_Oimage(X8,X7,X0),X12))
| ~ spl0_405 ),
inference(avatar_component_clause,[],[f5535]) ).
fof(f107505,plain,
( spl0_1745
| ~ spl0_92
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f5902,f5515,f1379,f107503]) ).
fof(f107503,plain,
( spl0_1745
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(c_in(X5,X2,X6))
| ~ hBOOL(c_in(X1,X7,X8))
| hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X8,tc_fun(X6,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f1379,plain,
( spl0_92
<=> ! [X4,X0,X8,X16,X3] : hAPP(c_Fun_Ofun__upd(X8,X3,X4,X0,X16),X3) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f5515,plain,
( spl0_400
<=> ! [X11,X0,X12,X3,X2,X7] :
( ~ hBOOL(c_in(X3,X11,X7))
| ~ hBOOL(c_in(X2,hAPP(X12,X3),X0))
| hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f5902,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(c_in(X5,X2,X6))
| ~ hBOOL(c_in(X1,X7,X8))
| hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X8,tc_fun(X6,tc_bool)),X6)) )
| ~ spl0_92
| ~ spl0_400 ),
inference(superposition,[],[f5516,f1380]) ).
fof(f1380,plain,
( ! [X3,X0,X8,X16,X4] : hAPP(c_Fun_Ofun__upd(X8,X3,X4,X0,X16),X3) = X4
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1379]) ).
fof(f5516,plain,
( ! [X2,X3,X0,X11,X7,X12] :
( ~ hBOOL(c_in(X2,hAPP(X12,X3),X0))
| ~ hBOOL(c_in(X3,X11,X7))
| hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool)),X0)) )
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f5515]) ).
fof(f107501,plain,
( spl0_1744
| ~ spl0_70
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106322,f106217,f1273,f107499]) ).
fof(f107499,plain,
( spl0_1744
<=> ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f106322,plain,
( ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),X1)
| ~ spl0_70
| ~ spl0_1672 ),
inference(superposition,[],[f1274,f106218]) ).
fof(f107497,plain,
( spl0_1743
| ~ spl0_100
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f5891,f5515,f1413,f107495]) ).
fof(f107495,plain,
( spl0_1743
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(c_in(X1,X4,X5))
| hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X5,tc_fun(X3,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f1413,plain,
( spl0_100
<=> ! [X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X11) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f5891,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(c_in(X1,X4,X5))
| hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X5,tc_fun(X3,tc_bool)),X3)) )
| ~ spl0_100
| ~ spl0_400 ),
inference(superposition,[],[f5516,f1414]) ).
fof(f1414,plain,
( ! [X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X11) = X11
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1413]) ).
fof(f107493,plain,
( spl0_1742
| ~ spl0_261
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5811,f5483,f2560,f107491]) ).
fof(f107491,plain,
( spl0_1742
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f5483,plain,
( spl0_392
<=> ! [X4,X0,X3,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f5811,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_392 ),
inference(resolution,[],[f5484,f2561]) ).
fof(f5484,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X10)) )
| ~ spl0_392 ),
inference(avatar_component_clause,[],[f5483]) ).
fof(f107489,plain,
( spl0_1741
| ~ spl0_256
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5793,f5483,f2540,f107487]) ).
fof(f107487,plain,
( spl0_1741
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f5793,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_392 ),
inference(resolution,[],[f5484,f2541]) ).
fof(f107485,plain,
( spl0_1740
| ~ spl0_261
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5773,f5479,f2560,f107483]) ).
fof(f107483,plain,
( spl0_1740
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f5479,plain,
( spl0_391
<=> ! [X4,X0,X3,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f5773,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_391 ),
inference(resolution,[],[f5480,f2561]) ).
fof(f5480,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X10))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X10)) )
| ~ spl0_391 ),
inference(avatar_component_clause,[],[f5479]) ).
fof(f107481,plain,
( spl0_1739
| ~ spl0_256
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5755,f5479,f2540,f107479]) ).
fof(f107479,plain,
( spl0_1739
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f5755,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_391 ),
inference(resolution,[],[f5480,f2541]) ).
fof(f107477,plain,
( spl0_1738
| ~ spl0_261
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5730,f5475,f2560,f107475]) ).
fof(f107475,plain,
( spl0_1738
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f5475,plain,
( spl0_390
<=> ! [X4,X0,X3,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f5730,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_390 ),
inference(resolution,[],[f5476,f2561]) ).
fof(f5476,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X4))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X3)) )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f5475]) ).
fof(f107473,plain,
( spl0_1737
| ~ spl0_256
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5712,f5475,f2540,f107471]) ).
fof(f107471,plain,
( spl0_1737
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f5712,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_390 ),
inference(resolution,[],[f5476,f2541]) ).
fof(f107469,plain,
( spl0_1736
| ~ spl0_261
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5691,f5471,f2560,f107467]) ).
fof(f107467,plain,
( spl0_1736
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f5471,plain,
( spl0_389
<=> ! [X4,X0,X3,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X10),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f5691,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_389 ),
inference(resolution,[],[f5472,f2561]) ).
fof(f5472,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X10),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X3)) )
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f5471]) ).
fof(f107465,plain,
( spl0_1735
| ~ spl0_256
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5673,f5471,f2540,f107463]) ).
fof(f107463,plain,
( spl0_1735
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f5673,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_389 ),
inference(resolution,[],[f5472,f2541]) ).
fof(f107461,plain,
( spl0_1734
| ~ spl0_228
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f5639,f5467,f2259,f107459]) ).
fof(f107459,plain,
( spl0_1734
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)),X3)
| ~ c_Fun_Oinj__on(c_COMBB(X0,X1,X2,X3,X4),X5,X4,X3)
| c_Finite__Set_Ofinite(X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f5467,plain,
( spl0_388
<=> ! [X17,X11,X0,X9,X8,X7] : hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_Set_Oimage(X9,X17,X7),X11)) = hAPP(c_Set_Oimage(c_COMBB(X8,X9,X7,X0,X17),X17,X0),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f5639,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)),X3)
| ~ c_Fun_Oinj__on(c_COMBB(X0,X1,X2,X3,X4),X5,X4,X3)
| c_Finite__Set_Ofinite(X5,X4) )
| ~ spl0_228
| ~ spl0_388 ),
inference(superposition,[],[f2260,f5468]) ).
fof(f5468,plain,
( ! [X0,X11,X8,X9,X7,X17] : hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_Set_Oimage(X9,X17,X7),X11)) = hAPP(c_Set_Oimage(c_COMBB(X8,X9,X7,X0,X17),X17,X0),X11)
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f5467]) ).
fof(f107457,plain,
( spl0_1733
| ~ spl0_160
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106321,f106217,f1722,f107455]) ).
fof(f107455,plain,
( spl0_1733
<=> ! [X0] : c_False = c_Inductive_Ocomplete__lattice__class_Olfp(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f1722,plain,
( spl0_160
<=> ! [X0] : c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,tc_bool,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f106321,plain,
( ! [X0] : c_False = c_Inductive_Ocomplete__lattice__class_Olfp(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),tc_bool)
| ~ spl0_160
| ~ spl0_1672 ),
inference(superposition,[],[f1723,f106218]) ).
fof(f1723,plain,
( ! [X0] : c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,tc_bool,tc_bool),tc_bool) = X0
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1722]) ).
fof(f107452,plain,
( spl0_1732
| ~ spl0_205
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f5625,f5467,f2029,f107450]) ).
fof(f107450,plain,
( spl0_1732
<=> ! [X5,X3,X4,X7,X0,X6,X2,X1] : hBOOL(c_in(hAPP(c_Set_Oimage(c_COMBB(X0,X3,X1,X2,X4),X4,X2),X5),hAPP(c_Set_Oimage(c_Set_Oimage(X0,X1,X2),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f5625,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hBOOL(c_in(hAPP(c_Set_Oimage(c_COMBB(X0,X3,X1,X2,X4),X4,X2),X5),hAPP(c_Set_Oimage(c_Set_Oimage(X0,X1,X2),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7))
| ~ spl0_205
| ~ spl0_388 ),
inference(superposition,[],[f2030,f5468]) ).
fof(f107448,plain,
( spl0_1731
| ~ spl0_292
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f5431,f5066,f3016,f107446]) ).
fof(f107446,plain,
( spl0_1731
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f3016,plain,
( spl0_292
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f5066,plain,
( spl0_384
<=> ! [X20,X0,X24] :
( c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X20,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X24,X0))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f5431,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_292
| ~ spl0_384 ),
inference(resolution,[],[f5067,f3017]) ).
fof(f3017,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3016]) ).
fof(f5067,plain,
( ! [X0,X24,X20] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24))
| ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X20,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X24,X0)) )
| ~ spl0_384 ),
inference(avatar_component_clause,[],[f5066]) ).
fof(f107444,plain,
( spl0_1730
| ~ spl0_292
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5384,f5062,f3016,f107442]) ).
fof(f107442,plain,
( spl0_1730
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X2,X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f5062,plain,
( spl0_383
<=> ! [X20,X0,X24] :
( c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X24,X0),c_SetInterval_Oord__class_OatLeastLessThan(X20,X24,X0))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f5384,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X2,X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_292
| ~ spl0_383 ),
inference(resolution,[],[f5063,f3017]) ).
fof(f5063,plain,
( ! [X0,X24,X20] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24))
| ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X24,X0),c_SetInterval_Oord__class_OatLeastLessThan(X20,X24,X0)) )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f5062]) ).
fof(f107109,plain,
( ~ spl0_24
| spl0_1729
| ~ spl0_378
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5331,f5058,f5042,f107107,f1077]) ).
fof(f107107,plain,
( spl0_1729
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X3,X2,tc_fun(X4,tc_bool)),X5)),hAPP(hAPP(X3,X0),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f5042,plain,
( spl0_378
<=> ! [X3,X0,X9,X8,X7] :
( ~ class_HOL_Oord(X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X8),X9))
| hBOOL(hAPP(hAPP(c_lessequals(X7),hAPP(X8,X3)),hAPP(X9,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f5058,plain,
( spl0_382
<=> ! [X11,X0,X12,X1,X7] :
( ~ hBOOL(c_in(X1,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X0,tc_fun(X7,tc_bool))),hAPP(X12,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f5331,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X3,X2,tc_fun(X4,tc_bool)),X5)),hAPP(hAPP(X3,X0),X5))) )
| ~ spl0_378
| ~ spl0_382 ),
inference(resolution,[],[f5059,f5043]) ).
fof(f5043,plain,
( ! [X3,X0,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X8),X9))
| ~ class_HOL_Oord(X7)
| hBOOL(hAPP(hAPP(c_lessequals(X7),hAPP(X8,X3)),hAPP(X9,X3))) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f5042]) ).
fof(f5059,plain,
( ! [X0,X11,X1,X7,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X0,tc_fun(X7,tc_bool))),hAPP(X12,X1)))
| ~ hBOOL(c_in(X1,X11,X0)) )
| ~ spl0_382 ),
inference(avatar_component_clause,[],[f5058]) ).
fof(f107105,plain,
( spl0_1728
| ~ spl0_379
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f5265,f5050,f5046,f107103]) ).
fof(f107103,plain,
( spl0_1728
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X4,X0),X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f5046,plain,
( spl0_379
<=> ! [X11,X0,X12,X2] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X2,X0),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f5050,plain,
( spl0_380
<=> ! [X11,X0,X12,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X11)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f5265,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X4,X0),X1)),X3)) )
| ~ spl0_379
| ~ spl0_380 ),
inference(resolution,[],[f5051,f5047]) ).
fof(f5047,plain,
( ! [X2,X0,X11,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X2,X0),X12)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) )
| ~ spl0_379 ),
inference(avatar_component_clause,[],[f5046]) ).
fof(f5051,plain,
( ! [X3,X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X11)),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) )
| ~ spl0_380 ),
inference(avatar_component_clause,[],[f5050]) ).
fof(f107101,plain,
( spl0_1727
| ~ spl0_234
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f5263,f5050,f2283,f107099]) ).
fof(f107099,plain,
( spl0_1727
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),hAPP(c_Set_Oinsert(X3,X0),X1)))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f2283,plain,
( spl0_234
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f5263,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),hAPP(c_Set_Oinsert(X3,X0),X1)))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) )
| ~ spl0_234
| ~ spl0_380 ),
inference(resolution,[],[f5051,f2284]) ).
fof(f2284,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2283]) ).
fof(f107097,plain,
( spl0_1726
| ~ spl0_243
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f5261,f5050,f2319,f107095]) ).
fof(f107095,plain,
( spl0_1726
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),hAPP(c_Set_Oinsert(X3,X0),X1)))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f2319,plain,
( spl0_243
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f5261,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),hAPP(c_Set_Oinsert(X3,X0),X1)))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) )
| ~ spl0_243
| ~ spl0_380 ),
inference(resolution,[],[f5051,f2320]) ).
fof(f2320,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2319]) ).
fof(f106857,plain,
( ~ spl0_24
| spl0_1725
| ~ spl0_378
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5244,f5046,f5042,f106855,f1077]) ).
fof(f106855,plain,
( spl0_1725
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X1,X3)),hAPP(hAPP(c_Set_Oinsert(X4,X0),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f5244,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X1,X3)),hAPP(hAPP(c_Set_Oinsert(X4,X0),X2),X3))) )
| ~ spl0_378
| ~ spl0_379 ),
inference(resolution,[],[f5047,f5043]) ).
fof(f106853,plain,
( spl0_1724
| ~ spl0_72
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106269,f106217,f1282,f106851]) ).
fof(f106851,plain,
( spl0_1724
<=> ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f1282,plain,
( spl0_72
<=> ! [X5,X0] : ~ hBOOL(c_in(X5,c_COMBK(c_False,tc_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f106269,plain,
( ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),tc_bool))
| ~ spl0_72
| ~ spl0_1672 ),
inference(superposition,[],[f1283,f106218]) ).
fof(f1283,plain,
( ! [X0,X5] : ~ hBOOL(c_in(X5,c_COMBK(c_False,tc_bool,X0),X0))
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1282]) ).
fof(f106507,plain,
( spl0_1723
| ~ spl0_24
| ~ spl0_377
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5217,f5042,f5038,f1077,f106505]) ).
fof(f106505,plain,
( spl0_1723
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(X0,X1),X2)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X0,X4,tc_fun(X5,tc_bool)),X2)))
| ~ hBOOL(c_in(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).
fof(f5038,plain,
( spl0_377
<=> ! [X11,X0,X12,X1,X7] :
( ~ hBOOL(c_in(X1,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),hAPP(X12,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f5217,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(X0,X1),X2)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X0,X4,tc_fun(X5,tc_bool)),X2)))
| ~ hBOOL(c_in(X1,X3,X4)) )
| ~ spl0_377
| ~ spl0_378 ),
inference(resolution,[],[f5043,f5039]) ).
fof(f5039,plain,
( ! [X0,X11,X1,X7,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),hAPP(X12,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool))))
| ~ hBOOL(c_in(X1,X11,X0)) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f5038]) ).
fof(f106503,plain,
( spl0_1722
| ~ spl0_234
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5199,f5042,f2283,f106501]) ).
fof(f106501,plain,
( spl0_1722
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X3,X2)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X4,X0)),X3),X1))
| ~ class_Orderings_Olinorder(tc_fun(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f5199,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X3,X2)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X4,X0)),X3),X1))
| ~ class_Orderings_Olinorder(tc_fun(X4,X0)) )
| ~ spl0_234
| ~ spl0_378 ),
inference(resolution,[],[f5043,f2284]) ).
fof(f106499,plain,
( spl0_1721
| ~ spl0_243
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5197,f5042,f2319,f106497]) ).
fof(f106497,plain,
( spl0_1721
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X3,X2)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,X0)),X3),X1))
| ~ class_Orderings_Olinorder(tc_fun(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f5197,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X3,X2)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,X0)),X3),X1))
| ~ class_Orderings_Olinorder(tc_fun(X4,X0)) )
| ~ spl0_243
| ~ spl0_378 ),
inference(resolution,[],[f5043,f2320]) ).
fof(f106495,plain,
( spl0_1720
| ~ spl0_364
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4990,f4392,f4388,f106493]) ).
fof(f106493,plain,
( spl0_1720
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).
fof(f4388,plain,
( spl0_364
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f4990,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X2)) )
| ~ spl0_364
| ~ spl0_365 ),
inference(duplicate_literal_removal,[],[f4967]) ).
fof(f4967,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X2))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_364
| ~ spl0_365 ),
inference(resolution,[],[f4393,f4389]) ).
fof(f4389,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f4388]) ).
fof(f106491,plain,
( spl0_1719
| ~ spl0_362
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4989,f4392,f4380,f106489]) ).
fof(f106489,plain,
( spl0_1719
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f4380,plain,
( spl0_362
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f4989,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X3)) )
| ~ spl0_362
| ~ spl0_365 ),
inference(duplicate_literal_removal,[],[f4968]) ).
fof(f4968,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_362
| ~ spl0_365 ),
inference(resolution,[],[f4393,f4381]) ).
fof(f4381,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f4380]) ).
fof(f106487,plain,
( spl0_1718
| ~ spl0_304
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4975,f4392,f3384,f106485]) ).
fof(f106485,plain,
( spl0_1718
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Finite__Set_Olinorder__class_OMax(X2,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f3384,plain,
( spl0_304
<=> ! [X0,X11,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Finite__Set_Olinorder__class_OMax(X11,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f4975,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Finite__Set_Olinorder__class_OMax(X2,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_304
| ~ spl0_365 ),
inference(resolution,[],[f4393,f3385]) ).
fof(f3385,plain,
( ! [X3,X0,X11] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Finite__Set_Olinorder__class_OMax(X11,X0)))
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X3,X11,X0))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_304 ),
inference(avatar_component_clause,[],[f3384]) ).
fof(f106483,plain,
( spl0_1717
| ~ spl0_361
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4951,f4388,f4376,f106481]) ).
fof(f106481,plain,
( spl0_1717
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f4951,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) )
| ~ spl0_361
| ~ spl0_364 ),
inference(duplicate_literal_removal,[],[f4937]) ).
fof(f4937,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_361
| ~ spl0_364 ),
inference(resolution,[],[f4389,f4377]) ).
fof(f106479,plain,
( spl0_1716
| ~ spl0_361
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4908,f4380,f4376,f106477]) ).
fof(f106477,plain,
( spl0_1716
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f4908,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3))) )
| ~ spl0_361
| ~ spl0_362 ),
inference(duplicate_literal_removal,[],[f4894]) ).
fof(f4894,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_361
| ~ spl0_362 ),
inference(resolution,[],[f4381,f4377]) ).
fof(f106475,plain,
( spl0_1715
| ~ spl0_304
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4853,f4376,f3384,f106473]) ).
fof(f106473,plain,
( spl0_1715
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Finite__Set_Olinorder__class_OMax(X2,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).
fof(f4853,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Finite__Set_Olinorder__class_OMax(X2,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_304
| ~ spl0_361 ),
inference(resolution,[],[f4377,f3385]) ).
fof(f106471,plain,
( spl0_1714
| ~ spl0_71
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106268,f106217,f1277,f106469]) ).
fof(f106469,plain,
( spl0_1714
<=> ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),tc_bool,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f1277,plain,
( spl0_71
<=> ! [X0,X7,X8] : c_Fun_Oinj__on(X8,c_COMBK(c_False,tc_bool,X0),X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f106268,plain,
( ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),tc_bool,X2)
| ~ spl0_71
| ~ spl0_1672 ),
inference(superposition,[],[f1278,f106218]) ).
fof(f1278,plain,
( ! [X0,X8,X7] : c_Fun_Oinj__on(X8,c_COMBK(c_False,tc_bool,X0),X0,X7)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f106467,plain,
( spl0_1713
| ~ spl0_238
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f4817,f4372,f2299,f106465]) ).
fof(f106465,plain,
( spl0_1713
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f4372,plain,
( spl0_360
<=> ! [X11,X0,X12] :
( X11 = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f4817,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X2 )
| ~ spl0_238
| ~ spl0_360 ),
inference(resolution,[],[f4373,f2300]) ).
fof(f4373,plain,
( ! [X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| X11 = X12 )
| ~ spl0_360 ),
inference(avatar_component_clause,[],[f4372]) ).
fof(f106463,plain,
( spl0_1712
| ~ spl0_237
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f4816,f4372,f2295,f106461]) ).
fof(f106461,plain,
( spl0_1712
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f4816,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X1 )
| ~ spl0_237
| ~ spl0_360 ),
inference(resolution,[],[f4373,f2296]) ).
fof(f106459,plain,
( spl0_1711
| ~ spl0_150
| ~ spl0_275
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4795,f4368,f2948,f1668,f106457]) ).
fof(f106457,plain,
( spl0_1711
<=> ! [X5,X4,X0,X6,X1,X7] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X6))
| ~ hBOOL(hAPP(X0,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,tc_fun(X7,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f1668,plain,
( spl0_150
<=> ! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X11) = c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f2948,plain,
( spl0_275
<=> ! [X11,X0,X12,X7] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool))) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f4368,plain,
( spl0_359
<=> ! [X11,X0,X12,X3,X2,X7] :
( ~ hBOOL(c_in(X3,X11,X0))
| ~ hBOOL(hAPP(hAPP(X12,X3),X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f4795,plain,
( ! [X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X6))
| ~ hBOOL(hAPP(X0,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,tc_fun(X7,tc_bool)),X4)) )
| ~ spl0_150
| ~ spl0_275
| ~ spl0_359 ),
inference(forward_demodulation,[],[f4762,f3192]) ).
fof(f3192,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X2) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X0),X1,X0,tc_fun(X2,tc_bool))
| ~ spl0_150
| ~ spl0_275 ),
inference(superposition,[],[f2949,f1669]) ).
fof(f1669,plain,
( ! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X11) = c_COMBK(c_False,tc_bool,X0)
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1668]) ).
fof(f2949,plain,
( ! [X0,X11,X7,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool))) = X11
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2948]) ).
fof(f4762,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X1,tc_bool)),X5,X6))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,tc_fun(X7,tc_bool)),X4)) )
| ~ spl0_275
| ~ spl0_359 ),
inference(superposition,[],[f4369,f2949]) ).
fof(f4369,plain,
( ! [X2,X3,X0,X11,X7,X12] :
( ~ hBOOL(hAPP(hAPP(X12,X3),X2))
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool)),X2)) )
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f4368]) ).
fof(f106455,plain,
( spl0_1710
| ~ spl0_240
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4787,f4368,f2307,f106453]) ).
fof(f106453,plain,
( spl0_1710
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f2307,plain,
( spl0_240
<=> ! [X0,X11] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f4787,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_240
| ~ spl0_359 ),
inference(superposition,[],[f4369,f2308]) ).
fof(f2308,plain,
( ! [X0,X11] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2307]) ).
fof(f106451,plain,
( spl0_1709
| ~ spl0_239
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4782,f4368,f2303,f106449]) ).
fof(f106449,plain,
( spl0_1709
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f4782,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_239
| ~ spl0_359 ),
inference(superposition,[],[f4369,f2304]) ).
fof(f106447,plain,
( spl0_1708
| ~ spl0_261
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4728,f4368,f2560,f106445]) ).
fof(f106445,plain,
( spl0_1708
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X5)))
| ~ hBOOL(c_in(X0,X5,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f4728,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X5)))
| ~ hBOOL(c_in(X0,X5,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_261
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2561]) ).
fof(f106443,plain,
( spl0_1707
| ~ spl0_256
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4703,f4368,f2540,f106441]) ).
fof(f106441,plain,
( spl0_1707
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_lessequals(X0),X3,tc_fun(X4,tc_bool)),X5))
| ~ hBOOL(c_in(X5,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f4703,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_lessequals(X0),X3,tc_fun(X4,tc_bool)),X5))
| ~ hBOOL(c_in(X5,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2541]) ).
fof(f106439,plain,
( spl0_1706
| ~ spl0_350
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4601,f4344,f4331,f106437]) ).
fof(f106437,plain,
( spl0_1706
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f4331,plain,
( spl0_350
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f4601,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3))) )
| ~ spl0_350
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4594]) ).
fof(f4594,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_350
| ~ spl0_353 ),
inference(resolution,[],[f4345,f4332]) ).
fof(f4332,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_350 ),
inference(avatar_component_clause,[],[f4331]) ).
fof(f106435,plain,
( spl0_1705
| ~ spl0_349
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4600,f4344,f4327,f106433]) ).
fof(f106433,plain,
( spl0_1705
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f4327,plain,
( spl0_349
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f4600,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3))) )
| ~ spl0_349
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4595]) ).
fof(f4595,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_349
| ~ spl0_353 ),
inference(resolution,[],[f4345,f4328]) ).
fof(f4328,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f4327]) ).
fof(f106431,plain,
( spl0_1704
| ~ spl0_305
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4593,f4344,f3388,f106429]) ).
fof(f106429,plain,
( spl0_1704
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X1,X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X1,X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f3388,plain,
( spl0_305
<=> ! [X0,X11,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X11,X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f4593,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X1,X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X1,X0))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_305
| ~ spl0_353 ),
inference(resolution,[],[f4345,f3389]) ).
fof(f3389,plain,
( ! [X3,X0,X11] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X11,X0)),X3))
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X3,X11,X0))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_305 ),
inference(avatar_component_clause,[],[f3388]) ).
fof(f106424,plain,
( spl0_1703
| ~ spl0_207
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4583,f4344,f2037,f106422]) ).
fof(f106422,plain,
( spl0_1703
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),tc_fun(X0,tc_bool)),X3)),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f2037,plain,
( spl0_207
<=> ! [X12,X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f4583,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),tc_fun(X0,tc_bool)),X3)),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_207
| ~ spl0_353 ),
inference(resolution,[],[f4345,f2038]) ).
fof(f2038,plain,
( ! [X0,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),X11))
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2037]) ).
fof(f106420,plain,
( spl0_1702
| ~ spl0_350
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4574,f4335,f4331,f106418]) ).
fof(f106418,plain,
( spl0_1702
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f4574,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4))) )
| ~ spl0_350
| ~ spl0_351 ),
inference(duplicate_literal_removal,[],[f4567]) ).
fof(f4567,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_350
| ~ spl0_351 ),
inference(resolution,[],[f4336,f4332]) ).
fof(f106416,plain,
( spl0_1701
| ~ spl0_349
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4573,f4335,f4327,f106414]) ).
fof(f106414,plain,
( spl0_1701
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f4573,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4))) )
| ~ spl0_349
| ~ spl0_351 ),
inference(duplicate_literal_removal,[],[f4568]) ).
fof(f4568,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_349
| ~ spl0_351 ),
inference(resolution,[],[f4336,f4328]) ).
fof(f106412,plain,
( spl0_1700
| ~ spl0_305
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4566,f4335,f3388,f106410]) ).
fof(f106410,plain,
( spl0_1700
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X1,X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X1,X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f4566,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X1,X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X1,X0))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_305
| ~ spl0_351 ),
inference(resolution,[],[f4336,f3389]) ).
fof(f106408,plain,
( spl0_1699
| ~ spl0_207
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4556,f4335,f2037,f106406]) ).
fof(f106406,plain,
( spl0_1699
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),tc_fun(X0,tc_bool)),X3)),X1))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f4556,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),tc_fun(X0,tc_bool)),X3)),X1))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_207
| ~ spl0_351 ),
inference(resolution,[],[f4336,f2038]) ).
fof(f106404,plain,
( spl0_1698
| ~ spl0_199
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f4522,f4331,f2005,f106402]) ).
fof(f106402,plain,
( spl0_1698
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3),X1),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f2005,plain,
( spl0_199
<=> ! [X11,X0,X12] :
( ~ c_Finite__Set_Ofinite(X12,X0)
| c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f4522,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3),X1),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_199
| ~ spl0_350 ),
inference(resolution,[],[f4332,f2006]) ).
fof(f2006,plain,
( ! [X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofinite(X12,X0) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f2005]) ).
fof(f106400,plain,
( spl0_1697
| ~ spl0_199
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4486,f4327,f2005,f106398]) ).
fof(f106398,plain,
( spl0_1697
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f4486,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_199
| ~ spl0_349 ),
inference(resolution,[],[f4328,f2006]) ).
fof(f106396,plain,
( spl0_1696
| ~ spl0_238
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4468,f4323,f2299,f106394]) ).
fof(f106394,plain,
( spl0_1696
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f4323,plain,
( spl0_348
<=> ! [X11,X0,X12] :
( X11 = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f4468,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0))) )
| ~ spl0_238
| ~ spl0_348 ),
inference(resolution,[],[f4324,f2300]) ).
fof(f4324,plain,
( ! [X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| X11 = X12
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12)) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f4323]) ).
fof(f106392,plain,
( spl0_1695
| ~ spl0_237
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4467,f4323,f2295,f106390]) ).
fof(f106390,plain,
( spl0_1695
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f4467,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2))) )
| ~ spl0_237
| ~ spl0_348 ),
inference(resolution,[],[f4324,f2296]) ).
fof(f106388,plain,
( spl0_1694
| ~ spl0_252
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f4257,f3961,f2524,f106386]) ).
fof(f106386,plain,
( spl0_1694
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X0,X1),X2),X1))
| hBOOL(c_in(X3,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X1))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f2524,plain,
( spl0_252
<=> ! [X11,X0,X2,X1] :
( X1 = X2
| hBOOL(c_in(X1,X11,X0))
| ~ hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X2,X0),X11),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f3961,plain,
( spl0_337
<=> ! [X11,X0,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(c_Set_Oinsert(X1,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f4257,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X0,X1),X2),X1))
| hBOOL(c_in(X3,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X1))
| X0 = X3 )
| ~ spl0_252
| ~ spl0_337 ),
inference(superposition,[],[f2525,f3962]) ).
fof(f3962,plain,
( ! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(c_Set_Oinsert(X1,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)))
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f3961]) ).
fof(f2525,plain,
( ! [X2,X0,X11,X1] :
( ~ hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X2,X0),X11),X0))
| hBOOL(c_in(X1,X11,X0))
| X1 = X2 )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2524]) ).
fof(f106384,plain,
( spl0_1693
| ~ spl0_47
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f106267,f106217,f1171,f106382]) ).
fof(f106382,plain,
( spl0_1693
<=> ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f1171,plain,
( spl0_47
<=> ! [X0] : c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f106267,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool),tc_bool)
| ~ spl0_47
| ~ spl0_1672 ),
inference(superposition,[],[f1172,f106218]) ).
fof(f1172,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f106380,plain,
( spl0_1692
| ~ spl0_165
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4234,f3949,f1768,f106378]) ).
fof(f106378,plain,
( spl0_1692
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X4),X0),v_x))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Inductive_Ocomplete__lattice__class_Olfp(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4)),v_x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f3949,plain,
( spl0_334
<=> ! [X0,X11,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X8,X11)),X11))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X8,X0)),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f4234,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X4),X0),v_x))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Inductive_Ocomplete__lattice__class_Olfp(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4)),v_x)) )
| ~ spl0_165
| ~ spl0_334 ),
inference(superposition,[],[f3950,f1769]) ).
fof(f3950,plain,
( ! [X0,X11,X8] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X8,X11)),X11))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X8,X0)),X11)) )
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f3949]) ).
fof(f106376,plain,
( spl0_1691
| ~ spl0_170
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4211,f3949,f1788,f106374]) ).
fof(f106374,plain,
( spl0_1691
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X1),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f1788,plain,
( spl0_170
<=> ! [X0,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X12) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f4211,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X1),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)),X1)) )
| ~ spl0_170
| ~ spl0_334 ),
inference(superposition,[],[f3950,f1789]) ).
fof(f1789,plain,
( ! [X0,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X12) = X12
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1788]) ).
fof(f106372,plain,
( spl0_1690
| ~ spl0_165
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4185,f3945,f1768,f106370]) ).
fof(f106370,plain,
( spl0_1690
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,X4)),X0))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f3945,plain,
( spl0_333
<=> ! [X44,X11,X0,X26,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| ~ hBOOL(c_in(X26,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X7),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X44,X0,X7)),hAPP(X44,X26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f4185,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,X4)),X0))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_165
| ~ spl0_333 ),
inference(superposition,[],[f3946,f1769]) ).
fof(f3946,plain,
( ! [X0,X11,X44,X26,X7] :
( hBOOL(hAPP(hAPP(c_lessequals(X7),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X44,X0,X7)),hAPP(X44,X26)))
| ~ hBOOL(c_in(X26,X11,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X7) )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f3945]) ).
fof(f106368,plain,
( spl0_1689
| ~ spl0_171
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4181,f3945,f1792,f106366]) ).
fof(f106366,plain,
( spl0_1689
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,c_Set_Oinsert(X0,X1),X4,X2)),hAPP(c_fequal(X1),X0)))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f4181,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,c_Set_Oinsert(X0,X1),X4,X2)),hAPP(c_fequal(X1),X0)))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_171
| ~ spl0_333 ),
inference(superposition,[],[f3946,f1793]) ).
fof(f106364,plain,
( spl0_1688
| ~ spl0_169
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4169,f3945,f1784,f106362]) ).
fof(f106362,plain,
( spl0_1688
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f1784,plain,
( spl0_169
<=> ! [X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_COMBK(c_False,tc_bool,X0)) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f4169,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_169
| ~ spl0_333 ),
inference(superposition,[],[f3946,f1785]) ).
fof(f1785,plain,
( ! [X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_COMBK(c_False,tc_bool,X0)) = X11
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1784]) ).
fof(f106360,plain,
( spl0_1687
| ~ spl0_170
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4162,f3945,f1788,f106358]) ).
fof(f106358,plain,
( spl0_1687
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).
fof(f4162,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_170
| ~ spl0_333 ),
inference(superposition,[],[f3946,f1789]) ).
fof(f106356,plain,
( spl0_1686
| ~ spl0_36
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4128,f3932,f1127,f106354]) ).
fof(f106354,plain,
( spl0_1686
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f1127,plain,
( spl0_36
<=> ! [X80,X79] :
( ~ class_Lattices_Olattice(X80)
| class_Lattices_Oupper__semilattice(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f3932,plain,
( spl0_330
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f4128,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_36
| ~ spl0_330 ),
inference(resolution,[],[f3933,f1128]) ).
fof(f1128,plain,
( ! [X80,X79] :
( class_Lattices_Oupper__semilattice(tc_fun(X79,X80))
| ~ class_Lattices_Olattice(X80) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f3933,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)) )
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f3932]) ).
fof(f106352,plain,
( spl0_1685
| ~ spl0_165
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4106,f3924,f1768,f106350]) ).
fof(f106350,plain,
( spl0_1685
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,X4)))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f3924,plain,
( spl0_328
<=> ! [X44,X11,X0,X26,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| ~ hBOOL(c_in(X26,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X7),hAPP(X44,X26)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X44,X0,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f4106,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,X4)))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_165
| ~ spl0_328 ),
inference(superposition,[],[f3925,f1769]) ).
fof(f3925,plain,
( ! [X0,X11,X44,X26,X7] :
( hBOOL(hAPP(hAPP(c_lessequals(X7),hAPP(X44,X26)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X44,X0,X7)))
| ~ hBOOL(c_in(X26,X11,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X7) )
| ~ spl0_328 ),
inference(avatar_component_clause,[],[f3924]) ).
fof(f106348,plain,
( spl0_1684
| ~ spl0_171
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4102,f3924,f1792,f106346]) ).
fof(f106346,plain,
( spl0_1684
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_fequal(X1),X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_Set_Oinsert(X0,X1),X4,X2)))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f4102,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_fequal(X1),X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_Set_Oinsert(X0,X1),X4,X2)))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_171
| ~ spl0_328 ),
inference(superposition,[],[f3925,f1793]) ).
fof(f106344,plain,
( spl0_1683
| ~ spl0_169
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4091,f3924,f1784,f106342]) ).
fof(f106342,plain,
( spl0_1683
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f4091,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_169
| ~ spl0_328 ),
inference(superposition,[],[f3925,f1785]) ).
fof(f106259,plain,
( spl0_1682
| ~ spl0_170
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4084,f3924,f1788,f106257]) ).
fof(f106257,plain,
( spl0_1682
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f4084,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_170
| ~ spl0_328 ),
inference(superposition,[],[f3925,f1789]) ).
fof(f106255,plain,
( spl0_1681
| ~ spl0_87
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4054,f3920,f1344,f106253]) ).
fof(f106253,plain,
( spl0_1681
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X0,X1)),X2))),X2))
| ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X1)),X2),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f1344,plain,
( spl0_87
<=> ! [X29] :
( ~ hBOOL(hAPP(X29,c_False))
| hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(X29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f3920,plain,
( spl0_327
<=> ! [X0,X9,X8,X7] :
( ~ class_HOL_Oord(X7)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X7)),X8),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X9),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f4054,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X0,X1)),X2))),X2))
| ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X1)),X2),c_False)) )
| ~ spl0_87
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1345]) ).
fof(f1345,plain,
( ! [X29] :
( hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(X29)))
| ~ hBOOL(hAPP(X29,c_False)) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1344]) ).
fof(f3921,plain,
( ! [X0,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X9),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X7)),X8),X9))
| ~ class_HOL_Oord(X7) )
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f3920]) ).
fof(f106251,plain,
( spl0_1680
| ~ spl0_233
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f4023,f3912,f2279,f106249]) ).
fof(f106249,plain,
( spl0_1680
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( c_Fun_Oinj__on(X0,hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X2,tc_bool)),X5)),X3,X6)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X0,X1,X3,X6,X2),X4,X2,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f3912,plain,
( spl0_325
<=> ! [X17,X11,X0,X9,X8,X7] :
( ~ c_Fun_Oinj__on(c_Fun_Ocomp(X9,X8,X17,X7,X0),X11,X0,X7)
| c_Fun_Oinj__on(X9,hAPP(c_Set_Oimage(X8,X0,X17),X11),X17,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f4023,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_Fun_Oinj__on(X0,hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X2,tc_bool)),X5)),X3,X6)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X0,X1,X3,X6,X2),X4,X2,X6) )
| ~ spl0_233
| ~ spl0_325 ),
inference(resolution,[],[f3913,f2280]) ).
fof(f3913,plain,
( ! [X0,X11,X8,X9,X7,X17] :
( ~ c_Fun_Oinj__on(c_Fun_Ocomp(X9,X8,X17,X7,X0),X11,X0,X7)
| c_Fun_Oinj__on(X9,hAPP(c_Set_Oimage(X8,X0,X17),X11),X17,X7) )
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f3912]) ).
fof(f106247,plain,
( spl0_1679
| ~ spl0_41
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4000,f3900,f1147,f106245]) ).
fof(f106245,plain,
( spl0_1679
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f1147,plain,
( spl0_41
<=> ! [X80,X79] :
( ~ class_Lattices_Olattice(X80)
| class_Lattices_Olattice(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f3900,plain,
( spl0_322
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f4000,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_41
| ~ spl0_322 ),
inference(resolution,[],[f3901,f1148]) ).
fof(f1148,plain,
( ! [X80,X79] :
( class_Lattices_Olattice(tc_fun(X79,X80))
| ~ class_Lattices_Olattice(X80) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f3901,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f3900]) ).
fof(f106243,plain,
( spl0_1678
| ~ spl0_87
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f3997,f3896,f1344,f106241]) ).
fof(f106241,plain,
( spl0_1678
<=> ! [X2,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X0)),X2),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X0)),X2))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X0)),X2),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f3896,plain,
( spl0_321
<=> ! [X0,X9,X8,X7] :
( ~ class_HOL_Oord(X7)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X7)),X8),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X8),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f3997,plain,
( ! [X2,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X0)),X2),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X0)),X2))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X0)),X2),c_False)) )
| ~ spl0_87
| ~ spl0_321 ),
inference(resolution,[],[f3897,f1345]) ).
fof(f3897,plain,
( ! [X0,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X7)),X8),X9))
| ~ class_HOL_Oord(X7)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X8),X9)) )
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f3896]) ).
fof(f106239,plain,
( spl0_1677
| ~ spl0_261
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3809,f3416,f2560,f106237]) ).
fof(f106237,plain,
( spl0_1677
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),X1))
| ~ hBOOL(c_in(X0,X3,X1))
| ~ hBOOL(c_in(X3,X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f3416,plain,
( spl0_312
<=> ! [X11,X0,X12,X5] :
( ~ hBOOL(c_in(X5,X11,X0))
| hBOOL(c_in(X5,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f3809,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),X1))
| ~ hBOOL(c_in(X0,X3,X1))
| ~ hBOOL(c_in(X3,X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) )
| ~ spl0_261
| ~ spl0_312 ),
inference(resolution,[],[f3417,f2561]) ).
fof(f3417,plain,
( ! [X0,X11,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(c_in(X5,X12,X0))
| ~ hBOOL(c_in(X5,X11,X0)) )
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f3416]) ).
fof(f106235,plain,
( spl0_1676
| ~ spl0_256
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3796,f3416,f2540,f106233]) ).
fof(f106233,plain,
( spl0_1676
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X3),X2))
| ~ hBOOL(c_in(X1,X3,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f3796,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X3),X2))
| ~ hBOOL(c_in(X1,X3,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) )
| ~ spl0_256
| ~ spl0_312 ),
inference(resolution,[],[f3417,f2541]) ).
fof(f106231,plain,
( spl0_1675
| ~ spl0_256
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3755,f3408,f2540,f106229]) ).
fof(f106229,plain,
( spl0_1675
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X2)) = X1
| ~ hBOOL(c_in(X1,X2,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f3408,plain,
( spl0_310
<=> ! [X12,X0,X11] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X11))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f3755,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X2)) = X1
| ~ hBOOL(c_in(X1,X2,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) )
| ~ spl0_256
| ~ spl0_310 ),
inference(resolution,[],[f3409,f2541]) ).
fof(f3409,plain,
( ! [X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X11))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = X11 )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f3408]) ).
fof(f106227,plain,
( spl0_1674
| ~ spl0_256
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3722,f3404,f2540,f106225]) ).
fof(f106225,plain,
( spl0_1674
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X1)),X2) = X2
| ~ hBOOL(c_in(X2,X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f3404,plain,
( spl0_309
<=> ! [X11,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f3722,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X1)),X2) = X2
| ~ hBOOL(c_in(X2,X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) )
| ~ spl0_256
| ~ spl0_309 ),
inference(resolution,[],[f3405,f2541]) ).
fof(f3405,plain,
( ! [X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = X12 )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f3404]) ).
fof(f106223,plain,
( spl0_1673
| ~ spl0_304
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3708,f3400,f3384,f106221]) ).
fof(f106221,plain,
( spl0_1673
<=> ! [X2,X0,X1] :
( c_Finite__Set_Olinorder__class_OMax(X0,X1) = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMax(X0,X1)),X2))
| ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f3400,plain,
( spl0_308
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f3708,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Olinorder__class_OMax(X0,X1) = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMax(X0,X1)),X2))
| ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_304
| ~ spl0_308 ),
inference(resolution,[],[f3401,f3385]) ).
fof(f3401,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| X3 = X4
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) )
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f3400]) ).
fof(f106219,plain,
( spl0_1672
| ~ spl0_20
| ~ spl0_288
| ~ spl0_587 ),
inference(avatar_split_clause,[],[f13382,f13333,f3000,f1057,f106217]) ).
fof(f1057,plain,
( spl0_20
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f3000,plain,
( spl0_288
<=> ! [X20,X0,X19] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f13333,plain,
( spl0_587
<=> ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_False),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f13382,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_bool)
| c_COMBK(c_False,tc_bool,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X0,c_False,tc_bool) )
| ~ spl0_288
| ~ spl0_587 ),
inference(resolution,[],[f13334,f3001]) ).
fof(f3001,plain,
( ! [X0,X19,X20] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X19))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3000]) ).
fof(f13334,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_False),X0))
| ~ spl0_587 ),
inference(avatar_component_clause,[],[f13333]) ).
fof(f106215,plain,
( spl0_1671
| ~ spl0_305
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3697,f3400,f3388,f106213]) ).
fof(f106213,plain,
( spl0_1671
<=> ! [X2,X0,X1] :
( c_Finite__Set_Olinorder__class_OMin(X1,X2) = X0
| ~ class_Orderings_Oorder(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X0),c_Finite__Set_Olinorder__class_OMin(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f3697,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Olinorder__class_OMin(X1,X2) = X0
| ~ class_Orderings_Oorder(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X0),c_Finite__Set_Olinorder__class_OMin(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_305
| ~ spl0_308 ),
inference(resolution,[],[f3401,f3389]) ).
fof(f106211,plain,
( spl0_1670
| ~ spl0_199
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3649,f3388,f2005,f106209]) ).
fof(f106209,plain,
( spl0_1670
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X2,X0,tc_fun(X1,tc_bool)))
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool))
| c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMin(X0,tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f3649,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X2,X0,tc_fun(X1,tc_bool)))
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool))
| c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMin(X0,tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) )
| ~ spl0_199
| ~ spl0_305 ),
inference(resolution,[],[f3389,f2006]) ).
fof(f106207,plain,
( spl0_1669
| ~ spl0_199
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3629,f3384,f2005,f106205]) ).
fof(f106205,plain,
( spl0_1669
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X2,X0,tc_fun(X1,tc_bool)))
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool))
| c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMax(X0,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f3629,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X2,X0,tc_fun(X1,tc_bool)))
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool))
| c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMax(X0,tc_fun(X1,tc_bool)),X1) )
| ~ spl0_199
| ~ spl0_304 ),
inference(resolution,[],[f3385,f2006]) ).
fof(f106203,plain,
( spl0_1668
| ~ spl0_185
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3615,f3376,f1880,f106201]) ).
fof(f106201,plain,
( spl0_1668
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(X0,hAPP(X1,X5)),X6)
| ~ hBOOL(c_in(X5,X7,X8))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,c_Fun_Ocomp(X0,X1,X2,X3,X4),X8,tc_fun(X6,tc_bool)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f3376,plain,
( spl0_302
<=> ! [X11,X0,X3,X28,X7] :
( ~ hBOOL(c_in(X3,X28,X0))
| ~ c_Finite__Set_Ofinite(hAPP(X11,X3),X7)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28,X11,X0,tc_fun(X7,tc_bool)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f3615,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(X0,hAPP(X1,X5)),X6)
| ~ hBOOL(c_in(X5,X7,X8))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,c_Fun_Ocomp(X0,X1,X2,X3,X4),X8,tc_fun(X6,tc_bool)),X6) )
| ~ spl0_185
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1881]) ).
fof(f3377,plain,
( ! [X3,X28,X0,X11,X7] :
( ~ c_Finite__Set_Ofinite(hAPP(X11,X3),X7)
| ~ hBOOL(c_in(X3,X28,X0))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28,X11,X0,tc_fun(X7,tc_bool)),X7) )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f3376]) ).
fof(f106199,plain,
( spl0_1667
| ~ spl0_178
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3606,f3376,f1852,f106197]) ).
fof(f106197,plain,
( spl0_1667
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(X0,hAPP(X1,X5)),X6)
| ~ hBOOL(c_in(X5,X7,X8))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,c_COMBB(X0,X1,X2,X3,X4),X8,tc_fun(X6,tc_bool)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f1852,plain,
( spl0_178
<=> ! [X7,X17,X0,X31,X29,X30] : hAPP(c_COMBB(X29,X30,X7,X0,X17),X31) = hAPP(X29,hAPP(X30,X31)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f3606,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(X0,hAPP(X1,X5)),X6)
| ~ hBOOL(c_in(X5,X7,X8))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,c_COMBB(X0,X1,X2,X3,X4),X8,tc_fun(X6,tc_bool)),X6) )
| ~ spl0_178
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1853]) ).
fof(f1853,plain,
( ! [X31,X29,X0,X7,X17,X30] : hAPP(c_COMBB(X29,X30,X7,X0,X17),X31) = hAPP(X29,hAPP(X30,X31))
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1852]) ).
fof(f106195,plain,
( spl0_1666
| ~ spl0_191
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3605,f3376,f1904,f106193]) ).
fof(f106193,plain,
( spl0_1666
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X2),X3)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X4,X5))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_Set_Oimage(X0,X1,X2),X5,tc_fun(X3,tc_bool)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f3605,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X2),X3)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X4,X5))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_Set_Oimage(X0,X1,X2),X5,tc_fun(X3,tc_bool)),X3) )
| ~ spl0_191
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1905]) ).
fof(f106191,plain,
( spl0_1665
| ~ spl0_261
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3520,f3364,f2560,f106189]) ).
fof(f106189,plain,
( spl0_1665
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X4),X2,X3)
| ~ hBOOL(c_in(X1,X4,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f3364,plain,
( spl0_299
<=> ! [X11,X0,X12,X8,X7] :
( ~ c_Fun_Oinj__on(X8,X12,X0,X7)
| c_Fun_Oinj__on(X8,X11,X0,X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f3520,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X4),X2,X3)
| ~ hBOOL(c_in(X1,X4,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) )
| ~ spl0_261
| ~ spl0_299 ),
inference(resolution,[],[f3365,f2561]) ).
fof(f3365,plain,
( ! [X0,X11,X8,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| c_Fun_Oinj__on(X8,X11,X0,X7)
| ~ c_Fun_Oinj__on(X8,X12,X0,X7) )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f3364]) ).
fof(f106187,plain,
( spl0_1664
| ~ spl0_256
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3508,f3364,f2540,f106185]) ).
fof(f106185,plain,
( spl0_1664
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_bool)),X2),X1,X3)
| ~ c_Fun_Oinj__on(X0,X4,X1,X3)
| ~ hBOOL(c_in(X4,X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f3508,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_bool)),X2),X1,X3)
| ~ c_Fun_Oinj__on(X0,X4,X1,X3)
| ~ hBOOL(c_in(X4,X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) )
| ~ spl0_256
| ~ spl0_299 ),
inference(resolution,[],[f3365,f2541]) ).
fof(f106183,plain,
( spl0_1663
| ~ spl0_272
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3334,f3016,f2936,f106181]) ).
fof(f106181,plain,
( spl0_1663
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Set_Oinsert(X1,X0),X2),X3,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f2936,plain,
( spl0_272
<=> ! [X11,X0,X12,X3] :
( hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X11)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f3334,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Set_Oinsert(X1,X0),X2),X3,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X3,X0)) )
| ~ spl0_272
| ~ spl0_292 ),
inference(resolution,[],[f3017,f2937]) ).
fof(f2937,plain,
( ! [X3,X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X11)),X12))
| hBOOL(c_in(X3,X12,X0)) )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f2936]) ).
fof(f106179,plain,
( spl0_1662
| ~ spl0_276
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3333,f3016,f2952,f106177]) ).
fof(f106177,plain,
( spl0_1662
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f2952,plain,
( spl0_276
<=> ! [X0,X11] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),c_COMBK(c_False,tc_bool,X0)))
| c_COMBK(c_False,tc_bool,X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f3333,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X0) = X1 )
| ~ spl0_276
| ~ spl0_292 ),
inference(resolution,[],[f3017,f2953]) ).
fof(f2953,plain,
( ! [X0,X11] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),c_COMBK(c_False,tc_bool,X0)))
| c_COMBK(c_False,tc_bool,X0) = X11 )
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f2952]) ).
fof(f106094,plain,
( spl0_1661
| ~ spl0_171
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3059,f2920,f1792,f106092]) ).
fof(f106092,plain,
( spl0_1661
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_Set_Oinsert(X0,X1),X2) != hAPP(c_fequal(X1),X0)
| c_COMBK(c_False,tc_bool,X1) = X2
| ~ c_Fun_Oinj__on(c_Set_Oinsert(X0,X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f2920,plain,
( spl0_269
<=> ! [X4,X7,X0,X3,X8] :
( X3 = X4
| hAPP(X8,X3) != hAPP(X8,X4)
| ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f3059,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(c_Set_Oinsert(X0,X1),X2) != hAPP(c_fequal(X1),X0)
| c_COMBK(c_False,tc_bool,X1) = X2
| ~ c_Fun_Oinj__on(c_Set_Oinsert(X0,X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_171
| ~ spl0_269 ),
inference(superposition,[],[f2921,f1793]) ).
fof(f2921,plain,
( ! [X3,X0,X8,X7,X4] :
( hAPP(X8,X3) != hAPP(X8,X4)
| X3 = X4
| ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f2920]) ).
fof(f106090,plain,
( spl0_1660
| ~ spl0_92
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3051,f2920,f1379,f106088]) ).
fof(f106088,plain,
( spl0_1660
<=> ! [X3,X4,X0,X7,X6,X5,X2,X1] :
( hAPP(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5) != X2
| X1 = X5
| ~ c_Fun_Oinj__on(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool)),X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f3051,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5) != X2
| X1 = X5
| ~ c_Fun_Oinj__on(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool)),X6,X7) )
| ~ spl0_92
| ~ spl0_269 ),
inference(superposition,[],[f2921,f1380]) ).
fof(f106086,plain,
( spl0_1659
| ~ spl0_100
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3041,f2920,f1413,f106084]) ).
fof(f106084,plain,
( spl0_1659
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) != X1
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f3041,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) != X1
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_100
| ~ spl0_269 ),
inference(superposition,[],[f2921,f1414]) ).
fof(f106082,plain,
( spl0_1658
| ~ spl0_240
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2714,f2520,f2307,f106080]) ).
fof(f106080,plain,
( spl0_1658
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f2520,plain,
( spl0_251
<=> ! [X11,X0,X3,X8,X7] :
( ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(hAPP(X8,X3),hAPP(c_Set_Oimage(X8,X0,X7),X11),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2714,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X4,X2)) )
| ~ spl0_240
| ~ spl0_251 ),
inference(superposition,[],[f2521,f2308]) ).
fof(f2521,plain,
( ! [X3,X0,X11,X8,X7] :
( hBOOL(c_in(hAPP(X8,X3),hAPP(c_Set_Oimage(X8,X0,X7),X11),X7))
| ~ hBOOL(c_in(X3,X11,X0)) )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2520]) ).
fof(f106078,plain,
( spl0_1657
| ~ spl0_239
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2710,f2520,f2303,f106076]) ).
fof(f106076,plain,
( spl0_1657
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2,X3),X4),X3))
| ~ hBOOL(c_in(X1,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f2710,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2,X3),X4),X3))
| ~ hBOOL(c_in(X1,X4,X2)) )
| ~ spl0_239
| ~ spl0_251 ),
inference(superposition,[],[f2521,f2304]) ).
fof(f106074,plain,
( spl0_1656
| ~ spl0_207
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2620,f2495,f2037,f106072]) ).
fof(f106072,plain,
( spl0_1656
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f2495,plain,
( spl0_247
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2620,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)) )
| ~ spl0_207
| ~ spl0_247 ),
inference(resolution,[],[f2496,f2038]) ).
fof(f2496,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = X4 )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f2495]) ).
fof(f106069,plain,
( spl0_1655
| ~ spl0_207
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2588,f2487,f2037,f106067]) ).
fof(f106067,plain,
( spl0_1655
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f2487,plain,
( spl0_245
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2588,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)),X1) )
| ~ spl0_207
| ~ spl0_245 ),
inference(resolution,[],[f2488,f2038]) ).
fof(f2488,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = X3 )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2487]) ).
fof(f105495,plain,
( spl0_1654
| ~ spl0_92
| ~ spl0_1652 ),
inference(avatar_split_clause,[],[f104625,f91796,f1379,f105493]) ).
fof(f105493,plain,
( spl0_1654
<=> ! [X1] : hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),c_False) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f91796,plain,
( spl0_1652
<=> ! [X0] : hAPP(X0,v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),c_False) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f104625,plain,
( ! [X1] : hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),c_False) = X1
| ~ spl0_92
| ~ spl0_1652 ),
inference(superposition,[],[f91797,f1380]) ).
fof(f91797,plain,
( ! [X0] : hAPP(X0,v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),c_False)
| ~ spl0_1652 ),
inference(avatar_component_clause,[],[f91796]) ).
fof(f101277,plain,
( spl0_1653
| ~ spl0_92
| ~ spl0_1651 ),
inference(avatar_split_clause,[],[f99675,f91179,f1379,f101275]) ).
fof(f101275,plain,
( spl0_1653
<=> ! [X1] : c_False = hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f91179,plain,
( spl0_1651
<=> ! [X0] : c_False = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(X0,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f99675,plain,
( ! [X1] : c_False = hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),X1)
| ~ spl0_92
| ~ spl0_1651 ),
inference(superposition,[],[f91180,f1380]) ).
fof(f91180,plain,
( ! [X0] : c_False = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(X0,v_x))
| ~ spl0_1651 ),
inference(avatar_component_clause,[],[f91179]) ).
fof(f91798,plain,
( spl0_1652
| ~ spl0_70
| ~ spl0_275
| ~ spl0_660
| ~ spl0_900 ),
inference(avatar_split_clause,[],[f39332,f36638,f28672,f2948,f1273,f91796]) ).
fof(f28672,plain,
( spl0_660
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X2) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X0),X1,X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f36638,plain,
( spl0_900
<=> ! [X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(t_a,tc_bool)),X1),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(X1,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f39332,plain,
( ! [X0] : hAPP(X0,v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),c_False)
| ~ spl0_70
| ~ spl0_275
| ~ spl0_660
| ~ spl0_900 ),
inference(forward_demodulation,[],[f39331,f1274]) ).
fof(f39331,plain,
( ! [X0] : hAPP(X0,v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(c_COMBK(c_False,tc_bool,t_a),v_x))
| ~ spl0_275
| ~ spl0_660
| ~ spl0_900 ),
inference(forward_demodulation,[],[f39279,f28673]) ).
fof(f28673,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X2) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X0),X1,X0,tc_fun(X2,tc_bool))
| ~ spl0_660 ),
inference(avatar_component_clause,[],[f28672]) ).
fof(f39279,plain,
( ! [X2,X0,X1] : hAPP(X0,v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X1),X2,X1,tc_fun(t_a,tc_bool)),v_x))
| ~ spl0_275
| ~ spl0_900 ),
inference(superposition,[],[f36639,f2949]) ).
fof(f36639,plain,
( ! [X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(t_a,tc_bool)),X1),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(X1,v_x))
| ~ spl0_900 ),
inference(avatar_component_clause,[],[f36638]) ).
fof(f91181,plain,
( spl0_1651
| ~ spl0_70
| ~ spl0_150
| ~ spl0_900 ),
inference(avatar_split_clause,[],[f39327,f36638,f1668,f1273,f91179]) ).
fof(f39327,plain,
( ! [X0] : c_False = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(X0,v_x))
| ~ spl0_70
| ~ spl0_150
| ~ spl0_900 ),
inference(forward_demodulation,[],[f39276,f1274]) ).
fof(f39276,plain,
( ! [X0] : hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(X0,v_x))
| ~ spl0_150
| ~ spl0_900 ),
inference(superposition,[],[f36639,f1669]) ).
fof(f89564,plain,
( spl0_1650
| ~ spl0_337
| ~ spl0_402
| ~ spl0_442
| ~ spl0_443
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f21891,f8454,f6756,f6752,f5523,f3961,f89562]) ).
fof(f89562,plain,
( spl0_1650
<=> ! [X0,X3,X2,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_Set_Oinsert(X1,X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f5523,plain,
( spl0_402
<=> ! [X12,X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f6756,plain,
( spl0_443
<=> ! [X18,X0,X12,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)),X18) = hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f8454,plain,
( spl0_481
<=> ! [X11,X0,X12,X1] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),tc_fun(X0,tc_bool)),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f21891,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_Set_Oinsert(X1,X0),X3))
| ~ spl0_337
| ~ spl0_402
| ~ spl0_442
| ~ spl0_443
| ~ spl0_481 ),
inference(forward_demodulation,[],[f21890,f7122]) ).
fof(f7122,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(c_Set_Oinsert(X0,X1),X2)) = hAPP(c_Set_Oinsert(X0,X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0))))
| ~ spl0_337
| ~ spl0_442 ),
inference(superposition,[],[f6753,f3962]) ).
fof(f21890,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3) = hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))))
| ~ spl0_402
| ~ spl0_443
| ~ spl0_481 ),
inference(forward_demodulation,[],[f21819,f9163]) ).
fof(f9163,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X3)))
| ~ spl0_402
| ~ spl0_481 ),
inference(superposition,[],[f5524,f8455]) ).
fof(f8455,plain,
( ! [X0,X11,X1,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),tc_fun(X0,tc_bool)),X12)
| ~ spl0_481 ),
inference(avatar_component_clause,[],[f8454]) ).
fof(f5524,plain,
( ! [X0,X11,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),X11))
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f5523]) ).
fof(f21819,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3) = hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2))))
| ~ spl0_402
| ~ spl0_443 ),
inference(superposition,[],[f6757,f5524]) ).
fof(f6757,plain,
( ! [X0,X1,X18,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)),X18) = hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18))
| ~ spl0_443 ),
inference(avatar_component_clause,[],[f6756]) ).
fof(f89560,plain,
( spl0_1649
| ~ spl0_149
| ~ spl0_171
| ~ spl0_558 ),
inference(avatar_split_clause,[],[f12337,f12204,f1792,f1664,f89558]) ).
fof(f89558,plain,
( spl0_1649
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),hAPP(c_fequal(X2),X0)))
| ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X0,c_COMBK(c_False,tc_bool,X2),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f1664,plain,
( spl0_149
<=> ! [X0,X11] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),c_COMBK(c_False,tc_bool,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f12204,plain,
( spl0_558
<=> ! [X11,X0,X12,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3))),X12))
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f12337,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),hAPP(c_fequal(X2),X0)))
| ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X0,c_COMBK(c_False,tc_bool,X2),X2)) )
| ~ spl0_149
| ~ spl0_171
| ~ spl0_558 ),
inference(forward_demodulation,[],[f12322,f1793]) ).
fof(f12322,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X0,c_COMBK(c_False,tc_bool,X2),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),hAPP(c_Set_Oinsert(X0,X2),c_COMBK(c_False,tc_bool,X2)))) )
| ~ spl0_149
| ~ spl0_558 ),
inference(resolution,[],[f12205,f1665]) ).
fof(f1665,plain,
( ! [X0,X11] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),c_COMBK(c_False,tc_bool,X0)))
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1664]) ).
fof(f12205,plain,
( ! [X3,X0,X11,X12] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3))),X12))
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) )
| ~ spl0_558 ),
inference(avatar_component_clause,[],[f12204]) ).
fof(f89556,plain,
( spl0_1648
| ~ spl0_163
| ~ spl0_535 ),
inference(avatar_split_clause,[],[f11458,f11053,f1760,f89554]) ).
fof(f89554,plain,
( spl0_1648
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f1760,plain,
( spl0_163
<=> ! [X13,X0,X14] :
( c_Finite__Set_Ofinite(X14,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X13),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f11053,plain,
( spl0_535
<=> ! [X44,X11,X0,X12,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X7,tc_bool)),X11),X12),X44,X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X44,X7,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X44,X7,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f11458,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_163
| ~ spl0_535 ),
inference(superposition,[],[f1761,f11054]) ).
fof(f11054,plain,
( ! [X0,X11,X44,X7,X12] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X7,tc_bool)),X11),X12),X44,X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X44,X7,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X44,X7,tc_fun(X0,tc_bool)))
| ~ spl0_535 ),
inference(avatar_component_clause,[],[f11053]) ).
fof(f1761,plain,
( ! [X0,X14,X13] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X13),X0)
| c_Finite__Set_Ofinite(X14,X0) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1760]) ).
fof(f89552,plain,
( spl0_1647
| ~ spl0_162
| ~ spl0_535 ),
inference(avatar_split_clause,[],[f11457,f11053,f1756,f89550]) ).
fof(f89550,plain,
( spl0_1647
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X3,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f1756,plain,
( spl0_162
<=> ! [X13,X0,X14] :
( c_Finite__Set_Ofinite(X13,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X13),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f11457,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X3,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_162
| ~ spl0_535 ),
inference(superposition,[],[f1757,f11054]) ).
fof(f1757,plain,
( ! [X0,X14,X13] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X13),X0)
| c_Finite__Set_Ofinite(X13,X0) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1756]) ).
fof(f89548,plain,
( spl0_1646
| ~ spl0_163
| ~ spl0_534 ),
inference(avatar_split_clause,[],[f11350,f11049,f1760,f89546]) ).
fof(f89546,plain,
( spl0_1646
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3),tc_fun(X0,tc_bool)),X2),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f11049,plain,
( spl0_534
<=> ! [X18,X11,X0,X12] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),tc_fun(X0,tc_bool)),X18) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X18)),hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),X18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f11350,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3),tc_fun(X0,tc_bool)),X2),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0) )
| ~ spl0_163
| ~ spl0_534 ),
inference(superposition,[],[f1761,f11050]) ).
fof(f11050,plain,
( ! [X0,X11,X18,X12] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),tc_fun(X0,tc_bool)),X18) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X18)),hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),X18))
| ~ spl0_534 ),
inference(avatar_component_clause,[],[f11049]) ).
fof(f89544,plain,
( spl0_1645
| ~ spl0_162
| ~ spl0_534 ),
inference(avatar_split_clause,[],[f11349,f11049,f1756,f89542]) ).
fof(f89542,plain,
( spl0_1645
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3),tc_fun(X0,tc_bool)),X2),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X0,tc_bool)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f11349,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3),tc_fun(X0,tc_bool)),X2),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X0,tc_bool)),X2),X0) )
| ~ spl0_162
| ~ spl0_534 ),
inference(superposition,[],[f1757,f11050]) ).
fof(f89540,plain,
( spl0_1644
| ~ spl0_213
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f10418,f10328,f2064,f89538]) ).
fof(f89538,plain,
( spl0_1644
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X0),X3),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f2064,plain,
( spl0_213
<=> ! [X12,X0,X11,X3] :
( ~ hBOOL(hAPP(X11,X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f10418,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X0),X3),X5)) )
| ~ spl0_213
| ~ spl0_517 ),
inference(superposition,[],[f2065,f10329]) ).
fof(f2065,plain,
( ! [X3,X0,X11,X12] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X3))
| ~ hBOOL(hAPP(X11,X3)) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2064]) ).
fof(f89536,plain,
( spl0_1643
| ~ spl0_212
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f10417,f10328,f2060,f89534]) ).
fof(f89534,plain,
( spl0_1643
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X0),X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f2060,plain,
( spl0_212
<=> ! [X11,X0,X12,X3] :
( ~ hBOOL(hAPP(X12,X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f10417,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X0),X4),X5)) )
| ~ spl0_212
| ~ spl0_517 ),
inference(superposition,[],[f2061,f10329]) ).
fof(f2061,plain,
( ! [X3,X0,X11,X12] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X3))
| ~ hBOOL(hAPP(X12,X3)) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2060]) ).
fof(f89532,plain,
( spl0_1642
| ~ spl0_606
| ~ spl0_1600 ),
inference(avatar_split_clause,[],[f89226,f89064,f13625,f89530]) ).
fof(f89530,plain,
( spl0_1642
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f13625,plain,
( spl0_606
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f89064,plain,
( spl0_1600
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f89226,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_606
| ~ spl0_1600 ),
inference(superposition,[],[f89065,f13626]) ).
fof(f13626,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X0)
| ~ spl0_606 ),
inference(avatar_component_clause,[],[f13625]) ).
fof(f89065,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0)
| ~ spl0_1600 ),
inference(avatar_component_clause,[],[f89064]) ).
fof(f89528,plain,
( spl0_1641
| ~ spl0_133
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f9154,f8454,f1598,f89526]) ).
fof(f89526,plain,
( spl0_1641
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X3)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f1598,plain,
( spl0_133
<=> ! [X12,X0,X11] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f9154,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X3)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)),X1) )
| ~ spl0_133
| ~ spl0_481 ),
inference(superposition,[],[f1599,f8455]) ).
fof(f1599,plain,
( ! [X0,X11,X12] :
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)
| ~ c_Finite__Set_Ofinite(X11,X0) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1598]) ).
fof(f89524,plain,
( spl0_1640
| ~ spl0_207
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f9098,f8450,f2037,f89522]) ).
fof(f89522,plain,
( spl0_1640
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X3,X1),X2))),hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f9098,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X3,X1),X2))),hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2)))
| ~ spl0_207
| ~ spl0_480 ),
inference(superposition,[],[f2038,f8451]) ).
fof(f89520,plain,
( spl0_1639
| ~ spl0_199
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f9028,f8446,f2005,f89518]) ).
fof(f89518,plain,
( spl0_1639
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X0,X4),X1),X4)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X0,X4),X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f9028,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X0,X4),X1),X4)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X0,X4),X2),X4) )
| ~ spl0_199
| ~ spl0_479 ),
inference(resolution,[],[f8447,f2006]) ).
fof(f89516,plain,
( spl0_1638
| ~ spl0_187
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f9027,f8446,f1888,f89514]) ).
fof(f89514,plain,
( spl0_1638
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(X3,X0,tc_Hoare__Mirabelle_Otriple(X4)),X2),hAPP(c_Set_Oimage(X3,X0,tc_Hoare__Mirabelle_Otriple(X4)),X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f1888,plain,
( spl0_187
<=> ! [X13,X69,X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X69),X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f9027,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(X3,X0,tc_Hoare__Mirabelle_Otriple(X4)),X2),hAPP(c_Set_Oimage(X3,X0,tc_Hoare__Mirabelle_Otriple(X4)),X1),X4) )
| ~ spl0_187
| ~ spl0_479 ),
inference(resolution,[],[f8447,f1889]) ).
fof(f1889,plain,
( ! [X0,X69,X13] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X69),X13))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1888]) ).
fof(f89512,plain,
( spl0_1637
| ~ spl0_238
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8756,f8434,f2299,f89510]) ).
fof(f89510,plain,
( spl0_1637
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f8756,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool))))
| ~ spl0_238
| ~ spl0_476 ),
inference(superposition,[],[f2300,f8435]) ).
fof(f89508,plain,
( spl0_1636
| ~ spl0_264
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8740,f8434,f2572,f89506]) ).
fof(f89506,plain,
( spl0_1636
<=> ! [X0,X3,X2,X1] : hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_fequal(X0),X3,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X1,X3),X2),c_fequal(X0),X3,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f2572,plain,
( spl0_264
<=> ! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f8740,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_fequal(X0),X3,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X1,X3),X2),c_fequal(X0),X3,tc_fun(X0,tc_bool))
| ~ spl0_264
| ~ spl0_476 ),
inference(superposition,[],[f8435,f2573]) ).
fof(f2573,plain,
( ! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X11)
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f2572]) ).
fof(f89504,plain,
( spl0_1635
| ~ spl0_238
| ~ spl0_468 ),
inference(avatar_split_clause,[],[f8383,f7953,f2299,f89502]) ).
fof(f89502,plain,
( spl0_1635
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f7953,plain,
( spl0_468
<=> ! [X18,X11,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f8383,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X2))) )
| ~ spl0_238
| ~ spl0_468 ),
inference(resolution,[],[f7954,f2300]) ).
fof(f7954,plain,
( ! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18)) )
| ~ spl0_468 ),
inference(avatar_component_clause,[],[f7953]) ).
fof(f89500,plain,
( spl0_1634
| ~ spl0_237
| ~ spl0_468 ),
inference(avatar_split_clause,[],[f8382,f7953,f2295,f89498]) ).
fof(f89498,plain,
( spl0_1634
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f8382,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))) )
| ~ spl0_237
| ~ spl0_468 ),
inference(resolution,[],[f7954,f2296]) ).
fof(f89496,plain,
( spl0_1633
| ~ spl0_187
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f8308,f7945,f1888,f89494]) ).
fof(f89494,plain,
( spl0_1633
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| ~ hBOOL(c_in(X3,X2,tc_Hoare__Mirabelle_Otriple(X0)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f8308,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| ~ hBOOL(c_in(X3,X2,tc_Hoare__Mirabelle_Otriple(X0)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X1),X0) )
| ~ spl0_187
| ~ spl0_466 ),
inference(resolution,[],[f7946,f1889]) ).
fof(f89492,plain,
( spl0_1632
| ~ spl0_238
| ~ spl0_457 ),
inference(avatar_split_clause,[],[f8022,f7909,f2299,f89490]) ).
fof(f89490,plain,
( spl0_1632
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f7909,plain,
( spl0_457
<=> ! [X18,X11,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X12),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f8022,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X3)) )
| ~ spl0_238
| ~ spl0_457 ),
inference(resolution,[],[f7910,f2300]) ).
fof(f7910,plain,
( ! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X12),X18))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X18)) )
| ~ spl0_457 ),
inference(avatar_component_clause,[],[f7909]) ).
fof(f89225,plain,
( spl0_1631
| ~ spl0_237
| ~ spl0_457 ),
inference(avatar_split_clause,[],[f8021,f7909,f2295,f89223]) ).
fof(f89223,plain,
( spl0_1631
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f8021,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X3)) )
| ~ spl0_237
| ~ spl0_457 ),
inference(resolution,[],[f7910,f2296]) ).
fof(f89221,plain,
( spl0_1630
| ~ spl0_238
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f7978,f7862,f2299,f89219]) ).
fof(f89219,plain,
( spl0_1630
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f7862,plain,
( spl0_456
<=> ! [X18,X11,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f7978,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X2))) )
| ~ spl0_238
| ~ spl0_456 ),
inference(resolution,[],[f7863,f2300]) ).
fof(f7863,plain,
( ! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X18)) )
| ~ spl0_456 ),
inference(avatar_component_clause,[],[f7862]) ).
fof(f89217,plain,
( spl0_1629
| ~ spl0_237
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f7977,f7862,f2295,f89215]) ).
fof(f89215,plain,
( spl0_1629
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f7977,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))) )
| ~ spl0_237
| ~ spl0_456 ),
inference(resolution,[],[f7863,f2296]) ).
fof(f89213,plain,
( spl0_1628
| ~ spl0_259
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f7598,f7488,f2552,f89211]) ).
fof(f89211,plain,
( spl0_1628
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f7488,plain,
( spl0_450
<=> ! [X18,X53,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X18),X53))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X18)),hAPP(c_Set_Oinsert(X1,X0),X53))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f7598,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X1),X4)) )
| ~ spl0_259
| ~ spl0_450 ),
inference(resolution,[],[f7489,f2553]) ).
fof(f7489,plain,
( ! [X0,X1,X18,X53] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X18)),hAPP(c_Set_Oinsert(X1,X0),X53)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X18),X53)) )
| ~ spl0_450 ),
inference(avatar_component_clause,[],[f7488]) ).
fof(f89209,plain,
( spl0_1627
| ~ spl0_377
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f7440,f6764,f5038,f89207]) ).
fof(f89207,plain,
( spl0_1627
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X4,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X1,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f6764,plain,
( spl0_445
<=> ! [X18,X11,X0,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f7440,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X4,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X1,X2,X4)) )
| ~ spl0_377
| ~ spl0_445 ),
inference(resolution,[],[f6765,f5039]) ).
fof(f6765,plain,
( ! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18)) )
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f6764]) ).
fof(f89205,plain,
( spl0_1626
| ~ spl0_264
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f7390,f6760,f2572,f89203]) ).
fof(f89203,plain,
( spl0_1626
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f6760,plain,
( spl0_444
<=> ! [X18,X11,X0,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f7390,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X3)) )
| ~ spl0_264
| ~ spl0_444 ),
inference(superposition,[],[f6761,f2573]) ).
fof(f6761,plain,
( ! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18)) )
| ~ spl0_444 ),
inference(avatar_component_clause,[],[f6760]) ).
fof(f89201,plain,
( spl0_1625
| ~ spl0_377
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f7382,f6760,f5038,f89199]) ).
fof(f89199,plain,
( spl0_1625
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X4,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f7382,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X4,X2,X3)) )
| ~ spl0_377
| ~ spl0_444 ),
inference(resolution,[],[f6761,f5039]) ).
fof(f89197,plain,
( spl0_1624
| ~ spl0_258
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7288,f6756,f2548,f89195]) ).
fof(f89195,plain,
( spl0_1624
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X1,X0),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f2548,plain,
( spl0_258
<=> ! [X11,X0,X12,X5] :
( ~ hBOOL(c_in(X5,X11,X0))
| hBOOL(c_in(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f7288,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X1,X0),X2),X0)) )
| ~ spl0_258
| ~ spl0_443 ),
inference(superposition,[],[f2549,f6757]) ).
fof(f2549,plain,
( ! [X0,X11,X5,X12] :
( hBOOL(c_in(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0))
| ~ hBOOL(c_in(X5,X11,X0)) )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f2548]) ).
fof(f89193,plain,
( spl0_1623
| ~ spl0_249
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7284,f6756,f2503,f89191]) ).
fof(f89191,plain,
( spl0_1623
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X1,X0),X2),X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f2503,plain,
( spl0_249
<=> ! [X11,X0,X12,X8,X7] :
( c_Fun_Oinj__on(X8,X11,X0,X7)
| ~ c_Fun_Oinj__on(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f7284,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X1,X0),X2),X0,X5) )
| ~ spl0_249
| ~ spl0_443 ),
inference(superposition,[],[f2504,f6757]) ).
fof(f2504,plain,
( ! [X0,X11,X8,X7,X12] :
( ~ c_Fun_Oinj__on(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0,X7)
| c_Fun_Oinj__on(X8,X11,X0,X7) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2503]) ).
fof(f89189,plain,
( spl0_1622
| ~ spl0_266
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7224,f6752,f2580,f89187]) ).
fof(f89187,plain,
( spl0_1622
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X3)),X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f2580,plain,
( spl0_266
<=> ! [X60,X13,X0,X69] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X60),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f7224,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X3)),X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),X0),X1) )
| ~ spl0_266
| ~ spl0_442 ),
inference(superposition,[],[f2581,f6753]) ).
fof(f2581,plain,
( ! [X0,X69,X60,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X60),X0) )
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f2580]) ).
fof(f89150,plain,
( spl0_1621
| ~ spl0_272
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7212,f6752,f2936,f89148]) ).
fof(f89148,plain,
( spl0_1621
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3))),X4))
| hBOOL(c_in(X0,X4,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f7212,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3))),X4))
| hBOOL(c_in(X0,X4,X1)) )
| ~ spl0_272
| ~ spl0_442 ),
inference(superposition,[],[f2937,f6753]) ).
fof(f89146,plain,
( spl0_1620
| ~ spl0_257
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7158,f6752,f2544,f89144]) ).
fof(f89144,plain,
( spl0_1620
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X0),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f7158,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X0),X3),X0)) )
| ~ spl0_257
| ~ spl0_442 ),
inference(superposition,[],[f2545,f6753]) ).
fof(f89142,plain,
( spl0_1619
| ~ spl0_248
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7154,f6752,f2499,f89140]) ).
fof(f89140,plain,
( spl0_1619
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X0),X3),X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f7154,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X0),X3),X0,X5) )
| ~ spl0_248
| ~ spl0_442 ),
inference(superposition,[],[f2500,f6753]) ).
fof(f89138,plain,
( spl0_1618
| ~ spl0_264
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7137,f6752,f2572,f89136]) ).
fof(f89136,plain,
( spl0_1618
<=> ! [X0,X3,X2,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_Set_Oinsert(X3,X0),X2)) = hAPP(c_Set_Oinsert(X3,X0),hAPP(c_Set_Oinsert(X1,X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f7137,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_Set_Oinsert(X3,X0),X2)) = hAPP(c_Set_Oinsert(X3,X0),hAPP(c_Set_Oinsert(X1,X0),X2))
| ~ spl0_264
| ~ spl0_442 ),
inference(superposition,[],[f6753,f2573]) ).
fof(f89134,plain,
( spl0_1617
| ~ spl0_250
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7135,f6752,f2516,f89132]) ).
fof(f89132,plain,
( spl0_1617
<=> ! [X0,X3,X2,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X3,X0),X2)) = hAPP(c_Set_Oinsert(X3,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f2516,plain,
( spl0_250
<=> ! [X12,X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f7135,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X3,X0),X2)) = hAPP(c_Set_Oinsert(X3,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_250
| ~ spl0_442 ),
inference(superposition,[],[f6753,f2517]) ).
fof(f2517,plain,
( ! [X0,X11,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X11)
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2516]) ).
fof(f89130,plain,
( spl0_1616
| ~ spl0_250
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7128,f6752,f2516,f89128]) ).
fof(f89128,plain,
( spl0_1616
<=> ! [X0,X3,X2,X1] : hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X2,X0),X3)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f7128,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X2,X0),X3)),X1)
| ~ spl0_250
| ~ spl0_442 ),
inference(superposition,[],[f6753,f2517]) ).
fof(f89126,plain,
( spl0_1615
| ~ spl0_221
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f6999,f6711,f2097,f89124]) ).
fof(f89124,plain,
( spl0_1615
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X3,X4,X5)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f6999,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X3,X4,X5)
| X1 = X2 )
| ~ spl0_221
| ~ spl0_432 ),
inference(trivial_inequality_removal,[],[f6998]) ).
fof(f6998,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_COMBK(c_False,tc_bool,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X3,X4,X5)
| X1 = X2 )
| ~ spl0_221
| ~ spl0_432 ),
inference(forward_demodulation,[],[f6923,f2098]) ).
fof(f6923,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X2)
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X3,X4,X5)
| X1 = X2 )
| ~ spl0_221
| ~ spl0_432 ),
inference(superposition,[],[f6712,f2098]) ).
fof(f89122,plain,
( spl0_1614
| ~ spl0_312
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f6613,f6432,f3416,f89120]) ).
fof(f89120,plain,
( spl0_1614
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(c_in(X3,c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0),X0))
| ~ hBOOL(c_in(X3,c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f6432,plain,
( spl0_422
<=> ! [X5,X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f6613,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(c_in(X3,c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0),X0))
| ~ hBOOL(c_in(X3,c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0)) )
| ~ spl0_312
| ~ spl0_422 ),
inference(resolution,[],[f6433,f3417]) ).
fof(f6433,plain,
( ! [X2,X0,X1,X6,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_422 ),
inference(avatar_component_clause,[],[f6432]) ).
fof(f89118,plain,
( spl0_1613
| ~ spl0_299
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f6610,f6432,f3364,f89116]) ).
fof(f89116,plain,
( spl0_1613
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_Fun_Oinj__on(X3,c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0,X4)
| ~ c_Fun_Oinj__on(X3,c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f6610,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_Fun_Oinj__on(X3,c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0,X4)
| ~ c_Fun_Oinj__on(X3,c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0),X0,X4) )
| ~ spl0_299
| ~ spl0_422 ),
inference(resolution,[],[f6433,f3365]) ).
fof(f89114,plain,
( spl0_1612
| ~ spl0_236
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f6338,f5559,f2291,f89112]) ).
fof(f89112,plain,
( spl0_1612
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f2291,plain,
( spl0_236
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f6338,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)))
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_236
| ~ spl0_411 ),
inference(resolution,[],[f5560,f2292]) ).
fof(f2292,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2291]) ).
fof(f89110,plain,
( ~ spl0_6
| spl0_1611
| ~ spl0_235
| ~ spl0_1579 ),
inference(avatar_split_clause,[],[f88960,f88917,f2287,f89108,f987]) ).
fof(f987,plain,
( spl0_6
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f89108,plain,
( spl0_1611
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f2287,plain,
( spl0_235
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f88917,plain,
( spl0_1579
<=> ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f88960,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)))
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_235
| ~ spl0_1579 ),
inference(resolution,[],[f88918,f2288]) ).
fof(f2288,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2287]) ).
fof(f88918,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0))
| ~ spl0_1579 ),
inference(avatar_component_clause,[],[f88917]) ).
fof(f89106,plain,
( spl0_1610
| ~ spl0_235
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f6337,f5559,f2287,f89104]) ).
fof(f89104,plain,
( spl0_1610
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f6337,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)))
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_235
| ~ spl0_411 ),
inference(resolution,[],[f5560,f2288]) ).
fof(f89102,plain,
( spl0_1609
| ~ spl0_234
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6302,f5555,f2283,f89100]) ).
fof(f89100,plain,
( spl0_1609
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f6302,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_410 ),
inference(resolution,[],[f5556,f2284]) ).
fof(f89098,plain,
( spl0_1608
| ~ spl0_243
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6300,f5555,f2319,f89096]) ).
fof(f89096,plain,
( spl0_1608
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f6300,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_410 ),
inference(resolution,[],[f5556,f2320]) ).
fof(f89094,plain,
( spl0_1607
| ~ spl0_292
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6286,f5551,f3016,f89092]) ).
fof(f89092,plain,
( spl0_1607
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f6286,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) )
| ~ spl0_292
| ~ spl0_409 ),
inference(duplicate_literal_removal,[],[f6260]) ).
fof(f6260,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) )
| ~ spl0_292
| ~ spl0_409 ),
inference(resolution,[],[f5552,f3017]) ).
fof(f89090,plain,
( spl0_1606
| ~ spl0_234
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6263,f5551,f2283,f89088]) ).
fof(f89088,plain,
( spl0_1606
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f6263,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_409 ),
inference(resolution,[],[f5552,f2284]) ).
fof(f89086,plain,
( spl0_1605
| ~ spl0_243
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6261,f5551,f2319,f89084]) ).
fof(f89084,plain,
( spl0_1605
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f6261,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_409 ),
inference(resolution,[],[f5552,f2320]) ).
fof(f89082,plain,
( spl0_1604
| ~ spl0_272
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6130,f5535,f2936,f89080]) ).
fof(f89080,plain,
( spl0_1604
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4))),X5))
| hBOOL(c_in(hAPP(X0,X1),X5,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f6130,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4))),X5))
| hBOOL(c_in(hAPP(X0,X1),X5,X2)) )
| ~ spl0_272
| ~ spl0_405 ),
inference(superposition,[],[f2937,f5536]) ).
fof(f89078,plain,
( spl0_1603
| ~ spl0_318
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f6007,f5523,f3462,f89076]) ).
fof(f89076,plain,
( spl0_1603
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)
| c_COMBK(c_False,tc_bool,X0) = hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f6007,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)
| c_COMBK(c_False,tc_bool,X0) = hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1) )
| ~ spl0_318
| ~ spl0_402 ),
inference(superposition,[],[f3463,f5524]) ).
fof(f89074,plain,
( spl0_1602
| ~ spl0_306
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f6005,f5523,f3392,f89072]) ).
fof(f89072,plain,
( spl0_1602
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f3392,plain,
( spl0_306
<=> ! [X11,X0,X12,X3] :
( hBOOL(hAPP(X12,X3))
| hBOOL(hAPP(X11,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f6005,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X3)) )
| ~ spl0_306
| ~ spl0_402 ),
inference(superposition,[],[f3393,f5524]) ).
fof(f3393,plain,
( ! [X3,X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X3))
| hBOOL(hAPP(X11,X3))
| hBOOL(hAPP(X12,X3)) )
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f3392]) ).
fof(f89070,plain,
( spl0_1601
| ~ spl0_319
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5946,f5519,f3466,f89068]) ).
fof(f89068,plain,
( spl0_1601
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)
| c_COMBK(c_False,tc_bool,X0) = hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f5519,plain,
( spl0_401
<=> ! [X12,X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),X11)),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f5946,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)
| c_COMBK(c_False,tc_bool,X0) = hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2) )
| ~ spl0_319
| ~ spl0_401 ),
inference(superposition,[],[f3467,f5520]) ).
fof(f5520,plain,
( ! [X0,X11,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),X11)),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X11)
| ~ spl0_401 ),
inference(avatar_component_clause,[],[f5519]) ).
fof(f89066,plain,
( spl0_1600
| ~ spl0_604
| ~ spl0_1537 ),
inference(avatar_split_clause,[],[f88538,f88493,f13614,f89064]) ).
fof(f13614,plain,
( spl0_604
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f88493,plain,
( spl0_1537
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f88538,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0)
| ~ spl0_604
| ~ spl0_1537 ),
inference(superposition,[],[f88494,f13615]) ).
fof(f13615,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1)) = X0
| ~ spl0_604 ),
inference(avatar_component_clause,[],[f13614]) ).
fof(f88494,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0) = X0
| ~ spl0_1537 ),
inference(avatar_component_clause,[],[f88493]) ).
fof(f89062,plain,
( spl0_1599
| ~ spl0_311
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5944,f5519,f3412,f89060]) ).
fof(f89060,plain,
( spl0_1599
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f3412,plain,
( spl0_311
<=> ! [X11,X0,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) != X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f5944,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)),X2)) )
| ~ spl0_311
| ~ spl0_401 ),
inference(superposition,[],[f3413,f5520]) ).
fof(f3413,plain,
( ! [X0,X11,X12] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) != X12
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) )
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f3412]) ).
fof(f89058,plain,
( spl0_1598
| ~ spl0_306
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5943,f5519,f3392,f89056]) ).
fof(f89056,plain,
( spl0_1598
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X3))
| hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f5943,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X3))
| hBOOL(hAPP(X2,X3)) )
| ~ spl0_306
| ~ spl0_401 ),
inference(superposition,[],[f3393,f5520]) ).
fof(f89054,plain,
( spl0_1597
| ~ spl0_291
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f5854,f5495,f3012,f89052]) ).
fof(f89052,plain,
( spl0_1597
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f3012,plain,
( spl0_291
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f5495,plain,
( spl0_395
<=> ! [X4,X0,X3,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f5854,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X0) )
| ~ spl0_291
| ~ spl0_395 ),
inference(duplicate_literal_removal,[],[f5845]) ).
fof(f5845,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X0) )
| ~ spl0_291
| ~ spl0_395 ),
inference(resolution,[],[f5496,f3013]) ).
fof(f3013,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f3012]) ).
fof(f5496,plain,
( ! [X3,X10,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X3)) )
| ~ spl0_395 ),
inference(avatar_component_clause,[],[f5495]) ).
fof(f89050,plain,
( spl0_1596
| ~ spl0_290
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f5853,f5495,f3008,f89048]) ).
fof(f89048,plain,
( spl0_1596
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f3008,plain,
( spl0_290
<=> ! [X20,X0,X19] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X19),X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f5853,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X0) )
| ~ spl0_290
| ~ spl0_395 ),
inference(duplicate_literal_removal,[],[f5846]) ).
fof(f5846,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X0) )
| ~ spl0_290
| ~ spl0_395 ),
inference(resolution,[],[f5496,f3009]) ).
fof(f3009,plain,
( ! [X0,X19,X20] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X19),X20))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f3008]) ).
fof(f89046,plain,
( spl0_1595
| ~ spl0_243
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5795,f5483,f2319,f89044]) ).
fof(f89044,plain,
( spl0_1595
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f5795,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_392 ),
inference(resolution,[],[f5484,f2320]) ).
fof(f89042,plain,
( spl0_1594
| ~ spl0_234
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5759,f5479,f2283,f89040]) ).
fof(f89040,plain,
( spl0_1594
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f5759,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_391 ),
inference(resolution,[],[f5480,f2284]) ).
fof(f89038,plain,
( spl0_1593
| ~ spl0_243
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5757,f5479,f2319,f89036]) ).
fof(f89036,plain,
( spl0_1593
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f5757,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_391 ),
inference(resolution,[],[f5480,f2320]) ).
fof(f89034,plain,
( spl0_1592
| ~ spl0_292
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5739,f5475,f3016,f89032]) ).
fof(f89032,plain,
( spl0_1592
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f5739,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X0) )
| ~ spl0_292
| ~ spl0_390 ),
inference(duplicate_literal_removal,[],[f5713]) ).
fof(f5713,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X0) )
| ~ spl0_292
| ~ spl0_390 ),
inference(resolution,[],[f5476,f3017]) ).
fof(f89030,plain,
( spl0_1591
| ~ spl0_243
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5714,f5475,f2319,f89028]) ).
fof(f89028,plain,
( spl0_1591
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f5714,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_390 ),
inference(resolution,[],[f5476,f2320]) ).
fof(f89026,plain,
( spl0_1590
| ~ spl0_292
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5700,f5471,f3016,f89024]) ).
fof(f89024,plain,
( spl0_1590
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f5700,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) )
| ~ spl0_292
| ~ spl0_389 ),
inference(duplicate_literal_removal,[],[f5674]) ).
fof(f5674,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) )
| ~ spl0_292
| ~ spl0_389 ),
inference(resolution,[],[f5472,f3017]) ).
fof(f88959,plain,
( spl0_1589
| ~ spl0_234
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5677,f5471,f2283,f88957]) ).
fof(f88957,plain,
( spl0_1589
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f5677,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_389 ),
inference(resolution,[],[f5472,f2284]) ).
fof(f88955,plain,
( spl0_1588
| ~ spl0_243
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5675,f5471,f2319,f88953]) ).
fof(f88953,plain,
( spl0_1588
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f5675,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_389 ),
inference(resolution,[],[f5472,f2320]) ).
fof(f88951,plain,
( spl0_1587
| ~ spl0_324
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f5636,f5467,f3908,f88949]) ).
fof(f88949,plain,
( spl0_1587
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X6),hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5))))
| c_Finite__Set_Ofinite(X6,X3)
| ~ c_Finite__Set_Ofinite(X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f3908,plain,
( spl0_324
<=> ! [X11,X0,X12,X8,X7] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(X12,X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X12),hAPP(c_Set_Oimage(X8,X0,X7),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f5636,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X6),hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5))))
| c_Finite__Set_Ofinite(X6,X3)
| ~ c_Finite__Set_Ofinite(X5,X4) )
| ~ spl0_324
| ~ spl0_388 ),
inference(superposition,[],[f3909,f5468]) ).
fof(f3909,plain,
( ! [X0,X11,X8,X7,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X12),hAPP(c_Set_Oimage(X8,X0,X7),X11)))
| c_Finite__Set_Ofinite(X12,X7)
| ~ c_Finite__Set_Ofinite(X11,X0) )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3908]) ).
fof(f88947,plain,
( spl0_1586
| ~ spl0_92
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5352,f5058,f1379,f88945]) ).
fof(f88945,plain,
( spl0_1586
<=> ! [X3,X4,X7,X0,X6,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,tc_fun(X5,tc_bool))),X2))
| ~ hBOOL(c_in(X1,X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f5352,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,tc_fun(X5,tc_bool))),X2))
| ~ hBOOL(c_in(X1,X6,X7)) )
| ~ spl0_92
| ~ spl0_382 ),
inference(superposition,[],[f5059,f1380]) ).
fof(f88943,plain,
( spl0_1585
| ~ spl0_100
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5341,f5058,f1413,f88941]) ).
fof(f88941,plain,
( spl0_1585
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))),X1))
| ~ hBOOL(c_in(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f5341,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))),X1))
| ~ hBOOL(c_in(X1,X3,X4)) )
| ~ spl0_100
| ~ spl0_382 ),
inference(superposition,[],[f5059,f1414]) ).
fof(f88939,plain,
( spl0_1584
| ~ spl0_310
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5315,f5058,f3408,f88937]) ).
fof(f88937,plain,
( spl0_1584
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f5315,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))) )
| ~ spl0_310
| ~ spl0_382 ),
inference(resolution,[],[f5059,f3409]) ).
fof(f88935,plain,
( spl0_1583
| ~ spl0_309
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5314,f5058,f3404,f88933]) ).
fof(f88933,plain,
( spl0_1583
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f5314,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0)) )
| ~ spl0_309
| ~ spl0_382 ),
inference(resolution,[],[f5059,f3405]) ).
fof(f88931,plain,
( spl0_1582
| ~ spl0_92
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5161,f5038,f1379,f88929]) ).
fof(f88929,plain,
( spl0_1582
<=> ! [X2,X6,X4,X7,X0,X5,X3,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,tc_fun(X5,tc_bool))))
| ~ hBOOL(c_in(X1,X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f5161,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,tc_fun(X5,tc_bool))))
| ~ hBOOL(c_in(X1,X6,X7)) )
| ~ spl0_92
| ~ spl0_377 ),
inference(superposition,[],[f5039,f1380]) ).
fof(f88927,plain,
( spl0_1581
| ~ spl0_100
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5150,f5038,f1413,f88925]) ).
fof(f88925,plain,
( spl0_1581
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))))
| ~ hBOOL(c_in(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f5150,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))))
| ~ hBOOL(c_in(X1,X3,X4)) )
| ~ spl0_100
| ~ spl0_377 ),
inference(superposition,[],[f5039,f1414]) ).
fof(f88923,plain,
( spl0_1580
| ~ spl0_147
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f5010,f4409,f1655,f88921]) ).
fof(f88921,plain,
( spl0_1580
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X2)),X3),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X0,X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X2)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f1655,plain,
( spl0_147
<=> ! [X13,X0,X69,X71] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X71,X69,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X71,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f4409,plain,
( spl0_369
<=> ! [X60,X13,X0,X69] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X60),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f5010,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X2)),X3),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X0,X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X2)),X1),X2) )
| ~ spl0_147
| ~ spl0_369 ),
inference(resolution,[],[f4410,f1656]) ).
fof(f1656,plain,
( ! [X0,X71,X69,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X71,X69,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X71,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1655]) ).
fof(f4410,plain,
( ! [X0,X69,X60,X13] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X60),X0) )
| ~ spl0_369 ),
inference(avatar_component_clause,[],[f4409]) ).
fof(f88919,plain,
( ~ spl0_7
| spl0_1579
| ~ spl0_181
| ~ spl0_1516 ),
inference(avatar_split_clause,[],[f88351,f88219,f1864,f88917,f992]) ).
fof(f992,plain,
( spl0_7
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1864,plain,
( spl0_181
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f88219,plain,
( spl0_1516
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f88351,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0))
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_181
| ~ spl0_1516 ),
inference(superposition,[],[f1865,f88220]) ).
fof(f88220,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) = X0
| ~ spl0_1516 ),
inference(avatar_component_clause,[],[f88219]) ).
fof(f1865,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1864]) ).
fof(f88915,plain,
( spl0_1578
| ~ spl0_131
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f5001,f4405,f1567,f88913]) ).
fof(f88913,plain,
( spl0_1578
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(X1),X2) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),hAPP(c_fequal(X1),X2)),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f1567,plain,
( spl0_131
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X2,hAPP(c_fequal(X0),X1),X0))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f4405,plain,
( spl0_368
<=> ! [X0,X11,X3] :
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)) = X11
| hBOOL(c_in(X3,X11,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f5001,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X1),X2) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),hAPP(c_fequal(X1),X2)),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0))
| X0 = X2 )
| ~ spl0_131
| ~ spl0_368 ),
inference(resolution,[],[f4406,f1568]) ).
fof(f1568,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X2,hAPP(c_fequal(X0),X1),X0))
| X1 = X2 )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1567]) ).
fof(f4406,plain,
( ! [X3,X0,X11] :
( hBOOL(c_in(X3,X11,X0))
| hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)) = X11 )
| ~ spl0_368 ),
inference(avatar_component_clause,[],[f4405]) ).
fof(f88911,plain,
( spl0_1577
| ~ spl0_292
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4958,f4392,f3016,f88909]) ).
fof(f88909,plain,
( spl0_1577
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f4958,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0) )
| ~ spl0_292
| ~ spl0_365 ),
inference(resolution,[],[f4393,f3017]) ).
fof(f88907,plain,
( spl0_1576
| ~ spl0_289
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4930,f4388,f3004,f88905]) ).
fof(f88905,plain,
( spl0_1576
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f3004,plain,
( spl0_289
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f4930,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3),X1,X0) )
| ~ spl0_289
| ~ spl0_364 ),
inference(resolution,[],[f4389,f3005]) ).
fof(f3005,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f3004]) ).
fof(f88903,plain,
( spl0_1575
| ~ spl0_288
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4929,f4388,f3000,f88901]) ).
fof(f88901,plain,
( spl0_1575
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f4929,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3),X1,X0) )
| ~ spl0_288
| ~ spl0_364 ),
inference(resolution,[],[f4389,f3001]) ).
fof(f88899,plain,
( spl0_1574
| ~ spl0_289
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4887,f4380,f3004,f88897]) ).
fof(f88897,plain,
( spl0_1574
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f4887,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2),X1,X0) )
| ~ spl0_289
| ~ spl0_362 ),
inference(resolution,[],[f4381,f3005]) ).
fof(f88895,plain,
( spl0_1573
| ~ spl0_288
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4886,f4380,f3000,f88893]) ).
fof(f88893,plain,
( spl0_1573
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f4886,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2),X1,X0) )
| ~ spl0_288
| ~ spl0_362 ),
inference(resolution,[],[f4381,f3001]) ).
fof(f88891,plain,
( spl0_1572
| ~ spl0_292
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4838,f4376,f3016,f88889]) ).
fof(f88889,plain,
( spl0_1572
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f4838,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0) )
| ~ spl0_292
| ~ spl0_361 ),
inference(resolution,[],[f4377,f3017]) ).
fof(f88887,plain,
( spl0_1571
| ~ spl0_206
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4786,f4368,f2033,f88885]) ).
fof(f88885,plain,
( spl0_1571
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ hBOOL(c_in(X4,X6,X7))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBC(X0,X1,X2,X3),X7,tc_fun(X8,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f2033,plain,
( spl0_206
<=> ! [X31,X0,X7,X29,X17,X30] : hAPP(hAPP(c_COMBC(X29,X7,X17,X0),X30),X31) = hAPP(hAPP(X29,X31),X30) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f4786,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ hBOOL(c_in(X4,X6,X7))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBC(X0,X1,X2,X3),X7,tc_fun(X8,tc_bool)),X5)) )
| ~ spl0_206
| ~ spl0_359 ),
inference(superposition,[],[f4369,f2034]) ).
fof(f2034,plain,
( ! [X31,X29,X0,X7,X17,X30] : hAPP(hAPP(c_COMBC(X29,X7,X17,X0),X30),X31) = hAPP(hAPP(X29,X31),X30)
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f2033]) ).
fof(f88883,plain,
( spl0_1570
| ~ spl0_238
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4727,f4368,f2299,f88881]) ).
fof(f88881,plain,
( spl0_1570
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X5),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f4727,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X5),X0))) )
| ~ spl0_238
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2300]) ).
fof(f88879,plain,
( spl0_1569
| ~ spl0_237
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4726,f4368,f2295,f88877]) ).
fof(f88877,plain,
( spl0_1569
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X0),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f4726,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X0),X5))) )
| ~ spl0_237
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2296]) ).
fof(f88875,plain,
( spl0_1568
| ~ spl0_234
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4713,f4368,f2283,f88873]) ).
fof(f88873,plain,
( spl0_1568
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_HOL_Oord__class_Oless(X3),X2,tc_fun(X4,tc_bool)),X5))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X5),X0))
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f4713,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_HOL_Oord__class_Oless(X3),X2,tc_fun(X4,tc_bool)),X5))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X5),X0))
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_234
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2284]) ).
fof(f88871,plain,
( spl0_1567
| ~ spl0_234
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4707,f4368,f2283,f88869]) ).
fof(f88869,plain,
( spl0_1567
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X5),X0))
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f4707,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X5),X0))
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_234
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2284]) ).
fof(f88867,plain,
( spl0_1566
| ~ spl0_243
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4705,f4368,f2319,f88865]) ).
fof(f88865,plain,
( spl0_1566
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X5))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X5),X0))
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f4705,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X5))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X5),X0))
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_243
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2320]) ).
fof(f88863,plain,
( spl0_1565
| ~ spl0_45
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4690,f4364,f1163,f88861]) ).
fof(f88861,plain,
( spl0_1565
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(t_a,tc_fun(X1,X2))),X3),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_fun(X1,X2)),hAPP(X3,v_x))
| ~ class_HOL_Ominus(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f1163,plain,
( spl0_45
<=> ! [X80,X79] :
( ~ class_HOL_Ominus(X80)
| class_HOL_Ominus(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f4364,plain,
( spl0_358
<=> ! [X11,X12,X7] :
( ~ class_HOL_Ominus(X7)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(t_a,X7)),X12),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X11,v_x),X7),hAPP(X12,v_x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f4690,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(t_a,tc_fun(X1,X2))),X3),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_fun(X1,X2)),hAPP(X3,v_x))
| ~ class_HOL_Ominus(X2) )
| ~ spl0_45
| ~ spl0_358 ),
inference(resolution,[],[f4365,f1164]) ).
fof(f1164,plain,
( ! [X80,X79] :
( class_HOL_Ominus(tc_fun(X79,X80))
| ~ class_HOL_Ominus(X80) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f4365,plain,
( ! [X11,X7,X12] :
( ~ class_HOL_Ominus(X7)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(t_a,X7)),X12),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X11,v_x),X7),hAPP(X12,v_x)) )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f4364]) ).
fof(f88859,plain,
( spl0_1564
| ~ spl0_286
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4633,f4352,f2992,f88857]) ).
fof(f88857,plain,
( spl0_1564
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f2992,plain,
( spl0_286
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f4352,plain,
( spl0_355
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f4633,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2),X1,X0) )
| ~ spl0_286
| ~ spl0_355 ),
inference(resolution,[],[f4353,f2993]) ).
fof(f2993,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f2992]) ).
fof(f4353,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_355 ),
inference(avatar_component_clause,[],[f4352]) ).
fof(f88855,plain,
( spl0_1563
| ~ spl0_286
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4608,f4348,f2992,f88853]) ).
fof(f88853,plain,
( spl0_1563
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f4348,plain,
( spl0_354
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f4608,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3),X1,X0) )
| ~ spl0_286
| ~ spl0_354 ),
inference(resolution,[],[f4349,f2993]) ).
fof(f4349,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_354 ),
inference(avatar_component_clause,[],[f4348]) ).
fof(f88851,plain,
( spl0_1562
| ~ spl0_292
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4589,f4344,f3016,f88849]) ).
fof(f88849,plain,
( spl0_1562
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f4589,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X0) )
| ~ spl0_292
| ~ spl0_353 ),
inference(resolution,[],[f4345,f3017]) ).
fof(f88847,plain,
( spl0_1561
| ~ spl0_292
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4562,f4335,f3016,f88845]) ).
fof(f88845,plain,
( spl0_1561
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f4562,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X0) )
| ~ spl0_292
| ~ spl0_351 ),
inference(resolution,[],[f4336,f3017]) ).
fof(f88843,plain,
( spl0_1560
| ~ spl0_289
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f4536,f4331,f3004,f88841]) ).
fof(f88841,plain,
( spl0_1560
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f4536,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X0) )
| ~ spl0_289
| ~ spl0_350 ),
inference(resolution,[],[f4332,f3005]) ).
fof(f88839,plain,
( spl0_1559
| ~ spl0_288
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f4535,f4331,f3000,f88837]) ).
fof(f88837,plain,
( spl0_1559
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f4535,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X0) )
| ~ spl0_288
| ~ spl0_350 ),
inference(resolution,[],[f4332,f3001]) ).
fof(f88835,plain,
( ~ spl0_1558
| spl0_56
| ~ spl0_86
| ~ spl0_608
| ~ spl0_1516
| ~ spl0_1537 ),
inference(avatar_split_clause,[],[f88776,f88493,f88219,f13633,f1340,f1213,f88832]) ).
fof(f88832,plain,
( spl0_1558
<=> hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f1340,plain,
( spl0_86
<=> ! [X29] :
( hBOOL(hAPP(X29,c_False))
| ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(X29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f13633,plain,
( spl0_608
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f88776,plain,
( hBOOL(c_False)
| ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat))))
| ~ spl0_86
| ~ spl0_608
| ~ spl0_1516
| ~ spl0_1537 ),
inference(forward_demodulation,[],[f88775,f88220]) ).
fof(f88775,plain,
( hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_False),c_Orderings_Obot__class_Obot(tc_nat)))
| ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat))))
| ~ spl0_86
| ~ spl0_608
| ~ spl0_1537 ),
inference(forward_demodulation,[],[f88737,f13634]) ).
fof(f13634,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X0)
| ~ spl0_608 ),
inference(avatar_component_clause,[],[f13633]) ).
fof(f88737,plain,
( ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat))))
| hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_False))
| ~ spl0_86
| ~ spl0_1537 ),
inference(superposition,[],[f1341,f88494]) ).
fof(f1341,plain,
( ! [X29] :
( ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(X29)))
| hBOOL(hAPP(X29,c_False)) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f88830,plain,
( spl0_1557
| ~ spl0_289
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4500,f4327,f3004,f88828]) ).
fof(f88828,plain,
( spl0_1557
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f4500,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3),X0) )
| ~ spl0_289
| ~ spl0_349 ),
inference(resolution,[],[f4328,f3005]) ).
fof(f88826,plain,
( spl0_1556
| ~ spl0_288
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4499,f4327,f3000,f88824]) ).
fof(f88824,plain,
( spl0_1556
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f4499,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3),X0) )
| ~ spl0_288
| ~ spl0_349 ),
inference(resolution,[],[f4328,f3001]) ).
fof(f88822,plain,
( spl0_1555
| ~ spl0_286
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4436,f4319,f2992,f88820]) ).
fof(f88820,plain,
( spl0_1555
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f4319,plain,
( spl0_347
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f4436,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X0) )
| ~ spl0_286
| ~ spl0_347 ),
inference(resolution,[],[f4320,f2993]) ).
fof(f4320,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f4319]) ).
fof(f88818,plain,
( spl0_1554
| ~ spl0_286
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4417,f4315,f2992,f88816]) ).
fof(f88816,plain,
( spl0_1554
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f4315,plain,
( spl0_346
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f4417,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3),X0) )
| ~ spl0_286
| ~ spl0_346 ),
inference(resolution,[],[f4316,f2993]) ).
fof(f4316,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f4315]) ).
fof(f88814,plain,
( spl0_1553
| ~ spl0_91
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f4263,f3961,f1375,f88812]) ).
fof(f88812,plain,
( spl0_1553
<=> ! [X4,X0,X3,X2,X1] : c_Set_Oinsert(X0,X1) = c_Fun_Ofun__upd(c_Set_Oinsert(X0,X1),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),hAPP(c_Set_Oinsert(X0,X1),X2),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f1375,plain,
( spl0_91
<=> ! [X0,X3,X8,X7] : c_Fun_Ofun__upd(X8,X3,hAPP(X8,X3),X7,X0) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f4263,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oinsert(X0,X1) = c_Fun_Ofun__upd(c_Set_Oinsert(X0,X1),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),hAPP(c_Set_Oinsert(X0,X1),X2),X3,X4)
| ~ spl0_91
| ~ spl0_337 ),
inference(superposition,[],[f1376,f3962]) ).
fof(f1376,plain,
( ! [X3,X0,X8,X7] : c_Fun_Ofun__upd(X8,X3,hAPP(X8,X3),X7,X0) = X8
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f88810,plain,
( spl0_1552
| ~ spl0_150
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4225,f3949,f1668,f88808]) ).
fof(f88808,plain,
( spl0_1552
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_COMBK(c_False,tc_bool,X1)),X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Inductive_Ocomplete__lattice__class_Olfp(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f4225,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_COMBK(c_False,tc_bool,X1)),X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Inductive_Ocomplete__lattice__class_Olfp(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2)),X0)) )
| ~ spl0_150
| ~ spl0_334 ),
inference(superposition,[],[f3950,f1669]) ).
fof(f88806,plain,
( spl0_1551
| ~ spl0_150
| ~ spl0_275
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4188,f3945,f2948,f1668,f88804]) ).
fof(f88804,plain,
( spl0_1551
<=> ! [X5,X4,X0,X6,X1] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,X4)),X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f4188,plain,
( ! [X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,X4)),X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_150
| ~ spl0_275
| ~ spl0_333 ),
inference(forward_demodulation,[],[f4178,f3192]) ).
fof(f4178,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,X4)),X0))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X1,tc_bool)),X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_275
| ~ spl0_333 ),
inference(superposition,[],[f3946,f2949]) ).
fof(f88802,plain,
( spl0_1550
| ~ spl0_150
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4176,f3945,f1668,f88800]) ).
fof(f88800,plain,
( spl0_1550
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X4,X2)),c_COMBK(c_False,tc_bool,X1)))
| ~ hBOOL(c_in(X0,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f4176,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X4,X2)),c_COMBK(c_False,tc_bool,X1)))
| ~ hBOOL(c_in(X0,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_150
| ~ spl0_333 ),
inference(superposition,[],[f3946,f1669]) ).
fof(f88798,plain,
( spl0_1549
| ~ spl0_255
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4147,f3945,f2536,f88796]) ).
fof(f88796,plain,
( spl0_1549
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)),hAPP(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f4147,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)),hAPP(X4,X0)) )
| ~ spl0_255
| ~ spl0_333 ),
inference(resolution,[],[f3946,f2537]) ).
fof(f88794,plain,
( spl0_1548
| ~ spl0_253
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4146,f3945,f2528,f88792]) ).
fof(f88792,plain,
( spl0_1548
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f4146,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)) )
| ~ spl0_253
| ~ spl0_333 ),
inference(resolution,[],[f3946,f2529]) ).
fof(f88535,plain,
( spl0_1547
| ~ spl0_150
| ~ spl0_275
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4109,f3924,f2948,f1668,f88533]) ).
fof(f88533,plain,
( spl0_1547
<=> ! [X5,X4,X0,X6,X1] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f4109,plain,
( ! [X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_150
| ~ spl0_275
| ~ spl0_328 ),
inference(forward_demodulation,[],[f4099,f3192]) ).
fof(f4099,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,X4)))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X1,tc_bool)),X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_275
| ~ spl0_328 ),
inference(superposition,[],[f3925,f2949]) ).
fof(f88531,plain,
( spl0_1546
| ~ spl0_150
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4097,f3924,f1668,f88529]) ).
fof(f88529,plain,
( spl0_1546
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_COMBK(c_False,tc_bool,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X4,X2)))
| ~ hBOOL(c_in(X0,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f4097,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_COMBK(c_False,tc_bool,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X4,X2)))
| ~ hBOOL(c_in(X0,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_150
| ~ spl0_328 ),
inference(superposition,[],[f3925,f1669]) ).
fof(f88527,plain,
( spl0_1545
| ~ spl0_247
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4068,f3924,f2495,f88525]) ).
fof(f88525,plain,
( spl0_1545
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f4068,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)) )
| ~ spl0_247
| ~ spl0_328 ),
inference(resolution,[],[f3925,f2496]) ).
fof(f88523,plain,
( spl0_1544
| ~ spl0_245
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4067,f3924,f2487,f88521]) ).
fof(f88521,plain,
( spl0_1544
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f4067,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)) )
| ~ spl0_245
| ~ spl0_328 ),
inference(resolution,[],[f3925,f2488]) ).
fof(f88519,plain,
( spl0_1543
| ~ spl0_252
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3834,f3420,f2524,f88517]) ).
fof(f88517,plain,
( spl0_1543
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1))
| hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X1),X3),X1))
| X0 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f3420,plain,
( spl0_313
<=> ! [X4,X11,X0,X3] : hAPP(c_Set_Oinsert(X3,X0),hAPP(c_Set_Oinsert(X4,X0),X11)) = hAPP(c_Set_Oinsert(X4,X0),hAPP(c_Set_Oinsert(X3,X0),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f3834,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1))
| hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X1),X3),X1))
| X0 = X4 )
| ~ spl0_252
| ~ spl0_313 ),
inference(superposition,[],[f2525,f3421]) ).
fof(f3421,plain,
( ! [X3,X0,X11,X4] : hAPP(c_Set_Oinsert(X3,X0),hAPP(c_Set_Oinsert(X4,X0),X11)) = hAPP(c_Set_Oinsert(X4,X0),hAPP(c_Set_Oinsert(X3,X0),X11))
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f3420]) ).
fof(f88515,plain,
( spl0_1542
| ~ spl0_87
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3813,f3416,f1344,f88513]) ).
fof(f88513,plain,
( spl0_1542
<=> ! [X2,X0,X1] :
( hBOOL(c_in(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2)),X1))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f3813,plain,
( ! [X2,X0,X1] :
( hBOOL(c_in(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2)),X1))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_False)) )
| ~ spl0_87
| ~ spl0_312 ),
inference(resolution,[],[f3417,f1345]) ).
fof(f88511,plain,
( spl0_1541
| ~ spl0_261
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3705,f3400,f2560,f88509]) ).
fof(f88509,plain,
( spl0_1541
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1) = X2
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f3705,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1) = X2
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_308 ),
inference(resolution,[],[f3401,f2561]) ).
fof(f88507,plain,
( spl0_1540
| ~ spl0_256
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3692,f3400,f2540,f88505]) ).
fof(f88505,plain,
( spl0_1540
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2)))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f3692,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2)))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_256
| ~ spl0_308 ),
inference(resolution,[],[f3401,f2541]) ).
fof(f88503,plain,
( spl0_1539
| ~ spl0_86
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3661,f3388,f1340,f88501]) ).
fof(f88501,plain,
( spl0_1539
<=> ! [X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1))),X0,X1))
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1)),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f3661,plain,
( ! [X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1))),X0,X1))
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1)),c_False)) )
| ~ spl0_86
| ~ spl0_305 ),
inference(resolution,[],[f3389,f1341]) ).
fof(f88499,plain,
( spl0_1538
| ~ spl0_87
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3623,f3380,f1344,f88497]) ).
fof(f88497,plain,
( spl0_1538
<=> ! [X2,X0,X1] :
( hBOOL(c_in(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2)),X1))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f3380,plain,
( spl0_303
<=> ! [X11,X0,X12,X5] :
( ~ hBOOL(c_in(X5,X11,X0))
| hBOOL(c_in(X5,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f3623,plain,
( ! [X2,X0,X1] :
( hBOOL(c_in(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2)),X1))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_False)) )
| ~ spl0_87
| ~ spl0_303 ),
inference(resolution,[],[f3381,f1345]) ).
fof(f3381,plain,
( ! [X0,X11,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(c_in(X5,X12,X0))
| ~ hBOOL(c_in(X5,X11,X0)) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f3380]) ).
fof(f88495,plain,
( spl0_1537
| ~ spl0_608
| ~ spl0_1516 ),
inference(avatar_split_clause,[],[f88262,f88219,f13633,f88493]) ).
fof(f88262,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0) = X0
| ~ spl0_608
| ~ spl0_1516 ),
inference(superposition,[],[f88220,f13634]) ).
fof(f88491,plain,
( spl0_1536
| ~ spl0_165
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3614,f3376,f1768,f88489]) ).
fof(f88489,plain,
( spl0_1536
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( ~ c_Finite__Set_Ofinite(X0,X4)
| ~ hBOOL(c_in(v_x,X5,X6))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,tc_fun(X4,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f3614,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Finite__Set_Ofinite(X0,X4)
| ~ hBOOL(c_in(v_x,X5,X6))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,tc_fun(X4,tc_bool)),X4) )
| ~ spl0_165
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1769]) ).
fof(f88487,plain,
( spl0_1535
| ~ spl0_171
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3612,f3376,f1792,f88485]) ).
fof(f88485,plain,
( spl0_1535
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X1),X0),X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,c_Set_Oinsert(X0,X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f3612,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X1),X0),X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,c_Set_Oinsert(X0,X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_171
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1793]) ).
fof(f88483,plain,
( spl0_1534
| ~ spl0_169
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3601,f3376,f1784,f88481]) ).
fof(f88481,plain,
( spl0_1534
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f3601,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_169
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1785]) ).
fof(f88479,plain,
( spl0_1533
| ~ spl0_170
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3594,f3376,f1788,f88477]) ).
fof(f88477,plain,
( spl0_1533
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f3594,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_170
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1789]) ).
fof(f88475,plain,
( spl0_1532
| ~ spl0_232
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3585,f3376,f2275,f88473]) ).
fof(f88473,plain,
( spl0_1532
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X0,X3)
| ~ c_Finite__Set_Ofinite(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f2275,plain,
( spl0_232
<=> ! [X13,X0,X14] :
( ~ c_Finite__Set_Ofinite(X14,X0)
| ~ c_Finite__Set_Ofinite(X13,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X13),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f3585,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X0,X3)
| ~ c_Finite__Set_Ofinite(X4,X3) )
| ~ spl0_232
| ~ spl0_302 ),
inference(resolution,[],[f3377,f2276]) ).
fof(f2276,plain,
( ! [X0,X14,X13] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X13),X0)
| ~ c_Finite__Set_Ofinite(X13,X0)
| ~ c_Finite__Set_Ofinite(X14,X0) )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2275]) ).
fof(f88471,plain,
( spl0_1531
| ~ spl0_261
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3575,f3372,f2560,f88469]) ).
fof(f88469,plain,
( spl0_1531
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X2) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X2)))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f3372,plain,
( spl0_301
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f3575,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X2) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X2)))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_261
| ~ spl0_301 ),
inference(resolution,[],[f3373,f2561]) ).
fof(f3373,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| X3 = X4
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f3372]) ).
fof(f88467,plain,
( spl0_1530
| ~ spl0_256
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3563,f3372,f2540,f88465]) ).
fof(f88465,plain,
( spl0_1530
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1) = X2
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f3563,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1) = X2
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_301 ),
inference(resolution,[],[f3373,f2541]) ).
fof(f88463,plain,
( spl0_1529
| ~ spl0_261
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3547,f3368,f2560,f88461]) ).
fof(f88461,plain,
( spl0_1529
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)))
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f3368,plain,
( spl0_300
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3547,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)))
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_300 ),
inference(resolution,[],[f3369,f2561]) ).
fof(f3369,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| X1 = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) )
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f3368]) ).
fof(f88459,plain,
( spl0_1528
| ~ spl0_256
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3535,f3368,f2540,f88457]) ).
fof(f88457,plain,
( spl0_1528
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2)),X0))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f3535,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2)),X0))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_256
| ~ spl0_300 ),
inference(resolution,[],[f3369,f2541]) ).
fof(f88455,plain,
( spl0_1527
| ~ spl0_87
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3523,f3364,f1344,f88453]) ).
fof(f88453,plain,
( spl0_1527
<=> ! [X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1)),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f3523,plain,
( ! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1)),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_False)) )
| ~ spl0_87
| ~ spl0_299 ),
inference(resolution,[],[f3365,f1345]) ).
fof(f88261,plain,
( spl0_1526
| ~ spl0_259
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3323,f3016,f2552,f88259]) ).
fof(f88259,plain,
( spl0_1526
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(X0,tc_bool))
| hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f3323,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(X0,tc_bool))
| hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ spl0_259
| ~ spl0_292 ),
inference(resolution,[],[f3017,f2553]) ).
fof(f88257,plain,
( spl0_1525
| ~ spl0_256
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3220,f2952,f2540,f88255]) ).
fof(f88255,plain,
( spl0_1525
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X1)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f3220,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X1)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) )
| ~ spl0_256
| ~ spl0_276 ),
inference(resolution,[],[f2953,f2541]) ).
fof(f88253,plain,
( spl0_1524
| ~ spl0_87
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3190,f2944,f1344,f88251]) ).
fof(f88251,plain,
( spl0_1524
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1)),X2,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f2944,plain,
( spl0_274
<=> ! [X13,X0,X69,X71] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X71,X69,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X71),X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f3190,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1)),X2,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),c_False)) )
| ~ spl0_87
| ~ spl0_274 ),
inference(resolution,[],[f2945,f1345]) ).
fof(f2945,plain,
( ! [X0,X71,X69,X13] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X71),X13))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X71,X69,X0) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2944]) ).
fof(f88249,plain,
( spl0_1523
| ~ spl0_87
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3164,f2940,f1344,f88247]) ).
fof(f88247,plain,
( spl0_1523
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1)),X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f2940,plain,
( spl0_273
<=> ! [X69,X0,X13,X70] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X70,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X69),X70)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f3164,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1)),X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1),c_False)) )
| ~ spl0_87
| ~ spl0_273 ),
inference(resolution,[],[f2941,f1345]) ).
fof(f2941,plain,
( ! [X70,X0,X69,X13] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X69),X70))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X70,X0) )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f2940]) ).
fof(f88245,plain,
( spl0_1522
| ~ spl0_261
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3127,f2936,f2560,f88243]) ).
fof(f88243,plain,
( spl0_1522
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),X1))
| ~ hBOOL(c_in(hAPP(c_Set_Oinsert(X0,X1),X3),X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f3127,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),X1))
| ~ hBOOL(c_in(hAPP(c_Set_Oinsert(X0,X1),X3),X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) )
| ~ spl0_261
| ~ spl0_272 ),
inference(resolution,[],[f2937,f2561]) ).
fof(f88241,plain,
( spl0_1521
| ~ spl0_205
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2899,f2572,f2029,f88239]) ).
fof(f88239,plain,
( spl0_1521
<=> ! [X2,X4,X0,X3,X1] : hBOOL(c_in(hAPP(c_Set_Oinsert(X1,X0),X2),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f2899,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(c_in(hAPP(c_Set_Oinsert(X1,X0),X2),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))),X4))
| ~ spl0_205
| ~ spl0_264 ),
inference(superposition,[],[f2030,f2573]) ).
fof(f88237,plain,
( spl0_1520
| ~ spl0_87
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2798,f2536,f1344,f88235]) ).
fof(f88235,plain,
( spl0_1520
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f2798,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_255 ),
inference(resolution,[],[f2537,f1345]) ).
fof(f88233,plain,
( spl0_1519
| ~ spl0_87
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2758,f2528,f1344,f88231]) ).
fof(f88231,plain,
( spl0_1519
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))),X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f2758,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))),X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_253 ),
inference(resolution,[],[f2529,f1345]) ).
fof(f88229,plain,
( spl0_1518
| ~ spl0_215
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2726,f2520,f2072,f88227]) ).
fof(f88227,plain,
( spl0_1518
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(c_in(hAPP(c_Set_Oinsert(X0,X1),X2),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X3,X4),X5),X4))
| ~ hBOOL(c_in(hAPP(c_Set_Oinsert(X0,X1),X2),X5,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f2072,plain,
( spl0_215
<=> ! [X0,X11,X3] : hAPP(c_Set_Oinsert(X3,X0),X11) = hAPP(c_Set_Oinsert(X3,X0),hAPP(c_Set_Oinsert(X3,X0),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2726,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(hAPP(c_Set_Oinsert(X0,X1),X2),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X3,X4),X5),X4))
| ~ hBOOL(c_in(hAPP(c_Set_Oinsert(X0,X1),X2),X5,X3)) )
| ~ spl0_215
| ~ spl0_251 ),
inference(superposition,[],[f2521,f2073]) ).
fof(f2073,plain,
( ! [X3,X0,X11] : hAPP(c_Set_Oinsert(X3,X0),X11) = hAPP(c_Set_Oinsert(X3,X0),hAPP(c_Set_Oinsert(X3,X0),X11))
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2072]) ).
fof(f88225,plain,
( spl0_1517
| ~ spl0_221
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2724,f2520,f2097,f88223]) ).
fof(f88223,plain,
( spl0_1517
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X2,X3),X4),X3))
| ~ hBOOL(c_in(X1,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f2724,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X2,X3),X4),X3))
| ~ hBOOL(c_in(X1,X4,X2)) )
| ~ spl0_221
| ~ spl0_251 ),
inference(superposition,[],[f2521,f2098]) ).
fof(f88221,plain,
( ~ spl0_2
| spl0_1516
| ~ spl0_9
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f14578,f13657,f1002,f88219,f967]) ).
fof(f967,plain,
( spl0_2
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1002,plain,
( spl0_9
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f13657,plain,
( spl0_614
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f14578,plain,
( ! [X0] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) = X0
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_9
| ~ spl0_614 ),
inference(resolution,[],[f13658,f1004]) ).
fof(f1004,plain,
( class_Orderings_Obot(tc_nat)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f1002]) ).
fof(f13658,plain,
( ! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_614 ),
inference(avatar_component_clause,[],[f13657]) ).
fof(f88217,plain,
( spl0_1515
| ~ spl0_219
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2723,f2520,f2089,f88215]) ).
fof(f88215,plain,
( spl0_1515
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f2089,plain,
( spl0_219
<=> ! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2723,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X4,X2)) )
| ~ spl0_219
| ~ spl0_251 ),
inference(superposition,[],[f2521,f2090]) ).
fof(f2090,plain,
( ! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = c_COMBK(c_False,tc_bool,X0)
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2089]) ).
fof(f88213,plain,
( spl0_1514
| ~ spl0_201
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2718,f2520,f2013,f88211]) ).
fof(f88211,plain,
( spl0_1514
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( hBOOL(c_in(hAPP(X0,X5),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6,X7),X8),X7))
| ~ hBOOL(c_in(X5,X8,X6))
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f2013,plain,
( spl0_201
<=> ! [X10,X0,X4,X3,X8,X7] :
( X3 = X10
| hAPP(X8,X10) = hAPP(c_Fun_Ofun__upd(X8,X3,X4,X0,X7),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2718,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( hBOOL(c_in(hAPP(X0,X5),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6,X7),X8),X7))
| ~ hBOOL(c_in(X5,X8,X6))
| X1 = X5 )
| ~ spl0_201
| ~ spl0_251 ),
inference(superposition,[],[f2521,f2014]) ).
fof(f2014,plain,
( ! [X3,X10,X0,X8,X7,X4] :
( hAPP(X8,X10) = hAPP(c_Fun_Ofun__upd(X8,X3,X4,X0,X7),X10)
| X3 = X10 )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2013]) ).
fof(f88209,plain,
( spl0_1513
| ~ spl0_206
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2713,f2520,f2033,f88207]) ).
fof(f88207,plain,
( spl0_1513
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( hBOOL(c_in(hAPP(hAPP(X0,X5),X4),hAPP(c_Set_Oimage(hAPP(c_COMBC(X0,X1,X2,X3),X4),X6,X7),X8),X7))
| ~ hBOOL(c_in(X5,X8,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f2713,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( hBOOL(c_in(hAPP(hAPP(X0,X5),X4),hAPP(c_Set_Oimage(hAPP(c_COMBC(X0,X1,X2,X3),X4),X6,X7),X8),X7))
| ~ hBOOL(c_in(X5,X8,X6)) )
| ~ spl0_206
| ~ spl0_251 ),
inference(superposition,[],[f2521,f2034]) ).
fof(f88205,plain,
( spl0_1512
| ~ spl0_91
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2679,f2516,f1375,f88203]) ).
fof(f88203,plain,
( spl0_1512
<=> ! [X4,X0,X3,X2,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f2679,plain,
( ! [X2,X3,X0,X1,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1),X3,X4)
| ~ spl0_91
| ~ spl0_250 ),
inference(superposition,[],[f1376,f2517]) ).
fof(f88201,plain,
( spl0_1511
| ~ spl0_205
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2678,f2516,f2029,f88199]) ).
fof(f88199,plain,
( spl0_1511
<=> ! [X2,X4,X0,X3,X1] : hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f2678,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))),X4))
| ~ spl0_205
| ~ spl0_250 ),
inference(superposition,[],[f2030,f2517]) ).
fof(f88197,plain,
( spl0_1510
| ~ spl0_91
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2241,f2097,f1375,f88195]) ).
fof(f88195,plain,
( spl0_1510
<=> ! [X0,X3,X2,X1] : c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)) = c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X1,c_COMBK(c_False,tc_bool,X0),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f2241,plain,
( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)) = c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X1,c_COMBK(c_False,tc_bool,X0),X2,X3)
| ~ spl0_91
| ~ spl0_221 ),
inference(superposition,[],[f1376,f2098]) ).
fof(f88193,plain,
( spl0_1509
| ~ spl0_87
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2213,f2068,f1344,f88191]) ).
fof(f88191,plain,
( spl0_1509
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_Set_Oinsert(X1,X2),X0))))
| c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_Set_Oinsert(X1,X2),X0)) = X1
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X0),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f2068,plain,
( spl0_214
<=> ! [X4,X11,X0,X3] :
( X3 = X4
| hBOOL(hAPP(X11,X3))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X4,X0),X11),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2213,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_Set_Oinsert(X1,X2),X0))))
| c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_Set_Oinsert(X1,X2),X0)) = X1
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X0),c_False)) )
| ~ spl0_87
| ~ spl0_214 ),
inference(resolution,[],[f2069,f1345]) ).
fof(f2069,plain,
( ! [X3,X0,X11,X4] :
( ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X4,X0),X11),X3))
| hBOOL(hAPP(X11,X3))
| X3 = X4 )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2068]) ).
fof(f87882,plain,
( spl0_1508
| ~ spl0_171
| ~ spl0_598 ),
inference(avatar_split_clause,[],[f13589,f13408,f1792,f87880]) ).
fof(f87880,plain,
( spl0_1508
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_fequal(X1),X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f13408,plain,
( spl0_598
<=> ! [X2,X0,X1,X3] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f13589,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_fequal(X1),X0)),X0))
| ~ spl0_171
| ~ spl0_598 ),
inference(superposition,[],[f13409,f1793]) ).
fof(f13409,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X0))
| ~ spl0_598 ),
inference(avatar_component_clause,[],[f13408]) ).
fof(f87173,plain,
( spl0_1507
| ~ spl0_65
| ~ spl0_582 ),
inference(avatar_split_clause,[],[f13313,f13041,f1252,f87171]) ).
fof(f87171,plain,
( spl0_1507
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f1252,plain,
( spl0_65
<=> ! [X13,X69,X0] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| c_Hoare__Mirabelle_Ohoare__valids(X13,X69,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f13041,plain,
( spl0_582
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f13313,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X1)
| ~ spl0_65
| ~ spl0_582 ),
inference(resolution,[],[f13042,f1253]) ).
fof(f1253,plain,
( ! [X0,X69,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| c_Hoare__Mirabelle_Ohoare__valids(X13,X69,X0) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1252]) ).
fof(f13042,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X1)
| ~ spl0_582 ),
inference(avatar_component_clause,[],[f13041]) ).
fof(f85849,plain,
( spl0_1506
| ~ spl0_217
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11663,f5030,f2081,f85847]) ).
fof(f85847,plain,
( spl0_1506
<=> ! [X0,X1] : c_The(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f2081,plain,
( spl0_217
<=> ! [X0,X1,X8] : c_The(c_Finite__Set_Ofold1Set(X8,hAPP(c_fequal(X0),X1),X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f5030,plain,
( spl0_375
<=> ! [X0] : hAPP(c_fequal(tc_bool),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f11663,plain,
( ! [X0,X1] : c_The(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),tc_bool) = X0
| ~ spl0_217
| ~ spl0_375 ),
inference(superposition,[],[f2082,f5031]) ).
fof(f5031,plain,
( ! [X0] : hAPP(c_fequal(tc_bool),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f5030]) ).
fof(f2082,plain,
( ! [X0,X1,X8] : c_The(c_Finite__Set_Ofold1Set(X8,hAPP(c_fequal(X0),X1),X0),X0) = X1
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f2081]) ).
fof(f85196,plain,
( spl0_1505
| ~ spl0_131
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11658,f5030,f1567,f85194]) ).
fof(f85194,plain,
( spl0_1505
<=> ! [X0,X1] :
( ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f11658,plain,
( ! [X0,X1] :
( ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool))
| X0 = X1 )
| ~ spl0_131
| ~ spl0_375 ),
inference(superposition,[],[f1568,f5031]) ).
fof(f82793,plain,
( spl0_1504
| ~ spl0_217
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7873,f4832,f2081,f82791]) ).
fof(f82791,plain,
( spl0_1504
<=> ! [X0,X1] : c_The(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f4832,plain,
( spl0_371
<=> ! [X0] : hAPP(c_fequal(tc_nat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f7873,plain,
( ! [X0,X1] : c_The(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat),tc_nat) = X0
| ~ spl0_217
| ~ spl0_371 ),
inference(superposition,[],[f2082,f4833]) ).
fof(f4833,plain,
( ! [X0] : hAPP(c_fequal(tc_nat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_371 ),
inference(avatar_component_clause,[],[f4832]) ).
fof(f81452,plain,
( spl0_1503
| ~ spl0_131
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7868,f4832,f1567,f81450]) ).
fof(f81450,plain,
( spl0_1503
<=> ! [X0,X1] :
( ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f7868,plain,
( ! [X0,X1] :
( ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat))
| X0 = X1 )
| ~ spl0_131
| ~ spl0_371 ),
inference(superposition,[],[f1568,f4833]) ).
fof(f74178,plain,
( spl0_1502
| ~ spl0_242
| ~ spl0_244
| ~ spl0_368
| ~ spl0_418
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f17449,f8450,f6416,f4405,f2328,f2315,f74176]) ).
fof(f74176,plain,
( spl0_1502
<=> ! [X0,X3,X2,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X3) = hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X0,X1),X3))
| ~ hBOOL(c_in(X0,X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f2315,plain,
( spl0_242
<=> ! [X11,X0,X12,X5] :
( ~ hBOOL(c_in(X5,X12,X0))
| ~ hBOOL(c_in(X5,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2328,plain,
( spl0_244
<=> ! [X0,X1] : hBOOL(c_in(X0,hAPP(c_fequal(X1),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f6416,plain,
( spl0_418
<=> ! [X11,X0,X12,X3] :
( ~ hBOOL(c_in(X3,X12,X0))
| hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f17449,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X3) = hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X0,X1),X3))
| ~ hBOOL(c_in(X0,X3,X1)) )
| ~ spl0_242
| ~ spl0_244
| ~ spl0_368
| ~ spl0_418
| ~ spl0_480 ),
inference(forward_demodulation,[],[f17448,f8451]) ).
fof(f17448,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X3) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0))
| ~ hBOOL(c_in(X0,X3,X1)) )
| ~ spl0_242
| ~ spl0_244
| ~ spl0_368
| ~ spl0_418 ),
inference(forward_demodulation,[],[f5002,f6505]) ).
fof(f6505,plain,
( ! [X2,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X2,X1),X0),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2))
| ~ spl0_244
| ~ spl0_418 ),
inference(resolution,[],[f6417,f2329]) ).
fof(f2329,plain,
( ! [X0,X1] : hBOOL(c_in(X0,hAPP(c_fequal(X1),X0),X1))
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2328]) ).
fof(f6417,plain,
( ! [X3,X0,X11,X12] :
( ~ hBOOL(c_in(X3,X12,X0))
| hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),X12) )
| ~ spl0_418 ),
inference(avatar_component_clause,[],[f6416]) ).
fof(f5002,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X3) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X3)),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0))
| ~ hBOOL(c_in(X0,X3,X1)) )
| ~ spl0_242
| ~ spl0_368 ),
inference(resolution,[],[f4406,f2316]) ).
fof(f2316,plain,
( ! [X0,X11,X5,X12] :
( ~ hBOOL(c_in(X5,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0))
| ~ hBOOL(c_in(X5,X12,X0)) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2315]) ).
fof(f74174,plain,
( spl0_1501
| ~ spl0_83
| ~ spl0_520 ),
inference(avatar_split_clause,[],[f10513,f10510,f1328,f74172]) ).
fof(f74172,plain,
( spl0_1501
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f1328,plain,
( spl0_83
<=> ! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f10510,plain,
( spl0_520
<=> ! [X18,X11,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X18,tc_fun(X0,tc_bool)),X11)) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f10513,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1)) = X1 )
| ~ spl0_83
| ~ spl0_520 ),
inference(resolution,[],[f10511,f1329]) ).
fof(f1329,plain,
( ! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X11))
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f10511,plain,
( ! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X18,tc_fun(X0,tc_bool)),X11)) = X11 )
| ~ spl0_520 ),
inference(avatar_component_clause,[],[f10510]) ).
fof(f74170,plain,
( spl0_1500
| ~ spl0_100
| ~ spl0_507 ),
inference(avatar_split_clause,[],[f10135,f9520,f1413,f74168]) ).
fof(f74168,plain,
( spl0_1500
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f9520,plain,
( spl0_507
<=> ! [X18,X11,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),X18))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f10135,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1)),X1)) )
| ~ spl0_100
| ~ spl0_507 ),
inference(superposition,[],[f9521,f1414]) ).
fof(f9521,plain,
( ! [X0,X11,X18,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),X18)) )
| ~ spl0_507 ),
inference(avatar_component_clause,[],[f9520]) ).
fof(f74166,plain,
( spl0_1499
| ~ spl0_258
| ~ spl0_503 ),
inference(avatar_split_clause,[],[f9798,f9504,f2548,f74164]) ).
fof(f74164,plain,
( spl0_1499
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f9798,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,X1,X0)) )
| ~ spl0_258
| ~ spl0_503 ),
inference(superposition,[],[f2549,f9505]) ).
fof(f74162,plain,
( spl0_1498
| ~ spl0_249
| ~ spl0_503 ),
inference(avatar_split_clause,[],[f9794,f9504,f2503,f74160]) ).
fof(f74160,plain,
( spl0_1498
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X1,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f9794,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X1,X0,X5) )
| ~ spl0_249
| ~ spl0_503 ),
inference(superposition,[],[f2504,f9505]) ).
fof(f74158,plain,
( spl0_1497
| ~ spl0_257
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f9636,f9500,f2544,f74156]) ).
fof(f74156,plain,
( spl0_1497
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f9636,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) )
| ~ spl0_257
| ~ spl0_502 ),
inference(superposition,[],[f2545,f9501]) ).
fof(f74154,plain,
( spl0_1496
| ~ spl0_248
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f9632,f9500,f2499,f74152]) ).
fof(f74152,plain,
( spl0_1496
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X3,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f9632,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X3,X0,X5) )
| ~ spl0_248
| ~ spl0_502 ),
inference(superposition,[],[f2500,f9501]) ).
fof(f74150,plain,
( spl0_1495
| ~ spl0_70
| ~ spl0_100
| ~ spl0_343
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8816,f8434,f3985,f1413,f1273,f74148]) ).
fof(f74148,plain,
( spl0_1495
<=> ! [X4,X0,X3,X2,X1] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X4,X3),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = X1
| c_COMBK(c_False,tc_bool,X3) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f3985,plain,
( spl0_343
<=> ! [X11,X0,X5,X7] :
( c_COMBK(c_False,tc_bool,X7) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(X5,tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f8816,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X4,X3),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = X1
| c_COMBK(c_False,tc_bool,X3) = X0 )
| ~ spl0_70
| ~ spl0_100
| ~ spl0_343
| ~ spl0_476 ),
inference(forward_demodulation,[],[f8815,f1414]) ).
fof(f8815,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X4,X3),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X1)
| c_COMBK(c_False,tc_bool,X3) = X0 )
| ~ spl0_70
| ~ spl0_343
| ~ spl0_476 ),
inference(forward_demodulation,[],[f8739,f1274]) ).
fof(f8739,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X4,X3),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_COMBK(X1,tc_fun(X2,tc_bool),X3),X4)),X1)
| c_COMBK(c_False,tc_bool,X3) = X0 )
| ~ spl0_343
| ~ spl0_476 ),
inference(superposition,[],[f8435,f3986]) ).
fof(f3986,plain,
( ! [X0,X11,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(X5,tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = X5
| c_COMBK(c_False,tc_bool,X7) = X11 )
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f3985]) ).
fof(f74146,plain,
( spl0_1494
| ~ spl0_319
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8766,f8434,f3466,f74144]) ).
fof(f74144,plain,
( spl0_1494
<=> ! [X2,X4,X0,X3,X1] :
( c_COMBK(c_False,tc_bool,X0) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X0) = hAPP(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f8766,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X0) = hAPP(X1,X2) )
| ~ spl0_319
| ~ spl0_476 ),
inference(superposition,[],[f3467,f8435]) ).
fof(f74142,plain,
( spl0_1493
| ~ spl0_212
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8752,f8434,f2060,f74140]) ).
fof(f74140,plain,
( spl0_1493
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f8752,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X5)) )
| ~ spl0_212
| ~ spl0_476 ),
inference(superposition,[],[f2061,f8435]) ).
fof(f74127,plain,
( spl0_1492
| ~ spl0_71
| ~ spl0_191
| ~ spl0_471 ),
inference(avatar_split_clause,[],[f8544,f8414,f1904,f1277,f74125]) ).
fof(f74125,plain,
( spl0_1492
<=> ! [X2,X4,X0,X3,X1] :
( c_Finite__Set_Osetsum(c_Fun_Ocomp(X1,X2,X4,X0,X3),c_COMBK(c_False,tc_bool,X3),X3,X0) = c_Finite__Set_Osetsum(X1,c_COMBK(c_False,tc_bool,X4),X4,X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f8414,plain,
( spl0_471
<=> ! [X15,X17,X0,X12,X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X17)
| ~ c_Fun_Oinj__on(X8,X12,X0,X7)
| c_Finite__Set_Osetsum(X15,hAPP(c_Set_Oimage(X8,X0,X7),X12),X7,X17) = c_Finite__Set_Osetsum(c_Fun_Ocomp(X15,X8,X7,X17,X0),X12,X0,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f8544,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Osetsum(c_Fun_Ocomp(X1,X2,X4,X0,X3),c_COMBK(c_False,tc_bool,X3),X3,X0) = c_Finite__Set_Osetsum(X1,c_COMBK(c_False,tc_bool,X4),X4,X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) )
| ~ spl0_71
| ~ spl0_191
| ~ spl0_471 ),
inference(forward_demodulation,[],[f8541,f1905]) ).
fof(f8541,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_Finite__Set_Osetsum(X1,hAPP(c_Set_Oimage(X2,X3,X4),c_COMBK(c_False,tc_bool,X3)),X4,X0) = c_Finite__Set_Osetsum(c_Fun_Ocomp(X1,X2,X4,X0,X3),c_COMBK(c_False,tc_bool,X3),X3,X0) )
| ~ spl0_71
| ~ spl0_471 ),
inference(resolution,[],[f8415,f1278]) ).
fof(f8415,plain,
( ! [X0,X8,X7,X17,X15,X12] :
( ~ c_Fun_Oinj__on(X8,X12,X0,X7)
| ~ class_OrderedGroup_Ocomm__monoid__add(X17)
| c_Finite__Set_Osetsum(X15,hAPP(c_Set_Oimage(X8,X0,X7),X12),X7,X17) = c_Finite__Set_Osetsum(c_Fun_Ocomp(X15,X8,X7,X17,X0),X12,X0,X17) )
| ~ spl0_471 ),
inference(avatar_component_clause,[],[f8414]) ).
fof(f74123,plain,
( spl0_1491
| ~ spl0_207
| ~ spl0_468 ),
inference(avatar_split_clause,[],[f8365,f7953,f2037,f74121]) ).
fof(f74121,plain,
( spl0_1491
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f8365,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) )
| ~ spl0_207
| ~ spl0_468 ),
inference(resolution,[],[f7954,f2038]) ).
fof(f74119,plain,
( spl0_1490
| ~ spl0_199
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f8309,f7945,f2005,f74117]) ).
fof(f74117,plain,
( spl0_1490
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(c_in(X3,X2,X0))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X0),X1),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f8309,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(c_in(X3,X2,X0))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X0),X1),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_199
| ~ spl0_466 ),
inference(resolution,[],[f7946,f2006]) ).
fof(f74115,plain,
( spl0_1489
| ~ spl0_107
| ~ spl0_461 ),
inference(avatar_split_clause,[],[f8186,f7925,f1442,f74113]) ).
fof(f74113,plain,
( spl0_1489
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0),tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Otop__class_Otop(X0),X0)) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(X0),X2,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f1442,plain,
( spl0_107
<=> ! [X0,X3] :
( ~ class_Orderings_Otop(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Orderings_Otop__class_Otop(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f7925,plain,
( spl0_461
<=> ! [X23,X0,X27,X26] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X26),X27))
| hAPP(c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X26,X23,X0),tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X26,X27,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(X27,X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f8186,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0),tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Otop__class_Otop(X0),X0)) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(X0),X2,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_461 ),
inference(resolution,[],[f7926,f1443]) ).
fof(f1443,plain,
( ! [X3,X0] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1442]) ).
fof(f7926,plain,
( ! [X0,X26,X27,X23] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X26),X27))
| ~ class_Orderings_Olinorder(X0)
| hAPP(c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X26,X23,X0),tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X26,X27,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(X27,X23,X0) )
| ~ spl0_461 ),
inference(avatar_component_clause,[],[f7925]) ).
fof(f74111,plain,
( spl0_1488
| ~ spl0_105
| ~ spl0_461 ),
inference(avatar_split_clause,[],[f8158,f7925,f1433,f74109]) ).
fof(f74109,plain,
( spl0_1488
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X2,X1,X0) = hAPP(c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(X0),X1,X0),tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(X0),X2,X0))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f1433,plain,
( spl0_105
<=> ! [X0,X3] :
( ~ class_Orderings_Obot(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f8158,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X2,X1,X0) = hAPP(c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(X0),X1,X0),tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(X0),X2,X0))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_461 ),
inference(resolution,[],[f7926,f1434]) ).
fof(f1434,plain,
( ! [X3,X0] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X3))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f74107,plain,
( spl0_1487
| ~ spl0_207
| ~ spl0_457 ),
inference(avatar_split_clause,[],[f8005,f7909,f2037,f74105]) ).
fof(f74105,plain,
( spl0_1487
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f8005,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X3)),X2)) )
| ~ spl0_207
| ~ spl0_457 ),
inference(resolution,[],[f7910,f2038]) ).
fof(f74103,plain,
( spl0_1486
| ~ spl0_207
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f7961,f7862,f2037,f74101]) ).
fof(f74101,plain,
( spl0_1486
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f7961,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2)) )
| ~ spl0_207
| ~ spl0_456 ),
inference(resolution,[],[f7863,f2038]) ).
fof(f74099,plain,
( spl0_1485
| ~ spl0_187
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f7596,f7488,f1888,f74097]) ).
fof(f74097,plain,
( spl0_1485
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X2),hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f7596,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X2),hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X1),X0) )
| ~ spl0_187
| ~ spl0_450 ),
inference(resolution,[],[f7489,f1889]) ).
fof(f74095,plain,
( spl0_1484
| ~ spl0_238
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f7566,f7484,f2299,f74093]) ).
fof(f74093,plain,
( spl0_1484
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(c_in(hAPP(X0,X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),hAPP(c_Set_Oimage(X0,X4,X2),X5)),X2))
| ~ hBOOL(c_in(X1,X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f7566,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(hAPP(X0,X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),hAPP(c_Set_Oimage(X0,X4,X2),X5)),X2))
| ~ hBOOL(c_in(X1,X5,X4)) )
| ~ spl0_238
| ~ spl0_449 ),
inference(resolution,[],[f7485,f2300]) ).
fof(f74091,plain,
( spl0_1483
| ~ spl0_237
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f7565,f7484,f2295,f74089]) ).
fof(f74089,plain,
( spl0_1483
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(c_in(hAPP(X0,X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X0,X3,X2),X4)),X5),X2))
| ~ hBOOL(c_in(X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f7565,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(hAPP(X0,X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X0,X3,X2),X4)),X5),X2))
| ~ hBOOL(c_in(X1,X4,X3)) )
| ~ spl0_237
| ~ spl0_449 ),
inference(resolution,[],[f7485,f2296]) ).
fof(f74083,plain,
( spl0_1482
| ~ spl0_79
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f7462,f6768,f1311,f74081]) ).
fof(f74081,plain,
( spl0_1482
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Osetsum(X0,X1,X2,tc_nat) = c_Finite__Set_Osetsum(X0,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X3)),X2,tc_nat)
| hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f1311,plain,
( spl0_79
<=> ! [X0,X43,X3] :
( hBOOL(hAPP(X43,X3))
| ~ hBOOL(c_in(X3,X43,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f6768,plain,
( spl0_446
<=> ! [X8,X11,X0,X1] :
( c_Finite__Set_Osetsum(X8,X11,X0,tc_nat) = c_Finite__Set_Osetsum(X8,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X0,tc_nat)
| hBOOL(c_in(X1,X11,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f7462,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Osetsum(X0,X1,X2,tc_nat) = c_Finite__Set_Osetsum(X0,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X3)),X2,tc_nat)
| hBOOL(hAPP(X1,X3)) )
| ~ spl0_79
| ~ spl0_446 ),
inference(resolution,[],[f6769,f1312]) ).
fof(f1312,plain,
( ! [X3,X0,X43] :
( ~ hBOOL(c_in(X3,X43,X0))
| hBOOL(hAPP(X43,X3)) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1311]) ).
fof(f6769,plain,
( ! [X0,X11,X1,X8] :
( hBOOL(c_in(X1,X11,X0))
| c_Finite__Set_Osetsum(X8,X11,X0,tc_nat) = c_Finite__Set_Osetsum(X8,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X0,tc_nat) )
| ~ spl0_446 ),
inference(avatar_component_clause,[],[f6768]) ).
fof(f74079,plain,
( spl0_1481
| ~ spl0_237
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7281,f6756,f2295,f74077]) ).
fof(f74077,plain,
( spl0_1481
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f7281,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))))
| ~ spl0_237
| ~ spl0_443 ),
inference(superposition,[],[f2296,f6757]) ).
fof(f74075,plain,
( spl0_1480
| ~ spl0_232
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7280,f6756,f2275,f74073]) ).
fof(f74073,plain,
( spl0_1480
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(X3,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f7280,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(X3,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X2),X0) )
| ~ spl0_232
| ~ spl0_443 ),
inference(superposition,[],[f2276,f6757]) ).
fof(f74071,plain,
( spl0_1479
| ~ spl0_98
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7203,f6752,f1405,f74069]) ).
fof(f74069,plain,
( spl0_1479
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X1)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f1405,plain,
( spl0_98
<=> ! [X0,X11,X1] :
( c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X11),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f7203,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X1)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) )
| ~ spl0_98
| ~ spl0_442 ),
inference(superposition,[],[f1406,f6753]) ).
fof(f1406,plain,
( ! [X0,X11,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X11),X0)
| c_Finite__Set_Ofinite(X11,X0) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1405]) ).
fof(f74067,plain,
( spl0_1478
| ~ spl0_97
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7202,f6752,f1401,f74065]) ).
fof(f74065,plain,
( spl0_1478
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f1401,plain,
( spl0_97
<=> ! [X0,X11,X1] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X11),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f7202,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) )
| ~ spl0_97
| ~ spl0_442 ),
inference(superposition,[],[f1402,f6753]) ).
fof(f1402,plain,
( ! [X0,X11,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X11),X0)
| ~ c_Finite__Set_Ofinite(X11,X0) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1401]) ).
fof(f74063,plain,
( spl0_1477
| ~ spl0_238
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7153,f6752,f2299,f74061]) ).
fof(f74061,plain,
( spl0_1477
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X2,X0),X3)),hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f7153,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X2,X0),X3)),hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))))
| ~ spl0_238
| ~ spl0_442 ),
inference(superposition,[],[f2300,f6753]) ).
fof(f74059,plain,
( spl0_1476
| ~ spl0_232
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7151,f6752,f2275,f74057]) ).
fof(f74057,plain,
( spl0_1476
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),X3),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f7151,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),X3),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_232
| ~ spl0_442 ),
inference(superposition,[],[f2276,f6753]) ).
fof(f74055,plain,
( spl0_1475
| ~ spl0_80
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f7022,f6715,f1315,f74053]) ).
fof(f74053,plain,
( spl0_1475
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2)
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X1,X2),X4),hAPP(X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f1315,plain,
( spl0_80
<=> ! [X0,X43,X3] :
( ~ hBOOL(hAPP(X43,X3))
| hBOOL(c_in(X3,X43,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f6715,plain,
( spl0_433
<=> ! [X11,X0,X8,X1,X7] :
( hBOOL(c_in(X1,X11,X0))
| ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| ~ hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),X11),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f7022,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2)
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X1,X2),X4),hAPP(X0,X3))) )
| ~ spl0_80
| ~ spl0_433 ),
inference(resolution,[],[f6716,f1316]) ).
fof(f1316,plain,
( ! [X3,X0,X43] :
( hBOOL(c_in(X3,X43,X0))
| ~ hBOOL(hAPP(X43,X3)) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1315]) ).
fof(f6716,plain,
( ! [X0,X11,X1,X8,X7] :
( ~ hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),X11),X7))
| ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hBOOL(c_in(X1,X11,X0)) )
| ~ spl0_433 ),
inference(avatar_component_clause,[],[f6715]) ).
fof(f74051,plain,
( spl0_1474
| ~ spl0_79
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f6786,f6687,f1311,f74049]) ).
fof(f74049,plain,
( spl0_1474
<=> ! [X5,X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X5,X0,X2,X3),X4,X2,X3)
| ~ c_Fun_Oinj__on(X1,X4,X2,X3)
| hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X3),X4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f6687,plain,
( spl0_426
<=> ! [X4,X11,X0,X3,X8,X7] :
( ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| hBOOL(c_in(X4,hAPP(c_Set_Oimage(X8,X0,X7),X11),X7))
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X8,X3,X4,X0,X7),X11,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f6786,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X5,X0,X2,X3),X4,X2,X3)
| ~ c_Fun_Oinj__on(X1,X4,X2,X3)
| hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X3),X4),X0)) )
| ~ spl0_79
| ~ spl0_426 ),
inference(resolution,[],[f6688,f1312]) ).
fof(f6688,plain,
( ! [X3,X0,X11,X8,X7,X4] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X8,X3,X4,X0,X7),X11,X0,X7)
| hBOOL(c_in(X4,hAPP(c_Set_Oimage(X8,X0,X7),X11),X7))
| ~ c_Fun_Oinj__on(X8,X11,X0,X7) )
| ~ spl0_426 ),
inference(avatar_component_clause,[],[f6687]) ).
fof(f74047,plain,
( spl0_1473
| ~ spl0_168
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6140,f5535,f1780,f74045]) ).
fof(f74045,plain,
( spl0_1473
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(c_Set_Oimage(X0,X3,tc_Hoare__Mirabelle_Otriple(X2)),hAPP(c_Set_Oinsert(X1,X3),X4)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(c_Set_Oimage(X0,X3,tc_Hoare__Mirabelle_Otriple(X2)),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f1780,plain,
( spl0_168
<=> ! [X60,X13,X0,X69] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f6140,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(c_Set_Oimage(X0,X3,tc_Hoare__Mirabelle_Otriple(X2)),hAPP(c_Set_Oinsert(X1,X3),X4)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(c_Set_Oimage(X0,X3,tc_Hoare__Mirabelle_Otriple(X2)),X4),X2) )
| ~ spl0_168
| ~ spl0_405 ),
inference(superposition,[],[f1781,f5536]) ).
fof(f1781,plain,
( ! [X0,X69,X60,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1780]) ).
fof(f74036,plain,
( spl0_1472
| ~ spl0_266
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6139,f5535,f2580,f74034]) ).
fof(f74034,plain,
( spl0_1472
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(c_Set_Oimage(X0,X3,tc_Hoare__Mirabelle_Otriple(X2)),hAPP(c_Set_Oinsert(X1,X3),X4)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X2)),hAPP(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f6139,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(c_Set_Oimage(X0,X3,tc_Hoare__Mirabelle_Otriple(X2)),hAPP(c_Set_Oinsert(X1,X3),X4)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X2)),hAPP(X0,X1)),X2) )
| ~ spl0_266
| ~ spl0_405 ),
inference(superposition,[],[f2581,f5536]) ).
fof(f74032,plain,
( spl0_1471
| ~ spl0_184
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6126,f5535,f1876,f74030]) ).
fof(f74030,plain,
( spl0_1471
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(c_in(X5,hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2))
| ~ hBOOL(c_in(X5,hAPP(c_Set_Oimage(X0,X3,X2),X4),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f1876,plain,
( spl0_184
<=> ! [X0,X12,X2,X1] :
( ~ hBOOL(c_in(X1,X12,X0))
| hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X2,X0),X12),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f6126,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(X5,hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2))
| ~ hBOOL(c_in(X5,hAPP(c_Set_Oimage(X0,X3,X2),X4),X2)) )
| ~ spl0_184
| ~ spl0_405 ),
inference(superposition,[],[f1877,f5536]) ).
fof(f1877,plain,
( ! [X2,X0,X1,X12] :
( hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X2,X0),X12),X0))
| ~ hBOOL(c_in(X1,X12,X0)) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1876]) ).
fof(f74028,plain,
( spl0_1470
| ~ spl0_179
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6125,f5535,f1856,f74026]) ).
fof(f74026,plain,
( spl0_1470
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ c_Fun_Oinj__on(X5,hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2,X6)
| c_Fun_Oinj__on(X5,hAPP(c_Set_Oimage(X0,X3,X2),X4),X2,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f1856,plain,
( spl0_179
<=> ! [X1,X11,X0,X8,X7] :
( c_Fun_Oinj__on(X8,X11,X0,X7)
| ~ c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f6125,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Fun_Oinj__on(X5,hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2,X6)
| c_Fun_Oinj__on(X5,hAPP(c_Set_Oimage(X0,X3,X2),X4),X2,X6) )
| ~ spl0_179
| ~ spl0_405 ),
inference(superposition,[],[f1857,f5536]) ).
fof(f1857,plain,
( ! [X0,X11,X1,X8,X7] :
( ~ c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7)
| c_Fun_Oinj__on(X8,X11,X0,X7) )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1856]) ).
fof(f74024,plain,
( spl0_1469
| ~ spl0_70
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f5922,f5515,f1273,f74022]) ).
fof(f74022,plain,
( spl0_1469
<=> ! [X2,X6,X4,X1,X0,X5,X3,X7] :
( ~ hBOOL(c_in(X4,X0,X5))
| ~ hBOOL(c_in(X3,X6,X7))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X0,X1,X2),X7,tc_fun(X5,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f5922,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(c_in(X4,X0,X5))
| ~ hBOOL(c_in(X3,X6,X7))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X0,X1,X2),X7,tc_fun(X5,tc_bool)),X5)) )
| ~ spl0_70
| ~ spl0_400 ),
inference(superposition,[],[f5516,f1274]) ).
fof(f74020,plain,
( spl0_1468
| ~ spl0_178
| ~ spl0_251
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f5660,f5467,f2520,f1852,f74018]) ).
fof(f74018,plain,
( spl0_1468
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( hBOOL(c_in(hAPP(X0,hAPP(X1,X6)),hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)),X3))
| ~ hBOOL(c_in(X6,X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f5660,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(c_in(hAPP(X0,hAPP(X1,X6)),hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)),X3))
| ~ hBOOL(c_in(X6,X5,X4)) )
| ~ spl0_178
| ~ spl0_251
| ~ spl0_388 ),
inference(forward_demodulation,[],[f5638,f1853]) ).
fof(f5638,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(c_in(hAPP(c_COMBB(X0,X1,X2,X3,X4),X6),hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)),X3))
| ~ hBOOL(c_in(X6,X5,X4)) )
| ~ spl0_251
| ~ spl0_388 ),
inference(superposition,[],[f2521,f5468]) ).
fof(f73831,plain,
( ~ spl0_24
| spl0_1467
| ~ spl0_327
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5332,f5058,f3920,f73829,f1077]) ).
fof(f73829,plain,
( spl0_1467
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f5332,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_327
| ~ spl0_382 ),
inference(resolution,[],[f5059,f3921]) ).
fof(f73775,plain,
( ~ spl0_24
| spl0_1466
| ~ spl0_327
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5245,f5046,f3920,f73773,f1077]) ).
fof(f73773,plain,
( spl0_1466
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f5245,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X2)),X1))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_327
| ~ spl0_379 ),
inference(resolution,[],[f5047,f3921]) ).
fof(f73771,plain,
( spl0_1465
| ~ spl0_181
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5209,f5042,f1864,f73769]) ).
fof(f73769,plain,
( spl0_1465
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X4),X1),X2)))
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f5209,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X4),X1),X2)))
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) )
| ~ spl0_181
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1865]) ).
fof(f73761,plain,
( spl0_1464
| ~ spl0_182
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5208,f5042,f1868,f73759]) ).
fof(f73759,plain,
( spl0_1464
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X4),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f1868,plain,
( spl0_182
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f5208,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X4),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X3,X0)) )
| ~ spl0_182
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1869]) ).
fof(f1869,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1868]) ).
fof(f73757,plain,
( spl0_1463
| ~ spl0_180
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5207,f5042,f1860,f73755]) ).
fof(f73755,plain,
( spl0_1463
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X1),X4),X2)))
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f1860,plain,
( spl0_180
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f5207,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X1),X4),X2)))
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) )
| ~ spl0_180
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1861]) ).
fof(f1861,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1860]) ).
fof(f73753,plain,
( spl0_1462
| ~ spl0_183
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5206,f5042,f1872,f73751]) ).
fof(f73751,plain,
( spl0_1462
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X1),X4),X2)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f1872,plain,
( spl0_183
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f5206,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X1),X4),X2)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X3,X0)) )
| ~ spl0_183
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1873]) ).
fof(f1873,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1872]) ).
fof(f73749,plain,
( spl0_1461
| ~ spl0_175
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5194,f5042,f1839,f73747]) ).
fof(f73747,plain,
( spl0_1461
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X3,X4)))
| ~ class_Lattices_Olattice(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f1839,plain,
( spl0_175
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f5194,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X3,X4)))
| ~ class_Lattices_Olattice(tc_fun(X1,X0)) )
| ~ spl0_175
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1840]) ).
fof(f1840,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X4))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1839]) ).
fof(f73745,plain,
( spl0_1460
| ~ spl0_176
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5193,f5042,f1844,f73743]) ).
fof(f73743,plain,
( spl0_1460
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X3,X4)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f1844,plain,
( spl0_176
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f5193,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X3,X4)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,X0)) )
| ~ spl0_176
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1845]) ).
fof(f1845,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X4))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1844]) ).
fof(f73741,plain,
( spl0_1459
| ~ spl0_174
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5189,f5042,f1835,f73739]) ).
fof(f73739,plain,
( spl0_1459
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X2,X4)))
| ~ class_Lattices_Olattice(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f1835,plain,
( spl0_174
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f5189,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X2,X4)))
| ~ class_Lattices_Olattice(tc_fun(X1,X0)) )
| ~ spl0_174
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1836]) ).
fof(f1836,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1835]) ).
fof(f73737,plain,
( spl0_1458
| ~ spl0_177
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5188,f5042,f1848,f73735]) ).
fof(f73735,plain,
( spl0_1458
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X2,X4)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f1848,plain,
( spl0_177
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f5188,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X2,X4)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,X0)) )
| ~ spl0_177
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1849]) ).
fof(f1849,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1848]) ).
fof(f73536,plain,
( ~ spl0_24
| spl0_1457
| ~ spl0_327
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5143,f5038,f3920,f73534,f1077]) ).
fof(f73534,plain,
( spl0_1457
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f5143,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0)))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_327
| ~ spl0_377 ),
inference(resolution,[],[f5039,f3921]) ).
fof(f73532,plain,
( spl0_1456
| ~ spl0_261
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4971,f4392,f2560,f73530]) ).
fof(f73530,plain,
( spl0_1456
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f4971,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_365 ),
inference(resolution,[],[f4393,f2561]) ).
fof(f73517,plain,
( spl0_1455
| ~ spl0_247
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4926,f4388,f2495,f73515]) ).
fof(f73515,plain,
( spl0_1455
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f4926,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1) = X1 )
| ~ spl0_247
| ~ spl0_364 ),
inference(resolution,[],[f4389,f2496]) ).
fof(f73513,plain,
( spl0_1454
| ~ spl0_245
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4925,f4388,f2487,f73511]) ).
fof(f73511,plain,
( spl0_1454
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f4925,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)) = X1 )
| ~ spl0_245
| ~ spl0_364 ),
inference(resolution,[],[f4389,f2488]) ).
fof(f73509,plain,
( spl0_1453
| ~ spl0_247
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4883,f4380,f2495,f73507]) ).
fof(f73507,plain,
( spl0_1453
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f4883,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1) = X1 )
| ~ spl0_247
| ~ spl0_362 ),
inference(resolution,[],[f4381,f2496]) ).
fof(f73505,plain,
( spl0_1452
| ~ spl0_245
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4882,f4380,f2487,f73503]) ).
fof(f73503,plain,
( spl0_1452
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f4882,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)) = X1 )
| ~ spl0_245
| ~ spl0_362 ),
inference(resolution,[],[f4381,f2488]) ).
fof(f73501,plain,
( spl0_1451
| ~ spl0_261
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4849,f4376,f2560,f73499]) ).
fof(f73499,plain,
( spl0_1451
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f4849,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_361 ),
inference(resolution,[],[f4377,f2561]) ).
fof(f73497,plain,
( spl0_1450
| ~ spl0_207
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f4802,f4372,f2037,f73495]) ).
fof(f73495,plain,
( spl0_1450
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)))
| hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f4802,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)))
| hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2) = X1 )
| ~ spl0_207
| ~ spl0_360 ),
inference(resolution,[],[f4373,f2038]) ).
fof(f73493,plain,
( spl0_1449
| ~ spl0_92
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4755,f4368,f1379,f73491]) ).
fof(f73491,plain,
( spl0_1449
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(X2,X5))
| ~ hBOOL(c_in(X1,X6,X7))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,tc_fun(X8,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f4755,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(X2,X5))
| ~ hBOOL(c_in(X1,X6,X7))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,tc_fun(X8,tc_bool)),X5)) )
| ~ spl0_92
| ~ spl0_359 ),
inference(superposition,[],[f4369,f1380]) ).
fof(f73489,plain,
( spl0_1448
| ~ spl0_87
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4736,f4368,f1344,f73487]) ).
fof(f73487,plain,
( spl0_1448
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(X3,X0))))
| ~ hBOOL(hAPP(hAPP(X3,X0),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f4736,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(X3,X0))))
| ~ hBOOL(hAPP(hAPP(X3,X0),c_False)) )
| ~ spl0_87
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1345]) ).
fof(f73485,plain,
( spl0_1447
| ~ spl0_212
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4716,f4368,f2060,f73483]) ).
fof(f73483,plain,
( spl0_1447
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X0,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f4716,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X0,X6)) )
| ~ spl0_212
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2061]) ).
fof(f73481,plain,
( spl0_1446
| ~ spl0_213
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4715,f4368,f2064,f73479]) ).
fof(f73479,plain,
( spl0_1446
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X4,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f4715,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X4,X6)) )
| ~ spl0_213
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2065]) ).
fof(f73473,plain,
( spl0_1445
| ~ spl0_207
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4698,f4368,f2037,f73471]) ).
fof(f73471,plain,
( spl0_1445
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(tc_fun(X1,tc_bool)),X4,tc_fun(X5,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f4698,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(tc_fun(X1,tc_bool)),X4,tc_fun(X5,tc_bool)),X0)) )
| ~ spl0_207
| ~ spl0_359 ),
inference(resolution,[],[f4369,f2038]) ).
fof(f73469,plain,
( spl0_1444
| ~ spl0_256
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4588,f4344,f2540,f73467]) ).
fof(f73467,plain,
( spl0_1444
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f4588,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_353 ),
inference(resolution,[],[f4345,f2541]) ).
fof(f73465,plain,
( spl0_1443
| ~ spl0_256
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4561,f4335,f2540,f73463]) ).
fof(f73463,plain,
( spl0_1443
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f4561,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_351 ),
inference(resolution,[],[f4336,f2541]) ).
fof(f73461,plain,
( spl0_1442
| ~ spl0_255
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f4534,f4331,f2536,f73459]) ).
fof(f73459,plain,
( spl0_1442
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f4534,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2) = X2 )
| ~ spl0_255
| ~ spl0_350 ),
inference(resolution,[],[f4332,f2537]) ).
fof(f72766,plain,
( spl0_1441
| ~ spl0_26
| ~ spl0_1435 ),
inference(avatar_split_clause,[],[f72714,f72708,f1086,f72764]) ).
fof(f72764,plain,
( spl0_1441
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| ~ class_Finite__Set_Ofinite_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f1086,plain,
( spl0_26
<=> ! [X0,X11] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f72708,plain,
( spl0_1435
<=> ! [X2,X3] :
( ~ c_Finite__Set_Ofinite(X3,X2)
| c_COMBK(c_False,tc_bool,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f72714,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| ~ class_Finite__Set_Ofinite_Ofinite(X0) )
| ~ spl0_26
| ~ spl0_1435 ),
inference(resolution,[],[f72709,f1087]) ).
fof(f1087,plain,
( ! [X0,X11] :
( c_Finite__Set_Ofinite(X11,X0)
| ~ class_Finite__Set_Ofinite_Ofinite(X0) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f72709,plain,
( ! [X2,X3] :
( ~ c_Finite__Set_Ofinite(X3,X2)
| c_COMBK(c_False,tc_bool,X2) = X3 )
| ~ spl0_1435 ),
inference(avatar_component_clause,[],[f72708]) ).
fof(f72762,plain,
( spl0_1440
| ~ spl0_253
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f4533,f4331,f2528,f72760]) ).
fof(f72760,plain,
( spl0_1440
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f4533,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)) = X2 )
| ~ spl0_253
| ~ spl0_350 ),
inference(resolution,[],[f4332,f2529]) ).
fof(f72758,plain,
( spl0_1439
| ~ spl0_255
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4498,f4327,f2536,f72756]) ).
fof(f72756,plain,
( spl0_1439
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f4498,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2) = X2 )
| ~ spl0_255
| ~ spl0_349 ),
inference(resolution,[],[f4328,f2537]) ).
fof(f72754,plain,
( spl0_1438
| ~ spl0_253
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4497,f4327,f2528,f72752]) ).
fof(f72752,plain,
( spl0_1438
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f4497,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)) = X2 )
| ~ spl0_253
| ~ spl0_349 ),
inference(resolution,[],[f4328,f2529]) ).
fof(f72750,plain,
( spl0_1437
| ~ spl0_207
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4455,f4323,f2037,f72748]) ).
fof(f72748,plain,
( spl0_1437
<=> ! [X2,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f4455,plain,
( ! [X2,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2)),X0)) )
| ~ spl0_207
| ~ spl0_348 ),
inference(resolution,[],[f4324,f2038]) ).
fof(f72713,plain,
( spl0_1435
| spl0_1436
| ~ spl0_324
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4293,f3989,f3908,f72711,f72708]) ).
fof(f72711,plain,
( spl0_1436
<=> ! [X4,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),hAPP(c_fequal(X1),X0)))
| c_Finite__Set_Ofinite(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f3989,plain,
( spl0_344
<=> ! [X11,X0,X5,X7] :
( hAPP(c_Set_Oimage(c_COMBK(X5,X0,X7),X7,X0),X11) = hAPP(c_fequal(X0),X5)
| c_COMBK(c_False,tc_bool,X7) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f4293,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),hAPP(c_fequal(X1),X0)))
| c_Finite__Set_Ofinite(X4,X1)
| ~ c_Finite__Set_Ofinite(X3,X2)
| c_COMBK(c_False,tc_bool,X2) = X3 )
| ~ spl0_324
| ~ spl0_344 ),
inference(superposition,[],[f3909,f3990]) ).
fof(f3990,plain,
( ! [X0,X11,X7,X5] :
( hAPP(c_Set_Oimage(c_COMBK(X5,X0,X7),X7,X0),X11) = hAPP(c_fequal(X0),X5)
| c_COMBK(c_False,tc_bool,X7) = X11 )
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f3989]) ).
fof(f72706,plain,
( spl0_1434
| ~ spl0_214
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f4255,f3961,f2068,f72704]) ).
fof(f72704,plain,
( spl0_1434
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X0,X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X3))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f4255,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X0,X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X3))
| X0 = X3 )
| ~ spl0_214
| ~ spl0_337 ),
inference(superposition,[],[f2069,f3962]) ).
fof(f72702,plain,
( spl0_1433
| ~ spl0_261
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4238,f3949,f2560,f72700]) ).
fof(f72700,plain,
( spl0_1433
<=> ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ hBOOL(c_in(hAPP(X1,hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)),X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f4238,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ hBOOL(c_in(hAPP(X1,hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)),X2,X0)) )
| ~ spl0_261
| ~ spl0_334 ),
inference(duplicate_literal_removal,[],[f4199]) ).
fof(f4199,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ hBOOL(c_in(hAPP(X1,hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)),X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_334 ),
inference(resolution,[],[f3950,f2561]) ).
fof(f72698,plain,
( spl0_1432
| ~ spl0_328
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4237,f3949,f3924,f72696]) ).
fof(f72696,plain,
( spl0_1432
<=> ! [X0,X3,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1,X3,X0)))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1,X3,X0),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f4237,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1,X3,X0)))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1,X3,X0),X2,X3)) )
| ~ spl0_328
| ~ spl0_334 ),
inference(duplicate_literal_removal,[],[f4202]) ).
fof(f4202,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1,X3,X0)))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1,X3,X0),X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_328
| ~ spl0_334 ),
inference(resolution,[],[f3950,f3925]) ).
fof(f72694,plain,
( spl0_1431
| ~ spl0_292
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4195,f3949,f3016,f72692]) ).
fof(f72692,plain,
( spl0_1431
<=> ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),X2))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(X1,X2),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f4195,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),X2))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(X1,X2),X2,X0) )
| ~ spl0_292
| ~ spl0_334 ),
inference(resolution,[],[f3950,f3017]) ).
fof(f72683,plain,
( spl0_1430
| ~ spl0_289
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4149,f3945,f3004,f72681]) ).
fof(f72681,plain,
( spl0_1430
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Orderings_Oorder(X3)
| c_COMBK(c_False,tc_bool,X3) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(X4,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f4149,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Orderings_Oorder(X3)
| c_COMBK(c_False,tc_bool,X3) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(X4,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3),X3) )
| ~ spl0_289
| ~ spl0_333 ),
inference(resolution,[],[f3946,f3005]) ).
fof(f72679,plain,
( spl0_1429
| ~ spl0_288
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4148,f3945,f3000,f72677]) ).
fof(f72677,plain,
( spl0_1429
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Orderings_Oorder(X3)
| c_COMBK(c_False,tc_bool,X3) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(X4,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f4148,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Orderings_Oorder(X3)
| c_COMBK(c_False,tc_bool,X3) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(X4,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3),X3) )
| ~ spl0_288
| ~ spl0_333 ),
inference(resolution,[],[f3946,f3001]) ).
fof(f72675,plain,
( spl0_1428
| ~ spl0_289
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4072,f3924,f3004,f72673]) ).
fof(f72673,plain,
( spl0_1428
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Orderings_Oorder(X3)
| c_COMBK(c_False,tc_bool,X3) = c_SetInterval_Oord__class_OatLeastLessThan(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3),hAPP(X4,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f4072,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Orderings_Oorder(X3)
| c_COMBK(c_False,tc_bool,X3) = c_SetInterval_Oord__class_OatLeastLessThan(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3),hAPP(X4,X0),X3) )
| ~ spl0_289
| ~ spl0_328 ),
inference(resolution,[],[f3925,f3005]) ).
fof(f72671,plain,
( spl0_1427
| ~ spl0_288
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4071,f3924,f3000,f72669]) ).
fof(f72669,plain,
( spl0_1427
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Orderings_Oorder(X3)
| c_COMBK(c_False,tc_bool,X3) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3),hAPP(X4,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f4071,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Orderings_Oorder(X3)
| c_COMBK(c_False,tc_bool,X3) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3),hAPP(X4,X0),X3) )
| ~ spl0_288
| ~ spl0_328 ),
inference(resolution,[],[f3925,f3001]) ).
fof(f72667,plain,
( spl0_1426
| ~ spl0_234
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4018,f3908,f2283,f72665]) ).
fof(f72665,plain,
( spl0_1426
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(X2,X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(c_Set_Oimage(X4,X3,X1),X2)),X0))
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f4018,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(X2,X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(c_Set_Oimage(X4,X3,X1),X2)),X0))
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool)) )
| ~ spl0_234
| ~ spl0_324 ),
inference(resolution,[],[f3909,f2284]) ).
fof(f72663,plain,
( spl0_1425
| ~ spl0_243
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4016,f3908,f2319,f72661]) ).
fof(f72661,plain,
( spl0_1425
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_Set_Oimage(X4,X3,X1),X2)),X0))
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f4016,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_Set_Oimage(X4,X3,X1),X2)),X0))
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool)) )
| ~ spl0_243
| ~ spl0_324 ),
inference(resolution,[],[f3909,f2320]) ).
fof(f72659,plain,
( spl0_1424
| ~ spl0_91
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3843,f3420,f1375,f72657]) ).
fof(f72657,plain,
( spl0_1424
<=> ! [X2,X3,X4,X0,X5,X1] : c_Set_Oinsert(X0,X1) = c_Fun_Ofun__upd(c_Set_Oinsert(X0,X1),hAPP(c_Set_Oinsert(X2,X1),X3),hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f3843,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_Set_Oinsert(X0,X1) = c_Fun_Ofun__upd(c_Set_Oinsert(X0,X1),hAPP(c_Set_Oinsert(X2,X1),X3),hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X4,X5)
| ~ spl0_91
| ~ spl0_313 ),
inference(superposition,[],[f1376,f3421]) ).
fof(f72655,plain,
( spl0_1423
| ~ spl0_238
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3763,f3408,f2299,f72653]) ).
fof(f72653,plain,
( spl0_1423
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f3763,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2)
| ~ spl0_238
| ~ spl0_310 ),
inference(resolution,[],[f3409,f2300]) ).
fof(f72651,plain,
( spl0_1422
| ~ spl0_237
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3762,f3408,f2295,f72649]) ).
fof(f72649,plain,
( spl0_1422
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f3762,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1)
| ~ spl0_237
| ~ spl0_310 ),
inference(resolution,[],[f3409,f2296]) ).
fof(f72647,plain,
( spl0_1421
| ~ spl0_238
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3730,f3404,f2299,f72645]) ).
fof(f72645,plain,
( spl0_1421
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f3730,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_238
| ~ spl0_309 ),
inference(resolution,[],[f3405,f2300]) ).
fof(f72637,plain,
( spl0_1420
| ~ spl0_181
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3702,f3400,f1864,f72635]) ).
fof(f72635,plain,
( spl0_1420
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f3702,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1865]) ).
fof(f72633,plain,
( spl0_1419
| ~ spl0_182
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3701,f3400,f1868,f72631]) ).
fof(f72631,plain,
( spl0_1419
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f3701,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1869]) ).
fof(f72629,plain,
( spl0_1418
| ~ spl0_180
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3700,f3400,f1860,f72627]) ).
fof(f72627,plain,
( spl0_1418
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f3700,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1861]) ).
fof(f72625,plain,
( spl0_1417
| ~ spl0_183
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3699,f3400,f1872,f72623]) ).
fof(f72623,plain,
( spl0_1417
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f3699,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1873]) ).
fof(f72621,plain,
( spl0_1416
| ~ spl0_175
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3691,f3400,f1839,f72619]) ).
fof(f72619,plain,
( spl0_1416
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f3691,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_175
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1840]) ).
fof(f72617,plain,
( spl0_1415
| ~ spl0_176
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3690,f3400,f1844,f72615]) ).
fof(f72615,plain,
( spl0_1415
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)))
| ~ class_Lattices_Olower__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f3690,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)))
| ~ class_Lattices_Olower__semilattice(X1) )
| ~ spl0_176
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1845]) ).
fof(f72613,plain,
( spl0_1414
| ~ spl0_174
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3686,f3400,f1835,f72611]) ).
fof(f72611,plain,
( spl0_1414
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f3686,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_174
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1836]) ).
fof(f72609,plain,
( spl0_1413
| ~ spl0_177
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3685,f3400,f1848,f72607]) ).
fof(f72607,plain,
( spl0_1413
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)))
| ~ class_Lattices_Olower__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f3685,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)))
| ~ class_Lattices_Olower__semilattice(X1) )
| ~ spl0_177
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1849]) ).
fof(f72605,plain,
( spl0_1412
| ~ spl0_301
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3663,f3388,f3372,f72603]) ).
fof(f72603,plain,
( spl0_1412
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMin(X0,X1) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f3663,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMin(X0,X1) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1)),X2)) )
| ~ spl0_301
| ~ spl0_305 ),
inference(duplicate_literal_removal,[],[f3659]) ).
fof(f3659,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMin(X0,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1)),X2)) )
| ~ spl0_301
| ~ spl0_305 ),
inference(resolution,[],[f3389,f3373]) ).
fof(f72601,plain,
( spl0_1411
| ~ spl0_247
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3653,f3388,f2495,f72599]) ).
fof(f72599,plain,
( spl0_1411
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Finite__Set_Olinorder__class_OMin(X0,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Finite__Set_Olinorder__class_OMin(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f3653,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Finite__Set_Olinorder__class_OMin(X0,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Finite__Set_Olinorder__class_OMin(X0,X1)) )
| ~ spl0_247
| ~ spl0_305 ),
inference(resolution,[],[f3389,f2496]) ).
fof(f72528,plain,
( spl0_1410
| ~ spl0_245
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3652,f3388,f2487,f72526]) ).
fof(f72526,plain,
( spl0_1410
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Finite__Set_Olinorder__class_OMin(X0,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f3652,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Finite__Set_Olinorder__class_OMin(X0,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1)),X2) )
| ~ spl0_245
| ~ spl0_305 ),
inference(resolution,[],[f3389,f2488]) ).
fof(f72524,plain,
( spl0_1409
| ~ spl0_301
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3642,f3384,f3372,f72522]) ).
fof(f72522,plain,
( spl0_1409
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMax(X0,X1) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Finite__Set_Olinorder__class_OMax(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f3642,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMax(X0,X1) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Finite__Set_Olinorder__class_OMax(X0,X1))) )
| ~ spl0_301
| ~ spl0_304 ),
inference(duplicate_literal_removal,[],[f3639]) ).
fof(f3639,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMax(X0,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Finite__Set_Olinorder__class_OMax(X0,X1))) )
| ~ spl0_301
| ~ spl0_304 ),
inference(resolution,[],[f3385,f3373]) ).
fof(f72520,plain,
( spl0_1408
| ~ spl0_255
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3635,f3384,f2536,f72518]) ).
fof(f72518,plain,
( spl0_1408
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Finite__Set_Olinorder__class_OMax(X0,X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Finite__Set_Olinorder__class_OMax(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f3635,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Finite__Set_Olinorder__class_OMax(X0,X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Finite__Set_Olinorder__class_OMax(X0,X1)) )
| ~ spl0_255
| ~ spl0_304 ),
inference(resolution,[],[f3385,f2537]) ).
fof(f72516,plain,
( spl0_1407
| ~ spl0_253
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3634,f3384,f2528,f72514]) ).
fof(f72514,plain,
( spl0_1407
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Finite__Set_Olinorder__class_OMax(X0,X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Finite__Set_Olinorder__class_OMax(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f3634,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Finite__Set_Olinorder__class_OMax(X0,X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Finite__Set_Olinorder__class_OMax(X0,X1)),X2) )
| ~ spl0_253
| ~ spl0_304 ),
inference(resolution,[],[f3385,f2529]) ).
fof(f72512,plain,
( spl0_1406
| ~ spl0_150
| ~ spl0_275
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3617,f3376,f2948,f1668,f72510]) ).
fof(f72510,plain,
( spl0_1406
<=> ! [X5,X4,X0,X6,X1] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X6))
| ~ c_Finite__Set_Ofinite(X0,X4)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,tc_fun(X4,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f3617,plain,
( ! [X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X6))
| ~ c_Finite__Set_Ofinite(X0,X4)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,tc_fun(X4,tc_bool)),X4) )
| ~ spl0_150
| ~ spl0_275
| ~ spl0_302 ),
inference(forward_demodulation,[],[f3609,f3192]) ).
fof(f3609,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Finite__Set_Ofinite(X0,X4)
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X1,tc_bool)),X5,X6))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X6,tc_fun(X4,tc_bool)),X4) )
| ~ spl0_275
| ~ spl0_302 ),
inference(superposition,[],[f3377,f2949]) ).
fof(f72508,plain,
( spl0_1405
| ~ spl0_150
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3607,f3376,f1668,f72506]) ).
fof(f72506,plain,
( spl0_1405
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X2)
| ~ hBOOL(c_in(X0,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f3607,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X2)
| ~ hBOOL(c_in(X0,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_150
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1669]) ).
fof(f72504,plain,
( spl0_1404
| ~ spl0_181
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3572,f3372,f1864,f72502]) ).
fof(f72502,plain,
( spl0_1404
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X0) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X0)))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f3572,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X0) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X0)))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_181
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1865]) ).
fof(f72500,plain,
( spl0_1403
| ~ spl0_182
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3571,f3372,f1868,f72498]) ).
fof(f72498,plain,
( spl0_1403
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X0) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X0)))
| ~ class_Lattices_Oupper__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f3571,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X0) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X0)))
| ~ class_Lattices_Oupper__semilattice(X1) )
| ~ spl0_182
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1869]) ).
fof(f72496,plain,
( spl0_1402
| ~ spl0_180
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3570,f3372,f1860,f72494]) ).
fof(f72494,plain,
( spl0_1402
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X0),X2) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X0),X2)))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f3570,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X0),X2) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X0),X2)))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_180
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1861]) ).
fof(f72492,plain,
( spl0_1401
| ~ spl0_183
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3569,f3372,f1872,f72490]) ).
fof(f72490,plain,
( spl0_1401
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X0),X2) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f3569,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X0),X2) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X1) )
| ~ spl0_183
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1873]) ).
fof(f72477,plain,
( spl0_1400
| ~ spl0_175
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3562,f3372,f1839,f72475]) ).
fof(f72475,plain,
( spl0_1400
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f3562,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1840]) ).
fof(f72473,plain,
( spl0_1399
| ~ spl0_176
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3561,f3372,f1844,f72471]) ).
fof(f72471,plain,
( spl0_1399
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f3561,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1845]) ).
fof(f72469,plain,
( spl0_1398
| ~ spl0_174
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3557,f3372,f1835,f72467]) ).
fof(f72467,plain,
( spl0_1398
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f3557,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1836]) ).
fof(f72465,plain,
( spl0_1397
| ~ spl0_177
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3556,f3372,f1848,f72463]) ).
fof(f72463,plain,
( spl0_1397
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f3556,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1849]) ).
fof(f72461,plain,
( spl0_1396
| ~ spl0_181
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3544,f3368,f1864,f72459]) ).
fof(f72459,plain,
( spl0_1396
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f3544,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1865]) ).
fof(f72457,plain,
( spl0_1395
| ~ spl0_182
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3543,f3368,f1868,f72455]) ).
fof(f72455,plain,
( spl0_1395
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f3543,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1869]) ).
fof(f72453,plain,
( spl0_1394
| ~ spl0_180
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3542,f3368,f1860,f72451]) ).
fof(f72451,plain,
( spl0_1394
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f3542,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1861]) ).
fof(f72449,plain,
( spl0_1393
| ~ spl0_183
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3541,f3368,f1872,f72447]) ).
fof(f72447,plain,
( spl0_1393
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f3541,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1873]) ).
fof(f72445,plain,
( spl0_1392
| ~ spl0_175
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3534,f3368,f1839,f72443]) ).
fof(f72443,plain,
( spl0_1392
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)),X0))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f3534,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)),X0))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_175
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1840]) ).
fof(f72441,plain,
( spl0_1391
| ~ spl0_176
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3533,f3368,f1844,f72439]) ).
fof(f72439,plain,
( spl0_1391
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)),X0))
| ~ class_Lattices_Olower__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f3533,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)),X0))
| ~ class_Lattices_Olower__semilattice(X1) )
| ~ spl0_176
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1845]) ).
fof(f72433,plain,
( spl0_1390
| ~ spl0_174
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3529,f3368,f1835,f72431]) ).
fof(f72431,plain,
( spl0_1390
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)),X0))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f3529,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)),X0))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_174
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1836]) ).
fof(f72429,plain,
( spl0_1389
| ~ spl0_177
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3528,f3368,f1848,f72427]) ).
fof(f72427,plain,
( spl0_1389
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)),X0))
| ~ class_Lattices_Olower__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f3528,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)),X0))
| ~ class_Lattices_Olower__semilattice(X1) )
| ~ spl0_177
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1849]) ).
fof(f72425,plain,
( spl0_1388
| ~ spl0_187
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3322,f3016,f1888,f72423]) ).
fof(f72423,plain,
( spl0_1388
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)) = c_COMBK(c_False,tc_bool,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f3322,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)) = c_COMBK(c_False,tc_bool,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X0) )
| ~ spl0_187
| ~ spl0_292 ),
inference(resolution,[],[f3017,f1889]) ).
fof(f72421,plain,
( spl0_1387
| ~ spl0_238
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3280,f3004,f2299,f72419]) ).
fof(f72419,plain,
( spl0_1387
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X2,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f3280,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_238
| ~ spl0_289 ),
inference(resolution,[],[f3005,f2300]) ).
fof(f72417,plain,
( spl0_1386
| ~ spl0_237
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3279,f3004,f2295,f72415]) ).
fof(f72415,plain,
( spl0_1386
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f3279,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_237
| ~ spl0_289 ),
inference(resolution,[],[f3005,f2296]) ).
fof(f72413,plain,
( spl0_1385
| ~ spl0_238
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3254,f3000,f2299,f72411]) ).
fof(f72411,plain,
( spl0_1385
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X2,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f3254,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_238
| ~ spl0_288 ),
inference(resolution,[],[f3001,f2300]) ).
fof(f72409,plain,
( spl0_1384
| ~ spl0_237
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3253,f3000,f2295,f72407]) ).
fof(f72407,plain,
( spl0_1384
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f3253,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_237
| ~ spl0_288 ),
inference(resolution,[],[f3001,f2296]) ).
fof(f72405,plain,
( spl0_1383
| ~ spl0_87
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3035,f2916,f1344,f72403]) ).
fof(f72403,plain,
( spl0_1383
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f2916,plain,
( spl0_268
<=> ! [X11,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f3035,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_False)) )
| ~ spl0_87
| ~ spl0_268 ),
inference(resolution,[],[f2917,f1345]) ).
fof(f2917,plain,
( ! [X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) )
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f2916]) ).
fof(f72401,plain,
( spl0_1382
| ~ spl0_259
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2860,f2560,f2552,f72399]) ).
fof(f72399,plain,
( spl0_1382
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X1),X3))
| ~ hBOOL(hAPP(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f2860,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X1),X3))
| ~ hBOOL(hAPP(X0,X3)) )
| ~ spl0_259
| ~ spl0_261 ),
inference(resolution,[],[f2561,f2553]) ).
fof(f72397,plain,
( spl0_1381
| ~ spl0_256
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2842,f2552,f2540,f72395]) ).
fof(f72395,plain,
( spl0_1381
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(c_in(X0,X3,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f2842,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(c_in(X0,X3,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) )
| ~ spl0_256
| ~ spl0_259 ),
inference(resolution,[],[f2553,f2541]) ).
fof(f72386,plain,
( spl0_1380
| ~ spl0_86
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2810,f2540,f1340,f72384]) ).
fof(f72384,plain,
( spl0_1380
<=> ! [X0,X1] :
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1))),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f2810,plain,
( ! [X0,X1] :
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1))),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),c_False)) )
| ~ spl0_86
| ~ spl0_256 ),
inference(resolution,[],[f2541,f1341]) ).
fof(f72382,plain,
( spl0_1379
| ~ spl0_185
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2728,f2520,f1880,f72380]) ).
fof(f72380,plain,
( spl0_1379
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X1,X2,X3,X4),X6,X7),X8),X7))
| ~ hBOOL(c_in(X5,X8,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f2728,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X1,X2,X3,X4),X6,X7),X8),X7))
| ~ hBOOL(c_in(X5,X8,X6)) )
| ~ spl0_185
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1881]) ).
fof(f72378,plain,
( spl0_1378
| ~ spl0_178
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2720,f2520,f1852,f72376]) ).
fof(f72376,plain,
( spl0_1378
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(c_COMBB(X0,X1,X2,X3,X4),X6,X7),X8),X7))
| ~ hBOOL(c_in(X5,X8,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f2720,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(c_COMBB(X0,X1,X2,X3,X4),X6,X7),X8),X7))
| ~ hBOOL(c_in(X5,X8,X6)) )
| ~ spl0_178
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1853]) ).
fof(f72374,plain,
( spl0_1377
| ~ spl0_191
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2719,f2520,f1904,f72372]) ).
fof(f72372,plain,
( spl0_1377
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(c_in(c_COMBK(c_False,tc_bool,X2),hAPP(c_Set_Oimage(c_Set_Oimage(X0,X1,X2),X3,X4),X5),X4))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f2719,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(c_COMBK(c_False,tc_bool,X2),hAPP(c_Set_Oimage(c_Set_Oimage(X0,X1,X2),X3,X4),X5),X4))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X5,X3)) )
| ~ spl0_191
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1905]) ).
fof(f72370,plain,
( spl0_1376
| ~ spl0_91
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2461,f2307,f1375,f72368]) ).
fof(f72368,plain,
( spl0_1376
<=> ! [X0,X3,X2,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f2461,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X3)
| ~ spl0_91
| ~ spl0_240 ),
inference(superposition,[],[f1376,f2308]) ).
fof(f72366,plain,
( spl0_1375
| ~ spl0_91
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2178,f2033,f1375,f72364]) ).
fof(f72364,plain,
( spl0_1375
<=> ! [X5,X4,X2,X7,X0,X6,X3,X1] : hAPP(c_COMBC(X0,X1,X2,X3),X4) = c_Fun_Ofun__upd(hAPP(c_COMBC(X0,X1,X2,X3),X4),X5,hAPP(hAPP(X0,X5),X4),X6,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f2178,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_COMBC(X0,X1,X2,X3),X4) = c_Fun_Ofun__upd(hAPP(c_COMBC(X0,X1,X2,X3),X4),X5,hAPP(hAPP(X0,X5),X4),X6,X7)
| ~ spl0_91
| ~ spl0_206 ),
inference(superposition,[],[f1376,f2034]) ).
fof(f72362,plain,
( spl0_1374
| ~ spl0_91
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1817,f1788,f1375,f72360]) ).
fof(f72360,plain,
( spl0_1374
<=> ! [X0,X3,X2,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X1,X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f1817,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X1,X1,X2,X3)
| ~ spl0_91
| ~ spl0_170 ),
inference(superposition,[],[f1376,f1789]) ).
fof(f70479,plain,
( spl0_1373
| ~ spl0_375
| ~ spl0_1186 ),
inference(avatar_split_clause,[],[f56183,f52620,f5030,f70477]) ).
fof(f70477,plain,
( spl0_1373
<=> ! [X0] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X0,c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f52620,plain,
( spl0_1186
<=> ! [X0,X1] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X0,hAPP(c_fequal(X1),c_False),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f56183,plain,
( ! [X0] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X0,c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_bool),tc_bool))
| ~ spl0_375
| ~ spl0_1186 ),
inference(superposition,[],[f52621,f5031]) ).
fof(f52621,plain,
( ! [X0,X1] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X0,hAPP(c_fequal(X1),c_False),X1))
| ~ spl0_1186 ),
inference(avatar_component_clause,[],[f52620]) ).
fof(f68320,plain,
( spl0_1372
| ~ spl0_371
| ~ spl0_1186 ),
inference(avatar_split_clause,[],[f56182,f52620,f4832,f68318]) ).
fof(f68318,plain,
( spl0_1372
<=> ! [X0] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X0,c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f56182,plain,
( ! [X0] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X0,c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_nat),tc_nat))
| ~ spl0_371
| ~ spl0_1186 ),
inference(superposition,[],[f52621,f4833]) ).
fof(f66125,plain,
( ~ spl0_18
| spl0_1371
| ~ spl0_236
| ~ spl0_1127 ),
inference(avatar_split_clause,[],[f47775,f47731,f2291,f66123,f1047]) ).
fof(f1047,plain,
( spl0_18
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f66123,plain,
( spl0_1371
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f47731,plain,
( spl0_1127
<=> ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f47775,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0))
| ~ class_Orderings_Opreorder(tc_bool) )
| ~ spl0_236
| ~ spl0_1127 ),
inference(resolution,[],[f47732,f2292]) ).
fof(f47732,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)))
| ~ spl0_1127 ),
inference(avatar_component_clause,[],[f47731]) ).
fof(f65119,plain,
( spl0_1370
| ~ spl0_118
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39092,f31067,f1504,f65117]) ).
fof(f65117,plain,
( spl0_1370
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f1504,plain,
( spl0_118
<=> ! [X0,X8,X3] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,c_COMBK(c_False,tc_bool,X0),X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f39092,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool),X2))
| ~ spl0_118
| ~ spl0_728 ),
inference(superposition,[],[f1505,f31068]) ).
fof(f1505,plain,
( ! [X3,X0,X8] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,c_COMBK(c_False,tc_bool,X0),X0),X3))
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f64222,plain,
( spl0_1369
| ~ spl0_116
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39091,f31067,f1484,f64220]) ).
fof(f64220,plain,
( spl0_1369
<=> ! [X2,X0,X1,X3] : c_Nitpick_Ofold__graph_H(X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),X2,tc_bool,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f1484,plain,
( spl0_116
<=> ! [X0,X7,X8,X10] : c_Nitpick_Ofold__graph_H(X8,X10,c_COMBK(c_False,tc_bool,X0),X10,X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f39091,plain,
( ! [X2,X3,X0,X1] : c_Nitpick_Ofold__graph_H(X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),X2,tc_bool,X3)
| ~ spl0_116
| ~ spl0_728 ),
inference(superposition,[],[f1485,f31068]) ).
fof(f1485,plain,
( ! [X10,X0,X8,X7] : c_Nitpick_Ofold__graph_H(X8,X10,c_COMBK(c_False,tc_bool,X0),X10,X0,X7)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1484]) ).
fof(f63275,plain,
( spl0_1368
| ~ spl0_115
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39090,f31067,f1480,f63273]) ).
fof(f63273,plain,
( spl0_1368
<=> ! [X2,X0,X1,X3] : c_Finite__Set_Ofold__graph(X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),X2,tc_bool,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f1480,plain,
( spl0_115
<=> ! [X0,X7,X8,X10] : c_Finite__Set_Ofold__graph(X8,X10,c_COMBK(c_False,tc_bool,X0),X10,X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f39090,plain,
( ! [X2,X3,X0,X1] : c_Finite__Set_Ofold__graph(X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),X2,tc_bool,X3)
| ~ spl0_115
| ~ spl0_728 ),
inference(superposition,[],[f1481,f31068]) ).
fof(f1481,plain,
( ! [X10,X0,X8,X7] : c_Finite__Set_Ofold__graph(X8,X10,c_COMBK(c_False,tc_bool,X0),X10,X0,X7)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f62430,plain,
( spl0_1367
| ~ spl0_113
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39089,f31067,f1467,f62428]) ).
fof(f62428,plain,
( spl0_1367
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool) != X1
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f39089,plain,
( ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool) != X1
| ~ hBOOL(hAPP(X1,X2)) )
| ~ spl0_113
| ~ spl0_728 ),
inference(superposition,[],[f1468,f31068]) ).
fof(f61671,plain,
( spl0_1366
| ~ spl0_579
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39084,f31067,f12851,f61669]) ).
fof(f61669,plain,
( spl0_1366
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f39084,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool))
| ~ spl0_579
| ~ spl0_728 ),
inference(superposition,[],[f12853,f31068]) ).
fof(f60639,plain,
( spl0_1365
| ~ spl0_118
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36506,f30644,f1504,f60637]) ).
fof(f60637,plain,
( spl0_1365
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f30644,plain,
( spl0_727
<=> ! [X0] : c_COMBK(c_False,tc_bool,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f36506,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat),X2))
| ~ spl0_118
| ~ spl0_727 ),
inference(superposition,[],[f1505,f30645]) ).
fof(f30645,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat)
| ~ spl0_727 ),
inference(avatar_component_clause,[],[f30644]) ).
fof(f59849,plain,
( spl0_1364
| ~ spl0_116
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36505,f30644,f1484,f59847]) ).
fof(f59847,plain,
( spl0_1364
<=> ! [X2,X0,X1,X3] : c_Nitpick_Ofold__graph_H(X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),X2,tc_nat,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f36505,plain,
( ! [X2,X3,X0,X1] : c_Nitpick_Ofold__graph_H(X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),X2,tc_nat,X3)
| ~ spl0_116
| ~ spl0_727 ),
inference(superposition,[],[f1485,f30645]) ).
fof(f59167,plain,
( spl0_1363
| ~ spl0_115
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36504,f30644,f1480,f59165]) ).
fof(f59165,plain,
( spl0_1363
<=> ! [X2,X0,X1,X3] : c_Finite__Set_Ofold__graph(X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),X2,tc_nat,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f36504,plain,
( ! [X2,X3,X0,X1] : c_Finite__Set_Ofold__graph(X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),X2,tc_nat,X3)
| ~ spl0_115
| ~ spl0_727 ),
inference(superposition,[],[f1481,f30645]) ).
fof(f58400,plain,
( spl0_1362
| ~ spl0_113
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36503,f30644,f1467,f58398]) ).
fof(f58398,plain,
( spl0_1362
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat) != X1
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f36503,plain,
( ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat) != X1
| ~ hBOOL(hAPP(X1,X2)) )
| ~ spl0_113
| ~ spl0_727 ),
inference(superposition,[],[f1468,f30645]) ).
fof(f57850,plain,
( spl0_1361
| ~ spl0_118
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33244,f30221,f1504,f57848]) ).
fof(f57848,plain,
( spl0_1361
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f33244,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool),X2))
| ~ spl0_118
| ~ spl0_726 ),
inference(superposition,[],[f1505,f30222]) ).
fof(f57649,plain,
( spl0_1360
| ~ spl0_116
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33243,f30221,f1484,f57647]) ).
fof(f57647,plain,
( spl0_1360
<=> ! [X2,X0,X1,X3] : c_Nitpick_Ofold__graph_H(X1,X2,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),X2,tc_bool,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f33243,plain,
( ! [X2,X3,X0,X1] : c_Nitpick_Ofold__graph_H(X1,X2,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),X2,tc_bool,X3)
| ~ spl0_116
| ~ spl0_726 ),
inference(superposition,[],[f1485,f30222]) ).
fof(f56839,plain,
( spl0_1359
| ~ spl0_115
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33242,f30221,f1480,f56837]) ).
fof(f56837,plain,
( spl0_1359
<=> ! [X2,X0,X1,X3] : c_Finite__Set_Ofold__graph(X1,X2,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),X2,tc_bool,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f33242,plain,
( ! [X2,X3,X0,X1] : c_Finite__Set_Ofold__graph(X1,X2,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),X2,tc_bool,X3)
| ~ spl0_115
| ~ spl0_726 ),
inference(superposition,[],[f1481,f30222]) ).
fof(f56480,plain,
( spl0_1358
| ~ spl0_163
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f10416,f10328,f1760,f56478]) ).
fof(f56478,plain,
( spl0_1358
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)),X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X0),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f10416,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)),X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X0),X3),X0) )
| ~ spl0_163
| ~ spl0_517 ),
inference(superposition,[],[f1761,f10329]) ).
fof(f56476,plain,
( spl0_1357
| ~ spl0_162
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f10415,f10328,f1756,f56474]) ).
fof(f56474,plain,
( spl0_1357
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)),X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X0),X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f10415,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)),X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X0),X4),X0) )
| ~ spl0_162
| ~ spl0_517 ),
inference(superposition,[],[f1757,f10329]) ).
fof(f56472,plain,
( spl0_1356
| ~ spl0_251
| ~ spl0_495 ),
inference(avatar_split_clause,[],[f9391,f9339,f2520,f56470]) ).
fof(f56470,plain,
( spl0_1356
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X0,hAPP(c_Set_Oinsert(X1,X2),X3),X2,X4)
| ~ hBOOL(c_in(X1,hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f9339,plain,
( spl0_495
<=> ! [X8,X11,X0,X1,X7] :
( ~ hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))),X7))
| ~ c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f9391,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X0,hAPP(c_Set_Oinsert(X1,X2),X3),X2,X4)
| ~ hBOOL(c_in(X1,hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),X2)) )
| ~ spl0_251
| ~ spl0_495 ),
inference(resolution,[],[f9340,f2521]) ).
fof(f9340,plain,
( ! [X0,X11,X1,X8,X7] :
( ~ hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))),X7))
| ~ c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) )
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f9339]) ).
fof(f56468,plain,
( spl0_1355
| ~ spl0_242
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f9101,f8450,f2315,f56466]) ).
fof(f56466,plain,
( spl0_1355
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X3,X1),X2)),X1))
| ~ hBOOL(c_in(X4,hAPP(c_fequal(X1),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f9101,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X3,X1),X2)),X1))
| ~ hBOOL(c_in(X4,hAPP(c_fequal(X1),X3),X1)) )
| ~ spl0_242
| ~ spl0_480 ),
inference(superposition,[],[f2316,f8451]) ).
fof(f56464,plain,
( spl0_1354
| ~ spl0_199
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f7597,f7488,f2005,f56462]) ).
fof(f56462,plain,
( spl0_1354
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X0),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f7597,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X0),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X0),X2),X0) )
| ~ spl0_199
| ~ spl0_450 ),
inference(resolution,[],[f7489,f2006]) ).
fof(f56460,plain,
( spl0_1353
| ~ spl0_238
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f7429,f6764,f2299,f56458]) ).
fof(f56458,plain,
( spl0_1353
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f7429,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X1))))
| ~ spl0_238
| ~ spl0_445 ),
inference(resolution,[],[f6765,f2300]) ).
fof(f56456,plain,
( spl0_1352
| ~ spl0_238
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f7371,f6760,f2299,f56454]) ).
fof(f56454,plain,
( spl0_1352
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f7371,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))))
| ~ spl0_238
| ~ spl0_444 ),
inference(resolution,[],[f6761,f2300]) ).
fof(f56452,plain,
( spl0_1351
| ~ spl0_213
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7279,f6756,f2064,f56450]) ).
fof(f56450,plain,
( spl0_1351
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f7279,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),X2),X4)) )
| ~ spl0_213
| ~ spl0_443 ),
inference(superposition,[],[f2065,f6757]) ).
fof(f56448,plain,
( spl0_1350
| ~ spl0_113
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33241,f30221,f1467,f56446]) ).
fof(f56446,plain,
( spl0_1350
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool) != X1
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f33241,plain,
( ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool) != X1
| ~ hBOOL(hAPP(X1,X2)) )
| ~ spl0_113
| ~ spl0_726 ),
inference(superposition,[],[f1468,f30222]) ).
fof(f56444,plain,
( spl0_1349
| ~ spl0_212
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7149,f6752,f2060,f56442]) ).
fof(f56442,plain,
( spl0_1349
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f7149,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X0),X3),X4)) )
| ~ spl0_212
| ~ spl0_442 ),
inference(superposition,[],[f2061,f6753]) ).
fof(f56440,plain,
( spl0_1348
| ~ spl0_19
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f7106,f6723,f1052,f56438]) ).
fof(f56438,plain,
( spl0_1348
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f1052,plain,
( spl0_19
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f6723,plain,
( spl0_435
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f7106,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X2))
| ~ spl0_19
| ~ spl0_435 ),
inference(resolution,[],[f6724,f1054]) ).
fof(f1054,plain,
( class_Lattices_Olattice(tc_bool)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f1052]) ).
fof(f6724,plain,
( ! [X3,X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10)) )
| ~ spl0_435 ),
inference(avatar_component_clause,[],[f6723]) ).
fof(f56436,plain,
( spl0_1347
| ~ spl0_7
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f7105,f6723,f992,f56434]) ).
fof(f56434,plain,
( spl0_1347
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X2)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f7105,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X2)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X2))
| ~ spl0_7
| ~ spl0_435 ),
inference(resolution,[],[f6724,f994]) ).
fof(f994,plain,
( class_Lattices_Olattice(tc_nat)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f56432,plain,
( spl0_1346
| ~ spl0_19
| ~ spl0_434 ),
inference(avatar_split_clause,[],[f7103,f6719,f1052,f56430]) ).
fof(f56430,plain,
( spl0_1346
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f6719,plain,
( spl0_434
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f7103,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2))
| ~ spl0_19
| ~ spl0_434 ),
inference(resolution,[],[f6720,f1054]) ).
fof(f6720,plain,
( ! [X3,X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) )
| ~ spl0_434 ),
inference(avatar_component_clause,[],[f6719]) ).
fof(f56428,plain,
( spl0_1345
| ~ spl0_7
| ~ spl0_434 ),
inference(avatar_split_clause,[],[f7102,f6719,f992,f56426]) ).
fof(f56426,plain,
( spl0_1345
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f7102,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X2))
| ~ spl0_7
| ~ spl0_434 ),
inference(resolution,[],[f6720,f994]) ).
fof(f56424,plain,
( spl0_1344
| ~ spl0_14
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f6807,f6695,f1027,f56422]) ).
fof(f56422,plain,
( spl0_1344
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f1027,plain,
( spl0_14
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f6695,plain,
( spl0_428
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f6807,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X2))
| ~ spl0_14
| ~ spl0_428 ),
inference(resolution,[],[f6696,f1029]) ).
fof(f1029,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f6696,plain,
( ! [X3,X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10)) )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f6695]) ).
fof(f56420,plain,
( spl0_1343
| ~ spl0_3
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f6806,f6695,f972,f56418]) ).
fof(f56418,plain,
( spl0_1343
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f972,plain,
( spl0_3
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f6806,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X2))
| ~ spl0_3
| ~ spl0_428 ),
inference(resolution,[],[f6696,f974]) ).
fof(f974,plain,
( class_Lattices_Olower__semilattice(tc_nat)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f972]) ).
fof(f56416,plain,
( spl0_1342
| ~ spl0_14
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f6776,f6668,f1027,f56414]) ).
fof(f56414,plain,
( spl0_1342
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f6668,plain,
( spl0_425
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f6776,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2))
| ~ spl0_14
| ~ spl0_425 ),
inference(resolution,[],[f6669,f1029]) ).
fof(f6669,plain,
( ! [X3,X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) )
| ~ spl0_425 ),
inference(avatar_component_clause,[],[f6668]) ).
fof(f56412,plain,
( spl0_1341
| ~ spl0_3
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f6775,f6668,f972,f56410]) ).
fof(f56410,plain,
( spl0_1341
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f6775,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2))
| ~ spl0_3
| ~ spl0_425 ),
inference(resolution,[],[f6669,f974]) ).
fof(f56408,plain,
( spl0_1340
| ~ spl0_259
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f6609,f6432,f2552,f56406]) ).
fof(f56406,plain,
( spl0_1340
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0),X5))
| ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f6609,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0),X5))
| ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X5)) )
| ~ spl0_259
| ~ spl0_422 ),
inference(resolution,[],[f6433,f2553]) ).
fof(f56404,plain,
( spl0_1339
| ~ spl0_579
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33236,f30221,f12851,f56402]) ).
fof(f56402,plain,
( spl0_1339
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f33236,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool))
| ~ spl0_579
| ~ spl0_726 ),
inference(superposition,[],[f12853,f30222]) ).
fof(f56400,plain,
( spl0_1338
| ~ spl0_187
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f6607,f6432,f1888,f56398]) ).
fof(f56398,plain,
( spl0_1338
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_Hoare__Mirabelle_Otriple(X0)),X1),X2))
| ~ class_Orderings_Oorder(tc_Hoare__Mirabelle_Otriple(X0))
| c_Hoare__Mirabelle_Ohoare__derivs(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,tc_Hoare__Mirabelle_Otriple(X0)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_Hoare__Mirabelle_Otriple(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f6607,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_Hoare__Mirabelle_Otriple(X0)),X1),X2))
| ~ class_Orderings_Oorder(tc_Hoare__Mirabelle_Otriple(X0))
| c_Hoare__Mirabelle_Ohoare__derivs(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,tc_Hoare__Mirabelle_Otriple(X0)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_Hoare__Mirabelle_Otriple(X0)),X0) )
| ~ spl0_187
| ~ spl0_422 ),
inference(resolution,[],[f6433,f1889]) ).
fof(f56396,plain,
( spl0_1337
| ~ spl0_80
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f6515,f6420,f1315,f56394]) ).
fof(f56394,plain,
( spl0_1337
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_Set_Oimage(X0,X1,X2),X3) = hAPP(c_Set_Oinsert(hAPP(X0,X4),X2),hAPP(c_Set_Oimage(X0,X1,X2),X3))
| ~ hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f6420,plain,
( spl0_419
<=> ! [X11,X0,X3,X8,X7] :
( ~ hBOOL(c_in(X3,X11,X0))
| hAPP(c_Set_Oimage(X8,X0,X7),X11) = hAPP(c_Set_Oinsert(hAPP(X8,X3),X7),hAPP(c_Set_Oimage(X8,X0,X7),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f6515,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(c_Set_Oimage(X0,X1,X2),X3) = hAPP(c_Set_Oinsert(hAPP(X0,X4),X2),hAPP(c_Set_Oimage(X0,X1,X2),X3))
| ~ hBOOL(hAPP(X3,X4)) )
| ~ spl0_80
| ~ spl0_419 ),
inference(resolution,[],[f6421,f1316]) ).
fof(f6421,plain,
( ! [X3,X0,X11,X8,X7] :
( ~ hBOOL(c_in(X3,X11,X0))
| hAPP(c_Set_Oimage(X8,X0,X7),X11) = hAPP(c_Set_Oinsert(hAPP(X8,X3),X7),hAPP(c_Set_Oimage(X8,X0,X7),X11)) )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f6420]) ).
fof(f56392,plain,
( spl0_1336
| ~ spl0_80
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f6499,f6416,f1315,f56390]) ).
fof(f56390,plain,
( spl0_1336
<=> ! [X0,X3,X2,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X1),X0),tc_fun(X1,tc_bool)),X2)
| ~ hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f6499,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X1),X0),tc_fun(X1,tc_bool)),X2)
| ~ hBOOL(hAPP(X2,X3)) )
| ~ spl0_80
| ~ spl0_418 ),
inference(resolution,[],[f6417,f1316]) ).
fof(f56388,plain,
( spl0_1335
| ~ spl0_217
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f6366,f5559,f2081,f56386]) ).
fof(f56386,plain,
( spl0_1335
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ hBOOL(c_in(X2,hAPP(c_fequal(X0),X1),X0))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f6366,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ hBOOL(c_in(X2,hAPP(c_fequal(X0),X1),X0))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_217
| ~ spl0_411 ),
inference(superposition,[],[f5560,f2082]) ).
fof(f56384,plain,
( spl0_1334
| ~ spl0_181
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6311,f5555,f1864,f56382]) ).
fof(f56382,plain,
( spl0_1334
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f6311,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_410 ),
inference(resolution,[],[f5556,f1865]) ).
fof(f56380,plain,
( spl0_1333
| ~ spl0_180
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6309,f5555,f1860,f56378]) ).
fof(f56378,plain,
( spl0_1333
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f6309,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_410 ),
inference(resolution,[],[f5556,f1861]) ).
fof(f56376,plain,
( spl0_1332
| ~ spl0_175
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6297,f5555,f1839,f56374]) ).
fof(f56374,plain,
( spl0_1332
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f6297,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_410 ),
inference(resolution,[],[f5556,f1840]) ).
fof(f56372,plain,
( spl0_1331
| ~ spl0_174
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6292,f5555,f1835,f56370]) ).
fof(f56370,plain,
( spl0_1331
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f6292,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_410 ),
inference(resolution,[],[f5556,f1836]) ).
fof(f56368,plain,
( spl0_1330
| ~ spl0_181
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6272,f5551,f1864,f56366]) ).
fof(f56366,plain,
( spl0_1330
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f6272,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_409 ),
inference(resolution,[],[f5552,f1865]) ).
fof(f56364,plain,
( spl0_1329
| ~ spl0_180
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6270,f5551,f1860,f56362]) ).
fof(f56362,plain,
( spl0_1329
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f6270,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_409 ),
inference(resolution,[],[f5552,f1861]) ).
fof(f56360,plain,
( spl0_1328
| ~ spl0_118
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f31850,f29833,f1504,f56358]) ).
fof(f56358,plain,
( spl0_1328
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f29833,plain,
( spl0_725
<=> ! [X0] : c_COMBK(c_False,tc_bool,tc_nat) = c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f31850,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat),X2))
| ~ spl0_118
| ~ spl0_725 ),
inference(superposition,[],[f1505,f29834]) ).
fof(f29834,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,tc_nat) = c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat)
| ~ spl0_725 ),
inference(avatar_component_clause,[],[f29833]) ).
fof(f56356,plain,
( spl0_1327
| ~ spl0_175
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6258,f5551,f1839,f56354]) ).
fof(f56354,plain,
( spl0_1327
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f6258,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_409 ),
inference(resolution,[],[f5552,f1840]) ).
fof(f56352,plain,
( spl0_1326
| ~ spl0_174
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6253,f5551,f1835,f56350]) ).
fof(f56350,plain,
( spl0_1326
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f6253,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_409 ),
inference(resolution,[],[f5552,f1836]) ).
fof(f56348,plain,
( spl0_1325
| ~ spl0_388
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f6187,f5547,f5467,f56346]) ).
fof(f56346,plain,
( spl0_1325
<=> ! [X3,X4,X0,X5,X2,X1] : hAPP(c_Set_Oimage(c_COMBB(X0,X3,X1,X2,X4),X4,X2),X5) = hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X3,X1,X2,X4),X4,X2),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f6187,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(c_Set_Oimage(c_COMBB(X0,X3,X1,X2,X4),X4,X2),X5) = hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X3,X1,X2,X4),X4,X2),X5)
| ~ spl0_388
| ~ spl0_408 ),
inference(superposition,[],[f5548,f5468]) ).
fof(f56344,plain,
( spl0_1324
| ~ spl0_167
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6124,f5535,f1776,f56342]) ).
fof(f56342,plain,
( spl0_1324
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X0,X3,X2),X4)),hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f6124,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X0,X3,X2),X4)),hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4))))
| ~ spl0_167
| ~ spl0_405 ),
inference(superposition,[],[f1777,f5536]) ).
fof(f56340,plain,
( spl0_1323
| ~ spl0_257
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f6003,f5523,f2544,f56338]) ).
fof(f56338,plain,
( spl0_1323
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f6003,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X0)) )
| ~ spl0_257
| ~ spl0_402 ),
inference(superposition,[],[f2545,f5524]) ).
fof(f56336,plain,
( spl0_1322
| ~ spl0_248
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f6001,f5523,f2499,f56334]) ).
fof(f56334,plain,
( spl0_1322
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f6001,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X0,X4) )
| ~ spl0_248
| ~ spl0_402 ),
inference(superposition,[],[f2500,f5524]) ).
fof(f56332,plain,
( spl0_1321
| ~ spl0_258
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5942,f5519,f2548,f56330]) ).
fof(f56330,plain,
( spl0_1321
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f5942,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0)) )
| ~ spl0_258
| ~ spl0_401 ),
inference(superposition,[],[f2549,f5520]) ).
fof(f56328,plain,
( spl0_1320
| ~ spl0_249
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5938,f5519,f2503,f56326]) ).
fof(f56326,plain,
( spl0_1320
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f5938,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0,X4) )
| ~ spl0_249
| ~ spl0_401 ),
inference(superposition,[],[f2504,f5520]) ).
fof(f56324,plain,
( spl0_1319
| ~ spl0_250
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5926,f5519,f2516,f56322]) ).
fof(f56322,plain,
( spl0_1319
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f5926,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2))
| ~ spl0_250
| ~ spl0_401 ),
inference(superposition,[],[f5520,f2517]) ).
fof(f56320,plain,
( spl0_1318
| ~ spl0_181
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5806,f5483,f1864,f56318]) ).
fof(f56318,plain,
( spl0_1318
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f5806,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_392 ),
inference(resolution,[],[f5484,f1865]) ).
fof(f56316,plain,
( spl0_1317
| ~ spl0_116
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f31849,f29833,f1484,f56314]) ).
fof(f56314,plain,
( spl0_1317
<=> ! [X2,X0,X1,X3] : c_Nitpick_Ofold__graph_H(X1,X2,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),X2,tc_nat,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f31849,plain,
( ! [X2,X3,X0,X1] : c_Nitpick_Ofold__graph_H(X1,X2,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),X2,tc_nat,X3)
| ~ spl0_116
| ~ spl0_725 ),
inference(superposition,[],[f1485,f29834]) ).
fof(f56312,plain,
( spl0_1316
| ~ spl0_180
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5804,f5483,f1860,f56310]) ).
fof(f56310,plain,
( spl0_1316
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f5804,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_392 ),
inference(resolution,[],[f5484,f1861]) ).
fof(f56308,plain,
( spl0_1315
| ~ spl0_175
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5792,f5483,f1839,f56306]) ).
fof(f56306,plain,
( spl0_1315
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f5792,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_392 ),
inference(resolution,[],[f5484,f1840]) ).
fof(f56304,plain,
( spl0_1314
| ~ spl0_176
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5791,f5483,f1844,f56302]) ).
fof(f56302,plain,
( spl0_1314
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f5791,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_392 ),
inference(resolution,[],[f5484,f1845]) ).
fof(f56300,plain,
( spl0_1313
| ~ spl0_174
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5787,f5483,f1835,f56298]) ).
fof(f56298,plain,
( spl0_1313
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f5787,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_392 ),
inference(resolution,[],[f5484,f1836]) ).
fof(f56296,plain,
( spl0_1312
| ~ spl0_177
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5786,f5483,f1848,f56294]) ).
fof(f56294,plain,
( spl0_1312
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f5786,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_392 ),
inference(resolution,[],[f5484,f1849]) ).
fof(f56292,plain,
( spl0_1311
| ~ spl0_181
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5768,f5479,f1864,f56290]) ).
fof(f56290,plain,
( spl0_1311
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f5768,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_391 ),
inference(resolution,[],[f5480,f1865]) ).
fof(f56288,plain,
( spl0_1310
| ~ spl0_182
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5767,f5479,f1868,f56286]) ).
fof(f56286,plain,
( spl0_1310
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f5767,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_391 ),
inference(resolution,[],[f5480,f1869]) ).
fof(f56284,plain,
( spl0_1309
| ~ spl0_180
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5766,f5479,f1860,f56282]) ).
fof(f56282,plain,
( spl0_1309
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f5766,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_391 ),
inference(resolution,[],[f5480,f1861]) ).
fof(f56280,plain,
( spl0_1308
| ~ spl0_183
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5765,f5479,f1872,f56278]) ).
fof(f56278,plain,
( spl0_1308
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f5765,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_391 ),
inference(resolution,[],[f5480,f1873]) ).
fof(f56276,plain,
( spl0_1307
| ~ spl0_175
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5754,f5479,f1839,f56274]) ).
fof(f56274,plain,
( spl0_1307
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f5754,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_391 ),
inference(resolution,[],[f5480,f1840]) ).
fof(f56272,plain,
( spl0_1306
| ~ spl0_115
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f31848,f29833,f1480,f56270]) ).
fof(f56270,plain,
( spl0_1306
<=> ! [X2,X0,X1,X3] : c_Finite__Set_Ofold__graph(X1,X2,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),X2,tc_nat,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f31848,plain,
( ! [X2,X3,X0,X1] : c_Finite__Set_Ofold__graph(X1,X2,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),X2,tc_nat,X3)
| ~ spl0_115
| ~ spl0_725 ),
inference(superposition,[],[f1481,f29834]) ).
fof(f56268,plain,
( spl0_1305
| ~ spl0_174
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5749,f5479,f1835,f56266]) ).
fof(f56266,plain,
( spl0_1305
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f5749,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_391 ),
inference(resolution,[],[f5480,f1836]) ).
fof(f56264,plain,
( spl0_1304
| ~ spl0_181
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5725,f5475,f1864,f56262]) ).
fof(f56262,plain,
( spl0_1304
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f5725,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_390 ),
inference(resolution,[],[f5476,f1865]) ).
fof(f56260,plain,
( spl0_1303
| ~ spl0_180
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5723,f5475,f1860,f56258]) ).
fof(f56258,plain,
( spl0_1303
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f5723,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_390 ),
inference(resolution,[],[f5476,f1861]) ).
fof(f56256,plain,
( spl0_1302
| ~ spl0_175
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5711,f5475,f1839,f56254]) ).
fof(f56254,plain,
( spl0_1302
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f5711,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_390 ),
inference(resolution,[],[f5476,f1840]) ).
fof(f56252,plain,
( spl0_1301
| ~ spl0_176
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5710,f5475,f1844,f56250]) ).
fof(f56250,plain,
( spl0_1301
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f5710,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_390 ),
inference(resolution,[],[f5476,f1845]) ).
fof(f56248,plain,
( spl0_1300
| ~ spl0_174
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5706,f5475,f1835,f56246]) ).
fof(f56246,plain,
( spl0_1300
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f5706,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_390 ),
inference(resolution,[],[f5476,f1836]) ).
fof(f56244,plain,
( spl0_1299
| ~ spl0_177
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5705,f5475,f1848,f56242]) ).
fof(f56242,plain,
( spl0_1299
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f5705,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_390 ),
inference(resolution,[],[f5476,f1849]) ).
fof(f56240,plain,
( spl0_1298
| ~ spl0_181
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5686,f5471,f1864,f56238]) ).
fof(f56238,plain,
( spl0_1298
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f5686,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_389 ),
inference(resolution,[],[f5472,f1865]) ).
fof(f56236,plain,
( spl0_1297
| ~ spl0_182
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5685,f5471,f1868,f56234]) ).
fof(f56234,plain,
( spl0_1297
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f5685,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_389 ),
inference(resolution,[],[f5472,f1869]) ).
fof(f56232,plain,
( spl0_1296
| ~ spl0_180
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5684,f5471,f1860,f56230]) ).
fof(f56230,plain,
( spl0_1296
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f5684,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_389 ),
inference(resolution,[],[f5472,f1861]) ).
fof(f56228,plain,
( spl0_1295
| ~ spl0_113
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f31847,f29833,f1467,f56226]) ).
fof(f56226,plain,
( spl0_1295
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat) != X1
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f31847,plain,
( ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat) != X1
| ~ hBOOL(hAPP(X1,X2)) )
| ~ spl0_113
| ~ spl0_725 ),
inference(superposition,[],[f1468,f29834]) ).
fof(f56224,plain,
( spl0_1294
| ~ spl0_183
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5683,f5471,f1872,f56222]) ).
fof(f56222,plain,
( spl0_1294
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f5683,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_389 ),
inference(resolution,[],[f5472,f1873]) ).
fof(f56220,plain,
( spl0_1293
| ~ spl0_175
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5672,f5471,f1839,f56218]) ).
fof(f56218,plain,
( spl0_1293
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f5672,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_389 ),
inference(resolution,[],[f5472,f1840]) ).
fof(f56216,plain,
( spl0_1292
| ~ spl0_174
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5667,f5471,f1835,f56214]) ).
fof(f56214,plain,
( spl0_1292
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f5667,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_389 ),
inference(resolution,[],[f5472,f1836]) ).
fof(f56212,plain,
( spl0_1291
| ~ spl0_70
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5370,f5058,f1273,f56210]) ).
fof(f56210,plain,
( spl0_1291
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool))),X0))
| ~ hBOOL(c_in(X3,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f5370,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool))),X0))
| ~ hBOOL(c_in(X3,X5,X6)) )
| ~ spl0_70
| ~ spl0_382 ),
inference(superposition,[],[f5059,f1274]) ).
fof(f56208,plain,
( spl0_1290
| ~ spl0_299
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5313,f5058,f3364,f56206]) ).
fof(f56206,plain,
( spl0_1290
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Fun_Oinj__on(X3,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X5,tc_bool)),X5,X6)
| ~ c_Fun_Oinj__on(X3,hAPP(X4,X0),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f5313,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Fun_Oinj__on(X3,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X5,tc_bool)),X5,X6)
| ~ c_Fun_Oinj__on(X3,hAPP(X4,X0),X5,X6) )
| ~ spl0_299
| ~ spl0_382 ),
inference(resolution,[],[f5059,f3365]) ).
fof(f56204,plain,
( spl0_1289
| ~ spl0_312
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5229,f5046,f3416,f56202]) ).
fof(f56202,plain,
( spl0_1289
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X4,X0),X2),X0))
| ~ hBOOL(c_in(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f5229,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X4,X0),X2),X0))
| ~ hBOOL(c_in(X3,X1,X0)) )
| ~ spl0_312
| ~ spl0_379 ),
inference(resolution,[],[f5047,f3417]) ).
fof(f56200,plain,
( spl0_1288
| ~ spl0_299
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5226,f5046,f3364,f56198]) ).
fof(f56198,plain,
( spl0_1288
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Fun_Oinj__on(X3,X1,X0,X4)
| ~ c_Fun_Oinj__on(X3,hAPP(c_Set_Oinsert(X5,X0),X2),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f5226,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Fun_Oinj__on(X3,X1,X0,X4)
| ~ c_Fun_Oinj__on(X3,hAPP(c_Set_Oinsert(X5,X0),X2),X0,X4) )
| ~ spl0_299
| ~ spl0_379 ),
inference(resolution,[],[f5047,f3365]) ).
fof(f56196,plain,
( spl0_1287
| ~ spl0_273
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5222,f5046,f2940,f56194]) ).
fof(f56194,plain,
( spl0_1287
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_Set_Oinsert(X4,tc_Hoare__Mirabelle_Otriple(X0)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f5222,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_Set_Oinsert(X4,tc_Hoare__Mirabelle_Otriple(X0)),X2),X0) )
| ~ spl0_273
| ~ spl0_379 ),
inference(resolution,[],[f5047,f2941]) ).
fof(f56192,plain,
( spl0_1286
| ~ spl0_274
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5221,f5046,f2944,f56190]) ).
fof(f56190,plain,
( spl0_1286
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X2),X4,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f5221,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X2),X4,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X0) )
| ~ spl0_274
| ~ spl0_379 ),
inference(resolution,[],[f5047,f2945]) ).
fof(f56188,plain,
( spl0_1285
| ~ spl0_70
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5179,f5038,f1273,f56186]) ).
fof(f56186,plain,
( spl0_1285
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool))))
| ~ hBOOL(c_in(X3,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f5179,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool))))
| ~ hBOOL(c_in(X3,X5,X6)) )
| ~ spl0_70
| ~ spl0_377 ),
inference(superposition,[],[f5039,f1274]) ).
fof(f56181,plain,
( spl0_1284
| ~ spl0_299
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5125,f5038,f3364,f56179]) ).
fof(f56179,plain,
( spl0_1284
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Fun_Oinj__on(X3,hAPP(X4,X0),X5,X6)
| ~ c_Fun_Oinj__on(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X5,tc_bool)),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f5125,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Fun_Oinj__on(X3,hAPP(X4,X0),X5,X6)
| ~ c_Fun_Oinj__on(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_299
| ~ spl0_377 ),
inference(resolution,[],[f5039,f3365]) ).
fof(f56177,plain,
( spl0_1283
| ~ spl0_144
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f4999,f4405,f1643,f56175]) ).
fof(f56175,plain,
( spl0_1283
<=> ! [X2,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),X2),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)) = X2
| hAPP(c_Set_Oinsert(X0,X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f1643,plain,
( spl0_144
<=> ! [X0,X11,X1] :
( ~ hBOOL(c_in(X1,X11,X0))
| hAPP(c_Set_Oinsert(X1,X0),X11) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f4999,plain,
( ! [X2,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),X2),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)) = X2
| hAPP(c_Set_Oinsert(X0,X1),X2) = X2 )
| ~ spl0_144
| ~ spl0_368 ),
inference(resolution,[],[f4406,f1644]) ).
fof(f1644,plain,
( ! [X0,X11,X1] :
( ~ hBOOL(c_in(X1,X11,X0))
| hAPP(c_Set_Oinsert(X1,X0),X11) = X11 )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1643]) ).
fof(f56173,plain,
( spl0_1282
| ~ spl0_328
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4974,f4392,f3924,f56171]) ).
fof(f56171,plain,
( spl0_1282
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(X4,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f4974,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(X4,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_328
| ~ spl0_365 ),
inference(resolution,[],[f4393,f3925]) ).
fof(f56169,plain,
( spl0_1281
| ~ spl0_234
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4961,f4392,f2283,f56167]) ).
fof(f56167,plain,
( spl0_1281
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f4961,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3)))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_365 ),
inference(resolution,[],[f4393,f2284]) ).
fof(f56165,plain,
( spl0_1280
| ~ spl0_243
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4959,f4392,f2319,f56163]) ).
fof(f56163,plain,
( spl0_1280
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f4959,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3)))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_365 ),
inference(resolution,[],[f4393,f2320]) ).
fof(f56161,plain,
( spl0_1279
| ~ spl0_236
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4924,f4388,f2291,f56159]) ).
fof(f56159,plain,
( spl0_1279
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f4924,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_236
| ~ spl0_364 ),
inference(resolution,[],[f4389,f2292]) ).
fof(f56157,plain,
( spl0_1278
| ~ spl0_235
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4923,f4388,f2287,f56155]) ).
fof(f56155,plain,
( spl0_1278
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f4923,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_235
| ~ spl0_364 ),
inference(resolution,[],[f4389,f2288]) ).
fof(f56153,plain,
( spl0_1277
| ~ spl0_236
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4881,f4380,f2291,f56151]) ).
fof(f56151,plain,
( spl0_1277
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f4881,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_236
| ~ spl0_362 ),
inference(resolution,[],[f4381,f2292]) ).
fof(f56149,plain,
( spl0_1276
| ~ spl0_235
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4880,f4380,f2287,f56147]) ).
fof(f56147,plain,
( spl0_1276
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f4880,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_235
| ~ spl0_362 ),
inference(resolution,[],[f4381,f2288]) ).
fof(f56145,plain,
( spl0_1275
| ~ spl0_328
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4852,f4376,f3924,f56143]) ).
fof(f56143,plain,
( spl0_1275
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(X1,X2,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f4852,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(X1,X2,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_328
| ~ spl0_361 ),
inference(resolution,[],[f4377,f3925]) ).
fof(f56088,plain,
( spl0_1274
| ~ spl0_234
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4841,f4376,f2283,f56086]) ).
fof(f56086,plain,
( spl0_1274
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f4841,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1)))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_361 ),
inference(resolution,[],[f4377,f2284]) ).
fof(f56084,plain,
( spl0_1273
| ~ spl0_243
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4839,f4376,f2319,f56082]) ).
fof(f56082,plain,
( spl0_1273
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f4839,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1)))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_361 ),
inference(resolution,[],[f4377,f2320]) ).
fof(f56080,plain,
( spl0_1272
| ~ spl0_169
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4788,f4368,f1784,f56078]) ).
fof(f56078,plain,
( spl0_1272
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_COMBK(c_False,tc_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f4788,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_COMBK(c_False,tc_bool,X0))) )
| ~ spl0_169
| ~ spl0_359 ),
inference(superposition,[],[f4369,f1785]) ).
fof(f56076,plain,
( spl0_1271
| ~ spl0_170
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4781,f4368,f1788,f56074]) ).
fof(f56074,plain,
( spl0_1271
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f4781,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_170
| ~ spl0_359 ),
inference(superposition,[],[f4369,f1789]) ).
fof(f56072,plain,
( spl0_1270
| ~ spl0_181
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4725,f4368,f1864,f56070]) ).
fof(f56070,plain,
( spl0_1270
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X5),X0)))
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f4725,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X5),X0)))
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_181
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1865]) ).
fof(f56068,plain,
( spl0_1269
| ~ spl0_182
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4724,f4368,f1868,f56066]) ).
fof(f56066,plain,
( spl0_1269
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X5),X0)))
| ~ class_Lattices_Oupper__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f4724,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X5),X0)))
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_182
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1869]) ).
fof(f56064,plain,
( spl0_1268
| ~ spl0_180
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4723,f4368,f1860,f56062]) ).
fof(f56062,plain,
( spl0_1268
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X0),X5)))
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f4723,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X0),X5)))
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_180
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1861]) ).
fof(f56060,plain,
( spl0_1267
| ~ spl0_183
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4722,f4368,f1872,f56058]) ).
fof(f56058,plain,
( spl0_1267
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X0),X5)))
| ~ class_Lattices_Oupper__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f4722,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X0),X5)))
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_183
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1873]) ).
fof(f56056,plain,
( spl0_1266
| ~ spl0_175
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4702,f4368,f1839,f56054]) ).
fof(f56054,plain,
( spl0_1266
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f4702,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1840]) ).
fof(f56052,plain,
( spl0_1265
| ~ spl0_176
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4701,f4368,f1844,f56050]) ).
fof(f56050,plain,
( spl0_1265
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f4701,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1845]) ).
fof(f56048,plain,
( spl0_1264
| ~ spl0_92
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f55922,f51777,f1379,f56046]) ).
fof(f56046,plain,
( spl0_1264
<=> ! [X1] : c_False = hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f51777,plain,
( spl0_1185
<=> ! [X0] : c_False = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f55922,plain,
( ! [X1] : c_False = hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_92
| ~ spl0_1185 ),
inference(superposition,[],[f51778,f1380]) ).
fof(f51778,plain,
( ! [X0] : c_False = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_1185 ),
inference(avatar_component_clause,[],[f51777]) ).
fof(f56044,plain,
( spl0_1263
| ~ spl0_174
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4697,f4368,f1835,f56042]) ).
fof(f56042,plain,
( spl0_1263
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X1))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f4697,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X1))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1836]) ).
fof(f56040,plain,
( spl0_1262
| ~ spl0_177
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4696,f4368,f1848,f56038]) ).
fof(f56038,plain,
( spl0_1262
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f4696,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1849]) ).
fof(f56036,plain,
( spl0_1261
| ~ spl0_225
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4638,f4352,f2247,f56034]) ).
fof(f56034,plain,
( spl0_1261
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f2247,plain,
( spl0_225
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f4638,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))) )
| ~ spl0_225
| ~ spl0_355 ),
inference(resolution,[],[f4353,f2248]) ).
fof(f2248,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2247]) ).
fof(f56032,plain,
( spl0_1260
| ~ spl0_227
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4637,f4352,f2255,f56030]) ).
fof(f56030,plain,
( spl0_1260
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f2255,plain,
( spl0_227
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f4637,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))) )
| ~ spl0_227
| ~ spl0_355 ),
inference(resolution,[],[f4353,f2256]) ).
fof(f2256,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) )
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2255]) ).
fof(f56028,plain,
( spl0_1259
| ~ spl0_229
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4636,f4352,f2263,f56026]) ).
fof(f56026,plain,
( spl0_1259
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f2263,plain,
( spl0_229
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f4636,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1)) )
| ~ spl0_229
| ~ spl0_355 ),
inference(resolution,[],[f4353,f2264]) ).
fof(f2264,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2)) )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2263]) ).
fof(f56024,plain,
( spl0_1258
| ~ spl0_230
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4635,f4352,f2267,f56022]) ).
fof(f56022,plain,
( spl0_1258
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f2267,plain,
( spl0_230
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f4635,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1)) )
| ~ spl0_230
| ~ spl0_355 ),
inference(resolution,[],[f4353,f2268]) ).
fof(f2268,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2267]) ).
fof(f56020,plain,
( spl0_1257
| ~ spl0_231
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4634,f4352,f2271,f56018]) ).
fof(f56018,plain,
( spl0_1257
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f2271,plain,
( spl0_231
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f4634,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_231
| ~ spl0_355 ),
inference(resolution,[],[f4353,f2272]) ).
fof(f2272,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2271]) ).
fof(f56016,plain,
( spl0_1256
| ~ spl0_225
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4613,f4348,f2247,f56014]) ).
fof(f56014,plain,
( spl0_1256
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f4613,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))) )
| ~ spl0_225
| ~ spl0_354 ),
inference(resolution,[],[f4349,f2248]) ).
fof(f56012,plain,
( spl0_1255
| ~ spl0_227
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4612,f4348,f2255,f56010]) ).
fof(f56010,plain,
( spl0_1255
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f4612,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))) )
| ~ spl0_227
| ~ spl0_354 ),
inference(resolution,[],[f4349,f2256]) ).
fof(f56008,plain,
( spl0_1254
| ~ spl0_229
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4611,f4348,f2263,f56006]) ).
fof(f56006,plain,
( spl0_1254
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f4611,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1)) )
| ~ spl0_229
| ~ spl0_354 ),
inference(resolution,[],[f4349,f2264]) ).
fof(f55885,plain,
( spl0_1253
| ~ spl0_230
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4610,f4348,f2267,f55883]) ).
fof(f55883,plain,
( spl0_1253
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f4610,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1)) )
| ~ spl0_230
| ~ spl0_354 ),
inference(resolution,[],[f4349,f2268]) ).
fof(f55881,plain,
( spl0_1252
| ~ spl0_231
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4609,f4348,f2271,f55879]) ).
fof(f55879,plain,
( spl0_1252
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f4609,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_231
| ~ spl0_354 ),
inference(resolution,[],[f4349,f2272]) ).
fof(f55877,plain,
( spl0_1251
| ~ spl0_234
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4592,f4344,f2283,f55875]) ).
fof(f55875,plain,
( spl0_1251
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2)),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f4592,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2)),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_353 ),
inference(resolution,[],[f4345,f2284]) ).
fof(f55873,plain,
( spl0_1250
| ~ spl0_243
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4590,f4344,f2319,f55871]) ).
fof(f55871,plain,
( spl0_1250
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2)),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f4590,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2)),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_353 ),
inference(resolution,[],[f4345,f2320]) ).
fof(f55869,plain,
( spl0_1249
| ~ spl0_333
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4577,f4344,f3945,f55867]) ).
fof(f55867,plain,
( spl0_1249
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3,X0)),X4))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(X4,X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f4577,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3,X0)),X4))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(X4,X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_333
| ~ spl0_353 ),
inference(resolution,[],[f4345,f3946]) ).
fof(f55865,plain,
( spl0_1248
| ~ spl0_234
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4565,f4335,f2283,f55863]) ).
fof(f55863,plain,
( spl0_1248
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f4565,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_351 ),
inference(resolution,[],[f4336,f2284]) ).
fof(f55861,plain,
( spl0_1247
| ~ spl0_243
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4563,f4335,f2319,f55859]) ).
fof(f55859,plain,
( spl0_1247
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f4563,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_351 ),
inference(resolution,[],[f4336,f2320]) ).
fof(f55857,plain,
( spl0_1246
| ~ spl0_333
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4550,f4335,f3945,f55855]) ).
fof(f55855,plain,
( spl0_1246
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3,X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(X4,X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f4550,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3,X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(X4,X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_333
| ~ spl0_351 ),
inference(resolution,[],[f4336,f3946]) ).
fof(f55853,plain,
( spl0_1245
| ~ spl0_236
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f4530,f4331,f2291,f55851]) ).
fof(f55851,plain,
( spl0_1245
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f4530,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_236
| ~ spl0_350 ),
inference(resolution,[],[f4332,f2292]) ).
fof(f55849,plain,
( spl0_1244
| ~ spl0_235
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f4529,f4331,f2287,f55847]) ).
fof(f55847,plain,
( spl0_1244
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f4529,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_235
| ~ spl0_350 ),
inference(resolution,[],[f4332,f2288]) ).
fof(f55764,plain,
( spl0_1243
| ~ spl0_236
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4494,f4327,f2291,f55762]) ).
fof(f55762,plain,
( spl0_1243
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f4494,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_236
| ~ spl0_349 ),
inference(resolution,[],[f4328,f2292]) ).
fof(f55760,plain,
( spl0_1242
| ~ spl0_235
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4493,f4327,f2287,f55758]) ).
fof(f55758,plain,
( spl0_1242
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f4493,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_235
| ~ spl0_349 ),
inference(resolution,[],[f4328,f2288]) ).
fof(f55756,plain,
( spl0_1241
| ~ spl0_225
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4441,f4319,f2247,f55754]) ).
fof(f55754,plain,
( spl0_1241
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f4441,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2)) )
| ~ spl0_225
| ~ spl0_347 ),
inference(resolution,[],[f4320,f2248]) ).
fof(f55752,plain,
( spl0_1240
| ~ spl0_227
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4440,f4319,f2255,f55750]) ).
fof(f55750,plain,
( spl0_1240
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f4440,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2)) )
| ~ spl0_227
| ~ spl0_347 ),
inference(resolution,[],[f4320,f2256]) ).
fof(f55748,plain,
( spl0_1239
| ~ spl0_229
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4439,f4319,f2263,f55746]) ).
fof(f55746,plain,
( spl0_1239
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f4439,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1))) )
| ~ spl0_229
| ~ spl0_347 ),
inference(resolution,[],[f4320,f2264]) ).
fof(f55744,plain,
( spl0_1238
| ~ spl0_230
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4438,f4319,f2267,f55742]) ).
fof(f55742,plain,
( spl0_1238
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f4438,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1))) )
| ~ spl0_230
| ~ spl0_347 ),
inference(resolution,[],[f4320,f2268]) ).
fof(f55740,plain,
( spl0_1237
| ~ spl0_231
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4437,f4319,f2271,f55738]) ).
fof(f55738,plain,
( spl0_1237
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f4437,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_231
| ~ spl0_347 ),
inference(resolution,[],[f4320,f2272]) ).
fof(f55736,plain,
( spl0_1236
| ~ spl0_225
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4422,f4315,f2247,f55734]) ).
fof(f55734,plain,
( spl0_1236
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f4422,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2)) )
| ~ spl0_225
| ~ spl0_346 ),
inference(resolution,[],[f4316,f2248]) ).
fof(f55732,plain,
( spl0_1235
| ~ spl0_227
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4421,f4315,f2255,f55730]) ).
fof(f55730,plain,
( spl0_1235
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f4421,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2)) )
| ~ spl0_227
| ~ spl0_346 ),
inference(resolution,[],[f4316,f2256]) ).
fof(f55728,plain,
( spl0_1234
| ~ spl0_229
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4420,f4315,f2263,f55726]) ).
fof(f55726,plain,
( spl0_1234
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f4420,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))) )
| ~ spl0_229
| ~ spl0_346 ),
inference(resolution,[],[f4316,f2264]) ).
fof(f55608,plain,
( spl0_1233
| ~ spl0_230
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4419,f4315,f2267,f55606]) ).
fof(f55606,plain,
( spl0_1233
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f4419,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))) )
| ~ spl0_230
| ~ spl0_346 ),
inference(resolution,[],[f4316,f2268]) ).
fof(f55604,plain,
( spl0_1232
| ~ spl0_231
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4418,f4315,f2271,f55602]) ).
fof(f55602,plain,
( spl0_1232
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f4418,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_231
| ~ spl0_346 ),
inference(resolution,[],[f4316,f2272]) ).
fof(f55600,plain,
( spl0_1231
| ~ spl0_228
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4296,f3989,f2259,f55598]) ).
fof(f55598,plain,
( spl0_1231
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X1),X0),X1)
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X3,X2,X1)
| c_Finite__Set_Ofinite(X3,X2)
| c_COMBK(c_False,tc_bool,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f4296,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X1),X0),X1)
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X3,X2,X1)
| c_Finite__Set_Ofinite(X3,X2)
| c_COMBK(c_False,tc_bool,X2) = X3 )
| ~ spl0_228
| ~ spl0_344 ),
inference(superposition,[],[f2260,f3990]) ).
fof(f55596,plain,
( spl0_1230
| ~ spl0_92
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4221,f3949,f1379,f55594]) ).
fof(f55594,plain,
( spl0_1230
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X5),X2),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| hBOOL(hAPP(hAPP(c_lessequals(X5),c_Inductive_Ocomplete__lattice__class_Olfp(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f4221,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X5),X2),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| hBOOL(hAPP(hAPP(c_lessequals(X5),c_Inductive_Ocomplete__lattice__class_Olfp(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5)),X1)) )
| ~ spl0_92
| ~ spl0_334 ),
inference(superposition,[],[f3950,f1380]) ).
fof(f55592,plain,
( spl0_1229
| ~ spl0_100
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4210,f3949,f1413,f55590]) ).
fof(f55590,plain,
( spl0_1229
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X1),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f4210,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X1),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1)) )
| ~ spl0_100
| ~ spl0_334 ),
inference(superposition,[],[f3950,f1414]) ).
fof(f55588,plain,
( spl0_1228
| ~ spl0_92
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4172,f3945,f1379,f55586]) ).
fof(f55586,plain,
( spl0_1228
<=> ! [X3,X4,X7,X0,X6,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X5),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,X5)),X2))
| ~ hBOOL(c_in(X1,X6,X7))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f4172,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X5),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,X5)),X2))
| ~ hBOOL(c_in(X1,X6,X7))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) )
| ~ spl0_92
| ~ spl0_333 ),
inference(superposition,[],[f3946,f1380]) ).
fof(f55584,plain,
( spl0_1227
| ~ spl0_100
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4161,f3945,f1413,f55582]) ).
fof(f55582,plain,
( spl0_1227
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f4161,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_100
| ~ spl0_333 ),
inference(superposition,[],[f3946,f1414]) ).
fof(f55580,plain,
( spl0_1226
| ~ spl0_92
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4093,f3924,f1379,f55578]) ).
fof(f55578,plain,
( spl0_1226
<=> ! [X2,X6,X4,X7,X0,X5,X3,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X5),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,X5)))
| ~ hBOOL(c_in(X1,X6,X7))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f4093,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X5),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,X5)))
| ~ hBOOL(c_in(X1,X6,X7))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) )
| ~ spl0_92
| ~ spl0_328 ),
inference(superposition,[],[f3925,f1380]) ).
fof(f55576,plain,
( spl0_1225
| ~ spl0_100
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4083,f3924,f1413,f55574]) ).
fof(f55574,plain,
( spl0_1225
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f4083,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_100
| ~ spl0_328 ),
inference(superposition,[],[f3925,f1414]) ).
fof(f55572,plain,
( spl0_1224
| ~ spl0_205
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3842,f3420,f2029,f55570]) ).
fof(f55570,plain,
( spl0_1224
<=> ! [X2,X3,X4,X0,X5,X1] : hBOOL(c_in(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f3842,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(c_in(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))),X5))
| ~ spl0_205
| ~ spl0_313 ),
inference(superposition,[],[f2030,f3421]) ).
fof(f55421,plain,
( spl0_1223
| ~ spl0_168
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3837,f3420,f1780,f55419]) ).
fof(f55419,plain,
( spl0_1223
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_Set_Oinsert(X2,tc_Hoare__Mirabelle_Otriple(X1)),hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X3)),X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_Set_Oinsert(X2,tc_Hoare__Mirabelle_Otriple(X1)),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f3837,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_Set_Oinsert(X2,tc_Hoare__Mirabelle_Otriple(X1)),hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X3)),X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_Set_Oinsert(X2,tc_Hoare__Mirabelle_Otriple(X1)),X3),X1) )
| ~ spl0_168
| ~ spl0_313 ),
inference(superposition,[],[f1781,f3421]) ).
fof(f55417,plain,
( spl0_1222
| ~ spl0_214
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3832,f3420,f2068,f55415]) ).
fof(f55415,plain,
( spl0_1222
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X4))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),X3),X4))
| X0 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f3832,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X4))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),X3),X4))
| X0 = X4 )
| ~ spl0_214
| ~ spl0_313 ),
inference(superposition,[],[f2069,f3421]) ).
fof(f55413,plain,
( spl0_1221
| ~ spl0_234
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3800,f3416,f2283,f55411]) ).
fof(f55411,plain,
( spl0_1221
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,X3,X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),X3))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f3800,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,X3,X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),X3))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_234
| ~ spl0_312 ),
inference(resolution,[],[f3417,f2284]) ).
fof(f55409,plain,
( spl0_1220
| ~ spl0_234
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3759,f3408,f2283,f55407]) ).
fof(f55407,plain,
( spl0_1220
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f3759,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) )
| ~ spl0_234
| ~ spl0_310 ),
inference(resolution,[],[f3409,f2284]) ).
fof(f55405,plain,
( spl0_1219
| ~ spl0_243
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3757,f3408,f2319,f55403]) ).
fof(f55403,plain,
( spl0_1219
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f3757,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) )
| ~ spl0_243
| ~ spl0_310 ),
inference(resolution,[],[f3409,f2320]) ).
fof(f55401,plain,
( spl0_1218
| ~ spl0_234
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3726,f3404,f2283,f55399]) ).
fof(f55399,plain,
( spl0_1218
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f3726,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) )
| ~ spl0_234
| ~ spl0_309 ),
inference(resolution,[],[f3405,f2284]) ).
fof(f55397,plain,
( spl0_1217
| ~ spl0_243
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3724,f3404,f2319,f55395]) ).
fof(f55395,plain,
( spl0_1217
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f3724,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) )
| ~ spl0_243
| ~ spl0_309 ),
inference(resolution,[],[f3405,f2320]) ).
fof(f55393,plain,
( spl0_1216
| ~ spl0_289
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3657,f3388,f3004,f55391]) ).
fof(f55391,plain,
( spl0_1216
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Oorder(X1)
| c_COMBK(c_False,tc_bool,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Finite__Set_Olinorder__class_OMin(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f3657,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Oorder(X1)
| c_COMBK(c_False,tc_bool,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Finite__Set_Olinorder__class_OMin(X0,X1),X1) )
| ~ spl0_289
| ~ spl0_305 ),
inference(resolution,[],[f3389,f3005]) ).
fof(f55389,plain,
( spl0_1215
| ~ spl0_288
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3656,f3388,f3000,f55387]) ).
fof(f55387,plain,
( spl0_1215
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Oorder(X1)
| c_COMBK(c_False,tc_bool,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,c_Finite__Set_Olinorder__class_OMin(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f3656,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Oorder(X1)
| c_COMBK(c_False,tc_bool,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,c_Finite__Set_Olinorder__class_OMin(X0,X1),X1) )
| ~ spl0_288
| ~ spl0_305 ),
inference(resolution,[],[f3389,f3001]) ).
fof(f55385,plain,
( spl0_1214
| ~ spl0_289
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3637,f3384,f3004,f55383]) ).
fof(f55383,plain,
( spl0_1214
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Oorder(X1)
| c_COMBK(c_False,tc_bool,X1) = c_SetInterval_Oord__class_OatLeastLessThan(c_Finite__Set_Olinorder__class_OMax(X0,X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f3637,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Oorder(X1)
| c_COMBK(c_False,tc_bool,X1) = c_SetInterval_Oord__class_OatLeastLessThan(c_Finite__Set_Olinorder__class_OMax(X0,X1),X2,X1) )
| ~ spl0_289
| ~ spl0_304 ),
inference(resolution,[],[f3385,f3005]) ).
fof(f55266,plain,
( spl0_1213
| ~ spl0_288
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3636,f3384,f3000,f55264]) ).
fof(f55264,plain,
( spl0_1213
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Oorder(X1)
| c_COMBK(c_False,tc_bool,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Finite__Set_Olinorder__class_OMax(X0,X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f3636,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Oorder(X1)
| c_COMBK(c_False,tc_bool,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Finite__Set_Olinorder__class_OMax(X0,X1),X2,X1) )
| ~ spl0_288
| ~ spl0_304 ),
inference(resolution,[],[f3385,f3001]) ).
fof(f55262,plain,
( spl0_1212
| ~ spl0_234
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3512,f3364,f2283,f55260]) ).
fof(f55260,plain,
( spl0_1212
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,X4,X2,X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X4),X1))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f3512,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,X4,X2,X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X4),X1))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_234
| ~ spl0_299 ),
inference(resolution,[],[f3365,f2284]) ).
fof(f55258,plain,
( spl0_1211
| ~ spl0_243
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3510,f3364,f2319,f55256]) ).
fof(f55256,plain,
( spl0_1211
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,X4,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X4),X1))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f3510,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,X4,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X4),X1))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_243
| ~ spl0_299 ),
inference(resolution,[],[f3365,f2320]) ).
fof(f55254,plain,
( spl0_1210
| ~ spl0_199
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3324,f3016,f2005,f55252]) ).
fof(f55252,plain,
( spl0_1210
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f3324,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_199
| ~ spl0_292 ),
inference(resolution,[],[f3017,f2006]) ).
fof(f55250,plain,
( spl0_1209
| ~ spl0_207
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3265,f3004,f2037,f55248]) ).
fof(f55248,plain,
( spl0_1209
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f3265,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),tc_fun(X0,tc_bool)) )
| ~ spl0_207
| ~ spl0_289 ),
inference(resolution,[],[f3005,f2038]) ).
fof(f55246,plain,
( spl0_1208
| ~ spl0_207
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3239,f3000,f2037,f55244]) ).
fof(f55244,plain,
( spl0_1208
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f3239,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),tc_fun(X0,tc_bool)) )
| ~ spl0_207
| ~ spl0_288 ),
inference(resolution,[],[f3001,f2038]) ).
fof(f55242,plain,
( spl0_1207
| ~ spl0_234
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3179,f2944,f2283,f55240]) ).
fof(f55240,plain,
( spl0_1207
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0),X3))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f3179,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0),X3))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) )
| ~ spl0_234
| ~ spl0_274 ),
inference(resolution,[],[f2945,f2284]) ).
fof(f55238,plain,
( spl0_1206
| ~ spl0_243
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3177,f2944,f2319,f55236]) ).
fof(f55236,plain,
( spl0_1206
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0),X3))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f3177,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0),X3))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) )
| ~ spl0_243
| ~ spl0_274 ),
inference(resolution,[],[f2945,f2320]) ).
fof(f55234,plain,
( spl0_1205
| ~ spl0_234
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3153,f2940,f2283,f55232]) ).
fof(f55232,plain,
( spl0_1205
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X1))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f3153,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X1))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) )
| ~ spl0_234
| ~ spl0_273 ),
inference(resolution,[],[f2941,f2284]) ).
fof(f55230,plain,
( spl0_1204
| ~ spl0_243
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3151,f2940,f2319,f55228]) ).
fof(f55228,plain,
( spl0_1204
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X2)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X1))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f3151,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X2)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X1))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) )
| ~ spl0_243
| ~ spl0_273 ),
inference(resolution,[],[f2941,f2320]) ).
fof(f55223,plain,
( spl0_1203
| ~ spl0_164
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3031,f2912,f1764,f55221]) ).
fof(f55221,plain,
( spl0_1203
<=> ! [X2,X3,X4,X0,X5,X1] :
( c_Fun_Ofun__upd(X0,X1,X2,X3,X4) != c_Fun_Ofun__upd(X0,X1,X5,X3,X4)
| hAPP(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X1) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f1764,plain,
( spl0_164
<=> ! [X4,X7,X0,X3,X8] :
( hAPP(X8,X3) = X4
| c_Fun_Ofun__upd(X8,X3,X4,X0,X7) != X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f2912,plain,
( spl0_267
<=> ! [X10,X0,X4,X3,X8,X7] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X8,X3,X4,X0,X7),X3,X10,X0,X7) = c_Fun_Ofun__upd(X8,X3,X10,X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f3031,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Fun_Ofun__upd(X0,X1,X2,X3,X4) != c_Fun_Ofun__upd(X0,X1,X5,X3,X4)
| hAPP(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X1) = X5 )
| ~ spl0_164
| ~ spl0_267 ),
inference(superposition,[],[f1765,f2913]) ).
fof(f2913,plain,
( ! [X3,X10,X0,X8,X7,X4] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X8,X3,X4,X0,X7),X3,X10,X0,X7) = c_Fun_Ofun__upd(X8,X3,X10,X0,X7)
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f2912]) ).
fof(f1765,plain,
( ! [X3,X0,X8,X7,X4] :
( c_Fun_Ofun__upd(X8,X3,X4,X0,X7) != X8
| hAPP(X8,X3) = X4 )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f55219,plain,
( spl0_1202
| ~ spl0_253
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2863,f2560,f2528,f55217]) ).
fof(f55217,plain,
( spl0_1202
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f2863,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0) )
| ~ spl0_253
| ~ spl0_261 ),
inference(resolution,[],[f2561,f2529]) ).
fof(f55215,plain,
( spl0_1201
| ~ spl0_255
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2862,f2560,f2536,f55213]) ).
fof(f55213,plain,
( spl0_1201
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f2862,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)) )
| ~ spl0_255
| ~ spl0_261 ),
inference(resolution,[],[f2561,f2537]) ).
fof(f55211,plain,
( spl0_1200
| ~ spl0_187
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2859,f2560,f1888,f55209]) ).
fof(f55209,plain,
( spl0_1200
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f2859,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1),X0,X2) )
| ~ spl0_187
| ~ spl0_261 ),
inference(resolution,[],[f2561,f1889]) ).
fof(f55207,plain,
( spl0_1199
| ~ spl0_87
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2855,f2552,f1344,f55205]) ).
fof(f55205,plain,
( spl0_1199
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f2855,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_False)) )
| ~ spl0_87
| ~ spl0_259 ),
inference(resolution,[],[f2553,f1345]) ).
fof(f55203,plain,
( spl0_1198
| ~ spl0_245
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2807,f2540,f2487,f55201]) ).
fof(f55201,plain,
( spl0_1198
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f2807,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)),X0) )
| ~ spl0_245
| ~ spl0_256 ),
inference(resolution,[],[f2541,f2488]) ).
fof(f55199,plain,
( spl0_1197
| ~ spl0_247
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2806,f2540,f2495,f55197]) ).
fof(f55197,plain,
( spl0_1197
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f2806,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)) )
| ~ spl0_247
| ~ spl0_256 ),
inference(resolution,[],[f2541,f2496]) ).
fof(f55195,plain,
( spl0_1196
| ~ spl0_187
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2802,f2540,f1888,f55193]) ).
fof(f55193,plain,
( spl0_1196
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f2802,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1),X2) )
| ~ spl0_187
| ~ spl0_256 ),
inference(resolution,[],[f2541,f1889]) ).
fof(f55191,plain,
( spl0_1195
| ~ spl0_165
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2727,f2520,f1768,f55189]) ).
fof(f55189,plain,
( spl0_1195
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4,X5),X6),X5))
| ~ hBOOL(c_in(v_x,X6,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f2727,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4,X5),X6),X5))
| ~ hBOOL(c_in(v_x,X6,X4)) )
| ~ spl0_165
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1769]) ).
fof(f55187,plain,
( spl0_1194
| ~ spl0_171
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2725,f2520,f1792,f55185]) ).
fof(f55185,plain,
( spl0_1194
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(hAPP(c_fequal(X1),X0),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f2725,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(hAPP(c_fequal(X1),X0),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X4,X2)) )
| ~ spl0_171
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1793]) ).
fof(f55174,plain,
( spl0_1193
| ~ spl0_169
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2715,f2520,f1784,f55172]) ).
fof(f55172,plain,
( spl0_1193
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f2715,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X4,X2)) )
| ~ spl0_169
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1785]) ).
fof(f55170,plain,
( spl0_1192
| ~ spl0_170
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2709,f2520,f1788,f55168]) ).
fof(f55168,plain,
( spl0_1192
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2,X3),X4),X3))
| ~ hBOOL(c_in(X1,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f2709,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2,X3),X4),X3))
| ~ hBOOL(c_in(X1,X4,X2)) )
| ~ spl0_170
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1789]) ).
fof(f55166,plain,
( spl0_1191
| ~ spl0_86
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2206,f2064,f1340,f55164]) ).
fof(f55164,plain,
( spl0_1191
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2))))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f2206,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2))))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2),c_False)) )
| ~ spl0_86
| ~ spl0_213 ),
inference(resolution,[],[f2065,f1341]) ).
fof(f55162,plain,
( spl0_1190
| ~ spl0_86
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2201,f2060,f1340,f55160]) ).
fof(f55160,plain,
( spl0_1190
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0))))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f2201,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0))))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0),c_False)) )
| ~ spl0_86
| ~ spl0_212 ),
inference(resolution,[],[f2061,f1341]) ).
fof(f55158,plain,
( spl0_1189
| ~ spl0_205
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2177,f2033,f2029,f55156]) ).
fof(f55156,plain,
( spl0_1189
<=> ! [X2,X4,X7,X0,X6,X5,X3,X1] : hBOOL(c_in(hAPP(hAPP(X0,X5),X4),hAPP(c_Set_Oimage(hAPP(c_COMBC(X0,X1,X2,X3),X4),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f2177,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hBOOL(c_in(hAPP(hAPP(X0,X5),X4),hAPP(c_Set_Oimage(hAPP(c_COMBC(X0,X1,X2,X3),X4),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7))
| ~ spl0_205
| ~ spl0_206 ),
inference(superposition,[],[f2030,f2034]) ).
fof(f55154,plain,
( spl0_1188
| ~ spl0_201
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2166,f2029,f2013,f55152]) ).
fof(f55152,plain,
( spl0_1188
<=> ! [X2,X4,X7,X0,X6,X5,X3,X1] :
( hBOOL(c_in(hAPP(X0,X5),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7))
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f2166,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(c_in(hAPP(X0,X5),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7))
| X1 = X5 )
| ~ spl0_201
| ~ spl0_205 ),
inference(superposition,[],[f2030,f2014]) ).
fof(f55150,plain,
( spl0_1187
| ~ spl0_91
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2145,f2013,f1375,f55148]) ).
fof(f55148,plain,
( spl0_1187
<=> ! [X5,X1,X4,X2,X0,X6,X3,X7] :
( c_Fun_Ofun__upd(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5,hAPP(X0,X5),X6,X7)
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f2145,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( c_Fun_Ofun__upd(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5,hAPP(X0,X5),X6,X7)
| X1 = X5 )
| ~ spl0_91
| ~ spl0_201 ),
inference(superposition,[],[f1376,f2014]) ).
fof(f52622,plain,
( spl0_1186
| ~ spl0_193
| ~ spl0_934 ),
inference(avatar_split_clause,[],[f41550,f40830,f1913,f52620]) ).
fof(f1913,plain,
( spl0_193
<=> ! [X0,X8,X3] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_fequal(X0),X3),X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f40830,plain,
( spl0_934
<=> ! [X2,X0,X1] :
( c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X1,hAPP(c_fequal(X2),X0),X2)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(c_fequal(X2),X0),X2),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f41550,plain,
( ! [X0,X1] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X0,hAPP(c_fequal(X1),c_False),X1))
| ~ spl0_193
| ~ spl0_934 ),
inference(resolution,[],[f40831,f1914]) ).
fof(f1914,plain,
( ! [X3,X0,X8] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_fequal(X0),X3),X0),X3))
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f1913]) ).
fof(f40831,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(c_fequal(X2),X0),X2),c_False))
| c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X1,hAPP(c_fequal(X2),X0),X2)) = X0 )
| ~ spl0_934 ),
inference(avatar_component_clause,[],[f40830]) ).
fof(f51779,plain,
( spl0_1185
| ~ spl0_70
| ~ spl0_219
| ~ spl0_345
| ~ spl0_900 ),
inference(avatar_split_clause,[],[f39330,f36638,f4278,f2089,f1273,f51777]) ).
fof(f4278,plain,
( spl0_345
<=> c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f39330,plain,
( ! [X0] : c_False = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_70
| ~ spl0_219
| ~ spl0_345
| ~ spl0_900 ),
inference(forward_demodulation,[],[f39329,f1274]) ).
fof(f39329,plain,
( ! [X0] : hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_219
| ~ spl0_345
| ~ spl0_900 ),
inference(forward_demodulation,[],[f39278,f4280]) ).
fof(f4280,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x)
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f4278]) ).
fof(f39278,plain,
( ! [X0] : hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x))
| ~ spl0_219
| ~ spl0_900 ),
inference(superposition,[],[f36639,f2090]) ).
fof(f50314,plain,
( spl0_1184
| ~ spl0_186
| ~ spl0_829 ),
inference(avatar_split_clause,[],[f35280,f33180,f1884,f50312]) ).
fof(f50312,plain,
( spl0_1184
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Set_Oinsert(c_False,tc_bool),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f1884,plain,
( spl0_186
<=> ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f33180,plain,
( spl0_829
<=> ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Set_Oinsert(X0,tc_bool),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f35280,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Set_Oinsert(c_False,tc_bool),X0))
| ~ spl0_186
| ~ spl0_829 ),
inference(superposition,[],[f33181,f1885]) ).
fof(f1885,plain,
( ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),X0)
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1884]) ).
fof(f33181,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Set_Oinsert(X0,tc_bool),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X1))
| ~ spl0_829 ),
inference(avatar_component_clause,[],[f33180]) ).
fof(f49992,plain,
( spl0_1183
| ~ spl0_7
| ~ spl0_588 ),
inference(avatar_split_clause,[],[f13414,f13337,f992,f49990]) ).
fof(f49990,plain,
( spl0_1183
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_nat)),X1),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f13337,plain,
( spl0_588
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f13414,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_nat)),X1),X1) = X1
| ~ spl0_7
| ~ spl0_588 ),
inference(resolution,[],[f13338,f994]) ).
fof(f13338,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X2) = X2 )
| ~ spl0_588 ),
inference(avatar_component_clause,[],[f13337]) ).
fof(f49622,plain,
( spl0_1182
| ~ spl0_19
| ~ spl0_586 ),
inference(avatar_split_clause,[],[f13412,f13329,f1052,f49620]) ).
fof(f49620,plain,
( spl0_1182
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f13329,plain,
( spl0_586
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f13412,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X1) = X1
| ~ spl0_19
| ~ spl0_586 ),
inference(resolution,[],[f13330,f1054]) ).
fof(f13330,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X2) = X2 )
| ~ spl0_586 ),
inference(avatar_component_clause,[],[f13329]) ).
fof(f49240,plain,
( spl0_1181
| ~ spl0_7
| ~ spl0_586 ),
inference(avatar_split_clause,[],[f13411,f13329,f992,f49238]) ).
fof(f49238,plain,
( spl0_1181
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_nat)),X1),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f13411,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_nat)),X1),X1) = X1
| ~ spl0_7
| ~ spl0_586 ),
inference(resolution,[],[f13330,f994]) ).
fof(f48205,plain,
( spl0_1180
| ~ spl0_193
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11662,f5030,f1913,f48203]) ).
fof(f48203,plain,
( spl0_1180
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f11662,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),X0))
| ~ spl0_193
| ~ spl0_375 ),
inference(superposition,[],[f1914,f5031]) ).
fof(f47977,plain,
( spl0_1179
| ~ spl0_150
| ~ spl0_169
| ~ spl0_534 ),
inference(avatar_split_clause,[],[f11428,f11049,f1784,f1668,f47975]) ).
fof(f47975,plain,
( spl0_1179
<=> ! [X2,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X0) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0),tc_fun(X1,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f11428,plain,
( ! [X2,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X0) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0),tc_fun(X1,tc_bool)),X0)
| ~ spl0_150
| ~ spl0_169
| ~ spl0_534 ),
inference(forward_demodulation,[],[f11337,f1785]) ).
fof(f11337,plain,
( ! [X2,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X0),tc_fun(X1,tc_bool)),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X0)),c_COMBK(c_False,tc_bool,X1))
| ~ spl0_150
| ~ spl0_534 ),
inference(superposition,[],[f11050,f1669]) ).
fof(f47973,plain,
( spl0_1178
| ~ spl0_150
| ~ spl0_170
| ~ spl0_534 ),
inference(avatar_split_clause,[],[f11421,f11049,f1788,f1668,f47971]) ).
fof(f47971,plain,
( spl0_1178
<=> ! [X2,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2),tc_fun(X1,tc_bool)),X0) = hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f11421,plain,
( ! [X2,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2),tc_fun(X1,tc_bool)),X0) = hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X0)
| ~ spl0_150
| ~ spl0_170
| ~ spl0_534 ),
inference(forward_demodulation,[],[f11329,f1789]) ).
fof(f11329,plain,
( ! [X2,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X0),X2),tc_fun(X1,tc_bool)),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1)),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),X0))
| ~ spl0_150
| ~ spl0_534 ),
inference(superposition,[],[f11050,f1669]) ).
fof(f47969,plain,
( spl0_1177
| ~ spl0_156
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f11020,f10604,f1694,f47967]) ).
fof(f47967,plain,
( spl0_1177
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq1__1(X1,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f10604,plain,
( spl0_528
<=> ! [X5,X13,X29,X76,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f11020,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq1__1(X1,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X1,X2))) )
| ~ spl0_156
| ~ spl0_528 ),
inference(resolution,[],[f10605,f1695]) ).
fof(f10605,plain,
( ! [X29,X76,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76))) )
| ~ spl0_528 ),
inference(avatar_component_clause,[],[f10604]) ).
fof(f47965,plain,
( spl0_1176
| ~ spl0_156
| ~ spl0_527 ),
inference(avatar_split_clause,[],[f11017,f10600,f1694,f47963]) ).
fof(f47963,plain,
( spl0_1176
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq2__1(X2,X1)),v_sko__Hoare__Mirabelle__Xconseq2__2(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f10600,plain,
( spl0_527
<=> ! [X5,X13,X75,X29,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| hBOOL(hAPP(hAPP(X75,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f11017,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq2__1(X2,X1)),v_sko__Hoare__Mirabelle__Xconseq2__2(X2,X1))) )
| ~ spl0_156
| ~ spl0_527 ),
inference(resolution,[],[f10601,f1695]) ).
fof(f10601,plain,
( ! [X29,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X75,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75))) )
| ~ spl0_527 ),
inference(avatar_component_clause,[],[f10600]) ).
fof(f47961,plain,
( spl0_1175
| ~ spl0_156
| ~ spl0_526 ),
inference(avatar_split_clause,[],[f11014,f10589,f1694,f47959]) ).
fof(f47959,plain,
( spl0_1175
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X1,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f10589,plain,
( spl0_526
<=> ! [X5,X13,X29,X76,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X76,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f11014,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X1,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X1,X2))) )
| ~ spl0_156
| ~ spl0_526 ),
inference(resolution,[],[f10590,f1695]) ).
fof(f10590,plain,
( ! [X29,X76,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X76,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76))) )
| ~ spl0_526 ),
inference(avatar_component_clause,[],[f10589]) ).
fof(f47957,plain,
( spl0_1174
| ~ spl0_156
| ~ spl0_525 ),
inference(avatar_split_clause,[],[f11011,f10585,f1694,f47955]) ).
fof(f47955,plain,
( spl0_1174
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq2__1(X2,X1)),v_sko__Hoare__Mirabelle__Xconseq2__2(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f10585,plain,
( spl0_525
<=> ! [X5,X13,X75,X29,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f11011,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq2__1(X2,X1)),v_sko__Hoare__Mirabelle__Xconseq2__2(X2,X1))) )
| ~ spl0_156
| ~ spl0_525 ),
inference(resolution,[],[f10586,f1695]) ).
fof(f10586,plain,
( ! [X29,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75))) )
| ~ spl0_525 ),
inference(avatar_component_clause,[],[f10585]) ).
fof(f47952,plain,
( spl0_1173
| ~ spl0_83
| ~ spl0_506 ),
inference(avatar_split_clause,[],[f10039,f9516,f1328,f47950]) ).
fof(f47950,plain,
( spl0_1173
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),tc_fun(X0,tc_bool)),X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f9516,plain,
( spl0_506
<=> ! [X18,X11,X0,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f10039,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),tc_fun(X0,tc_bool)),X1)),X2))
| ~ spl0_83
| ~ spl0_506 ),
inference(resolution,[],[f9517,f1329]) ).
fof(f9517,plain,
( ! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),X18)) )
| ~ spl0_506 ),
inference(avatar_component_clause,[],[f9516]) ).
fof(f47948,plain,
( spl0_1172
| ~ spl0_213
| ~ spl0_503 ),
inference(avatar_split_clause,[],[f9789,f9504,f2064,f47946]) ).
fof(f47946,plain,
( spl0_1172
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f9789,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(X1,X4)) )
| ~ spl0_213
| ~ spl0_503 ),
inference(superposition,[],[f2065,f9505]) ).
fof(f47944,plain,
( spl0_1171
| ~ spl0_212
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f9627,f9500,f2060,f47942]) ).
fof(f47942,plain,
( spl0_1171
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f9627,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(X3,X4)) )
| ~ spl0_212
| ~ spl0_502 ),
inference(superposition,[],[f2061,f9501]) ).
fof(f47940,plain,
( spl0_1170
| ~ spl0_110
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11657,f5030,f1455,f47938]) ).
fof(f47938,plain,
( spl0_1170
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f11657,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1))
| X0 = X1 )
| ~ spl0_110
| ~ spl0_375 ),
inference(superposition,[],[f1456,f5031]) ).
fof(f47936,plain,
( spl0_1169
| ~ spl0_258
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8762,f8434,f2548,f47934]) ).
fof(f47934,plain,
( spl0_1169
<=> ! [X2,X4,X0,X3,X5,X1] :
( hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X5,hAPP(X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f8762,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X5,hAPP(X1,X2),X0)) )
| ~ spl0_258
| ~ spl0_476 ),
inference(superposition,[],[f2549,f8435]) ).
fof(f47932,plain,
( spl0_1168
| ~ spl0_249
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8758,f8434,f2503,f47930]) ).
fof(f47930,plain,
( spl0_1168
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( ~ c_Fun_Oinj__on(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0,X6)
| c_Fun_Oinj__on(X5,hAPP(X1,X2),X0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f8758,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Fun_Oinj__on(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0,X6)
| c_Fun_Oinj__on(X5,hAPP(X1,X2),X0,X6) )
| ~ spl0_249
| ~ spl0_476 ),
inference(superposition,[],[f2504,f8435]) ).
fof(f47928,plain,
( spl0_1167
| ~ spl0_162
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8750,f8434,f1756,f47926]) ).
fof(f47926,plain,
( spl0_1167
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f8750,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_162
| ~ spl0_476 ),
inference(superposition,[],[f1757,f8435]) ).
fof(f47924,plain,
( spl0_1166
| ~ spl0_167
| ~ spl0_457 ),
inference(avatar_split_clause,[],[f8019,f7909,f1776,f47922]) ).
fof(f47922,plain,
( spl0_1166
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f8019,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X3)) )
| ~ spl0_167
| ~ spl0_457 ),
inference(resolution,[],[f7910,f1777]) ).
fof(f47920,plain,
( spl0_1165
| ~ spl0_167
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f7975,f7862,f1776,f47918]) ).
fof(f47918,plain,
( spl0_1165
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X3,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f7975,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X3,X0),X2))) )
| ~ spl0_167
| ~ spl0_456 ),
inference(resolution,[],[f7863,f1777]) ).
fof(f47916,plain,
( spl0_1164
| ~ spl0_185
| ~ spl0_201
| ~ spl0_431 ),
inference(avatar_split_clause,[],[f6884,f6707,f2013,f1880,f47914]) ).
fof(f47914,plain,
( spl0_1164
<=> ! [X5,X6,X4,X7,X0,X3,X2,X1] :
( hAPP(X0,hAPP(X1,X7)) = hAPP(c_Fun_Ocomp(X0,c_Fun_Ofun__upd(X1,X5,X6,X4,X2),X2,X3,X4),X7)
| X5 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f6884,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(X0,hAPP(X1,X7)) = hAPP(c_Fun_Ocomp(X0,c_Fun_Ofun__upd(X1,X5,X6,X4,X2),X2,X3,X4),X7)
| X5 = X7 )
| ~ spl0_185
| ~ spl0_201
| ~ spl0_431 ),
inference(forward_demodulation,[],[f6878,f1881]) ).
fof(f6878,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(c_Fun_Ocomp(X0,X1,X2,X3,X4),X7) = hAPP(c_Fun_Ocomp(X0,c_Fun_Ofun__upd(X1,X5,X6,X4,X2),X2,X3,X4),X7)
| X5 = X7 )
| ~ spl0_201
| ~ spl0_431 ),
inference(superposition,[],[f2014,f6708]) ).
fof(f47912,plain,
( spl0_1163
| ~ spl0_148
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6123,f5535,f1660,f47910]) ).
fof(f47910,plain,
( spl0_1163
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X3,X2),X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f6123,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X3,X2),X4),X5)) )
| ~ spl0_148
| ~ spl0_405 ),
inference(superposition,[],[f1661,f5536]) ).
fof(f47908,plain,
( spl0_1162
| ~ spl0_238
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f6000,f5523,f2299,f47906]) ).
fof(f47906,plain,
( spl0_1162
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f6000,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)))
| ~ spl0_238
| ~ spl0_402 ),
inference(superposition,[],[f2300,f5524]) ).
fof(f47904,plain,
( spl0_1161
| ~ spl0_232
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f5998,f5523,f2275,f47902]) ).
fof(f47902,plain,
( spl0_1161
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f5998,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_232
| ~ spl0_402 ),
inference(superposition,[],[f2276,f5524]) ).
fof(f47900,plain,
( spl0_1160
| ~ spl0_237
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5935,f5519,f2295,f47898]) ).
fof(f47898,plain,
( spl0_1160
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f5935,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)))
| ~ spl0_237
| ~ spl0_401 ),
inference(superposition,[],[f2296,f5520]) ).
fof(f47896,plain,
( spl0_1159
| ~ spl0_193
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7872,f4832,f1913,f47894]) ).
fof(f47894,plain,
( spl0_1159
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f7872,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat),X0))
| ~ spl0_193
| ~ spl0_371 ),
inference(superposition,[],[f1914,f4833]) ).
fof(f47892,plain,
( spl0_1158
| ~ spl0_232
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5934,f5519,f2275,f47890]) ).
fof(f47890,plain,
( spl0_1158
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f5934,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0) )
| ~ spl0_232
| ~ spl0_401 ),
inference(superposition,[],[f2276,f5520]) ).
fof(f47888,plain,
( spl0_1157
| ~ spl0_80
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f5880,f5515,f1315,f47886]) ).
fof(f47886,plain,
( spl0_1157
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X5,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f5880,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X5,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X0),X3)) )
| ~ spl0_80
| ~ spl0_400 ),
inference(resolution,[],[f5516,f1316]) ).
fof(f47884,plain,
( spl0_1156
| ~ spl0_80
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f5866,f5511,f1315,f47882]) ).
fof(f47882,plain,
( spl0_1156
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(c_in(X0,hAPP(X1,X2),X3))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X3,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f5511,plain,
( spl0_399
<=> ! [X2,X11,X0,X12,X1,X7] :
( ~ hBOOL(c_in(X1,X11,X7))
| hBOOL(c_in(X2,hAPP(X12,X1),X0))
| ~ hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X7,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f5866,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(X0,hAPP(X1,X2),X3))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X3,tc_bool)),X0)) )
| ~ spl0_80
| ~ spl0_399 ),
inference(resolution,[],[f5512,f1316]) ).
fof(f5512,plain,
( ! [X2,X0,X11,X1,X7,X12] :
( ~ hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X7,tc_fun(X0,tc_bool)),X0))
| hBOOL(c_in(X2,hAPP(X12,X1),X0))
| ~ hBOOL(c_in(X1,X11,X7)) )
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f5511]) ).
fof(f47880,plain,
( spl0_1155
| ~ spl0_79
| ~ spl0_393 ),
inference(avatar_split_clause,[],[f5824,f5487,f1311,f47878]) ).
fof(f47878,plain,
( spl0_1155
<=> ! [X3,X4,X0,X5,X2,X1] :
( hAPP(c_Set_Oimage(X0,X1,X2),X3) = hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X4,X5,X1,X2),X1,X2),X3)
| hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f5487,plain,
( spl0_393
<=> ! [X4,X11,X0,X3,X8,X7] :
( hBOOL(c_in(X3,X11,X7))
| hAPP(c_Set_Oimage(X8,X7,X0),X11) = hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X8,X3,X4,X7,X0),X7,X0),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f5824,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hAPP(c_Set_Oimage(X0,X1,X2),X3) = hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X4,X5,X1,X2),X1,X2),X3)
| hBOOL(hAPP(X3,X4)) )
| ~ spl0_79
| ~ spl0_393 ),
inference(resolution,[],[f5488,f1312]) ).
fof(f5488,plain,
( ! [X3,X0,X11,X8,X7,X4] :
( hBOOL(c_in(X3,X11,X7))
| hAPP(c_Set_Oimage(X8,X7,X0),X11) = hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X8,X3,X4,X7,X0),X7,X0),X11) )
| ~ spl0_393 ),
inference(avatar_component_clause,[],[f5487]) ).
fof(f47876,plain,
( spl0_1154
| ~ spl0_178
| ~ spl0_205
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f5661,f5467,f2029,f1852,f47874]) ).
fof(f47874,plain,
( spl0_1154
<=> ! [X5,X4,X0,X3,X2,X1] : hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)))),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f5661,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)))),X3))
| ~ spl0_178
| ~ spl0_205
| ~ spl0_388 ),
inference(forward_demodulation,[],[f5641,f1853]) ).
fof(f5641,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(c_in(hAPP(c_COMBB(X0,X1,X2,X3,X4),X5),hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)))),X3))
| ~ spl0_205
| ~ spl0_388 ),
inference(superposition,[],[f2030,f5468]) ).
fof(f47872,plain,
( spl0_1153
| ~ spl0_265
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f5637,f5467,f2576,f47870]) ).
fof(f47870,plain,
( spl0_1153
<=> ! [X3,X4,X0,X5,X2,X1] :
( hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)) != c_COMBK(c_False,tc_bool,X3)
| c_COMBK(c_False,tc_bool,X4) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f2576,plain,
( spl0_265
<=> ! [X11,X0,X8,X7] :
( hAPP(c_Set_Oimage(X8,X7,X0),X11) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X7) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f5637,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)) != c_COMBK(c_False,tc_bool,X3)
| c_COMBK(c_False,tc_bool,X4) = X5 )
| ~ spl0_265
| ~ spl0_388 ),
inference(superposition,[],[f2577,f5468]) ).
fof(f2577,plain,
( ! [X0,X11,X8,X7] :
( hAPP(c_Set_Oimage(X8,X7,X0),X11) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X7) = X11 )
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f2576]) ).
fof(f47868,plain,
( spl0_1152
| ~ spl0_243
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f5461,f5066,f2319,f47866]) ).
fof(f47866,plain,
( spl0_1152
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f5461,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) )
| ~ spl0_243
| ~ spl0_384 ),
inference(duplicate_literal_removal,[],[f5432]) ).
fof(f5432,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_384 ),
inference(resolution,[],[f5067,f2320]) ).
fof(f47864,plain,
( spl0_1151
| ~ spl0_234
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f5459,f5066,f2283,f47862]) ).
fof(f47862,plain,
( spl0_1151
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f5459,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) )
| ~ spl0_234
| ~ spl0_384 ),
inference(duplicate_literal_removal,[],[f5434]) ).
fof(f5434,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_384 ),
inference(resolution,[],[f5067,f2284]) ).
fof(f47860,plain,
( spl0_1150
| ~ spl0_243
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5414,f5062,f2319,f47858]) ).
fof(f47858,plain,
( spl0_1150
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X2,X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f5414,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X2,X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) )
| ~ spl0_243
| ~ spl0_383 ),
inference(duplicate_literal_removal,[],[f5385]) ).
fof(f5385,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X2,X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_383 ),
inference(resolution,[],[f5063,f2320]) ).
fof(f47856,plain,
( spl0_1149
| ~ spl0_234
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5412,f5062,f2283,f47854]) ).
fof(f47854,plain,
( spl0_1149
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X2,X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f5412,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X2,X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) )
| ~ spl0_234
| ~ spl0_383 ),
inference(duplicate_literal_removal,[],[f5387]) ).
fof(f5387,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = hAPP(c_Set_Oinsert(X2,X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_383 ),
inference(resolution,[],[f5063,f2284]) ).
fof(f47852,plain,
( spl0_1148
| ~ spl0_110
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7867,f4832,f1455,f47850]) ).
fof(f47850,plain,
( spl0_1148
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),X1))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f7867,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),X1))
| X0 = X1 )
| ~ spl0_110
| ~ spl0_371 ),
inference(superposition,[],[f1456,f4833]) ).
fof(f47848,plain,
( spl0_1147
| ~ spl0_273
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5309,f5058,f2940,f47846]) ).
fof(f47846,plain,
( spl0_1147
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(X4,X0),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f5309,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(X4,X0),X5) )
| ~ spl0_273
| ~ spl0_382 ),
inference(resolution,[],[f5059,f2941]) ).
fof(f47844,plain,
( spl0_1146
| ~ spl0_274
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5308,f5058,f2944,f47842]) ).
fof(f47842,plain,
( spl0_1146
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(X3,X0),X4,X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X3,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f5308,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(X3,X0),X4,X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X3,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),X4,X5) )
| ~ spl0_274
| ~ spl0_382 ),
inference(resolution,[],[f5059,f2945]) ).
fof(f47840,plain,
( spl0_1145
| ~ spl0_264
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f5300,f5054,f2572,f47838]) ).
fof(f47838,plain,
( spl0_1145
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X1,X0),X2),X0))
| hBOOL(c_in(X3,hAPP(c_fequal(X0),X1),X0))
| hBOOL(c_in(X3,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f5054,plain,
( spl0_381
<=> ! [X11,X0,X12,X5] :
( hBOOL(c_in(X5,X12,X0))
| hBOOL(c_in(X5,X11,X0))
| ~ hBOOL(c_in(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f5300,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X1,X0),X2),X0))
| hBOOL(c_in(X3,hAPP(c_fequal(X0),X1),X0))
| hBOOL(c_in(X3,X2,X0)) )
| ~ spl0_264
| ~ spl0_381 ),
inference(superposition,[],[f5055,f2573]) ).
fof(f5055,plain,
( ! [X0,X11,X5,X12] :
( ~ hBOOL(c_in(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0))
| hBOOL(c_in(X5,X11,X0))
| hBOOL(c_in(X5,X12,X0)) )
| ~ spl0_381 ),
inference(avatar_component_clause,[],[f5054]) ).
fof(f47836,plain,
( spl0_1144
| ~ spl0_377
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f5278,f5050,f5038,f47834]) ).
fof(f47834,plain,
( spl0_1144
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Set_Oinsert(X3,X0),X4,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X1,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f5278,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Set_Oinsert(X3,X0),X4,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X1,X2,X4)) )
| ~ spl0_377
| ~ spl0_380 ),
inference(resolution,[],[f5051,f5039]) ).
fof(f47832,plain,
( spl0_1143
| ~ spl0_272
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5246,f5046,f2936,f47830]) ).
fof(f47830,plain,
( spl0_1143
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3))
| hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X4,X0),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f5246,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X3))
| hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X4,X0),X3),X0)) )
| ~ spl0_272
| ~ spl0_379 ),
inference(resolution,[],[f5047,f2937]) ).
fof(f47828,plain,
( spl0_1142
| ~ spl0_273
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5121,f5038,f2940,f47826]) ).
fof(f47826,plain,
( spl0_1142
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(X4,X0),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f5121,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(X4,X0),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),X5) )
| ~ spl0_273
| ~ spl0_377 ),
inference(resolution,[],[f5039,f2941]) ).
fof(f47824,plain,
( spl0_1141
| ~ spl0_274
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5120,f5038,f2944,f47822]) ).
fof(f47822,plain,
( spl0_1141
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),X5,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(X3,X0),X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f5120,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),X5,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(X3,X0),X5,X4) )
| ~ spl0_274
| ~ spl0_377 ),
inference(resolution,[],[f5039,f2945]) ).
fof(f47820,plain,
( spl0_1140
| ~ spl0_70
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4773,f4368,f1273,f47818]) ).
fof(f47818,plain,
( spl0_1140
<=> ! [X5,X1,X4,X2,X0,X6,X3,X7] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(c_in(X3,X5,X6))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X7,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f4773,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(c_in(X3,X5,X6))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X7,tc_bool)),X4)) )
| ~ spl0_70
| ~ spl0_359 ),
inference(superposition,[],[f4369,f1274]) ).
fof(f47816,plain,
( spl0_1139
| ~ spl0_167
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4721,f4368,f1776,f47814]) ).
fof(f47814,plain,
( spl0_1139
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(c_Set_Oinsert(X5,X3),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f4721,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(c_Set_Oinsert(X5,X3),X0))) )
| ~ spl0_167
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1777]) ).
fof(f47812,plain,
( spl0_1138
| ~ spl0_234
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4198,f3949,f2283,f47810]) ).
fof(f47810,plain,
( spl0_1138
<=> ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(X1,X2)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f4198,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(X1,X2)))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_334 ),
inference(resolution,[],[f3950,f2284]) ).
fof(f47773,plain,
( spl0_1137
| ~ spl0_243
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4196,f3949,f2319,f47771]) ).
fof(f47771,plain,
( spl0_1137
<=> ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(X1,X2)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f4196,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X0)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(X1,X2)))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_334 ),
inference(resolution,[],[f3950,f2320]) ).
fof(f47769,plain,
( spl0_1136
| ~ spl0_236
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4143,f3945,f2291,f47767]) ).
fof(f47767,plain,
( spl0_1136
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)))
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f4143,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)))
| ~ class_Orderings_Opreorder(X3) )
| ~ spl0_236
| ~ spl0_333 ),
inference(resolution,[],[f3946,f2292]) ).
fof(f47765,plain,
( spl0_1135
| ~ spl0_235
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4142,f3945,f2287,f47763]) ).
fof(f47763,plain,
( spl0_1135
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)))
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f4142,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)))
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_235
| ~ spl0_333 ),
inference(resolution,[],[f3946,f2288]) ).
fof(f47761,plain,
( spl0_1134
| ~ spl0_236
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4066,f3924,f2291,f47759]) ).
fof(f47759,plain,
( spl0_1134
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)))
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f4066,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)))
| ~ class_Orderings_Opreorder(X3) )
| ~ spl0_236
| ~ spl0_328 ),
inference(resolution,[],[f3925,f2292]) ).
fof(f47757,plain,
( spl0_1133
| ~ spl0_235
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4065,f3924,f2287,f47755]) ).
fof(f47755,plain,
( spl0_1133
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)))
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f4065,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)))
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_235
| ~ spl0_328 ),
inference(resolution,[],[f3925,f2288]) ).
fof(f47753,plain,
( spl0_1132
| ~ spl0_181
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4049,f3920,f1864,f47751]) ).
fof(f47751,plain,
( spl0_1132
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)),X3))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olattice(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f4049,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)),X3))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olattice(tc_fun(X0,X1)) )
| ~ spl0_181
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1865]) ).
fof(f47749,plain,
( spl0_1131
| ~ spl0_182
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4048,f3920,f1868,f47747]) ).
fof(f47747,plain,
( spl0_1131
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)),X3))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Oupper__semilattice(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f4048,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)),X3))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Oupper__semilattice(tc_fun(X0,X1)) )
| ~ spl0_182
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1869]) ).
fof(f47745,plain,
( spl0_1130
| ~ spl0_180
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4047,f3920,f1860,f47743]) ).
fof(f47743,plain,
( spl0_1130
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)),X2))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olattice(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f4047,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)),X2))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olattice(tc_fun(X0,X1)) )
| ~ spl0_180
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1861]) ).
fof(f47741,plain,
( spl0_1129
| ~ spl0_183
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4046,f3920,f1872,f47739]) ).
fof(f47739,plain,
( spl0_1129
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)),X2))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Oupper__semilattice(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f4046,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)),X2))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Oupper__semilattice(tc_fun(X0,X1)) )
| ~ spl0_183
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1873]) ).
fof(f47737,plain,
( spl0_1128
| ~ spl0_175
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4036,f3920,f1839,f47735]) ).
fof(f47735,plain,
( spl0_1128
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X3),X2)))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olattice(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f4036,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X3),X2)))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olattice(tc_fun(X0,X1)) )
| ~ spl0_175
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1840]) ).
fof(f47733,plain,
( ~ spl0_19
| spl0_1127
| ~ spl0_174
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f6372,f3137,f1835,f47731,f1052]) ).
fof(f3137,plain,
( spl0_295
<=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f6372,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)))
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_174
| ~ spl0_295 ),
inference(superposition,[],[f1836,f3138]) ).
fof(f3138,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) = X0
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f3137]) ).
fof(f47729,plain,
( spl0_1126
| ~ spl0_176
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4035,f3920,f1844,f47727]) ).
fof(f47727,plain,
( spl0_1126
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X3),X2)))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f4035,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X3),X2)))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,X1)) )
| ~ spl0_176
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1845]) ).
fof(f47725,plain,
( spl0_1125
| ~ spl0_174
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4031,f3920,f1835,f47723]) ).
fof(f47723,plain,
( spl0_1125
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3)))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olattice(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f4031,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3)))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olattice(tc_fun(X0,X1)) )
| ~ spl0_174
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1836]) ).
fof(f47721,plain,
( spl0_1124
| ~ spl0_177
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4030,f3920,f1848,f47719]) ).
fof(f47719,plain,
( spl0_1124
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3)))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f4030,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3)))
| ~ class_HOL_Oord(X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,X1)) )
| ~ spl0_177
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1849]) ).
fof(f47717,plain,
( spl0_1123
| ~ spl0_175
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4013,f3908,f1839,f47715]) ).
fof(f47715,plain,
( spl0_1123
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oimage(X2,X3,X0),X4)),X0)
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f4013,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oimage(X2,X3,X0),X4)),X0)
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) )
| ~ spl0_175
| ~ spl0_324 ),
inference(resolution,[],[f3909,f1840]) ).
fof(f47713,plain,
( spl0_1122
| ~ spl0_176
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4012,f3908,f1844,f47711]) ).
fof(f47711,plain,
( spl0_1122
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oimage(X2,X3,X0),X4)),X0)
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f4012,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oimage(X2,X3,X0),X4)),X0)
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_176
| ~ spl0_324 ),
inference(resolution,[],[f3909,f1845]) ).
fof(f47709,plain,
( spl0_1121
| ~ spl0_174
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4008,f3908,f1835,f47707]) ).
fof(f47707,plain,
( spl0_1121
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X0),X3)),X4),X0)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f4008,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X0),X3)),X4),X0)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) )
| ~ spl0_174
| ~ spl0_324 ),
inference(resolution,[],[f3909,f1836]) ).
fof(f47705,plain,
( spl0_1120
| ~ spl0_177
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4007,f3908,f1848,f47703]) ).
fof(f47703,plain,
( spl0_1120
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X0),X3)),X4),X0)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f4007,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X0),X3)),X4),X0)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_177
| ~ spl0_324 ),
inference(resolution,[],[f3909,f1849]) ).
fof(f47701,plain,
( spl0_1119
| ~ spl0_266
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3836,f3420,f2580,f47699]) ).
fof(f47699,plain,
( spl0_1119
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_Set_Oinsert(X2,tc_Hoare__Mirabelle_Otriple(X1)),hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X3)),X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f3836,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_Set_Oinsert(X2,tc_Hoare__Mirabelle_Otriple(X1)),hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X3)),X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),X0),X1) )
| ~ spl0_266
| ~ spl0_313 ),
inference(superposition,[],[f2581,f3421]) ).
fof(f47697,plain,
( spl0_1118
| ~ spl0_272
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3835,f3420,f2936,f47695]) ).
fof(f47695,plain,
( spl0_1118
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3))),X4))
| hBOOL(c_in(X0,X4,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f3835,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3))),X4))
| hBOOL(c_in(X0,X4,X1)) )
| ~ spl0_272
| ~ spl0_313 ),
inference(superposition,[],[f2937,f3421]) ).
fof(f47693,plain,
( spl0_1117
| ~ spl0_184
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3831,f3420,f1876,f47691]) ).
fof(f47691,plain,
( spl0_1117
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1))
| ~ hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X1),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f3831,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1))
| ~ hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X1),X3),X1)) )
| ~ spl0_184
| ~ spl0_313 ),
inference(superposition,[],[f1877,f3421]) ).
fof(f47641,plain,
( spl0_1116
| ~ spl0_179
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3830,f3420,f1856,f47639]) ).
fof(f47639,plain,
( spl0_1116
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1,X5)
| c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X1),X3),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f3830,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1,X5)
| c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X1),X3),X1,X5) )
| ~ spl0_179
| ~ spl0_313 ),
inference(superposition,[],[f1857,f3421]) ).
fof(f47637,plain,
( spl0_1115
| ~ spl0_255
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3655,f3388,f2536,f47635]) ).
fof(f47635,plain,
( spl0_1115
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f3655,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Finite__Set_Olinorder__class_OMin(X0,X1)),X2) = X2 )
| ~ spl0_255
| ~ spl0_305 ),
inference(resolution,[],[f3389,f2537]) ).
fof(f47633,plain,
( spl0_1114
| ~ spl0_253
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3654,f3388,f2528,f47631]) ).
fof(f47631,plain,
( spl0_1114
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Finite__Set_Olinorder__class_OMin(X0,X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f3654,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Finite__Set_Olinorder__class_OMin(X0,X1)) = X2 )
| ~ spl0_253
| ~ spl0_305 ),
inference(resolution,[],[f3389,f2529]) ).
fof(f47629,plain,
( spl0_1113
| ~ spl0_247
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3633,f3384,f2495,f47627]) ).
fof(f47627,plain,
( spl0_1113
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Finite__Set_Olinorder__class_OMax(X0,X1)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f3633,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Finite__Set_Olinorder__class_OMax(X0,X1)),X2) = X2 )
| ~ spl0_247
| ~ spl0_304 ),
inference(resolution,[],[f3385,f2496]) ).
fof(f47625,plain,
( spl0_1112
| ~ spl0_245
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3632,f3384,f2487,f47623]) ).
fof(f47623,plain,
( spl0_1112
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Finite__Set_Olinorder__class_OMax(X0,X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f3632,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Finite__Set_Olinorder__class_OMax(X0,X1)) = X2 )
| ~ spl0_245
| ~ spl0_304 ),
inference(resolution,[],[f3385,f2488]) ).
fof(f47621,plain,
( spl0_1111
| ~ spl0_92
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3603,f3376,f1379,f47619]) ).
fof(f47619,plain,
( spl0_1111
<=> ! [X5,X3,X4,X7,X0,X6,X2,X1] :
( ~ c_Finite__Set_Ofinite(X2,X5)
| ~ hBOOL(c_in(X1,X6,X7))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,tc_fun(X5,tc_bool)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f3603,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ c_Finite__Set_Ofinite(X2,X5)
| ~ hBOOL(c_in(X1,X6,X7))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X7,tc_fun(X5,tc_bool)),X5) )
| ~ spl0_92
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1380]) ).
fof(f47617,plain,
( spl0_1110
| ~ spl0_100
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3593,f3376,f1413,f47615]) ).
fof(f47615,plain,
( spl0_1110
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f3593,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_100
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1414]) ).
fof(f47613,plain,
( spl0_1109
| ~ spl0_86
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3335,f3016,f1340,f47611]) ).
fof(f47611,plain,
( spl0_1109
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_lessequals(X0),X1)),X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f3335,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_lessequals(X0),X1)),X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) )
| ~ spl0_86
| ~ spl0_292 ),
inference(resolution,[],[f3017,f1341]) ).
fof(f47609,plain,
( spl0_1108
| ~ spl0_86
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3315,f3012,f1340,f47607]) ).
fof(f47607,plain,
( spl0_1108
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1)),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f3315,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1)),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) )
| ~ spl0_86
| ~ spl0_291 ),
inference(resolution,[],[f3013,f1341]) ).
fof(f47605,plain,
( spl0_1107
| ~ spl0_86
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3298,f3008,f1340,f47603]) ).
fof(f47603,plain,
( spl0_1107
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1)),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f3298,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1)),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) )
| ~ spl0_86
| ~ spl0_290 ),
inference(resolution,[],[f3009,f1341]) ).
fof(f47570,plain,
( spl0_1106
| ~ spl0_87
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3284,f3004,f1344,f47568]) ).
fof(f47568,plain,
( spl0_1106
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f3284,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1345]) ).
fof(f47566,plain,
( spl0_1105
| ~ spl0_87
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3258,f3000,f1344,f47564]) ).
fof(f47564,plain,
( spl0_1105
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f3258,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1)),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1345]) ).
fof(f47562,plain,
( spl0_1104
| ~ spl0_87
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3233,f2992,f1344,f47560]) ).
fof(f47560,plain,
( spl0_1104
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1)),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f3233,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1)),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_286 ),
inference(resolution,[],[f2993,f1345]) ).
fof(f47558,plain,
( spl0_1103
| ~ spl0_35
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3227,f2980,f1123,f47556]) ).
fof(f47556,plain,
( spl0_1103
<=> ! [X4,X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X2,tc_fun(X3,X4),X0),X0,tc_fun(X3,X4)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1123,plain,
( spl0_35
<=> ! [X80,X79] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X80)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f2980,plain,
( spl0_283
<=> ! [X44,X11,X0,X7] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(X44,X7,X0),X0,X7) = X44 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3227,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X2,tc_fun(X3,X4),X0),X0,tc_fun(X3,X4)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_35
| ~ spl0_283 ),
inference(resolution,[],[f2981,f1124]) ).
fof(f1124,plain,
( ! [X80,X79] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X79,X80))
| ~ class_Complete__Lattice_Ocomplete__lattice(X80) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f2981,plain,
( ! [X0,X11,X44,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| c_COMBK(c_False,tc_bool,X0) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(X44,X7,X0),X0,X7) = X44 )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f2980]) ).
fof(f47554,plain,
( spl0_1102
| ~ spl0_35
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3225,f2976,f1123,f47552]) ).
fof(f47552,plain,
( spl0_1102
<=> ! [X4,X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_fun(X3,X4),X0),X0,tc_fun(X3,X4)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f2976,plain,
( spl0_282
<=> ! [X44,X11,X0,X7] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBK(X44,X7,X0),X0,X7) = X44 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f3225,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_fun(X3,X4),X0),X0,tc_fun(X3,X4)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_35
| ~ spl0_282 ),
inference(resolution,[],[f2977,f1124]) ).
fof(f2977,plain,
( ! [X0,X11,X44,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| c_COMBK(c_False,tc_bool,X0) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBK(X44,X7,X0),X0,X7) = X44 )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f2976]) ).
fof(f47550,plain,
( spl0_1101
| ~ spl0_234
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3119,f2936,f2283,f47548]) ).
fof(f47548,plain,
( spl0_1101
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),hAPP(c_Set_Oinsert(X0,X2),X3)))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f3119,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),hAPP(c_Set_Oinsert(X0,X2),X3)))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_234
| ~ spl0_272 ),
inference(resolution,[],[f2937,f2284]) ).
fof(f47546,plain,
( spl0_1100
| ~ spl0_243
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3117,f2936,f2319,f47544]) ).
fof(f47544,plain,
( spl0_1100
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),hAPP(c_Set_Oinsert(X0,X2),X3)))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f3117,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),hAPP(c_Set_Oinsert(X0,X2),X3)))
| ~ class_Orderings_Olinorder(tc_fun(X2,tc_bool)) )
| ~ spl0_243
| ~ spl0_272 ),
inference(resolution,[],[f2937,f2320]) ).
fof(f47542,plain,
( spl0_1099
| ~ spl0_199
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2861,f2560,f2005,f47540]) ).
fof(f47540,plain,
( spl0_1099
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(X0,X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f2861,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(X0,X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X1),X2) )
| ~ spl0_199
| ~ spl0_261 ),
inference(resolution,[],[f2561,f2006]) ).
fof(f47538,plain,
( spl0_1098
| ~ spl0_199
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2803,f2540,f2005,f47536]) ).
fof(f47536,plain,
( spl0_1098
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X1),X2)
| ~ c_Finite__Set_Ofinite(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f2803,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X1),X2)
| ~ c_Finite__Set_Ofinite(X0,X2) )
| ~ spl0_199
| ~ spl0_256 ),
inference(resolution,[],[f2541,f2006]) ).
fof(f47534,plain,
( spl0_1097
| ~ spl0_151
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2722,f2520,f1672,f47532]) ).
fof(f47532,plain,
( spl0_1097
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1672,plain,
( spl0_151
<=> ! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f2722,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),X4),X3))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),X4,X2)) )
| ~ spl0_151
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1673]) ).
fof(f1673,plain,
( ! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)) = X11
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1672]) ).
fof(f47502,plain,
( spl0_1096
| ~ spl0_150
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2721,f2520,f1668,f47500]) ).
fof(f47500,plain,
( spl0_1096
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),X4),X3))
| ~ hBOOL(c_in(X0,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f2721,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),X4),X3))
| ~ hBOOL(c_in(X0,X4,X2)) )
| ~ spl0_150
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1669]) ).
fof(f47498,plain,
( spl0_1095
| ~ spl0_91
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2234,f2089,f1375,f47496]) ).
fof(f47496,plain,
( spl0_1095
<=> ! [X0,X3,X2,X1] : c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)) = c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f2234,plain,
( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)) = c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1),X2,X3)
| ~ spl0_91
| ~ spl0_219 ),
inference(superposition,[],[f1376,f2090]) ).
fof(f47494,plain,
( spl0_1094
| ~ spl0_185
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2173,f2029,f1880,f47492]) ).
fof(f47492,plain,
( spl0_1094
<=> ! [X2,X4,X7,X0,X6,X5,X3,X1] : hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X1,X2,X3,X4),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f2173,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X1,X2,X3,X4),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7))
| ~ spl0_185
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1881]) ).
fof(f47490,plain,
( spl0_1093
| ~ spl0_178
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2168,f2029,f1852,f47488]) ).
fof(f47488,plain,
( spl0_1093
<=> ! [X2,X4,X7,X0,X6,X5,X3,X1] : hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(c_COMBB(X0,X1,X2,X3,X4),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f2168,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hBOOL(c_in(hAPP(X0,hAPP(X1,X5)),hAPP(c_Set_Oimage(c_COMBB(X0,X1,X2,X3,X4),X6,X7),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool))),X7))
| ~ spl0_178
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1853]) ).
fof(f47486,plain,
( spl0_1092
| ~ spl0_91
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1962,f1880,f1375,f47484]) ).
fof(f47484,plain,
( spl0_1092
<=> ! [X5,X3,X4,X2,X7,X0,X6,X1] : c_Fun_Ocomp(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_Fun_Ocomp(X0,X1,X2,X3,X4),X5,hAPP(X0,hAPP(X1,X5)),X6,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f1962,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Fun_Ocomp(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_Fun_Ocomp(X0,X1,X2,X3,X4),X5,hAPP(X0,hAPP(X1,X5)),X6,X7)
| ~ spl0_91
| ~ spl0_185 ),
inference(superposition,[],[f1376,f1881]) ).
fof(f47482,plain,
( spl0_1091
| ~ spl0_91
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1931,f1852,f1375,f47480]) ).
fof(f47480,plain,
( spl0_1091
<=> ! [X5,X3,X4,X2,X7,X0,X6,X1] : c_COMBB(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_COMBB(X0,X1,X2,X3,X4),X5,hAPP(X0,hAPP(X1,X5)),X6,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f1931,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_COMBB(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_COMBB(X0,X1,X2,X3,X4),X5,hAPP(X0,hAPP(X1,X5)),X6,X7)
| ~ spl0_91
| ~ spl0_178 ),
inference(superposition,[],[f1376,f1853]) ).
fof(f44963,plain,
( spl0_1090
| ~ spl0_386
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39085,f31067,f5416,f44961]) ).
fof(f44961,plain,
( spl0_1090
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f39085,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool))
| ~ spl0_386
| ~ spl0_728 ),
inference(superposition,[],[f5418,f31068]) ).
fof(f44784,plain,
( spl0_1089
| ~ spl0_726
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39082,f31067,f30221,f44782]) ).
fof(f44782,plain,
( spl0_1089
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f39082,plain,
( ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,tc_bool)
| ~ spl0_726
| ~ spl0_728 ),
inference(superposition,[],[f31068,f30222]) ).
fof(f44607,plain,
( spl0_1088
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39081,f31067,f44605]) ).
fof(f44605,plain,
( spl0_1088
<=> ! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f39081,plain,
( ! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,tc_bool)
| ~ spl0_728 ),
inference(superposition,[],[f31068,f31068]) ).
fof(f44544,plain,
( spl0_1087
| ~ spl0_237
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8755,f8434,f2295,f44542]) ).
fof(f44542,plain,
( spl0_1087
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X1,X2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f8755,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X1,X2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool))))
| ~ spl0_237
| ~ spl0_476 ),
inference(superposition,[],[f2296,f8435]) ).
fof(f44540,plain,
( spl0_1086
| ~ spl0_155
| ~ spl0_468 ),
inference(avatar_split_clause,[],[f8367,f7953,f1690,f44538]) ).
fof(f44538,plain,
( spl0_1086
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f8367,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) )
| ~ spl0_155
| ~ spl0_468 ),
inference(resolution,[],[f7954,f1691]) ).
fof(f44536,plain,
( spl0_1085
| ~ spl0_155
| ~ spl0_457 ),
inference(avatar_split_clause,[],[f8007,f7909,f1690,f44534]) ).
fof(f44534,plain,
( spl0_1085
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f8007,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)) )
| ~ spl0_155
| ~ spl0_457 ),
inference(resolution,[],[f7910,f1691]) ).
fof(f44532,plain,
( spl0_1084
| ~ spl0_146
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f7991,f7862,f1651,f44530]) ).
fof(f44530,plain,
( spl0_1084
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f7991,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_146
| ~ spl0_456 ),
inference(resolution,[],[f7863,f1652]) ).
fof(f44501,plain,
( spl0_1083
| spl0_56
| ~ spl0_70
| ~ spl0_221
| ~ spl0_453 ),
inference(avatar_split_clause,[],[f7722,f7500,f2097,f1273,f1213,f44499]) ).
fof(f44499,plain,
( spl0_1083
<=> ! [X2,X0,X1,X3] : c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X3,X2,t_a)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f7722,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_False)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X3,X2,t_a)),t_a) )
| ~ spl0_70
| ~ spl0_221
| ~ spl0_453 ),
inference(forward_demodulation,[],[f7715,f1274]) ).
fof(f7715,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_COMBK(c_False,tc_bool,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X2,X3)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X3,X2,t_a)),t_a) )
| ~ spl0_221
| ~ spl0_453 ),
inference(superposition,[],[f7501,f2098]) ).
fof(f44497,plain,
( spl0_1082
| ~ spl0_725
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36498,f30644,f29833,f44495]) ).
fof(f44495,plain,
( spl0_1082
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f36498,plain,
( ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,tc_nat)
| ~ spl0_725
| ~ spl0_727 ),
inference(superposition,[],[f30645,f29834]) ).
fof(f44493,plain,
( spl0_1081
| ~ spl0_167
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f7563,f7484,f1776,f44491]) ).
fof(f44491,plain,
( spl0_1081
<=> ! [X2,X4,X0,X5,X3,X1] :
( hBOOL(c_in(hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X3),hAPP(c_Set_Oimage(X0,X4,X3),X5)),X3))
| ~ hBOOL(c_in(X1,X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f7563,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X3),hAPP(c_Set_Oimage(X0,X4,X3),X5)),X3))
| ~ hBOOL(c_in(X1,X5,X4)) )
| ~ spl0_167
| ~ spl0_449 ),
inference(resolution,[],[f7485,f1777]) ).
fof(f44489,plain,
( spl0_1080
| ~ spl0_240
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f7396,f6760,f2307,f44487]) ).
fof(f44487,plain,
( spl0_1080
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f7396,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) )
| ~ spl0_240
| ~ spl0_444 ),
inference(superposition,[],[f6761,f2308]) ).
fof(f44485,plain,
( spl0_1079
| ~ spl0_257
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7287,f6756,f2544,f44483]) ).
fof(f44483,plain,
( spl0_1079
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f7287,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) )
| ~ spl0_257
| ~ spl0_443 ),
inference(superposition,[],[f2545,f6757]) ).
fof(f44481,plain,
( spl0_1078
| ~ spl0_248
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7283,f6756,f2499,f44479]) ).
fof(f44479,plain,
( spl0_1078
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X3,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f7283,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X3,X0,X5) )
| ~ spl0_248
| ~ spl0_443 ),
inference(superposition,[],[f2500,f6757]) ).
fof(f44477,plain,
( spl0_1077
| ~ spl0_163
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7277,f6756,f1760,f44475]) ).
fof(f44475,plain,
( spl0_1077
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f7277,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X2),X0) )
| ~ spl0_163
| ~ spl0_443 ),
inference(superposition,[],[f1761,f6757]) ).
fof(f44473,plain,
( spl0_1076
| ~ spl0_258
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7159,f6752,f2548,f44471]) ).
fof(f44471,plain,
( spl0_1076
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f7159,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,X1,X0)) )
| ~ spl0_258
| ~ spl0_442 ),
inference(superposition,[],[f2549,f6753]) ).
fof(f44469,plain,
( spl0_1075
| ~ spl0_249
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7155,f6752,f2503,f44467]) ).
fof(f44467,plain,
( spl0_1075
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X1,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f7155,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X1,X0,X5) )
| ~ spl0_249
| ~ spl0_442 ),
inference(superposition,[],[f2504,f6753]) ).
fof(f44465,plain,
( spl0_1074
| ~ spl0_162
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7147,f6752,f1756,f44463]) ).
fof(f44463,plain,
( spl0_1074
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f7147,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),X3),X0) )
| ~ spl0_162
| ~ spl0_442 ),
inference(superposition,[],[f1757,f6753]) ).
fof(f44461,plain,
( spl0_1073
| ~ spl0_70
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f7005,f6711,f1273,f44459]) ).
fof(f44459,plain,
( spl0_1073
<=> ! [X5,X4,X2,X7,X0,X6,X3,X1] :
( ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X5,X6,X7)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f7005,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X5,X6,X7)
| X3 = X4 )
| ~ spl0_70
| ~ spl0_432 ),
inference(trivial_inequality_removal,[],[f7004]) ).
fof(f7004,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X0 != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X5,X6,X7)
| X3 = X4 )
| ~ spl0_70
| ~ spl0_432 ),
inference(forward_demodulation,[],[f6933,f1274]) ).
fof(f6933,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(c_COMBK(X0,X1,X2),X4) != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X5,X6,X7)
| X3 = X4 )
| ~ spl0_70
| ~ spl0_432 ),
inference(superposition,[],[f6712,f1274]) ).
fof(f44457,plain,
( spl0_1072
| ~ spl0_199
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f6608,f6432,f2005,f44455]) ).
fof(f44455,plain,
( spl0_1072
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0)
| ~ c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f6608,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0)
| ~ c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0),X0) )
| ~ spl0_199
| ~ spl0_422 ),
inference(resolution,[],[f6433,f2006]) ).
fof(f44453,plain,
( spl0_1071
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36497,f30644,f44451]) ).
fof(f44451,plain,
( spl0_1071
<=> ! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f36497,plain,
( ! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,tc_nat)
| ~ spl0_727 ),
inference(superposition,[],[f30645,f30645]) ).
fof(f44449,plain,
( spl0_1070
| ~ spl0_264
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f6533,f6424,f2572,f44447]) ).
fof(f44447,plain,
( spl0_1070
<=> ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X1,X0),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_Set_Oinsert(X1,X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f6424,plain,
( spl0_420
<=> ! [X11,X0,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f6533,plain,
( ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X1,X0),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_Set_Oinsert(X1,X0),X2))
| ~ spl0_264
| ~ spl0_420 ),
inference(superposition,[],[f6425,f2573]) ).
fof(f6425,plain,
( ! [X0,X11,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12))
| ~ spl0_420 ),
inference(avatar_component_clause,[],[f6424]) ).
fof(f44445,plain,
( spl0_1069
| ~ spl0_122
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f6219,f5547,f1531,f44443]) ).
fof(f44443,plain,
( spl0_1069
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X3,X1,X2,X4),X4,X2),X5),X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X4,X1),X5),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f1531,plain,
( spl0_122
<=> ! [X0,X7,X14,X15] :
( ~ c_Finite__Set_Ofinite(X14,X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X15,X0,X7),X14),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f6219,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Fun_Ocomp(X0,X3,X1,X2,X4),X4,X2),X5),X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X4,X1),X5),X1) )
| ~ spl0_122
| ~ spl0_408 ),
inference(superposition,[],[f1532,f5548]) ).
fof(f1532,plain,
( ! [X0,X7,X14,X15] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X15,X0,X7),X14),X7)
| ~ c_Finite__Set_Ofinite(X14,X0) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1531]) ).
fof(f44441,plain,
( spl0_1068
| ~ spl0_185
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f6174,f5539,f1880,f44439]) ).
fof(f44439,plain,
( spl0_1068
<=> ! [X2,X6,X4,X3,X7,X0,X5,X1] : hAPP(c_Fun_Ocomp(X0,c_Fun_Ocomp(X1,X5,X4,X2,X6),X2,X3,X6),X7) = hAPP(X0,hAPP(X1,hAPP(X5,X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f5539,plain,
( spl0_406
<=> ! [X17,X58,X0,X8,X9,X15,X7] : c_Fun_Ocomp(X8,c_Fun_Ocomp(X9,X15,X58,X17,X0),X17,X7,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X8,X9,X17,X7,X58),X15,X58,X7,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f6174,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ocomp(X0,c_Fun_Ocomp(X1,X5,X4,X2,X6),X2,X3,X6),X7) = hAPP(X0,hAPP(X1,hAPP(X5,X7)))
| ~ spl0_185
| ~ spl0_406 ),
inference(forward_demodulation,[],[f6172,f1881]) ).
fof(f6172,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ocomp(X0,X1,X2,X3,X4),hAPP(X5,X7)) = hAPP(c_Fun_Ocomp(X0,c_Fun_Ocomp(X1,X5,X4,X2,X6),X2,X3,X6),X7)
| ~ spl0_185
| ~ spl0_406 ),
inference(superposition,[],[f1881,f5540]) ).
fof(f5540,plain,
( ! [X58,X0,X8,X9,X7,X17,X15] : c_Fun_Ocomp(X8,c_Fun_Ocomp(X9,X15,X58,X17,X0),X17,X7,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X8,X9,X17,X7,X58),X15,X58,X7,X0)
| ~ spl0_406 ),
inference(avatar_component_clause,[],[f5539]) ).
fof(f44437,plain,
( spl0_1067
| ~ spl0_185
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f6173,f5539,f1880,f44435]) ).
fof(f44435,plain,
( spl0_1067
<=> ! [X6,X4,X3,X0,X7,X5,X2,X1] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(X0,X1,X4,X6,X3),X2,X3,X6,X5),X7) = hAPP(X0,hAPP(X1,hAPP(X2,X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f6173,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(X0,X1,X4,X6,X3),X2,X3,X6,X5),X7) = hAPP(X0,hAPP(X1,hAPP(X2,X7)))
| ~ spl0_185
| ~ spl0_406 ),
inference(forward_demodulation,[],[f6170,f1881]) ).
fof(f6170,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X0,hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X7)) = hAPP(c_Fun_Ocomp(c_Fun_Ocomp(X0,X1,X4,X6,X3),X2,X3,X6,X5),X7)
| ~ spl0_185
| ~ spl0_406 ),
inference(superposition,[],[f1881,f5540]) ).
fof(f44433,plain,
( spl0_1066
| ~ spl0_122
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6099,f5535,f1531,f44431]) ).
fof(f44431,plain,
( spl0_1066
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(hAPP(X0,X3),X2),hAPP(c_Set_Oimage(X0,X1,X2),X4)),X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X1),X4),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f6099,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(hAPP(X0,X3),X2),hAPP(c_Set_Oimage(X0,X1,X2),X4)),X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X1),X4),X1) )
| ~ spl0_122
| ~ spl0_405 ),
inference(superposition,[],[f1532,f5536]) ).
fof(f44429,plain,
( spl0_1065
| ~ spl0_212
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f5996,f5523,f2060,f44427]) ).
fof(f44427,plain,
( spl0_1065
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f5996,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X3)) )
| ~ spl0_212
| ~ spl0_402 ),
inference(superposition,[],[f2061,f5524]) ).
fof(f44425,plain,
( spl0_1064
| ~ spl0_213
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5933,f5519,f2064,f44423]) ).
fof(f44423,plain,
( spl0_1064
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f5933,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X3)) )
| ~ spl0_213
| ~ spl0_401 ),
inference(superposition,[],[f2065,f5520]) ).
fof(f44421,plain,
( spl0_1063
| ~ spl0_19
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f5862,f5507,f1052,f44419]) ).
fof(f44419,plain,
( spl0_1063
<=> ! [X0,X1] : hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(X0,v_x)),hAPP(X1,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f5507,plain,
( spl0_398
<=> ! [X9,X7,X8] :
( ~ class_Lattices_Olattice(X7)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X7)),X8),X9),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7),hAPP(X8,v_x)),hAPP(X9,v_x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f5862,plain,
( ! [X0,X1] : hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(X0,v_x)),hAPP(X1,v_x))
| ~ spl0_19
| ~ spl0_398 ),
inference(resolution,[],[f5508,f1054]) ).
fof(f5508,plain,
( ! [X8,X9,X7] :
( ~ class_Lattices_Olattice(X7)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X7)),X8),X9),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7),hAPP(X8,v_x)),hAPP(X9,v_x)) )
| ~ spl0_398 ),
inference(avatar_component_clause,[],[f5507]) ).
fof(f44417,plain,
( spl0_1062
| ~ spl0_7
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f5861,f5507,f992,f44415]) ).
fof(f44415,plain,
( spl0_1062
<=> ! [X0,X1] : hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_nat)),X0),X1),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(X0,v_x)),hAPP(X1,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f5861,plain,
( ! [X0,X1] : hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_nat)),X0),X1),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(X0,v_x)),hAPP(X1,v_x))
| ~ spl0_7
| ~ spl0_398 ),
inference(resolution,[],[f5508,f994]) ).
fof(f44412,plain,
( spl0_1061
| ~ spl0_122
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f5622,f5467,f1531,f44410]) ).
fof(f44410,plain,
( spl0_1061
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_COMBB(X0,X3,X1,X2,X4),X4,X2),X5),X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X4,X1),X5),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f5622,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_COMBB(X0,X3,X1,X2,X4),X4,X2),X5),X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X4,X1),X5),X1) )
| ~ spl0_122
| ~ spl0_388 ),
inference(superposition,[],[f1532,f5468]) ).
fof(f44408,plain,
( spl0_1060
| ~ spl0_386
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33237,f30221,f5416,f44406]) ).
fof(f44406,plain,
( spl0_1060
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f33237,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool))
| ~ spl0_386
| ~ spl0_726 ),
inference(superposition,[],[f5418,f30222]) ).
fof(f44404,plain,
( spl0_1059
| ~ spl0_80
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f5292,f5054,f1315,f44402]) ).
fof(f44402,plain,
( spl0_1059
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X0,X3,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f5292,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X0,X3,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X0)) )
| ~ spl0_80
| ~ spl0_381 ),
inference(resolution,[],[f5055,f1316]) ).
fof(f44400,plain,
( spl0_1058
| ~ spl0_259
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5225,f5046,f2552,f44398]) ).
fof(f44398,plain,
( spl0_1058
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X2),X4))
| ~ hBOOL(hAPP(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f5225,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X2),X4))
| ~ hBOOL(hAPP(X1,X4)) )
| ~ spl0_259
| ~ spl0_379 ),
inference(resolution,[],[f5047,f2553]) ).
fof(f44396,plain,
( spl0_1057
| ~ spl0_65
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f5011,f4409,f1252,f44394]) ).
fof(f44394,plain,
( spl0_1057
<=> ! [X0,X3,X2,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X2)),X3),X2)
| c_Hoare__Mirabelle_Ohoare__valids(X0,hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X2)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f5011,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X2)),X3),X2)
| c_Hoare__Mirabelle_Ohoare__valids(X0,hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X2)),X1),X2) )
| ~ spl0_65
| ~ spl0_369 ),
inference(resolution,[],[f4410,f1253]) ).
fof(f44392,plain,
( spl0_1056
| ~ spl0_146
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4733,f4368,f1651,f44390]) ).
fof(f44390,plain,
( spl0_1056
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f4733,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))) )
| ~ spl0_146
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1652]) ).
fof(f44388,plain,
( spl0_1055
| ~ spl0_148
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4714,f4368,f1660,f44386]) ).
fof(f44386,plain,
( spl0_1055
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_Set_Oinsert(X3,X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X0,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f4714,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_Set_Oinsert(X3,X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X0,X6)) )
| ~ spl0_148
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1661]) ).
fof(f44384,plain,
( spl0_1054
| ~ spl0_155
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4700,f4368,f1690,f44382]) ).
fof(f44382,plain,
( spl0_1054
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X0,tc_bool)),X2,tc_fun(X3,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f4700,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X0,tc_bool)),X2,tc_fun(X3,tc_bool)),X4)) )
| ~ spl0_155
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1691]) ).
fof(f44380,plain,
( spl0_1053
| ~ spl0_70
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4236,f3949,f1273,f44378]) ).
fof(f44378,plain,
( spl0_1053
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X4),X0),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,X1,X2),X4)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f4236,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X4),X0),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,X1,X2),X4)),X3)) )
| ~ spl0_70
| ~ spl0_334 ),
inference(superposition,[],[f3950,f1274]) ).
fof(f44376,plain,
( spl0_1052
| ~ spl0_207
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4191,f3949,f2037,f44374]) ).
fof(f44374,plain,
( spl0_1052
<=> ! [X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Inductive_Ocomplete__lattice__class_Olfp(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f4191,plain,
( ! [X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Inductive_Ocomplete__lattice__class_Olfp(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),X1)) )
| ~ spl0_207
| ~ spl0_334 ),
inference(resolution,[],[f3950,f2038]) ).
fof(f44372,plain,
( spl0_1051
| ~ spl0_70
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4187,f3945,f1273,f44370]) ).
fof(f44370,plain,
( spl0_1051
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,X4)),X0))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f4187,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,X4)),X0))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_70
| ~ spl0_333 ),
inference(superposition,[],[f3946,f1274]) ).
fof(f44368,plain,
( spl0_1050
| ~ spl0_70
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4108,f3924,f1273,f44366]) ).
fof(f44366,plain,
( spl0_1050
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,X4)))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f4108,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,X4)))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_70
| ~ spl0_328 ),
inference(superposition,[],[f3925,f1274]) ).
fof(f44364,plain,
( spl0_1049
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33235,f30221,f44362]) ).
fof(f44362,plain,
( spl0_1049
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f33235,plain,
( ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,tc_bool)
| ~ spl0_726 ),
inference(superposition,[],[f30222,f30222]) ).
fof(f44252,plain,
( ~ spl0_47
| ~ spl0_1047 ),
inference(avatar_contradiction_clause,[],[f44246]) ).
fof(f44246,plain,
( $false
| ~ spl0_47
| ~ spl0_1047 ),
inference(resolution,[],[f44241,f1172]) ).
fof(f44241,plain,
( ! [X1] : ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X1)
| ~ spl0_1047 ),
inference(avatar_component_clause,[],[f44240]) ).
fof(f44240,plain,
( spl0_1047
<=> ! [X1] : ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f44245,plain,
( spl0_1047
| spl0_1048
| ~ spl0_191
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4020,f3908,f1904,f44243,f44240]) ).
fof(f44243,plain,
( spl0_1048
<=> ! [X2,X3] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),c_COMBK(c_False,tc_bool,X2)))
| c_Finite__Set_Ofinite(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f4020,plain,
( ! [X2,X3,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),c_COMBK(c_False,tc_bool,X2)))
| c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X1) )
| ~ spl0_191
| ~ spl0_324 ),
inference(superposition,[],[f3909,f1905]) ).
fof(f44238,plain,
( spl0_1046
| ~ spl0_167
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3829,f3420,f1776,f44236]) ).
fof(f44236,plain,
( spl0_1046
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X3)),hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f3829,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X3)),hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3))))
| ~ spl0_167
| ~ spl0_313 ),
inference(superposition,[],[f1777,f3421]) ).
fof(f44234,plain,
( spl0_1045
| ~ spl0_175
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3795,f3416,f1839,f44232]) ).
fof(f44232,plain,
( spl0_1045
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f3795,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) )
| ~ spl0_175
| ~ spl0_312 ),
inference(resolution,[],[f3417,f1840]) ).
fof(f44230,plain,
( spl0_1044
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f31843,f29833,f44228]) ).
fof(f44228,plain,
( spl0_1044
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f31843,plain,
( ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,tc_nat)
| ~ spl0_725 ),
inference(superposition,[],[f29834,f29834]) ).
fof(f44226,plain,
( spl0_1043
| ~ spl0_176
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3794,f3416,f1844,f44224]) ).
fof(f44224,plain,
( spl0_1043
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f3794,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) )
| ~ spl0_176
| ~ spl0_312 ),
inference(resolution,[],[f3417,f1845]) ).
fof(f44222,plain,
( spl0_1042
| ~ spl0_174
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3790,f3416,f1835,f44220]) ).
fof(f44220,plain,
( spl0_1042
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f3790,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) )
| ~ spl0_174
| ~ spl0_312 ),
inference(resolution,[],[f3417,f1836]) ).
fof(f44218,plain,
( spl0_1041
| ~ spl0_177
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3789,f3416,f1848,f44216]) ).
fof(f44216,plain,
( spl0_1041
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f3789,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) )
| ~ spl0_177
| ~ spl0_312 ),
inference(resolution,[],[f3417,f1849]) ).
fof(f44214,plain,
( spl0_1040
| ~ spl0_175
| ~ spl0_250
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3744,f3404,f2516,f1839,f44212]) ).
fof(f44212,plain,
( spl0_1040
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)) = X2
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f3744,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)) = X2
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) )
| ~ spl0_175
| ~ spl0_250
| ~ spl0_309 ),
inference(forward_demodulation,[],[f3721,f2517]) ).
fof(f3721,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X2) = X2
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) )
| ~ spl0_175
| ~ spl0_309 ),
inference(resolution,[],[f3405,f1840]) ).
fof(f44210,plain,
( spl0_1039
| ~ spl0_176
| ~ spl0_250
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3743,f3404,f2516,f1844,f44208]) ).
fof(f44208,plain,
( spl0_1039
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)) = X2
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f3743,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)) = X2
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_176
| ~ spl0_250
| ~ spl0_309 ),
inference(forward_demodulation,[],[f3720,f2517]) ).
fof(f3720,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X2) = X2
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_176
| ~ spl0_309 ),
inference(resolution,[],[f3405,f1845]) ).
fof(f44206,plain,
( spl0_1038
| ~ spl0_292
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3710,f3400,f3016,f44204]) ).
fof(f44204,plain,
( spl0_1038
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ class_Orderings_Oorder(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X0),X1))
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f3710,plain,
( ! [X2,X0,X1] :
( X0 = X1
| ~ class_Orderings_Oorder(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X0),X1))
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) )
| ~ spl0_292
| ~ spl0_308 ),
inference(duplicate_literal_removal,[],[f3693]) ).
fof(f3693,plain,
( ! [X2,X0,X1] :
( X0 = X1
| ~ class_Orderings_Oorder(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X0),X1))
| ~ class_Orderings_Oorder(X2)
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) )
| ~ spl0_292
| ~ spl0_308 ),
inference(resolution,[],[f3401,f3017]) ).
fof(f44202,plain,
( spl0_1037
| ~ spl0_133
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3583,f3376,f1598,f44200]) ).
fof(f44200,plain,
( spl0_1037
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_HOL_Ominus__class_Ominus(X3,tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f3583,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_HOL_Ominus__class_Ominus(X3,tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X3,X4) )
| ~ spl0_133
| ~ spl0_302 ),
inference(resolution,[],[f3377,f1599]) ).
fof(f44198,plain,
( spl0_1036
| ~ spl0_292
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3551,f3368,f3016,f44196]) ).
fof(f44196,plain,
( spl0_1036
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ class_Orderings_Oorder(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X1),X0))
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f3551,plain,
( ! [X2,X0,X1] :
( X0 = X1
| ~ class_Orderings_Oorder(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X1),X0))
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) )
| ~ spl0_292
| ~ spl0_300 ),
inference(duplicate_literal_removal,[],[f3536]) ).
fof(f3536,plain,
( ! [X2,X0,X1] :
( X0 = X1
| ~ class_Orderings_Oorder(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2)
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) )
| ~ spl0_292
| ~ spl0_300 ),
inference(resolution,[],[f3369,f3017]) ).
fof(f44194,plain,
( spl0_1035
| ~ spl0_175
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3507,f3364,f1839,f44192]) ).
fof(f44192,plain,
( spl0_1035
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X3,X1,X4)
| ~ class_Lattices_Olattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f3507,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X3,X1,X4)
| ~ class_Lattices_Olattice(tc_fun(X1,tc_bool)) )
| ~ spl0_175
| ~ spl0_299 ),
inference(resolution,[],[f3365,f1840]) ).
fof(f44190,plain,
( spl0_1034
| ~ spl0_176
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3506,f3364,f1844,f44188]) ).
fof(f44188,plain,
( spl0_1034
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X3,X1,X4)
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f3506,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X3,X1,X4)
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,tc_bool)) )
| ~ spl0_176
| ~ spl0_299 ),
inference(resolution,[],[f3365,f1845]) ).
fof(f44171,plain,
( spl0_1033
| ~ spl0_174
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3502,f3364,f1835,f44169]) ).
fof(f44169,plain,
( spl0_1033
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X2,X1,X4)
| ~ class_Lattices_Olattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f3502,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X2,X1,X4)
| ~ class_Lattices_Olattice(tc_fun(X1,tc_bool)) )
| ~ spl0_174
| ~ spl0_299 ),
inference(resolution,[],[f3365,f1836]) ).
fof(f44167,plain,
( spl0_1032
| ~ spl0_177
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3501,f3364,f1848,f44165]) ).
fof(f44165,plain,
( spl0_1032
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X2,X1,X4)
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f3501,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X2,X1,X4)
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,tc_bool)) )
| ~ spl0_177
| ~ spl0_299 ),
inference(resolution,[],[f3365,f1849]) ).
fof(f44163,plain,
( spl0_1031
| ~ spl0_255
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3330,f3016,f2536,f44161]) ).
fof(f44161,plain,
( spl0_1031
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f3330,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 )
| ~ spl0_255
| ~ spl0_292 ),
inference(resolution,[],[f3017,f2537]) ).
fof(f44159,plain,
( spl0_1030
| ~ spl0_253
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3329,f3016,f2528,f44157]) ).
fof(f44157,plain,
( spl0_1030
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f3329,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = X2 )
| ~ spl0_253
| ~ spl0_292 ),
inference(resolution,[],[f3017,f2529]) ).
fof(f44155,plain,
( spl0_1029
| ~ spl0_247
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3328,f3016,f2495,f44153]) ).
fof(f44153,plain,
( spl0_1029
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f3328,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = X1 )
| ~ spl0_247
| ~ spl0_292 ),
inference(resolution,[],[f3017,f2496]) ).
fof(f44151,plain,
( spl0_1028
| ~ spl0_245
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3327,f3016,f2487,f44149]) ).
fof(f44149,plain,
( spl0_1028
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f3327,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 )
| ~ spl0_245
| ~ spl0_292 ),
inference(resolution,[],[f3017,f2488]) ).
fof(f44147,plain,
( spl0_1027
| ~ spl0_261
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3281,f3004,f2560,f44145]) ).
fof(f44145,plain,
( spl0_1027
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1),X2,X0)
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f3281,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1),X2,X0)
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_289 ),
inference(resolution,[],[f3005,f2561]) ).
fof(f44143,plain,
( spl0_1026
| ~ spl0_167
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3274,f3004,f1776,f44141]) ).
fof(f44141,plain,
( spl0_1026
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Set_Oinsert(X1,X0),X2),X2,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f3274,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Set_Oinsert(X1,X0),X2),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_167
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1777]) ).
fof(f44139,plain,
( spl0_1025
| ~ spl0_256
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3270,f3004,f2540,f44137]) ).
fof(f44137,plain,
( spl0_1025
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2),X0)
| ~ hBOOL(c_in(X1,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f3270,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2),X0)
| ~ hBOOL(c_in(X1,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_289 ),
inference(resolution,[],[f3005,f2541]) ).
fof(f44135,plain,
( spl0_1024
| ~ spl0_261
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3255,f3000,f2560,f44133]) ).
fof(f44133,plain,
( spl0_1024
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1),X2,X0)
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f3255,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1),X2,X0)
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_261
| ~ spl0_288 ),
inference(resolution,[],[f3001,f2561]) ).
fof(f44131,plain,
( ~ spl0_18
| spl0_1003
| ~ spl0_236
| ~ spl0_587 ),
inference(avatar_split_clause,[],[f13377,f13333,f2291,f44046,f1047]) ).
fof(f44046,plain,
( spl0_1003
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X0),c_False)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f13377,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X0),c_False))
| ~ class_Orderings_Opreorder(tc_bool) )
| ~ spl0_236
| ~ spl0_587 ),
inference(resolution,[],[f13334,f2292]) ).
fof(f44130,plain,
( spl0_1023
| ~ spl0_167
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3248,f3000,f1776,f44128]) ).
fof(f44128,plain,
( spl0_1023
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(c_Set_Oinsert(X1,X0),X2),X2,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f3248,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(c_Set_Oinsert(X1,X0),X2),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_167
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1777]) ).
fof(f44126,plain,
( spl0_1022
| ~ spl0_256
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3244,f3000,f2540,f44124]) ).
fof(f44124,plain,
( spl0_1022
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2),X0)
| ~ hBOOL(c_in(X1,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f3244,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2),X0)
| ~ hBOOL(c_in(X1,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_288 ),
inference(resolution,[],[f3001,f2541]) ).
fof(f44122,plain,
( spl0_1021
| ~ spl0_175
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3175,f2944,f1839,f44120]) ).
fof(f44120,plain,
( spl0_1021
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X0),X1,X2)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f3175,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X0),X1,X2)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) )
| ~ spl0_175
| ~ spl0_274 ),
inference(resolution,[],[f2945,f1840]) ).
fof(f44118,plain,
( spl0_1020
| ~ spl0_176
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3174,f2944,f1844,f44116]) ).
fof(f44116,plain,
( spl0_1020
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X0),X1,X2)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f3174,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X0),X1,X2)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) )
| ~ spl0_176
| ~ spl0_274 ),
inference(resolution,[],[f2945,f1845]) ).
fof(f44114,plain,
( spl0_1019
| ~ spl0_174
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3170,f2944,f1835,f44112]) ).
fof(f44112,plain,
( spl0_1019
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0),X3),X1,X2)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f3170,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0),X3),X1,X2)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) )
| ~ spl0_174
| ~ spl0_274 ),
inference(resolution,[],[f2945,f1836]) ).
fof(f44110,plain,
( spl0_1018
| ~ spl0_177
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3169,f2944,f1848,f44108]) ).
fof(f44108,plain,
( spl0_1018
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0),X3),X1,X2)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f3169,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0),X3),X1,X2)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) )
| ~ spl0_177
| ~ spl0_274 ),
inference(resolution,[],[f2945,f1849]) ).
fof(f44106,plain,
( spl0_1017
| ~ spl0_175
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3149,f2940,f1839,f44104]) ).
fof(f44104,plain,
( spl0_1017
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X1)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f3149,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X1)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) )
| ~ spl0_175
| ~ spl0_273 ),
inference(resolution,[],[f2941,f1840]) ).
fof(f44102,plain,
( spl0_1016
| ~ spl0_176
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3148,f2940,f1844,f44100]) ).
fof(f44100,plain,
( spl0_1016
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f3148,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) )
| ~ spl0_176
| ~ spl0_273 ),
inference(resolution,[],[f2941,f1845]) ).
fof(f44098,plain,
( spl0_1015
| ~ spl0_174
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3144,f2940,f1835,f44096]) ).
fof(f44096,plain,
( spl0_1015
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X2,X1)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f3144,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X2,X1)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) )
| ~ spl0_174
| ~ spl0_273 ),
inference(resolution,[],[f2941,f1836]) ).
fof(f44094,plain,
( spl0_1014
| ~ spl0_177
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3143,f2940,f1848,f44092]) ).
fof(f44092,plain,
( spl0_1014
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X2,X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f3143,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X2,X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) )
| ~ spl0_177
| ~ spl0_273 ),
inference(resolution,[],[f2941,f1849]) ).
fof(f44090,plain,
( spl0_1013
| ~ spl0_87
| ~ spl0_250
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2906,f2572,f2516,f1344,f44088]) ).
fof(f44088,plain,
( spl0_1013
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_False))
| hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f2906,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_False))
| hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))))) )
| ~ spl0_87
| ~ spl0_250
| ~ spl0_264 ),
inference(forward_demodulation,[],[f2905,f2869]) ).
fof(f2869,plain,
( ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X1,X0),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1))
| ~ spl0_250
| ~ spl0_264 ),
inference(superposition,[],[f2573,f2517]) ).
fof(f2905,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_False),hAPP(c_fequal(X0),X1)))
| hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))))) )
| ~ spl0_87
| ~ spl0_250
| ~ spl0_264 ),
inference(forward_demodulation,[],[f2897,f2517]) ).
fof(f2897,plain,
( ! [X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)))))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_False)) )
| ~ spl0_87
| ~ spl0_264 ),
inference(superposition,[],[f1345,f2573]) ).
fof(f44086,plain,
( spl0_1012
| ~ spl0_86
| ~ spl0_250
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2904,f2572,f2516,f1340,f44084]) ).
fof(f44084,plain,
( spl0_1012
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_False))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f2904,plain,
( ! [X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_False))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))))) )
| ~ spl0_86
| ~ spl0_250
| ~ spl0_264 ),
inference(forward_demodulation,[],[f2903,f2869]) ).
fof(f2903,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_False),hAPP(c_fequal(X0),X1)))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))))) )
| ~ spl0_86
| ~ spl0_250
| ~ spl0_264 ),
inference(forward_demodulation,[],[f2896,f2517]) ).
fof(f2896,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X0),c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)))))
| hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_False)) )
| ~ spl0_86
| ~ spl0_264 ),
inference(superposition,[],[f1341,f2573]) ).
fof(f44082,plain,
( spl0_1011
| ~ spl0_234
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2845,f2552,f2283,f44080]) ).
fof(f44080,plain,
( spl0_1011
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X0),X2))
| ~ class_Orderings_Olinorder(tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f2845,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X0),X2))
| ~ class_Orderings_Olinorder(tc_fun(X3,tc_bool)) )
| ~ spl0_234
| ~ spl0_259 ),
inference(resolution,[],[f2553,f2284]) ).
fof(f44078,plain,
( spl0_1010
| ~ spl0_243
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2843,f2552,f2319,f44076]) ).
fof(f44076,plain,
( spl0_1010
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X0),X2))
| ~ class_Orderings_Olinorder(tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f2843,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X0),X2))
| ~ class_Orderings_Olinorder(tc_fun(X3,tc_bool)) )
| ~ spl0_243
| ~ spl0_259 ),
inference(resolution,[],[f2553,f2320]) ).
fof(f44074,plain,
( spl0_1009
| ~ spl0_87
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2637,f2495,f1344,f44072]) ).
fof(f44072,plain,
( spl0_1009
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))),X1) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f2637,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))),X1) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_247 ),
inference(resolution,[],[f2496,f1345]) ).
fof(f44069,plain,
( spl0_1008
| ~ spl0_238
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2634,f2495,f2299,f44067]) ).
fof(f44067,plain,
( spl0_1008
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f2634,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2) = X2 )
| ~ spl0_238
| ~ spl0_247 ),
inference(resolution,[],[f2496,f2300]) ).
fof(f44064,plain,
( spl0_1007
| ~ spl0_237
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2633,f2495,f2295,f44062]) ).
fof(f44062,plain,
( spl0_1007
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f2633,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1) = X1 )
| ~ spl0_237
| ~ spl0_247 ),
inference(resolution,[],[f2496,f2296]) ).
fof(f44060,plain,
( spl0_1006
| ~ spl0_87
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2605,f2487,f1344,f44058]) ).
fof(f44058,plain,
( spl0_1006
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f2605,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_245 ),
inference(resolution,[],[f2488,f1345]) ).
fof(f44056,plain,
( spl0_1005
| ~ spl0_238
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2602,f2487,f2299,f44054]) ).
fof(f44054,plain,
( spl0_1005
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f2602,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) = X1 )
| ~ spl0_238
| ~ spl0_245 ),
inference(resolution,[],[f2488,f2300]) ).
fof(f44052,plain,
( spl0_1004
| ~ spl0_205
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2460,f2307,f2029,f44050]) ).
fof(f44050,plain,
( spl0_1004
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f2460,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3))
| ~ spl0_205
| ~ spl0_240 ),
inference(superposition,[],[f2030,f2308]) ).
fof(f44048,plain,
( ~ spl0_1002
| spl0_1003
| ~ spl0_235
| ~ spl0_587 ),
inference(avatar_split_clause,[],[f13376,f13333,f2287,f44046,f44042]) ).
fof(f44042,plain,
( spl0_1002
<=> class_Orderings_Olinorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f13376,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X0),c_False))
| ~ class_Orderings_Olinorder(tc_bool) )
| ~ spl0_235
| ~ spl0_587 ),
inference(resolution,[],[f13334,f2288]) ).
fof(f44040,plain,
( spl0_1001
| ~ spl0_165
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2172,f2029,f1768,f44038]) ).
fof(f44038,plain,
( spl0_1001
<=> ! [X2,X3,X4,X0,X5,X1] : hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f2172,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))),X5))
| ~ spl0_165
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1769]) ).
fof(f44036,plain,
( spl0_1000
| ~ spl0_170
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2159,f2029,f1788,f44034]) ).
fof(f44034,plain,
( spl0_1000
<=> ! [X2,X0,X1,X3] : hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f2159,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3))
| ~ spl0_170
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1789]) ).
fof(f44032,plain,
( spl0_999
| ~ spl0_87
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2139,f2005,f1344,f44030]) ).
fof(f44030,plain,
( spl0_999
<=> ! [X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X0)),X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X0),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f2139,plain,
( ! [X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X0)),X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X0),c_False)) )
| ~ spl0_87
| ~ spl0_199 ),
inference(resolution,[],[f2006,f1345]) ).
fof(f44028,plain,
( spl0_998
| ~ spl0_87
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1981,f1888,f1344,f44026]) ).
fof(f44026,plain,
( spl0_998
<=> ! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1)),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f1981,plain,
( ! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1)),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),c_False)) )
| ~ spl0_87
| ~ spl0_187 ),
inference(resolution,[],[f1889,f1345]) ).
fof(f44024,plain,
( spl0_997
| ~ spl0_91
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1812,f1784,f1375,f44022]) ).
fof(f44022,plain,
( spl0_997
<=> ! [X0,X3,X2,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0),X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f1812,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0),X1,X2,X3)
| ~ spl0_91
| ~ spl0_169 ),
inference(superposition,[],[f1376,f1785]) ).
fof(f42852,plain,
( spl0_996
| ~ spl0_92
| ~ spl0_995 ),
inference(avatar_split_clause,[],[f42359,f42037,f1379,f42850]) ).
fof(f42850,plain,
( spl0_996
<=> ! [X1] : c_False = hAPP(c_HOL_Ominus__class_Ominus(c_False,tc_bool),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f42037,plain,
( spl0_995
<=> ! [X0] : c_False = hAPP(c_HOL_Ominus__class_Ominus(c_False,tc_bool),hAPP(X0,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f42359,plain,
( ! [X1] : c_False = hAPP(c_HOL_Ominus__class_Ominus(c_False,tc_bool),X1)
| ~ spl0_92
| ~ spl0_995 ),
inference(superposition,[],[f42038,f1380]) ).
fof(f42038,plain,
( ! [X0] : c_False = hAPP(c_HOL_Ominus__class_Ominus(c_False,tc_bool),hAPP(X0,v_x))
| ~ spl0_995 ),
inference(avatar_component_clause,[],[f42037]) ).
fof(f42039,plain,
( spl0_995
| ~ spl0_70
| ~ spl0_221
| ~ spl0_900 ),
inference(avatar_split_clause,[],[f39334,f36638,f2097,f1273,f42037]) ).
fof(f39334,plain,
( ! [X0] : c_False = hAPP(c_HOL_Ominus__class_Ominus(c_False,tc_bool),hAPP(X0,v_x))
| ~ spl0_70
| ~ spl0_221
| ~ spl0_900 ),
inference(forward_demodulation,[],[f39281,f1274]) ).
fof(f39281,plain,
( ! [X0] : hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_COMBK(c_False,tc_bool,t_a),v_x),tc_bool),hAPP(X0,v_x))
| ~ spl0_221
| ~ spl0_900 ),
inference(superposition,[],[f36639,f2098]) ).
fof(f41547,plain,
( spl0_994
| ~ spl0_163
| ~ spl0_503 ),
inference(avatar_split_clause,[],[f9787,f9504,f1760,f41545]) ).
fof(f41545,plain,
( spl0_994
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f9787,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_163
| ~ spl0_503 ),
inference(superposition,[],[f1761,f9505]) ).
fof(f41543,plain,
( spl0_993
| ~ spl0_162
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f9625,f9500,f1756,f41541]) ).
fof(f41541,plain,
( spl0_993
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f9625,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(X3,X0) )
| ~ spl0_162
| ~ spl0_502 ),
inference(superposition,[],[f1757,f9501]) ).
fof(f41539,plain,
( spl0_992
| ~ spl0_242
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f9159,f8454,f2315,f41537]) ).
fof(f41537,plain,
( spl0_992
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X3)),X1))
| ~ hBOOL(c_in(X4,X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f9159,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X3)),X1))
| ~ hBOOL(c_in(X4,X3,X1)) )
| ~ spl0_242
| ~ spl0_481 ),
inference(superposition,[],[f2316,f8455]) ).
fof(f41535,plain,
( spl0_991
| ~ spl0_324
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f9023,f8446,f3908,f41533]) ).
fof(f41533,plain,
( spl0_991
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X0,X4),X1),X4)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f9023,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X0,X4),X1),X4)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_324
| ~ spl0_479 ),
inference(resolution,[],[f8447,f3909]) ).
fof(f41531,plain,
( spl0_990
| ~ spl0_213
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8753,f8434,f2064,f41529]) ).
fof(f41529,plain,
( spl0_990
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f8753,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) )
| ~ spl0_213
| ~ spl0_476 ),
inference(superposition,[],[f2065,f8435]) ).
fof(f41527,plain,
( spl0_989
| ~ spl0_238
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7282,f6756,f2299,f41525]) ).
fof(f41525,plain,
( spl0_989
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f7282,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))))
| ~ spl0_238
| ~ spl0_443 ),
inference(superposition,[],[f2300,f6757]) ).
fof(f41523,plain,
( spl0_988
| ~ spl0_98
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6121,f5535,f1405,f41521]) ).
fof(f41521,plain,
( spl0_988
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X3,X2),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f6121,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X3,X2),X4),X2) )
| ~ spl0_98
| ~ spl0_405 ),
inference(superposition,[],[f1406,f5536]) ).
fof(f41519,plain,
( spl0_987
| ~ spl0_97
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6120,f5535,f1401,f41517]) ).
fof(f41517,plain,
( spl0_987
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X3,X2),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f6120,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X3,X2),X4),X2) )
| ~ spl0_97
| ~ spl0_405 ),
inference(superposition,[],[f1402,f5536]) ).
fof(f41515,plain,
( spl0_986
| ~ spl0_107
| ~ spl0_387 ),
inference(avatar_split_clause,[],[f5601,f5463,f1442,f41513]) ).
fof(f41513,plain,
( spl0_986
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f5463,plain,
( spl0_387
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f5601,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_387 ),
inference(resolution,[],[f5464,f1443]) ).
fof(f5464,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) )
| ~ spl0_387 ),
inference(avatar_component_clause,[],[f5463]) ).
fof(f41511,plain,
( spl0_985
| ~ spl0_105
| ~ spl0_387 ),
inference(avatar_split_clause,[],[f5576,f5463,f1433,f41509]) ).
fof(f41509,plain,
( spl0_985
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f5576,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_387 ),
inference(resolution,[],[f5464,f1434]) ).
fof(f41495,plain,
( spl0_984
| ~ spl0_105
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f5426,f5066,f1433,f41493]) ).
fof(f41493,plain,
( spl0_984
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(c_Orderings_Obot__class_Obot(X0),X1,X0) = hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(X0),X0),c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Obot__class_Obot(X0),X1,X0))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f5426,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(c_Orderings_Obot__class_Obot(X0),X1,X0) = hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(X0),X0),c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Obot__class_Obot(X0),X1,X0))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_384 ),
inference(resolution,[],[f5067,f1434]) ).
fof(f41491,plain,
( spl0_983
| ~ spl0_107
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5404,f5062,f1442,f41489]) ).
fof(f41489,plain,
( spl0_983
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,c_Orderings_Otop__class_Otop(X0),X0) = hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(X0),X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Otop__class_Otop(X0),X0))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f5404,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,c_Orderings_Otop__class_Otop(X0),X0) = hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(X0),X0),c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Otop__class_Otop(X0),X0))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_383 ),
inference(resolution,[],[f5063,f1443]) ).
fof(f41487,plain,
( spl0_982
| ~ spl0_237
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f5286,f5050,f2295,f41485]) ).
fof(f41485,plain,
( spl0_982
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f5286,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))))
| ~ spl0_237
| ~ spl0_380 ),
inference(forward_demodulation,[],[f5266,f411]) ).
fof(f411,axiom,
! [X0,X1,X18,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)),X18) = hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
fof(f5266,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X2,X0),X1)),X3)))
| ~ spl0_237
| ~ spl0_380 ),
inference(resolution,[],[f5051,f2296]) ).
fof(f41483,plain,
( spl0_981
| ~ spl0_238
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f5267,f5050,f2299,f41481]) ).
fof(f41481,plain,
( spl0_981
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_Set_Oinsert(X3,X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f5267,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_Set_Oinsert(X3,X0),X1))))
| ~ spl0_238
| ~ spl0_380 ),
inference(resolution,[],[f5051,f2300]) ).
fof(f41479,plain,
( spl0_980
| ~ spl0_107
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5214,f5042,f1442,f41477]) ).
fof(f41477,plain,
( spl0_980
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,X0)),X2)))
| ~ class_Orderings_Otop(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f5214,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,X0)),X2)))
| ~ class_Orderings_Otop(tc_fun(X3,X0)) )
| ~ spl0_107
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1443]) ).
fof(f41306,plain,
( spl0_979
| ~ spl0_24
| ~ spl0_237
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5204,f5042,f2295,f1077,f41304]) ).
fof(f41304,plain,
( spl0_979
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X0),X3),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f5204,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X0),X3),X1))) )
| ~ spl0_237
| ~ spl0_378 ),
inference(resolution,[],[f5043,f2296]) ).
fof(f41302,plain,
( spl0_978
| ~ spl0_105
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5191,f5042,f1433,f41300]) ).
fof(f41300,plain,
( spl0_978
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2)),hAPP(X3,X2)))
| ~ class_Orderings_Obot(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f5191,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2)),hAPP(X3,X2)))
| ~ class_Orderings_Obot(tc_fun(X1,X0)) )
| ~ spl0_105
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1434]) ).
fof(f41011,plain,
( spl0_977
| ~ spl0_244
| ~ spl0_418
| ~ spl0_976 ),
inference(avatar_split_clause,[],[f41001,f40998,f6416,f2328,f41009]) ).
fof(f41009,plain,
( spl0_977
<=> ! [X2,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)) = X2
| hBOOL(hAPP(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f40998,plain,
( spl0_976
<=> ! [X2,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),X2),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)) = X2
| hBOOL(hAPP(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f41001,plain,
( ! [X2,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)) = X2
| hBOOL(hAPP(X2,X0)) )
| ~ spl0_244
| ~ spl0_418
| ~ spl0_976 ),
inference(forward_demodulation,[],[f40999,f6505]) ).
fof(f40999,plain,
( ! [X2,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),X2),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)) = X2
| hBOOL(hAPP(X2,X0)) )
| ~ spl0_976 ),
inference(avatar_component_clause,[],[f40998]) ).
fof(f41000,plain,
( spl0_976
| ~ spl0_79
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f5000,f4405,f1311,f40998]) ).
fof(f5000,plain,
( ! [X2,X0,X1] :
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),X2),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)) = X2
| hBOOL(hAPP(X2,X0)) )
| ~ spl0_79
| ~ spl0_368 ),
inference(resolution,[],[f4406,f1312]) ).
fof(f40996,plain,
( spl0_975
| ~ spl0_167
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f4815,f4372,f1776,f40994]) ).
fof(f40994,plain,
( spl0_975
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X2))
| hAPP(c_Set_Oinsert(X1,X0),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f4815,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X2))
| hAPP(c_Set_Oinsert(X1,X0),X2) = X2 )
| ~ spl0_167
| ~ spl0_360 ),
inference(resolution,[],[f4373,f1777]) ).
fof(f40992,plain,
( spl0_974
| ~ spl0_100
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4780,f4368,f1413,f40990]) ).
fof(f40990,plain,
( spl0_974
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f4780,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_100
| ~ spl0_359 ),
inference(superposition,[],[f4369,f1414]) ).
fof(f40988,plain,
( spl0_973
| ~ spl0_79
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f4681,f4360,f1311,f40986]) ).
fof(f40986,plain,
( spl0_973
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,X3,X2))
| hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f4360,plain,
( spl0_357
<=> ! [X11,X0,X12,X5] :
( ~ hBOOL(c_in(X5,X11,X0))
| hBOOL(c_in(X5,X12,X0))
| hBOOL(c_in(X5,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f4681,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,X3,X2))
| hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1),X0)) )
| ~ spl0_79
| ~ spl0_357 ),
inference(resolution,[],[f4361,f1312]) ).
fof(f4361,plain,
( ! [X0,X11,X5,X12] :
( hBOOL(c_in(X5,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0))
| hBOOL(c_in(X5,X12,X0))
| ~ hBOOL(c_in(X5,X11,X0)) )
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f4360]) ).
fof(f40984,plain,
( spl0_972
| ~ spl0_167
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4466,f4323,f1776,f40982]) ).
fof(f40982,plain,
( spl0_972
<=> ! [X2,X0,X1] :
( hAPP(c_Set_Oinsert(X1,X2),X0) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X0),hAPP(c_Set_Oinsert(X1,X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f4466,plain,
( ! [X2,X0,X1] :
( hAPP(c_Set_Oinsert(X1,X2),X0) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X0),hAPP(c_Set_Oinsert(X1,X2),X0))) )
| ~ spl0_167
| ~ spl0_348 ),
inference(resolution,[],[f4324,f1777]) ).
fof(f40980,plain,
( spl0_971
| ~ spl0_77
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4434,f4319,f1303,f40978]) ).
fof(f40978,plain,
( spl0_971
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f1303,plain,
( spl0_77
<=> ! [X0,X3] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f4434,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_77
| ~ spl0_347 ),
inference(resolution,[],[f4320,f1304]) ).
fof(f1304,plain,
( ! [X3,X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X3),X3))
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1303]) ).
fof(f40976,plain,
( spl0_970
| ~ spl0_77
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4415,f4315,f1303,f40974]) ).
fof(f40974,plain,
( spl0_970
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f4415,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_77
| ~ spl0_346 ),
inference(resolution,[],[f4316,f1304]) ).
fof(f40972,plain,
( spl0_969
| ~ spl0_148
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3828,f3420,f1660,f40970]) ).
fof(f40970,plain,
( spl0_969
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f3828,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),X3),X4)) )
| ~ spl0_148
| ~ spl0_313 ),
inference(superposition,[],[f1661,f3421]) ).
fof(f40968,plain,
( spl0_968
| ~ spl0_70
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3616,f3376,f1273,f40966]) ).
fof(f40966,plain,
( spl0_968
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( ~ c_Finite__Set_Ofinite(X0,X4)
| ~ hBOOL(c_in(X3,X5,X6))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f3616,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Finite__Set_Ofinite(X0,X4)
| ~ hBOOL(c_in(X3,X5,X6))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool)),X4) )
| ~ spl0_70
| ~ spl0_302 ),
inference(superposition,[],[f3377,f1274]) ).
fof(f40964,plain,
( spl0_967
| ~ spl0_122
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3584,f3376,f1531,f40962]) ).
fof(f40962,plain,
( spl0_967
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_Set_Oimage(X3,X4,X5),X2,tc_fun(X5,tc_bool)),X5)
| ~ c_Finite__Set_Ofinite(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f3584,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_Set_Oimage(X3,X4,X5),X2,tc_fun(X5,tc_bool)),X5)
| ~ c_Finite__Set_Ofinite(X0,X4) )
| ~ spl0_122
| ~ spl0_302 ),
inference(resolution,[],[f3377,f1532]) ).
fof(f40960,plain,
( spl0_966
| ~ spl0_70
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39122,f31067,f1273,f40958]) ).
fof(f40958,plain,
( spl0_966
<=> ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f39122,plain,
( ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),X1)
| ~ spl0_70
| ~ spl0_728 ),
inference(superposition,[],[f1274,f31068]) ).
fof(f40956,plain,
( spl0_965
| ~ spl0_286
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3318,f3012,f2992,f40954]) ).
fof(f40954,plain,
( spl0_965
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f3318,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X0) )
| ~ spl0_286
| ~ spl0_291 ),
inference(duplicate_literal_removal,[],[f3308]) ).
fof(f3308,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X0) )
| ~ spl0_286
| ~ spl0_291 ),
inference(resolution,[],[f3013,f2993]) ).
fof(f40952,plain,
( spl0_964
| ~ spl0_286
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3301,f3008,f2992,f40950]) ).
fof(f40950,plain,
( spl0_964
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f3301,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X0) )
| ~ spl0_286
| ~ spl0_290 ),
inference(duplicate_literal_removal,[],[f3291]) ).
fof(f3291,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X0) )
| ~ spl0_286
| ~ spl0_290 ),
inference(resolution,[],[f3009,f2993]) ).
fof(f40948,plain,
( spl0_963
| ~ spl0_146
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3283,f3004,f1651,f40946]) ).
fof(f40946,plain,
( spl0_963
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f3283,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_146
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1652]) ).
fof(f40944,plain,
( spl0_962
| ~ spl0_155
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3267,f3004,f1690,f40942]) ).
fof(f40942,plain,
( spl0_962
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f3267,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)) )
| ~ spl0_155
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1691]) ).
fof(f40940,plain,
( spl0_961
| ~ spl0_146
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3257,f3000,f1651,f40938]) ).
fof(f40938,plain,
( spl0_961
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f3257,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) )
| ~ spl0_146
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1652]) ).
fof(f40936,plain,
( spl0_960
| ~ spl0_155
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3241,f3000,f1690,f40934]) ).
fof(f40934,plain,
( spl0_960
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f3241,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)) )
| ~ spl0_155
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1691]) ).
fof(f40932,plain,
( spl0_959
| ~ spl0_201
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3030,f2912,f2013,f40930]) ).
fof(f40930,plain,
( spl0_959
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( hAPP(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6) = hAPP(c_Fun_Ofun__upd(X0,X1,X5,X3,X4),X6)
| X1 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f3030,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X6) = hAPP(c_Fun_Ofun__upd(X0,X1,X5,X3,X4),X6)
| X1 = X6 )
| ~ spl0_201
| ~ spl0_267 ),
inference(superposition,[],[f2014,f2913]) ).
fof(f40928,plain,
( spl0_958
| ~ spl0_245
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2865,f2560,f2487,f40926]) ).
fof(f40926,plain,
( spl0_958
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2865,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)) = X0 )
| ~ spl0_245
| ~ spl0_261 ),
inference(resolution,[],[f2561,f2488]) ).
fof(f40924,plain,
( spl0_957
| ~ spl0_247
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2864,f2560,f2495,f40922]) ).
fof(f40922,plain,
( spl0_957
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2864,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0) = X0 )
| ~ spl0_247
| ~ spl0_261 ),
inference(resolution,[],[f2561,f2496]) ).
fof(f40920,plain,
( spl0_956
| ~ spl0_253
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2805,f2540,f2528,f40918]) ).
fof(f40918,plain,
( spl0_956
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f2805,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)) = X0 )
| ~ spl0_253
| ~ spl0_256 ),
inference(resolution,[],[f2541,f2529]) ).
fof(f40916,plain,
( spl0_955
| ~ spl0_160
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39121,f31067,f1722,f40914]) ).
fof(f40914,plain,
( spl0_955
<=> ! [X0] : c_False = c_Inductive_Ocomplete__lattice__class_Olfp(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f39121,plain,
( ! [X0] : c_False = c_Inductive_Ocomplete__lattice__class_Olfp(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool)
| ~ spl0_160
| ~ spl0_728 ),
inference(superposition,[],[f1723,f31068]) ).
fof(f40912,plain,
( spl0_954
| ~ spl0_255
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2804,f2540,f2536,f40910]) ).
fof(f40910,plain,
( spl0_954
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f2804,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)),X0) = X0 )
| ~ spl0_255
| ~ spl0_256 ),
inference(resolution,[],[f2541,f2537]) ).
fof(f40908,plain,
( spl0_953
| ~ spl0_182
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2799,f2536,f1868,f40906]) ).
fof(f40906,plain,
( spl0_953
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f2799,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) )
| ~ spl0_182
| ~ spl0_255 ),
inference(duplicate_literal_removal,[],[f2792]) ).
fof(f2792,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_255 ),
inference(resolution,[],[f2537,f1869]) ).
fof(f40904,plain,
( spl0_952
| ~ spl0_183
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2760,f2528,f1872,f40902]) ).
fof(f40902,plain,
( spl0_952
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f2760,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) )
| ~ spl0_183
| ~ spl0_253 ),
inference(duplicate_literal_removal,[],[f2750]) ).
fof(f2750,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_253 ),
inference(resolution,[],[f2529,f1873]) ).
fof(f40900,plain,
( spl0_951
| ~ spl0_182
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2759,f2528,f1868,f40898]) ).
fof(f40898,plain,
( spl0_951
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f2759,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) )
| ~ spl0_182
| ~ spl0_253 ),
inference(duplicate_literal_removal,[],[f2752]) ).
fof(f2752,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_253 ),
inference(resolution,[],[f2529,f1869]) ).
fof(f40896,plain,
( spl0_950
| ~ spl0_92
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2717,f2520,f1379,f40894]) ).
fof(f40894,plain,
( spl0_950
<=> ! [X5,X4,X2,X7,X0,X6,X3,X1] :
( hBOOL(c_in(X2,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5,X6),X7),X6))
| ~ hBOOL(c_in(X1,X7,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f2717,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(c_in(X2,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5,X6),X7),X6))
| ~ hBOOL(c_in(X1,X7,X5)) )
| ~ spl0_92
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1380]) ).
fof(f40892,plain,
( spl0_949
| ~ spl0_100
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2708,f2520,f1413,f40890]) ).
fof(f40890,plain,
( spl0_949
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),X4),X3))
| ~ hBOOL(c_in(X1,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f2708,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),X4),X3))
| ~ hBOOL(c_in(X1,X4,X2)) )
| ~ spl0_100
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1414]) ).
fof(f40888,plain,
( spl0_948
| ~ spl0_176
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2638,f2495,f1844,f40886]) ).
fof(f40886,plain,
( spl0_948
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f2638,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) )
| ~ spl0_176
| ~ spl0_247 ),
inference(duplicate_literal_removal,[],[f2623]) ).
fof(f2623,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_247 ),
inference(resolution,[],[f2496,f1845]) ).
fof(f40884,plain,
( spl0_947
| ~ spl0_177
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2607,f2487,f1848,f40882]) ).
fof(f40882,plain,
( spl0_947
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f2607,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) )
| ~ spl0_177
| ~ spl0_245 ),
inference(duplicate_literal_removal,[],[f2586]) ).
fof(f2586,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_245 ),
inference(resolution,[],[f2488,f1849]) ).
fof(f40880,plain,
( spl0_946
| ~ spl0_176
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2606,f2487,f1844,f40878]) ).
fof(f40878,plain,
( spl0_946
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f2606,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) )
| ~ spl0_176
| ~ spl0_245 ),
inference(duplicate_literal_removal,[],[f2591]) ).
fof(f2591,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_245 ),
inference(resolution,[],[f2488,f1845]) ).
fof(f40876,plain,
( spl0_945
| ~ spl0_87
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2397,f2291,f1344,f40874]) ).
fof(f40874,plain,
( spl0_945
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f2397,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1345]) ).
fof(f40872,plain,
( spl0_944
| ~ spl0_72
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39088,f31067,f1282,f40870]) ).
fof(f40870,plain,
( spl0_944
<=> ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f39088,plain,
( ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool))
| ~ spl0_72
| ~ spl0_728 ),
inference(superposition,[],[f1283,f31068]) ).
fof(f40868,plain,
( spl0_943
| ~ spl0_87
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2377,f2287,f1344,f40866]) ).
fof(f40866,plain,
( spl0_943
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f2377,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_lessequals(X0),X1))),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1345]) ).
fof(f40864,plain,
( spl0_942
| ~ spl0_87
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2333,f2271,f1344,f40862]) ).
fof(f40862,plain,
( spl0_942
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f2333,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_231 ),
inference(resolution,[],[f2272,f1345]) ).
fof(f40860,plain,
( spl0_941
| ~ spl0_87
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2332,f2267,f1344,f40858]) ).
fof(f40858,plain,
( spl0_941
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f2332,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_230 ),
inference(resolution,[],[f2268,f1345]) ).
fof(f40856,plain,
( spl0_940
| ~ spl0_87
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2331,f2263,f1344,f40854]) ).
fof(f40854,plain,
( spl0_940
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f2331,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_229 ),
inference(resolution,[],[f2264,f1345]) ).
fof(f40852,plain,
( spl0_939
| ~ spl0_87
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2323,f2255,f1344,f40850]) ).
fof(f40850,plain,
( spl0_939
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f2323,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_227 ),
inference(resolution,[],[f2256,f1345]) ).
fof(f40848,plain,
( spl0_938
| ~ spl0_87
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2322,f2247,f1344,f40846]) ).
fof(f40846,plain,
( spl0_938
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f2322,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_HOL_Oord__class_Oless(X0),X1))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_False)) )
| ~ spl0_87
| ~ spl0_225 ),
inference(resolution,[],[f2248,f1345]) ).
fof(f40844,plain,
( spl0_937
| ~ spl0_91
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2229,f2072,f1375,f40842]) ).
fof(f40842,plain,
( spl0_937
<=> ! [X4,X0,X3,X2,X1] : c_Set_Oinsert(X0,X1) = c_Fun_Ofun__upd(c_Set_Oinsert(X0,X1),hAPP(c_Set_Oinsert(X0,X1),X2),hAPP(c_Set_Oinsert(X0,X1),X2),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f2229,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oinsert(X0,X1) = c_Fun_Ofun__upd(c_Set_Oinsert(X0,X1),hAPP(c_Set_Oinsert(X0,X1),X2),hAPP(c_Set_Oinsert(X0,X1),X2),X3,X4)
| ~ spl0_91
| ~ spl0_215 ),
inference(superposition,[],[f1376,f2073]) ).
fof(f40840,plain,
( spl0_936
| ~ spl0_150
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2169,f2029,f1668,f40838]) ).
fof(f40838,plain,
( spl0_936
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f2169,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(c_COMBK(c_False,tc_bool,X1),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3))
| ~ spl0_150
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1669]) ).
fof(f40836,plain,
( spl0_935
| ~ spl0_91
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1987,f1904,f1375,f40834]) ).
fof(f40834,plain,
( spl0_935
<=> ! [X4,X0,X3,X2,X1] : c_Set_Oimage(X0,X1,X2) = c_Fun_Ofun__upd(c_Set_Oimage(X0,X1,X2),c_COMBK(c_False,tc_bool,X1),c_COMBK(c_False,tc_bool,X2),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1987,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(X0,X1,X2) = c_Fun_Ofun__upd(c_Set_Oimage(X0,X1,X2),c_COMBK(c_False,tc_bool,X1),c_COMBK(c_False,tc_bool,X2),X3,X4)
| ~ spl0_91
| ~ spl0_191 ),
inference(superposition,[],[f1376,f1905]) ).
fof(f40832,plain,
( spl0_934
| ~ spl0_87
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1833,f1800,f1344,f40830]) ).
fof(f1800,plain,
( spl0_173
<=> ! [X0,X8,X2,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_fequal(X0),X1),X0),X2))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1833,plain,
( ! [X2,X0,X1] :
( c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Finite__Set_Ofold1Set(X1,hAPP(c_fequal(X2),X0),X2)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(c_fequal(X2),X0),X2),c_False)) )
| ~ spl0_87
| ~ spl0_173 ),
inference(resolution,[],[f1801,f1345]) ).
fof(f1801,plain,
( ! [X2,X0,X1,X8] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_fequal(X0),X1),X0),X2))
| X1 = X2 )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1800]) ).
fof(f40828,plain,
( spl0_933
| ~ spl0_71
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39087,f31067,f1277,f40826]) ).
fof(f40826,plain,
( spl0_933
<=> ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f39087,plain,
( ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool,X2)
| ~ spl0_71
| ~ spl0_728 ),
inference(superposition,[],[f1278,f31068]) ).
fof(f40035,plain,
( spl0_932
| ~ spl0_47
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f39086,f31067,f1171,f40033]) ).
fof(f40033,plain,
( spl0_932
<=> ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f39086,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool),tc_bool)
| ~ spl0_47
| ~ spl0_728 ),
inference(superposition,[],[f1172,f31068]) ).
fof(f36915,plain,
( spl0_931
| ~ spl0_150
| ~ spl0_221
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f9200,f8454,f2097,f1668,f36913]) ).
fof(f36913,plain,
( spl0_931
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f9200,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2))
| ~ spl0_150
| ~ spl0_221
| ~ spl0_481 ),
inference(forward_demodulation,[],[f9140,f2098]) ).
fof(f9140,plain,
( ! [X2,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X2) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2))
| ~ spl0_150
| ~ spl0_481 ),
inference(superposition,[],[f8455,f1669]) ).
fof(f36911,plain,
( spl0_930
| ~ spl0_70
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36532,f30644,f1273,f36909]) ).
fof(f36909,plain,
( spl0_930
<=> ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f36532,plain,
( ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),X1)
| ~ spl0_70
| ~ spl0_727 ),
inference(superposition,[],[f1274,f30645]) ).
fof(f36907,plain,
( spl0_929
| ~ spl0_94
| ~ spl0_458 ),
inference(avatar_split_clause,[],[f8044,f7913,f1387,f36905]) ).
fof(f36905,plain,
( spl0_929
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ c_Finite__Set_Ofold__graph(X0,X1,X2,X3,X4,X5)
| hBOOL(c_in(X6,X2,X4))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X6,X4),X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f1387,plain,
( spl0_94
<=> ! [X10,X11,X0,X3,X8,X7] :
( c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofold__graph(X8,X10,X11,X3,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f7913,plain,
( spl0_458
<=> ! [X4,X11,X0,X3,X10,X8,X7] :
( hBOOL(c_in(X3,X11,X0))
| ~ c_Finite__Set_Ofold__graph(X8,X10,X11,X4,X0,X7)
| c_Finite__Set_Ofold__graph(X8,X10,hAPP(c_Set_Oinsert(X3,X0),X11),hAPP(hAPP(X8,X3),X4),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f8044,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Finite__Set_Ofold__graph(X0,X1,X2,X3,X4,X5)
| hBOOL(c_in(X6,X2,X4))
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X6,X4),X2),X4) )
| ~ spl0_94
| ~ spl0_458 ),
inference(resolution,[],[f7914,f1388]) ).
fof(f1388,plain,
( ! [X3,X10,X0,X11,X8,X7] :
( ~ c_Finite__Set_Ofold__graph(X8,X10,X11,X3,X0,X7)
| c_Finite__Set_Ofinite(X11,X0) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1387]) ).
fof(f7914,plain,
( ! [X3,X10,X0,X11,X8,X7,X4] :
( c_Finite__Set_Ofold__graph(X8,X10,hAPP(c_Set_Oinsert(X3,X0),X11),hAPP(hAPP(X8,X3),X4),X0,X7)
| ~ c_Finite__Set_Ofold__graph(X8,X10,X11,X4,X0,X7)
| hBOOL(c_in(X3,X11,X0)) )
| ~ spl0_458 ),
inference(avatar_component_clause,[],[f7913]) ).
fof(f36903,plain,
( spl0_928
| ~ spl0_212
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7278,f6756,f2060,f36901]) ).
fof(f36901,plain,
( spl0_928
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f7278,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(X3,X4)) )
| ~ spl0_212
| ~ spl0_443 ),
inference(superposition,[],[f2061,f6757]) ).
fof(f36899,plain,
( spl0_927
| ~ spl0_213
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7150,f6752,f2064,f36897]) ).
fof(f36897,plain,
( spl0_927
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f7150,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(X1,X4)) )
| ~ spl0_213
| ~ spl0_442 ),
inference(superposition,[],[f2065,f6753]) ).
fof(f36895,plain,
( spl0_926
| ~ spl0_105
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6294,f5555,f1433,f36893]) ).
fof(f36893,plain,
( spl0_926
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f6294,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_410 ),
inference(resolution,[],[f5556,f1434]) ).
fof(f36891,plain,
( spl0_925
| ~ spl0_107
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f6280,f5551,f1442,f36889]) ).
fof(f36889,plain,
( spl0_925
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f6280,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_409 ),
inference(resolution,[],[f5552,f1443]) ).
fof(f36887,plain,
( spl0_924
| ~ spl0_162
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f5994,f5523,f1756,f36885]) ).
fof(f36885,plain,
( spl0_924
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f5994,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X0,tc_bool)),X1),X0) )
| ~ spl0_162
| ~ spl0_402 ),
inference(superposition,[],[f1757,f5524]) ).
fof(f36883,plain,
( spl0_923
| ~ spl0_163
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f5931,f5519,f1760,f36881]) ).
fof(f36881,plain,
( spl0_923
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f5931,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2),X0) )
| ~ spl0_163
| ~ spl0_401 ),
inference(superposition,[],[f1761,f5520]) ).
fof(f36879,plain,
( spl0_922
| ~ spl0_107
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f5814,f5483,f1442,f36877]) ).
fof(f36877,plain,
( spl0_922
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f5814,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_392 ),
inference(resolution,[],[f5484,f1443]) ).
fof(f36875,plain,
( spl0_921
| ~ spl0_105
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5751,f5479,f1433,f36873]) ).
fof(f36873,plain,
( spl0_921
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X2))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f5751,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X2))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_391 ),
inference(resolution,[],[f5480,f1434]) ).
fof(f36871,plain,
( spl0_920
| ~ spl0_107
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5733,f5475,f1442,f36869]) ).
fof(f36869,plain,
( spl0_920
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f5733,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_390 ),
inference(resolution,[],[f5476,f1443]) ).
fof(f36867,plain,
( spl0_919
| ~ spl0_72
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36502,f30644,f1282,f36865]) ).
fof(f36865,plain,
( spl0_919
<=> ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f36502,plain,
( ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat))
| ~ spl0_72
| ~ spl0_727 ),
inference(superposition,[],[f1283,f30645]) ).
fof(f36863,plain,
( spl0_918
| ~ spl0_105
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5708,f5475,f1433,f36861]) ).
fof(f36861,plain,
( spl0_918
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f5708,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_390 ),
inference(resolution,[],[f5476,f1434]) ).
fof(f36859,plain,
( spl0_917
| ~ spl0_107
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5694,f5471,f1442,f36857]) ).
fof(f36857,plain,
( spl0_917
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f5694,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_389 ),
inference(resolution,[],[f5472,f1443]) ).
fof(f36855,plain,
( spl0_916
| ~ spl0_105
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5669,f5471,f1433,f36853]) ).
fof(f36853,plain,
( spl0_916
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X2))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f5669,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X2))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_389 ),
inference(resolution,[],[f5472,f1434]) ).
fof(f36851,plain,
( spl0_915
| ~ spl0_107
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f5451,f5066,f1442,f36849]) ).
fof(f36849,plain,
( spl0_915
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,c_Orderings_Otop__class_Otop(X0),X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_Orderings_Otop__class_Otop(X0),X0))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f5451,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,c_Orderings_Otop__class_Otop(X0),X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_Orderings_Otop__class_Otop(X0),X0))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_384 ),
inference(resolution,[],[f5067,f1443]) ).
fof(f36847,plain,
( spl0_914
| ~ spl0_105
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5379,f5062,f1433,f36845]) ).
fof(f36845,plain,
( spl0_914
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(c_Orderings_Obot__class_Obot(X0),X1,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(X0),X1,X0))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f5379,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(c_Orderings_Obot__class_Obot(X0),X1,X0) = hAPP(c_Set_Oinsert(X1,X0),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(X0),X1,X0))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_383 ),
inference(resolution,[],[f5063,f1434]) ).
fof(f36843,plain,
( spl0_913
| ~ spl0_199
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5224,f5046,f2005,f36841]) ).
fof(f36841,plain,
( spl0_913
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f5224,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X0),X2),X0) )
| ~ spl0_199
| ~ spl0_379 ),
inference(resolution,[],[f5047,f2006]) ).
fof(f36839,plain,
( spl0_912
| ~ spl0_187
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5223,f5046,f1888,f36837]) ).
fof(f36837,plain,
( spl0_912
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f5223,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X3,tc_Hoare__Mirabelle_Otriple(X0)),X2),X1,X0) )
| ~ spl0_187
| ~ spl0_379 ),
inference(resolution,[],[f5047,f1889]) ).
fof(f36684,plain,
( spl0_911
| ~ spl0_24
| ~ spl0_207
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5190,f5042,f2037,f1077,f36682]) ).
fof(f36682,plain,
( spl0_911
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X3)),hAPP(X0,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f5190,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X3)),hAPP(X0,X3))) )
| ~ spl0_207
| ~ spl0_378 ),
inference(resolution,[],[f5043,f2038]) ).
fof(f36680,plain,
( spl0_910
| ~ spl0_199
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5123,f5038,f2005,f36678]) ).
fof(f36678,plain,
( spl0_910
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(hAPP(X3,X0),X4)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f5123,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(hAPP(X3,X0),X4)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4) )
| ~ spl0_199
| ~ spl0_377 ),
inference(resolution,[],[f5039,f2006]) ).
fof(f36676,plain,
( spl0_909
| ~ spl0_71
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36501,f30644,f1277,f36674]) ).
fof(f36674,plain,
( spl0_909
<=> ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f36501,plain,
( ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat,X2)
| ~ spl0_71
| ~ spl0_727 ),
inference(superposition,[],[f1278,f30645]) ).
fof(f36672,plain,
( spl0_908
| ~ spl0_202
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f5092,f5026,f2017,f36670]) ).
fof(f36670,plain,
( spl0_908
<=> ! [X2,X0,X1,X3] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X1)
| c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f2017,plain,
( spl0_202
<=> ! [X11,X0,X12] :
( ~ c_Finite__Set_Ofinite(X12,X0)
| c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f5026,plain,
( spl0_374
<=> ! [X11,X0,X12,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f5092,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2),X1)
| c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X3,X1),X2),X1) )
| ~ spl0_202
| ~ spl0_374 ),
inference(resolution,[],[f5027,f2018]) ).
fof(f2018,plain,
( ! [X0,X11,X12] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)
| c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofinite(X12,X0) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2017]) ).
fof(f5027,plain,
( ! [X0,X11,X1,X12] :
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0) )
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f5026]) ).
fof(f36668,plain,
( spl0_907
| ~ spl0_150
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f5086,f5022,f1668,f36666]) ).
fof(f36666,plain,
( spl0_907
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X1)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),X2),tc_fun(X1,tc_bool)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f5022,plain,
( spl0_373
<=> ! [X11,X0,X12,X1] :
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f5086,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X1)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X0,X1),X2),tc_fun(X1,tc_bool)),X2),X1) )
| ~ spl0_150
| ~ spl0_373 ),
inference(superposition,[],[f5023,f1669]) ).
fof(f5023,plain,
( ! [X0,X11,X1,X12] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f5022]) ).
fof(f36664,plain,
( spl0_906
| ~ spl0_183
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4992,f4392,f1872,f36662]) ).
fof(f36662,plain,
( spl0_906
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f4992,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_365 ),
inference(duplicate_literal_removal,[],[f4963]) ).
fof(f4963,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_365 ),
inference(resolution,[],[f4393,f1873]) ).
fof(f36660,plain,
( spl0_905
| ~ spl0_182
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4991,f4392,f1868,f36658]) ).
fof(f36658,plain,
( spl0_905
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f4991,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_365 ),
inference(duplicate_literal_removal,[],[f4965]) ).
fof(f4965,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_365 ),
inference(resolution,[],[f4393,f1869]) ).
fof(f36656,plain,
( spl0_904
| ~ spl0_183
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4868,f4376,f1872,f36654]) ).
fof(f36654,plain,
( spl0_904
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f4868,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_361 ),
inference(duplicate_literal_removal,[],[f4843]) ).
fof(f4843,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_361 ),
inference(resolution,[],[f4377,f1873]) ).
fof(f36652,plain,
( spl0_903
| ~ spl0_182
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4867,f4376,f1868,f36650]) ).
fof(f36650,plain,
( spl0_903
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f4867,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_361 ),
inference(duplicate_literal_removal,[],[f4845]) ).
fof(f4845,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1))))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_361 ),
inference(resolution,[],[f4377,f1869]) ).
fof(f36648,plain,
( spl0_902
| ~ spl0_107
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4732,f4368,f1442,f36646]) ).
fof(f36646,plain,
( spl0_902
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(X3)))
| ~ class_Orderings_Otop(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f4732,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(X3)))
| ~ class_Orderings_Otop(X3) )
| ~ spl0_107
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1443]) ).
fof(f36644,plain,
( spl0_901
| ~ spl0_105
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4699,f4368,f1433,f36642]) ).
fof(f36642,plain,
( spl0_901
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(c_Orderings_Obot__class_Obot(X0),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X0),X2,tc_fun(X3,tc_bool)),X4))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f4699,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(c_Orderings_Obot__class_Obot(X0),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X0),X2,tc_fun(X3,tc_bool)),X4))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1434]) ).
fof(f36640,plain,
( spl0_900
| ~ spl0_23
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4689,f4364,f1072,f36638]) ).
fof(f1072,plain,
( spl0_23
<=> class_HOL_Ominus(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f4689,plain,
( ! [X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(t_a,tc_bool)),X1),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_bool),hAPP(X1,v_x))
| ~ spl0_23
| ~ spl0_358 ),
inference(resolution,[],[f4365,f1074]) ).
fof(f1074,plain,
( class_HOL_Ominus(tc_bool)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f36636,plain,
( spl0_899
| ~ spl0_10
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4688,f4364,f1007,f36634]) ).
fof(f36634,plain,
( spl0_899
<=> ! [X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(t_a,tc_nat)),X1),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_nat),hAPP(X1,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f1007,plain,
( spl0_10
<=> class_HOL_Ominus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f4688,plain,
( ! [X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(t_a,tc_nat)),X1),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),tc_nat),hAPP(X1,v_x))
| ~ spl0_10
| ~ spl0_358 ),
inference(resolution,[],[f4365,f1009]) ).
fof(f1009,plain,
( class_HOL_Ominus(tc_nat)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f1007]) ).
fof(f36631,plain,
( spl0_898
| ~ spl0_177
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4603,f4344,f1848,f36629]) ).
fof(f36629,plain,
( spl0_898
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f4603,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4581]) ).
fof(f4581,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_353 ),
inference(resolution,[],[f4345,f1849]) ).
fof(f36627,plain,
( spl0_897
| ~ spl0_176
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4602,f4344,f1844,f36625]) ).
fof(f36625,plain,
( spl0_897
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X3))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f4602,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4586]) ).
fof(f4586,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_353 ),
inference(resolution,[],[f4345,f1845]) ).
fof(f36623,plain,
( spl0_896
| ~ spl0_177
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4576,f4335,f1848,f36621]) ).
fof(f36621,plain,
( spl0_896
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f4576,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_351 ),
inference(duplicate_literal_removal,[],[f4554]) ).
fof(f4554,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X1))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_351 ),
inference(resolution,[],[f4336,f1849]) ).
fof(f36619,plain,
( spl0_895
| ~ spl0_176
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4575,f4335,f1844,f36617]) ).
fof(f36617,plain,
( spl0_895
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f4575,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_351 ),
inference(duplicate_literal_removal,[],[f4559]) ).
fof(f4559,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_351 ),
inference(resolution,[],[f4336,f1845]) ).
fof(f36615,plain,
( spl0_894
| ~ spl0_97
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f4248,f3961,f1401,f36613]) ).
fof(f36613,plain,
( spl0_894
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X0,X1),X2),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f4248,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X0,X1),X2),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X1) )
| ~ spl0_97
| ~ spl0_337 ),
inference(superposition,[],[f1402,f3962]) ).
fof(f36611,plain,
( spl0_893
| ~ spl0_264
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f3780,f3412,f2572,f36609]) ).
fof(f36609,plain,
( spl0_893
<=> ! [X2,X0,X1] :
( hAPP(c_Set_Oinsert(X1,X0),X2) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f3780,plain,
( ! [X2,X0,X1] :
( hAPP(c_Set_Oinsert(X1,X0),X2) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2)) )
| ~ spl0_264
| ~ spl0_311 ),
inference(superposition,[],[f3413,f2573]) ).
fof(f36607,plain,
( spl0_892
| ~ spl0_250
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f3778,f3412,f2516,f36605]) ).
fof(f36605,plain,
( spl0_892
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f3778,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) )
| ~ spl0_250
| ~ spl0_311 ),
inference(superposition,[],[f3413,f2517]) ).
fof(f36603,plain,
( spl0_891
| ~ spl0_264
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f3678,f3392,f2572,f36601]) ).
fof(f36601,plain,
( spl0_891
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),X2),X3))
| hBOOL(hAPP(hAPP(c_fequal(X0),X1),X3))
| hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f3678,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),X2),X3))
| hBOOL(hAPP(hAPP(c_fequal(X0),X1),X3))
| hBOOL(hAPP(X2,X3)) )
| ~ spl0_264
| ~ spl0_306 ),
inference(superposition,[],[f3393,f2573]) ).
fof(f36599,plain,
( spl0_890
| ~ spl0_235
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3664,f3388,f2287,f36597]) ).
fof(f36597,plain,
( spl0_890
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Finite__Set_Olinorder__class_OMin(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f3664,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Finite__Set_Olinorder__class_OMin(X0,X1))) )
| ~ spl0_235
| ~ spl0_305 ),
inference(duplicate_literal_removal,[],[f3650]) ).
fof(f3650,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Finite__Set_Olinorder__class_OMin(X0,X1)))
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_235
| ~ spl0_305 ),
inference(resolution,[],[f3389,f2288]) ).
fof(f36595,plain,
( spl0_889
| ~ spl0_235
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3643,f3384,f2287,f36593]) ).
fof(f36593,plain,
( spl0_889
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Finite__Set_Olinorder__class_OMax(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f3643,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Finite__Set_Olinorder__class_OMax(X0,X1)),X2)) )
| ~ spl0_235
| ~ spl0_304 ),
inference(duplicate_literal_removal,[],[f3630]) ).
fof(f3630,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Finite__Set_Olinorder__class_OMax(X0,X1)),X2))
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_235
| ~ spl0_304 ),
inference(resolution,[],[f3385,f2288]) ).
fof(f36591,plain,
( spl0_888
| ~ spl0_47
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f36500,f30644,f1171,f36589]) ).
fof(f36589,plain,
( spl0_888
<=> ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f36500,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat)
| ~ spl0_47
| ~ spl0_727 ),
inference(superposition,[],[f1172,f30645]) ).
fof(f36587,plain,
( spl0_887
| ~ spl0_97
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3582,f3376,f1401,f36585]) ).
fof(f36585,plain,
( spl0_887
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_Set_Oinsert(X3,X4),X2,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f3582,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_Set_Oinsert(X3,X4),X2,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X0,X4) )
| ~ spl0_97
| ~ spl0_302 ),
inference(resolution,[],[f3377,f1402]) ).
fof(f36579,plain,
( spl0_885
| spl0_886
| ~ spl0_70
| ~ spl0_165
| ~ spl0_185
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3105,f2920,f1880,f1768,f1273,f36577,f36574]) ).
fof(f36574,plain,
( spl0_885
<=> ! [X5,X3,X0,X6,X2,X1] : ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f36577,plain,
( spl0_886
<=> ! [X4] : v_x = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f3105,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( v_x = X4
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_70
| ~ spl0_165
| ~ spl0_185
| ~ spl0_269 ),
inference(trivial_inequality_removal,[],[f3104]) ).
fof(f3104,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( X0 != X0
| v_x = X4
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_70
| ~ spl0_165
| ~ spl0_185
| ~ spl0_269 ),
inference(forward_demodulation,[],[f3103,f1274]) ).
fof(f3103,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_COMBK(X0,X1,X2),hAPP(X3,X4)) != X0
| v_x = X4
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_165
| ~ spl0_185
| ~ spl0_269 ),
inference(forward_demodulation,[],[f3061,f1881]) ).
fof(f3061,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4) != X0
| v_x = X4
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_165
| ~ spl0_269 ),
inference(superposition,[],[f2921,f1769]) ).
fof(f36572,plain,
( spl0_884
| spl0_630
| ~ spl0_239
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3097,f2920,f2303,f14664,f36570]) ).
fof(f36570,plain,
( spl0_884
<=> ! [X4,X0,X3] : ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f14664,plain,
( spl0_630
<=> ! [X4,X3] : X3 = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f3097,plain,
( ! [X2,X3,X0,X1,X4] :
( X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_239
| ~ spl0_269 ),
inference(trivial_inequality_removal,[],[f3096]) ).
fof(f3096,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_239
| ~ spl0_269 ),
inference(forward_demodulation,[],[f3043,f2304]) ).
fof(f3043,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2)
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_239
| ~ spl0_269 ),
inference(superposition,[],[f2921,f2304]) ).
fof(f36568,plain,
( spl0_883
| ~ spl0_235
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2867,f2560,f2287,f36566]) ).
fof(f36566,plain,
( spl0_883
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f2867,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0))
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_235
| ~ spl0_261 ),
inference(resolution,[],[f2561,f2288]) ).
fof(f36564,plain,
( spl0_882
| ~ spl0_236
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2866,f2560,f2291,f36562]) ).
fof(f36562,plain,
( spl0_882
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0))
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f2866,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0))
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_236
| ~ spl0_261 ),
inference(resolution,[],[f2561,f2292]) ).
fof(f36560,plain,
( spl0_881
| ~ spl0_175
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2841,f2552,f1839,f36558]) ).
fof(f36558,plain,
( spl0_881
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X0),X1))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f2841,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X0),X1))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) )
| ~ spl0_175
| ~ spl0_259 ),
inference(resolution,[],[f2553,f1840]) ).
fof(f36556,plain,
( spl0_880
| ~ spl0_176
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2840,f2552,f1844,f36554]) ).
fof(f36554,plain,
( spl0_880
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X0),X1))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f2840,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X0),X1))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) )
| ~ spl0_176
| ~ spl0_259 ),
inference(resolution,[],[f2553,f1845]) ).
fof(f36552,plain,
( spl0_879
| ~ spl0_174
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2836,f2552,f1835,f36550]) ).
fof(f36550,plain,
( spl0_879
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X0),X3),X1))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f2836,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X0),X3),X1))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) )
| ~ spl0_174
| ~ spl0_259 ),
inference(resolution,[],[f2553,f1836]) ).
fof(f36496,plain,
( spl0_878
| ~ spl0_177
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2835,f2552,f1848,f36494]) ).
fof(f36494,plain,
( spl0_878
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X0),X3),X1))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f2835,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X0),X3),X1))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) )
| ~ spl0_177
| ~ spl0_259 ),
inference(resolution,[],[f2553,f1849]) ).
fof(f36492,plain,
( spl0_877
| ~ spl0_235
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2809,f2540,f2287,f36490]) ).
fof(f36490,plain,
( spl0_877
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f2809,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)))
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_235
| ~ spl0_256 ),
inference(resolution,[],[f2541,f2288]) ).
fof(f36488,plain,
( spl0_876
| ~ spl0_236
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2808,f2540,f2291,f36486]) ).
fof(f36486,plain,
( spl0_876
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)))
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f2808,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)))
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_236
| ~ spl0_256 ),
inference(resolution,[],[f2541,f2292]) ).
fof(f36484,plain,
( spl0_875
| ~ spl0_234
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2788,f2536,f2283,f36482]) ).
fof(f36482,plain,
( spl0_875
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f2788,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_255 ),
inference(resolution,[],[f2537,f2284]) ).
fof(f36480,plain,
( spl0_874
| ~ spl0_243
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2786,f2536,f2319,f36478]) ).
fof(f36478,plain,
( spl0_874
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f2786,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_255 ),
inference(resolution,[],[f2537,f2320]) ).
fof(f36476,plain,
( spl0_873
| ~ spl0_234
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2748,f2528,f2283,f36474]) ).
fof(f36474,plain,
( spl0_873
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f2748,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_253 ),
inference(resolution,[],[f2529,f2284]) ).
fof(f36472,plain,
( spl0_872
| ~ spl0_243
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2746,f2528,f2319,f36470]) ).
fof(f36470,plain,
( spl0_872
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2746,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_253 ),
inference(resolution,[],[f2529,f2320]) ).
fof(f36468,plain,
( spl0_871
| ~ spl0_234
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2627,f2495,f2283,f36466]) ).
fof(f36466,plain,
( spl0_871
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2627,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_247 ),
inference(resolution,[],[f2496,f2284]) ).
fof(f36464,plain,
( spl0_870
| ~ spl0_243
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2625,f2495,f2319,f36462]) ).
fof(f36462,plain,
( spl0_870
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2625,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_247 ),
inference(resolution,[],[f2496,f2320]) ).
fof(f36460,plain,
( spl0_869
| ~ spl0_234
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2595,f2487,f2283,f36458]) ).
fof(f36458,plain,
( spl0_869
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f2595,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_234
| ~ spl0_245 ),
inference(resolution,[],[f2488,f2284]) ).
fof(f36391,plain,
( spl0_868
| ~ spl0_243
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2593,f2487,f2319,f36389]) ).
fof(f36389,plain,
( spl0_868
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2593,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243
| ~ spl0_245 ),
inference(resolution,[],[f2488,f2320]) ).
fof(f36387,plain,
( spl0_867
| ~ spl0_199
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2474,f2319,f2005,f36385]) ).
fof(f36385,plain,
( spl0_867
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2474,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_199
| ~ spl0_243 ),
inference(resolution,[],[f2320,f2006]) ).
fof(f36383,plain,
( spl0_866
| ~ spl0_187
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2473,f2319,f1888,f36381]) ).
fof(f36381,plain,
( spl0_866
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2473,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X0) )
| ~ spl0_187
| ~ spl0_243 ),
inference(resolution,[],[f2320,f1889]) ).
fof(f36379,plain,
( spl0_865
| ~ spl0_199
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2345,f2283,f2005,f36377]) ).
fof(f36377,plain,
( spl0_865
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f2345,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_199
| ~ spl0_234 ),
inference(resolution,[],[f2284,f2006]) ).
fof(f36375,plain,
( spl0_864
| ~ spl0_187
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2344,f2283,f1888,f36373]) ).
fof(f36373,plain,
( spl0_864
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f2344,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X2),X1))
| ~ class_Orderings_Olinorder(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X0) )
| ~ spl0_187
| ~ spl0_234 ),
inference(resolution,[],[f2284,f1889]) ).
fof(f36371,plain,
( spl0_863
| ~ spl0_36
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2187,f2041,f1127,f36369]) ).
fof(f36369,plain,
( spl0_863
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X3),X2)
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f2041,plain,
( spl0_208
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f2187,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X3),X2)
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_36
| ~ spl0_208 ),
inference(resolution,[],[f2042,f1128]) ).
fof(f2042,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f2041]) ).
fof(f36367,plain,
( spl0_862
| ~ spl0_87
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2180,f2033,f1344,f36365]) ).
fof(f36365,plain,
( spl0_862
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(X0,c_False),X4))
| hBOOL(hAPP(hAPP(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_COMBC(X0,X1,X2,X3),X4))),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f2180,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(X0,c_False),X4))
| hBOOL(hAPP(hAPP(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_COMBC(X0,X1,X2,X3),X4))),X4)) )
| ~ spl0_87
| ~ spl0_206 ),
inference(forward_demodulation,[],[f2176,f2034]) ).
fof(f2176,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(X0,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_COMBC(X0,X1,X2,X3),X4))),X4))
| ~ hBOOL(hAPP(hAPP(c_COMBC(X0,X1,X2,X3),X4),c_False)) )
| ~ spl0_87
| ~ spl0_206 ),
inference(superposition,[],[f1345,f2034]) ).
fof(f36363,plain,
( spl0_861
| ~ spl0_86
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2179,f2033,f1340,f36361]) ).
fof(f36361,plain,
( spl0_861
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X0,c_False),X4))
| ~ hBOOL(hAPP(hAPP(X0,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_COMBC(X0,X1,X2,X3),X4))),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f2179,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(X0,c_False),X4))
| ~ hBOOL(hAPP(hAPP(X0,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_COMBC(X0,X1,X2,X3),X4))),X4)) )
| ~ spl0_86
| ~ spl0_206 ),
inference(forward_demodulation,[],[f2175,f2034]) ).
fof(f2175,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(X0,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_COMBC(X0,X1,X2,X3),X4))),X4))
| hBOOL(hAPP(hAPP(c_COMBC(X0,X1,X2,X3),X4),c_False)) )
| ~ spl0_86
| ~ spl0_206 ),
inference(superposition,[],[f1341,f2034]) ).
fof(f36359,plain,
( spl0_860
| ~ spl0_191
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2167,f2029,f1904,f36357]) ).
fof(f36357,plain,
( spl0_860
<=> ! [X4,X0,X3,X2,X1] : hBOOL(c_in(c_COMBK(c_False,tc_bool,X2),hAPP(c_Set_Oimage(c_Set_Oimage(X0,X1,X2),X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f2167,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(c_in(c_COMBK(c_False,tc_bool,X2),hAPP(c_Set_Oimage(c_Set_Oimage(X0,X1,X2),X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))),X4))
| ~ spl0_191
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1905]) ).
fof(f36355,plain,
( spl0_859
| ~ spl0_37
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2152,f2021,f1131,f36353]) ).
fof(f36353,plain,
( spl0_859
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X3),X2)
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f1131,plain,
( spl0_37
<=> ! [X80,X79] :
( ~ class_Lattices_Olattice(X80)
| class_Lattices_Olower__semilattice(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f2021,plain,
( spl0_203
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2152,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X3),X2)
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_37
| ~ spl0_203 ),
inference(resolution,[],[f2022,f1132]) ).
fof(f1132,plain,
( ! [X80,X79] :
( class_Lattices_Olower__semilattice(tc_fun(X79,X80))
| ~ class_Lattices_Olattice(X80) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f2022,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2021]) ).
fof(f36350,plain,
( spl0_858
| ~ spl0_41
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2118,f1993,f1147,f36348]) ).
fof(f36348,plain,
( spl0_858
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f1993,plain,
( spl0_196
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2118,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_41
| ~ spl0_196 ),
inference(resolution,[],[f1994,f1148]) ).
fof(f1994,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)) = X3 )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f1993]) ).
fof(f36346,plain,
( spl0_857
| ~ spl0_41
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2115,f1989,f1147,f36344]) ).
fof(f36344,plain,
( spl0_857
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1989,plain,
( spl0_195
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2115,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_41
| ~ spl0_195 ),
inference(resolution,[],[f1990,f1148]) ).
fof(f1990,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)) = X3 )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f1989]) ).
fof(f36342,plain,
( spl0_856
| ~ spl0_91
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1745,f1672,f1375,f36340]) ).
fof(f36340,plain,
( spl0_856
<=> ! [X0,X3,X2,X1] : c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)) = c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1),X0,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f1745,plain,
( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)) = c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1),X0,X2,X3)
| ~ spl0_91
| ~ spl0_151 ),
inference(superposition,[],[f1376,f1673]) ).
fof(f36338,plain,
( spl0_855
| ~ spl0_91
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1739,f1668,f1375,f36336]) ).
fof(f36336,plain,
( spl0_855
<=> ! [X0,X3,X2,X1] : c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)) = c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X0,c_COMBK(c_False,tc_bool,X1),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f1739,plain,
( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)) = c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X0,c_COMBK(c_False,tc_bool,X1),X2,X3)
| ~ spl0_91
| ~ spl0_150 ),
inference(superposition,[],[f1376,f1669]) ).
fof(f34864,plain,
( spl0_854
| ~ spl0_70
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33268,f30221,f1273,f34862]) ).
fof(f34862,plain,
( spl0_854
<=> ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f33268,plain,
( ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),X1)
| ~ spl0_70
| ~ spl0_726 ),
inference(superposition,[],[f1274,f30222]) ).
fof(f34326,plain,
( spl0_853
| ~ spl0_160
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33267,f30221,f1722,f34324]) ).
fof(f34324,plain,
( spl0_853
<=> ! [X0] : c_False = c_Inductive_Ocomplete__lattice__class_Olfp(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f33267,plain,
( ! [X0] : c_False = c_Inductive_Ocomplete__lattice__class_Olfp(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool)
| ~ spl0_160
| ~ spl0_726 ),
inference(superposition,[],[f1723,f30222]) ).
fof(f34292,plain,
( spl0_852
| ~ spl0_72
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33240,f30221,f1282,f34290]) ).
fof(f34290,plain,
( spl0_852
<=> ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f33240,plain,
( ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool))
| ~ spl0_72
| ~ spl0_726 ),
inference(superposition,[],[f1283,f30222]) ).
fof(f33978,plain,
( spl0_851
| ~ spl0_71
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33239,f30221,f1277,f33976]) ).
fof(f33976,plain,
( spl0_851
<=> ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f33239,plain,
( ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool,X2)
| ~ spl0_71
| ~ spl0_726 ),
inference(superposition,[],[f1278,f30222]) ).
fof(f33348,plain,
( spl0_850
| ~ spl0_163
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8751,f8434,f1760,f33346]) ).
fof(f33346,plain,
( spl0_850
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(hAPP(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f8751,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X2,X4),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(hAPP(X1,X2),X0) )
| ~ spl0_163
| ~ spl0_476 ),
inference(superposition,[],[f1761,f8435]) ).
fof(f33344,plain,
( spl0_849
| ~ spl0_92
| ~ spl0_448 ),
inference(avatar_split_clause,[],[f7543,f7480,f1379,f33342]) ).
fof(f33342,plain,
( spl0_849
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( hAPP(c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X5,X6,X3,X4),X1,X2,X3,X4),X5) = X6
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f7480,plain,
( spl0_448
<=> ! [X2,X6,X23,X7,X0,X5,X1] :
( X1 = X5
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X23,X1,X2,X0,X7),X5,X6,X0,X7) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X23,X5,X6,X0,X7),X1,X2,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f7543,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X5,X6,X3,X4),X1,X2,X3,X4),X5) = X6
| X1 = X5 )
| ~ spl0_92
| ~ spl0_448 ),
inference(superposition,[],[f1380,f7481]) ).
fof(f7481,plain,
( ! [X2,X0,X1,X6,X7,X5,X23] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X23,X1,X2,X0,X7),X5,X6,X0,X7) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X23,X5,X6,X0,X7),X1,X2,X0,X7)
| X1 = X5 )
| ~ spl0_448 ),
inference(avatar_component_clause,[],[f7480]) ).
fof(f33340,plain,
( spl0_848
| ~ spl0_165
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f6168,f5539,f1768,f33338]) ).
fof(f33338,plain,
( spl0_848
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,X5),X4,X5,X1,t_a),v_x) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f6168,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,X5),X4,X5,X1,t_a),v_x) = X0
| ~ spl0_165
| ~ spl0_406 ),
inference(superposition,[],[f1769,f5540]) ).
fof(f33336,plain,
( spl0_847
| ~ spl0_187
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5310,f5058,f1888,f33334]) ).
fof(f33334,plain,
( spl0_847
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(X3,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X3,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f5310,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(X3,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X3,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),X4) )
| ~ spl0_187
| ~ spl0_382 ),
inference(resolution,[],[f5059,f1889]) ).
fof(f33332,plain,
( spl0_846
| ~ spl0_187
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5122,f5038,f1888,f33330]) ).
fof(f33330,plain,
( spl0_846
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),hAPP(X3,X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f5122,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),hAPP(X3,X0),X4) )
| ~ spl0_187
| ~ spl0_377 ),
inference(resolution,[],[f5039,f1889]) ).
fof(f33328,plain,
( spl0_845
| ~ spl0_272
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5116,f5038,f2936,f33326]) ).
fof(f33326,plain,
( spl0_845
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_Set_Oinsert(X3,X4),X2,tc_fun(X4,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f5116,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_Set_Oinsert(X3,X4),X2,tc_fun(X4,tc_bool)),X4)) )
| ~ spl0_272
| ~ spl0_377 ),
inference(resolution,[],[f5039,f2937]) ).
fof(f33324,plain,
( spl0_844
| ~ spl0_47
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f33238,f30221,f1171,f33322]) ).
fof(f33322,plain,
( spl0_844
<=> ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f33238,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool),tc_bool)
| ~ spl0_47
| ~ spl0_726 ),
inference(superposition,[],[f1172,f30222]) ).
fof(f33320,plain,
( spl0_843
| ~ spl0_146
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f4825,f4372,f1651,f33318]) ).
fof(f33318,plain,
( spl0_843
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f4825,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_146
| ~ spl0_360 ),
inference(resolution,[],[f4373,f1652]) ).
fof(f33316,plain,
( spl0_842
| ~ spl0_84
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4695,f4368,f1332,f33314]) ).
fof(f33314,plain,
( spl0_842
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X0))
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f1332,plain,
( spl0_84
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f4695,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X0))
| ~ class_Orderings_Oorder(X3) )
| ~ spl0_84
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1333]) ).
fof(f1333,plain,
( ! [X3,X0] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3))
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1332]) ).
fof(f33312,plain,
( spl0_841
| ~ spl0_85
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4694,f4368,f1336,f33310]) ).
fof(f33310,plain,
( spl0_841
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X0))
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f1336,plain,
( spl0_85
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f4694,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X0))
| ~ class_Orderings_Opreorder(X3) )
| ~ spl0_85
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1337]) ).
fof(f1337,plain,
( ! [X3,X0] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1336]) ).
fof(f33308,plain,
( spl0_840
| ~ spl0_83
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4693,f4368,f1328,f33306]) ).
fof(f33306,plain,
( spl0_840
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f4693,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),X0)) )
| ~ spl0_83
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1329]) ).
fof(f33304,plain,
( spl0_839
| ~ spl0_146
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4476,f4323,f1651,f33302]) ).
fof(f33302,plain,
( spl0_839
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f4476,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))) )
| ~ spl0_146
| ~ spl0_348 ),
inference(resolution,[],[f4324,f1652]) ).
fof(f33300,plain,
( spl0_838
| ~ spl0_155
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4457,f4323,f1690,f33298]) ).
fof(f33298,plain,
( spl0_838
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f4457,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X1)) )
| ~ spl0_155
| ~ spl0_348 ),
inference(resolution,[],[f4324,f1691]) ).
fof(f33296,plain,
( spl0_837
| ~ spl0_12
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f4275,f3969,f1017,f33294]) ).
fof(f33294,plain,
( spl0_837
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_Set_Oinsert(X0,tc_bool),hAPP(c_fequal(tc_bool),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f1017,plain,
( spl0_12
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f3969,plain,
( spl0_339
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f4275,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_Set_Oinsert(X0,tc_bool),hAPP(c_fequal(tc_bool),X1)))
| ~ spl0_12
| ~ spl0_339 ),
inference(resolution,[],[f3970,f1019]) ).
fof(f1019,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f3970,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2))) )
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f3969]) ).
fof(f33292,plain,
( spl0_836
| ~ spl0_12
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4273,f3965,f1017,f33290]) ).
fof(f33290,plain,
( spl0_836
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Set_Oinsert(X0,tc_bool),hAPP(c_fequal(tc_bool),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f3965,plain,
( spl0_338
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f4273,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Set_Oinsert(X0,tc_bool),hAPP(c_fequal(tc_bool),X1)))
| ~ spl0_12
| ~ spl0_338 ),
inference(resolution,[],[f3966,f1019]) ).
fof(f3966,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2))) )
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f3965]) ).
fof(f33288,plain,
( spl0_835
| ~ spl0_13
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4127,f3932,f1022,f33286]) ).
fof(f33286,plain,
( spl0_835
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f1022,plain,
( spl0_13
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f4127,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1))
| ~ spl0_13
| ~ spl0_330 ),
inference(resolution,[],[f3933,f1024]) ).
fof(f1024,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f33284,plain,
( spl0_834
| ~ spl0_2
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4126,f3932,f967,f33282]) ).
fof(f33282,plain,
( spl0_834
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f4126,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1))
| ~ spl0_2
| ~ spl0_330 ),
inference(resolution,[],[f3933,f969]) ).
fof(f969,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f967]) ).
fof(f33234,plain,
( spl0_833
| ~ spl0_12
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f4124,f3928,f1017,f33232]) ).
fof(f33232,plain,
( spl0_833
<=> ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_Set_Oinsert(X0,tc_bool),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f3928,plain,
( spl0_329
<=> ! [X0,X11,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f4124,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_Set_Oinsert(X0,tc_bool),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),X1))
| ~ spl0_12
| ~ spl0_329 ),
inference(resolution,[],[f3929,f1019]) ).
fof(f3929,plain,
( ! [X0,X11,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X11)) )
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f3928]) ).
fof(f33230,plain,
( spl0_832
| ~ spl0_107
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4051,f3920,f1442,f33228]) ).
fof(f33228,plain,
( spl0_832
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2))
| ~ class_HOL_Oord(X1)
| ~ class_Orderings_Otop(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f4051,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2))
| ~ class_HOL_Oord(X1)
| ~ class_Orderings_Otop(tc_fun(X0,X1)) )
| ~ spl0_107
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1443]) ).
fof(f33190,plain,
( ~ spl0_24
| spl0_831
| ~ spl0_237
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4044,f3920,f2295,f33188,f1077]) ).
fof(f33188,plain,
( spl0_831
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f4044,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_237
| ~ spl0_327 ),
inference(resolution,[],[f3921,f2296]) ).
fof(f33186,plain,
( spl0_830
| ~ spl0_105
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4033,f3920,f1433,f33184]) ).
fof(f33184,plain,
( spl0_830
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))))
| ~ class_HOL_Oord(X1)
| ~ class_Orderings_Obot(tc_fun(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f4033,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))))
| ~ class_HOL_Oord(X1)
| ~ class_Orderings_Obot(tc_fun(X0,X1)) )
| ~ spl0_105
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1434]) ).
fof(f33182,plain,
( spl0_829
| ~ spl0_12
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f4025,f3916,f1017,f33180]) ).
fof(f3916,plain,
( spl0_326
<=> ! [X0,X11,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f4025,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Set_Oinsert(X0,tc_bool),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X1))
| ~ spl0_12
| ~ spl0_326 ),
inference(resolution,[],[f3917,f1019]) ).
fof(f3917,plain,
( ! [X0,X11,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X11)) )
| ~ spl0_326 ),
inference(avatar_component_clause,[],[f3916]) ).
fof(f33178,plain,
( spl0_828
| ~ spl0_19
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f3999,f3900,f1052,f33176]) ).
fof(f33176,plain,
( spl0_828
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f3999,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1))
| ~ spl0_19
| ~ spl0_322 ),
inference(resolution,[],[f3901,f1054]) ).
fof(f33174,plain,
( spl0_827
| ~ spl0_7
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f3998,f3900,f992,f33172]) ).
fof(f33172,plain,
( spl0_827
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f3998,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1))
| ~ spl0_7
| ~ spl0_322 ),
inference(resolution,[],[f3901,f994]) ).
fof(f33170,plain,
( spl0_826
| ~ spl0_82
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f3869,f3439,f1324,f33168]) ).
fof(f33168,plain,
( spl0_826
<=> ! [X4,X0,X3,X2,X1] : hAPP(c_fequal(X1),X0) = hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X2,X1),hAPP(c_Set_Oinsert(X3,X2),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f1324,plain,
( spl0_82
<=> ! [X0,X12,X3] : hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X3,X0),X12),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f3439,plain,
( spl0_317
<=> ! [X11,X0,X5,X3,X7] :
( hAPP(c_Set_Oimage(c_COMBK(X5,X7,X0),X0,X7),X11) = hAPP(c_fequal(X7),X5)
| ~ hBOOL(c_in(X3,X11,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f3869,plain,
( ! [X2,X3,X0,X1,X4] : hAPP(c_fequal(X1),X0) = hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X2,X1),hAPP(c_Set_Oinsert(X3,X2),X4))
| ~ spl0_82
| ~ spl0_317 ),
inference(resolution,[],[f3440,f1325]) ).
fof(f1325,plain,
( ! [X3,X0,X12] : hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X3,X0),X12),X0))
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1324]) ).
fof(f3440,plain,
( ! [X3,X0,X11,X7,X5] :
( ~ hBOOL(c_in(X3,X11,X0))
| hAPP(c_Set_Oimage(c_COMBK(X5,X7,X0),X0,X7),X11) = hAPP(c_fequal(X7),X5) )
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f3439]) ).
fof(f33166,plain,
( spl0_825
| ~ spl0_80
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f3868,f3439,f1315,f33164]) ).
fof(f33164,plain,
( spl0_825
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_fequal(X1),X0) = hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X2,X1),X3)
| ~ hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f3868,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(c_fequal(X1),X0) = hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X2,X1),X3)
| ~ hBOOL(hAPP(X3,X4)) )
| ~ spl0_80
| ~ spl0_317 ),
inference(resolution,[],[f3440,f1316]) ).
fof(f33114,plain,
( spl0_824
| ~ spl0_98
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3826,f3420,f1405,f33112]) ).
fof(f33112,plain,
( spl0_824
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X1),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f3826,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X1),X3),X1) )
| ~ spl0_98
| ~ spl0_313 ),
inference(superposition,[],[f1406,f3421]) ).
fof(f33110,plain,
( spl0_823
| ~ spl0_97
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3825,f3420,f1401,f33108]) ).
fof(f33108,plain,
( spl0_823
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X1),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f3825,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X1),X3),X1) )
| ~ spl0_97
| ~ spl0_313 ),
inference(superposition,[],[f1402,f3421]) ).
fof(f33106,plain,
( spl0_822
| ~ spl0_169
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f3782,f3412,f1784,f33104]) ).
fof(f33104,plain,
( spl0_822
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f3782,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0))) )
| ~ spl0_169
| ~ spl0_311 ),
inference(superposition,[],[f3413,f1785]) ).
fof(f33102,plain,
( spl0_821
| ~ spl0_239
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f3777,f3412,f2303,f33100]) ).
fof(f33100,plain,
( spl0_821
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f3777,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1)) )
| ~ spl0_239
| ~ spl0_311 ),
inference(superposition,[],[f3413,f2304]) ).
fof(f33098,plain,
( spl0_820
| ~ spl0_167
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3761,f3408,f1776,f33096]) ).
fof(f33096,plain,
( spl0_820
<=> ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X1,X0),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f3761,plain,
( ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X1,X0),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X2)
| ~ spl0_167
| ~ spl0_310 ),
inference(resolution,[],[f3409,f1777]) ).
fof(f33094,plain,
( spl0_819
| ~ spl0_167
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3728,f3404,f1776,f33092]) ).
fof(f33092,plain,
( spl0_819
<=> ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X2,X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f3728,plain,
( ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X2,X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),X1))
| ~ spl0_167
| ~ spl0_309 ),
inference(resolution,[],[f3405,f1777]) ).
fof(f33090,plain,
( spl0_818
| ~ spl0_229
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3317,f3012,f2263,f33088]) ).
fof(f33088,plain,
( spl0_818
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f3317,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) )
| ~ spl0_229
| ~ spl0_291 ),
inference(duplicate_literal_removal,[],[f3311]) ).
fof(f3311,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) )
| ~ spl0_229
| ~ spl0_291 ),
inference(resolution,[],[f3013,f2264]) ).
fof(f33086,plain,
( spl0_817
| ~ spl0_225
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3316,f3012,f2247,f33084]) ).
fof(f33084,plain,
( spl0_817
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f3316,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) )
| ~ spl0_225
| ~ spl0_291 ),
inference(duplicate_literal_removal,[],[f3313]) ).
fof(f3313,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) )
| ~ spl0_225
| ~ spl0_291 ),
inference(resolution,[],[f3013,f2248]) ).
fof(f33082,plain,
( spl0_816
| ~ spl0_229
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3300,f3008,f2263,f33080]) ).
fof(f33080,plain,
( spl0_816
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f3300,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) )
| ~ spl0_229
| ~ spl0_290 ),
inference(duplicate_literal_removal,[],[f3294]) ).
fof(f3294,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) )
| ~ spl0_229
| ~ spl0_290 ),
inference(resolution,[],[f3009,f2264]) ).
fof(f33078,plain,
( spl0_815
| ~ spl0_225
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3299,f3008,f2247,f33076]) ).
fof(f33076,plain,
( spl0_815
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f3299,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) )
| ~ spl0_225
| ~ spl0_290 ),
inference(duplicate_literal_removal,[],[f3296]) ).
fof(f3296,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) )
| ~ spl0_225
| ~ spl0_290 ),
inference(resolution,[],[f3009,f2248]) ).
fof(f33062,plain,
( spl0_814
| ~ spl0_181
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3278,f3004,f1864,f33060]) ).
fof(f33060,plain,
( spl0_814
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f3278,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1865]) ).
fof(f33058,plain,
( spl0_813
| ~ spl0_182
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3277,f3004,f1868,f33056]) ).
fof(f33056,plain,
( spl0_813
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f3277,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1869]) ).
fof(f33054,plain,
( spl0_812
| ~ spl0_180
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3276,f3004,f1860,f33052]) ).
fof(f33052,plain,
( spl0_812
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f3276,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1861]) ).
fof(f33050,plain,
( spl0_811
| ~ spl0_183
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3275,f3004,f1872,f33048]) ).
fof(f33048,plain,
( spl0_811
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f3275,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1873]) ).
fof(f33046,plain,
( spl0_810
| ~ spl0_175
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3269,f3004,f1839,f33044]) ).
fof(f33044,plain,
( spl0_810
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f3269,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1840]) ).
fof(f33042,plain,
( spl0_809
| ~ spl0_176
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3268,f3004,f1844,f33040]) ).
fof(f33040,plain,
( spl0_809
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f3268,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1845]) ).
fof(f33038,plain,
( spl0_808
| ~ spl0_174
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3264,f3004,f1835,f33036]) ).
fof(f33036,plain,
( spl0_808
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f3264,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1836]) ).
fof(f33034,plain,
( spl0_807
| ~ spl0_177
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3263,f3004,f1848,f33032]) ).
fof(f33032,plain,
( spl0_807
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f3263,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1849]) ).
fof(f33030,plain,
( spl0_806
| ~ spl0_181
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3252,f3000,f1864,f33028]) ).
fof(f33028,plain,
( spl0_806
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f3252,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1865]) ).
fof(f33026,plain,
( spl0_805
| ~ spl0_182
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3251,f3000,f1868,f33024]) ).
fof(f33024,plain,
( spl0_805
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f3251,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1869]) ).
fof(f33016,plain,
( spl0_804
| ~ spl0_180
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3250,f3000,f1860,f33014]) ).
fof(f33014,plain,
( spl0_804
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f3250,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1861]) ).
fof(f33012,plain,
( spl0_803
| ~ spl0_183
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3249,f3000,f1872,f33010]) ).
fof(f33010,plain,
( spl0_803
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f3249,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1873]) ).
fof(f33008,plain,
( spl0_802
| ~ spl0_175
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3243,f3000,f1839,f33006]) ).
fof(f33006,plain,
( spl0_802
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f3243,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1840]) ).
fof(f33004,plain,
( spl0_801
| ~ spl0_176
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3242,f3000,f1844,f33002]) ).
fof(f33002,plain,
( spl0_801
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f3242,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1845]) ).
fof(f33000,plain,
( spl0_800
| ~ spl0_174
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3238,f3000,f1835,f32998]) ).
fof(f32998,plain,
( spl0_800
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f3238,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1836]) ).
fof(f32996,plain,
( spl0_799
| ~ spl0_177
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3237,f3000,f1848,f32994]) ).
fof(f32994,plain,
( spl0_799
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f3237,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1849]) ).
fof(f32991,plain,
( spl0_798
| spl0_630
| ~ spl0_221
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3102,f2920,f2097,f14664,f32989]) ).
fof(f32989,plain,
( spl0_798
<=> ! [X4,X0,X3] : ~ c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f3102,plain,
( ! [X2,X3,X0,X1,X4] :
( X1 = X2
| ~ c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_221
| ~ spl0_269 ),
inference(trivial_inequality_removal,[],[f3101]) ).
fof(f3101,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) != c_COMBK(c_False,tc_bool,X0)
| X1 = X2
| ~ c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_221
| ~ spl0_269 ),
inference(forward_demodulation,[],[f3058,f2098]) ).
fof(f3058,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X2)
| X1 = X2
| ~ c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_221
| ~ spl0_269 ),
inference(superposition,[],[f2921,f2098]) ).
fof(f32987,plain,
( spl0_797
| ~ spl0_70
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2729,f2520,f1273,f32985]) ).
fof(f32985,plain,
( spl0_797
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X4,X5),X6),X5))
| ~ hBOOL(c_in(X3,X6,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f2729,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X4,X5),X6),X5))
| ~ hBOOL(c_in(X3,X6,X4)) )
| ~ spl0_70
| ~ spl0_251 ),
inference(superposition,[],[f2521,f1274]) ).
fof(f32983,plain,
( spl0_796
| ~ spl0_167
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2628,f2495,f1776,f32981]) ).
fof(f32981,plain,
( spl0_796
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2628,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X2) = X2 )
| ~ spl0_167
| ~ spl0_247 ),
inference(resolution,[],[f2496,f1777]) ).
fof(f32979,plain,
( spl0_795
| ~ spl0_70
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f31877,f29833,f1273,f32977]) ).
fof(f32977,plain,
( spl0_795
<=> ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f31877,plain,
( ! [X0,X1] : c_False = hAPP(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),X1)
| ~ spl0_70
| ~ spl0_725 ),
inference(superposition,[],[f1274,f29834]) ).
fof(f32975,plain,
( spl0_794
| ~ spl0_167
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2596,f2487,f1776,f32973]) ).
fof(f32973,plain,
( spl0_794
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f2596,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),X1)) = X1 )
| ~ spl0_167
| ~ spl0_245 ),
inference(resolution,[],[f2488,f1777]) ).
fof(f32971,plain,
( spl0_793
| ~ spl0_171
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2171,f2029,f1792,f32969]) ).
fof(f32969,plain,
( spl0_793
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(hAPP(c_fequal(X1),X0),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f2171,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(hAPP(c_fequal(X1),X0),hAPP(c_Set_Oimage(c_Set_Oinsert(X0,X1),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3))
| ~ spl0_171
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1793]) ).
fof(f32967,plain,
( spl0_792
| ~ spl0_92
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2165,f2029,f1379,f32965]) ).
fof(f32965,plain,
( spl0_792
<=> ! [X5,X4,X2,X0,X6,X3,X1] : hBOOL(c_in(X2,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5,X6),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool))),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f2165,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(c_in(X2,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X5,X6),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool))),X6))
| ~ spl0_92
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1380]) ).
fof(f32963,plain,
( spl0_791
| ~ spl0_100
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2158,f2029,f1413,f32961]) ).
fof(f32961,plain,
( spl0_791
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f2158,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X1,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3))
| ~ spl0_100
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1414]) ).
fof(f32959,plain,
( spl0_790
| ~ spl0_87
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1964,f1880,f1344,f32957]) ).
fof(f32957,plain,
( spl0_790
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,hAPP(X1,c_False)))
| hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Fun_Ocomp(X0,X1,X2,X3,X4))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f1964,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,hAPP(X1,c_False)))
| hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Fun_Ocomp(X0,X1,X2,X3,X4))))) )
| ~ spl0_87
| ~ spl0_185 ),
inference(forward_demodulation,[],[f1961,f1881]) ).
fof(f1961,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_Fun_Ocomp(X0,X1,X2,X3,X4)))))
| ~ hBOOL(hAPP(c_Fun_Ocomp(X0,X1,X2,X3,X4),c_False)) )
| ~ spl0_87
| ~ spl0_185 ),
inference(superposition,[],[f1345,f1881]) ).
fof(f32955,plain,
( spl0_789
| ~ spl0_86
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1963,f1880,f1340,f32953]) ).
fof(f32953,plain,
( spl0_789
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(X0,hAPP(X1,c_False)))
| ~ hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(c_Fun_Ocomp(X0,X1,X2,X3,X4))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f1963,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,hAPP(X1,c_False)))
| ~ hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(c_Fun_Ocomp(X0,X1,X2,X3,X4))))) )
| ~ spl0_86
| ~ spl0_185 ),
inference(forward_demodulation,[],[f1960,f1881]) ).
fof(f1960,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(c_Fun_Ocomp(X0,X1,X2,X3,X4)))))
| hBOOL(hAPP(c_Fun_Ocomp(X0,X1,X2,X3,X4),c_False)) )
| ~ spl0_86
| ~ spl0_185 ),
inference(superposition,[],[f1341,f1881]) ).
fof(f32951,plain,
( spl0_788
| ~ spl0_87
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1933,f1852,f1344,f32949]) ).
fof(f32949,plain,
( spl0_788
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,hAPP(X1,c_False)))
| hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_COMBB(X0,X1,X2,X3,X4))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f1933,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,hAPP(X1,c_False)))
| hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_COMBB(X0,X1,X2,X3,X4))))) )
| ~ spl0_87
| ~ spl0_178 ),
inference(forward_demodulation,[],[f1930,f1853]) ).
fof(f1930,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_COMBB(X0,X1,X2,X3,X4)))))
| ~ hBOOL(hAPP(c_COMBB(X0,X1,X2,X3,X4),c_False)) )
| ~ spl0_87
| ~ spl0_178 ),
inference(superposition,[],[f1345,f1853]) ).
fof(f32947,plain,
( spl0_787
| ~ spl0_86
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1932,f1852,f1340,f32945]) ).
fof(f32945,plain,
( spl0_787
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(X0,hAPP(X1,c_False)))
| ~ hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(c_COMBB(X0,X1,X2,X3,X4))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f1932,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,hAPP(X1,c_False)))
| ~ hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(c_COMBB(X0,X1,X2,X3,X4))))) )
| ~ spl0_86
| ~ spl0_178 ),
inference(forward_demodulation,[],[f1929,f1853]) ).
fof(f1929,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,hAPP(X1,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(c_COMBB(X0,X1,X2,X3,X4)))))
| hBOOL(hAPP(c_COMBB(X0,X1,X2,X3,X4),c_False)) )
| ~ spl0_86
| ~ spl0_178 ),
inference(superposition,[],[f1341,f1853]) ).
fof(f32943,plain,
( spl0_786
| ~ spl0_91
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1830,f1792,f1375,f32941]) ).
fof(f32941,plain,
( spl0_786
<=> ! [X0,X3,X2,X1] : c_Set_Oinsert(X0,X1) = c_Fun_Ofun__upd(c_Set_Oinsert(X0,X1),c_COMBK(c_False,tc_bool,X1),hAPP(c_fequal(X1),X0),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f1830,plain,
( ! [X2,X3,X0,X1] : c_Set_Oinsert(X0,X1) = c_Fun_Ofun__upd(c_Set_Oinsert(X0,X1),c_COMBK(c_False,tc_bool,X1),hAPP(c_fequal(X1),X0),X2,X3)
| ~ spl0_91
| ~ spl0_171 ),
inference(superposition,[],[f1376,f1793]) ).
fof(f32939,plain,
( spl0_785
| ~ spl0_35
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1753,f1707,f1123,f32937]) ).
fof(f32937,plain,
( spl0_785
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),c_COMBK(c_False,tc_bool,tc_fun(X0,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f1707,plain,
( spl0_159
<=> ! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_COMBK(c_False,tc_bool,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1753,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),c_COMBK(c_False,tc_bool,tc_fun(X0,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_35
| ~ spl0_159 ),
inference(resolution,[],[f1708,f1124]) ).
fof(f1708,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_COMBK(c_False,tc_bool,X0)) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1707]) ).
fof(f32935,plain,
( spl0_784
| ~ spl0_72
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f31846,f29833,f1282,f32933]) ).
fof(f32933,plain,
( spl0_784
<=> ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f31846,plain,
( ! [X0,X1] : ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat))
| ~ spl0_72
| ~ spl0_725 ),
inference(superposition,[],[f1283,f29834]) ).
fof(f32931,plain,
( spl0_783
| ~ spl0_35
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1751,f1703,f1123,f32929]) ).
fof(f32929,plain,
( spl0_783
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),c_COMBK(c_False,tc_bool,tc_fun(X0,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f1703,plain,
( spl0_158
<=> ! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_COMBK(c_False,tc_bool,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1751,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),c_COMBK(c_False,tc_bool,tc_fun(X0,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_35
| ~ spl0_158 ),
inference(resolution,[],[f1704,f1124]) ).
fof(f1704,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_COMBK(c_False,tc_bool,X0)) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1703]) ).
fof(f32927,plain,
( spl0_782
| ~ spl0_35
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1734,f1647,f1123,f32925]) ).
fof(f32925,plain,
( spl0_782
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f1647,plain,
( spl0_145
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1734,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_35
| ~ spl0_145 ),
inference(resolution,[],[f1648,f1124]) ).
fof(f1648,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1647]) ).
fof(f32923,plain,
( spl0_781
| ~ spl0_35
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1728,f1639,f1123,f32921]) ).
fof(f32921,plain,
( spl0_781
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f1639,plain,
( spl0_143
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1728,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_35
| ~ spl0_143 ),
inference(resolution,[],[f1640,f1124]) ).
fof(f1640,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1639]) ).
fof(f32919,plain,
( spl0_780
| ~ spl0_39
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1719,f1619,f1139,f32917]) ).
fof(f32917,plain,
( spl0_780
<=> ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2)
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f1139,plain,
( spl0_39
<=> ! [X80,X79] :
( ~ class_Lattices_Obounded__lattice(X80)
| class_Lattices_Obounded__lattice(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1619,plain,
( spl0_138
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1719,plain,
( ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2)
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_39
| ~ spl0_138 ),
inference(resolution,[],[f1620,f1140]) ).
fof(f1140,plain,
( ! [X80,X79] :
( class_Lattices_Obounded__lattice(tc_fun(X79,X80))
| ~ class_Lattices_Obounded__lattice(X80) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f1620,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X3) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1619]) ).
fof(f32915,plain,
( spl0_779
| ~ spl0_39
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1717,f1610,f1139,f32913]) ).
fof(f32913,plain,
( spl0_779
<=> ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1)))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f1610,plain,
( spl0_136
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Otop__class_Otop(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1717,plain,
( ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1)))
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_39
| ~ spl0_136 ),
inference(resolution,[],[f1611,f1140]) ).
fof(f1611,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Otop__class_Otop(X0)) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1610]) ).
fof(f32911,plain,
( spl0_778
| ~ spl0_39
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1714,f1606,f1139,f32909]) ).
fof(f32909,plain,
( spl0_778
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1)))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f1606,plain,
( spl0_135
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Obot__class_Obot(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1714,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1)))
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_39
| ~ spl0_135 ),
inference(resolution,[],[f1607,f1140]) ).
fof(f1607,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Obot__class_Obot(X0)) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1606]) ).
fof(f32907,plain,
( spl0_777
| ~ spl0_39
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1711,f1602,f1139,f32905]) ).
fof(f32905,plain,
( spl0_777
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2)
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f1602,plain,
( spl0_134
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1711,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2)
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_39
| ~ spl0_134 ),
inference(resolution,[],[f1603,f1140]) ).
fof(f1603,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X3) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1602]) ).
fof(f32903,plain,
( spl0_776
| ~ spl0_91
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1492,f1413,f1375,f32901]) ).
fof(f32901,plain,
( spl0_776
<=> ! [X0,X3,X2,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X1,X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f1492,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1) = c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X1,X1,X2,X3)
| ~ spl0_91
| ~ spl0_100 ),
inference(superposition,[],[f1376,f1414]) ).
fof(f32899,plain,
( spl0_775
| ~ spl0_91
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1471,f1379,f1375,f32897]) ).
fof(f32897,plain,
( spl0_775
<=> ! [X5,X3,X4,X0,X6,X2,X1] : c_Fun_Ofun__upd(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X1,X2,X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f1471,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : c_Fun_Ofun__upd(X0,X1,X2,X3,X4) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X1,X2,X5,X6)
| ~ spl0_91
| ~ spl0_92 ),
inference(superposition,[],[f1376,f1380]) ).
fof(f32868,plain,
( spl0_774
| ~ spl0_71
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f31845,f29833,f1277,f32866]) ).
fof(f32866,plain,
( spl0_774
<=> ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f31845,plain,
( ! [X2,X0,X1] : c_Fun_Oinj__on(X1,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat,X2)
| ~ spl0_71
| ~ spl0_725 ),
inference(superposition,[],[f1278,f29834]) ).
fof(f31926,plain,
( spl0_773
| ~ spl0_47
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f31844,f29833,f1171,f31924]) ).
fof(f31924,plain,
( spl0_773
<=> ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f31844,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat)
| ~ spl0_47
| ~ spl0_725 ),
inference(superposition,[],[f1172,f29834]) ).
fof(f31738,plain,
( spl0_772
| ~ spl0_162
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7276,f6756,f1756,f31736]) ).
fof(f31736,plain,
( spl0_772
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f7276,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(X3,X0) )
| ~ spl0_162
| ~ spl0_443 ),
inference(superposition,[],[f1757,f6757]) ).
fof(f31734,plain,
( spl0_771
| ~ spl0_119
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7204,f6752,f1510,f31732]) ).
fof(f31732,plain,
( spl0_771
<=> ! [X0,X3,X2,X1] : c_COMBK(c_False,tc_bool,X1) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f1510,plain,
( spl0_119
<=> ! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) != c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f7204,plain,
( ! [X2,X3,X0,X1] : c_COMBK(c_False,tc_bool,X1) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3))
| ~ spl0_119
| ~ spl0_442 ),
inference(superposition,[],[f1511,f6753]) ).
fof(f1511,plain,
( ! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) != c_COMBK(c_False,tc_bool,X0)
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1510]) ).
fof(f31730,plain,
( spl0_770
| ~ spl0_163
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7148,f6752,f1760,f31728]) ).
fof(f31728,plain,
( spl0_770
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f7148,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X2,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_163
| ~ spl0_442 ),
inference(superposition,[],[f1761,f6753]) ).
fof(f31726,plain,
( spl0_769
| ~ spl0_92
| ~ spl0_431 ),
inference(avatar_split_clause,[],[f6880,f6707,f1379,f31724]) ).
fof(f31724,plain,
( spl0_769
<=> ! [X3,X4,X0,X6,X5,X2,X1] : hAPP(X0,X6) = hAPP(c_Fun_Ocomp(X0,c_Fun_Ofun__upd(X1,X5,X6,X4,X2),X2,X3,X4),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f6880,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hAPP(X0,X6) = hAPP(c_Fun_Ocomp(X0,c_Fun_Ofun__upd(X1,X5,X6,X4,X2),X2,X3,X4),X5)
| ~ spl0_92
| ~ spl0_431 ),
inference(superposition,[],[f1380,f6708]) ).
fof(f31722,plain,
( spl0_768
| ~ spl0_167
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f5264,f5050,f1776,f31720]) ).
fof(f31720,plain,
( spl0_768
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),hAPP(c_Set_Oinsert(X3,X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f5264,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(c_Set_Oinsert(X2,X0),hAPP(c_Set_Oinsert(X3,X0),X1))))
| ~ spl0_167
| ~ spl0_380 ),
inference(resolution,[],[f5051,f1777]) ).
fof(f31588,plain,
( spl0_767
| ~ spl0_24
| ~ spl0_167
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5203,f5042,f1776,f1077,f31586]) ).
fof(f31586,plain,
( spl0_767
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(hAPP(c_Set_Oinsert(X2,X3),X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f5203,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(hAPP(c_Set_Oinsert(X2,X3),X0),X1))) )
| ~ spl0_167
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1777]) ).
fof(f31584,plain,
( spl0_766
| ~ spl0_84
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5187,f5042,f1332,f31582]) ).
fof(f31582,plain,
( spl0_766
<=> ! [X2,X0,X1,X3] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X1,X2)))
| ~ class_Orderings_Oorder(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f5187,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X1,X2)))
| ~ class_Orderings_Oorder(tc_fun(X3,X0)) )
| ~ spl0_84
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1333]) ).
fof(f31580,plain,
( spl0_765
| ~ spl0_85
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5186,f5042,f1336,f31578]) ).
fof(f31578,plain,
( spl0_765
<=> ! [X2,X0,X1,X3] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X1,X2)))
| ~ class_Orderings_Opreorder(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f5186,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X1,X2)))
| ~ class_Orderings_Opreorder(tc_fun(X3,X0)) )
| ~ spl0_85
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1337]) ).
fof(f31575,plain,
( spl0_764
| ~ spl0_66
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4691,f4368,f1256,f31573]) ).
fof(f31573,plain,
( spl0_764
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_Set_Oinsert(X3,X4),X2,tc_fun(X5,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f1256,plain,
( spl0_66
<=> ! [X0,X11,X3] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X11),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f4691,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_Set_Oinsert(X3,X4),X2,tc_fun(X5,tc_bool)),X3)) )
| ~ spl0_66
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1257]) ).
fof(f1257,plain,
( ! [X3,X0,X11] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X11),X3))
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f31571,plain,
( spl0_763
| ~ spl0_256
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4239,f3949,f2540,f31569]) ).
fof(f31569,plain,
( spl0_763
<=> ! [X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(c_Complete__Lattice_OInf__class_OInf(X0),X0)),X1))
| ~ hBOOL(c_in(X1,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f4239,plain,
( ! [X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(c_Complete__Lattice_OInf__class_OInf(X0),X0)),X1))
| ~ hBOOL(c_in(X1,X1,X0)) )
| ~ spl0_256
| ~ spl0_334 ),
inference(duplicate_literal_removal,[],[f4194]) ).
fof(f4194,plain,
( ! [X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(c_Complete__Lattice_OInf__class_OInf(X0),X0)),X1))
| ~ hBOOL(c_in(X1,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_256
| ~ spl0_334 ),
inference(resolution,[],[f3950,f2541]) ).
fof(f31543,plain,
( ~ spl0_24
| spl0_762
| ~ spl0_207
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4032,f3920,f2037,f31541,f1077]) ).
fof(f31541,plain,
( spl0_762
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f4032,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_207
| ~ spl0_327 ),
inference(resolution,[],[f3921,f2038]) ).
fof(f31539,plain,
( spl0_761
| ~ spl0_207
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4009,f3908,f2037,f31537]) ).
fof(f31537,plain,
( spl0_761
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X0,X1,X2),X3),tc_fun(X2,tc_bool)),X4),X2)
| ~ c_Finite__Set_Ofinite(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f4009,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X0,X1,X2),X3),tc_fun(X2,tc_bool)),X4),X2)
| ~ c_Finite__Set_Ofinite(X3,X1) )
| ~ spl0_207
| ~ spl0_324 ),
inference(resolution,[],[f3909,f2038]) ).
fof(f31535,plain,
( spl0_760
| ~ spl0_63
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f3867,f3439,f1244,f31533]) ).
fof(f31533,plain,
( spl0_760
<=> ! [X2,X0,X1] : hAPP(c_fequal(X1),X0) = hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X2,X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f1244,plain,
( spl0_63
<=> ! [X0,X3] : hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f3867,plain,
( ! [X2,X0,X1] : hAPP(c_fequal(X1),X0) = hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X2,X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)))
| ~ spl0_63
| ~ spl0_317 ),
inference(resolution,[],[f3440,f1245]) ).
fof(f1245,plain,
( ! [X3,X0] : hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0))
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1244]) ).
fof(f31531,plain,
( spl0_759
| ~ spl0_171
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3865,f3420,f1792,f31529]) ).
fof(f31529,plain,
( spl0_759
<=> ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X0,X1),hAPP(c_fequal(X1),X2)) = hAPP(c_Set_Oinsert(X2,X1),hAPP(c_fequal(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f3865,plain,
( ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X0,X1),hAPP(c_fequal(X1),X2)) = hAPP(c_Set_Oinsert(X2,X1),hAPP(c_fequal(X1),X0))
| ~ spl0_171
| ~ spl0_313 ),
inference(forward_demodulation,[],[f3815,f1793]) ).
fof(f3815,plain,
( ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X0,X1),hAPP(c_Set_Oinsert(X2,X1),c_COMBK(c_False,tc_bool,X1))) = hAPP(c_Set_Oinsert(X2,X1),hAPP(c_fequal(X1),X0))
| ~ spl0_171
| ~ spl0_313 ),
inference(superposition,[],[f3421,f1793]) ).
fof(f31527,plain,
( spl0_758
| ~ spl0_79
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3353,f3024,f1311,f31525]) ).
fof(f31525,plain,
( spl0_758
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| c_COMBK(c_False,tc_bool,X0) = X1
| hBOOL(hAPP(X1,c_Finite__Set_Olinorder__class_OMin(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f3024,plain,
( spl0_294
<=> ! [X0,X11] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X11,X0),X11,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3353,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| c_COMBK(c_False,tc_bool,X0) = X1
| hBOOL(hAPP(X1,c_Finite__Set_Olinorder__class_OMin(X1,X0))) )
| ~ spl0_79
| ~ spl0_294 ),
inference(resolution,[],[f3025,f1312]) ).
fof(f3025,plain,
( ! [X0,X11] :
( hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X11,X0),X11,X0))
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| c_COMBK(c_False,tc_bool,X0) = X11 )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3024]) ).
fof(f31523,plain,
( spl0_757
| ~ spl0_79
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3340,f3020,f1311,f31521]) ).
fof(f31521,plain,
( spl0_757
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| c_COMBK(c_False,tc_bool,X0) = X1
| hBOOL(hAPP(X1,c_Finite__Set_Olinorder__class_OMax(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f3020,plain,
( spl0_293
<=> ! [X0,X11] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X11,X0),X11,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f3340,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| c_COMBK(c_False,tc_bool,X0) = X1
| hBOOL(hAPP(X1,c_Finite__Set_Olinorder__class_OMax(X1,X0))) )
| ~ spl0_79
| ~ spl0_293 ),
inference(resolution,[],[f3021,f1312]) ).
fof(f3021,plain,
( ! [X0,X11] :
( hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X11,X0),X11,X0))
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| c_COMBK(c_False,tc_bool,X0) = X11 )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3020]) ).
fof(f31519,plain,
( spl0_756
| ~ spl0_171
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3131,f2936,f1792,f31517]) ).
fof(f31517,plain,
( spl0_756
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X2))
| hBOOL(c_in(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f3131,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X2))
| hBOOL(c_in(X0,X2,X1)) )
| ~ spl0_171
| ~ spl0_272 ),
inference(superposition,[],[f2937,f1793]) ).
fof(f31514,plain,
( spl0_755
| ~ spl0_258
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2886,f2572,f2548,f31512]) ).
fof(f31512,plain,
( spl0_755
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X1,X0),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(c_fequal(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f2886,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X1,X0),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(c_fequal(X0),X1),X0)) )
| ~ spl0_258
| ~ spl0_264 ),
inference(superposition,[],[f2549,f2573]) ).
fof(f31510,plain,
( spl0_754
| ~ spl0_249
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2882,f2572,f2503,f31508]) ).
fof(f31508,plain,
( spl0_754
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X3,hAPP(c_Set_Oinsert(X1,X0),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(c_fequal(X0),X1),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f2882,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X3,hAPP(c_Set_Oinsert(X1,X0),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(c_fequal(X0),X1),X0,X4) )
| ~ spl0_249
| ~ spl0_264 ),
inference(superposition,[],[f2504,f2573]) ).
fof(f31506,plain,
( spl0_753
| ~ spl0_250
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2869,f2572,f2516,f31504]) ).
fof(f31504,plain,
( spl0_753
<=> ! [X2,X0,X1] : hAPP(c_Set_Oinsert(X1,X0),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f31502,plain,
( spl0_752
| ~ spl0_175
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2785,f2536,f1839,f31500]) ).
fof(f31500,plain,
( spl0_752
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f2785,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_255 ),
inference(resolution,[],[f2537,f1840]) ).
fof(f31498,plain,
( spl0_751
| ~ spl0_176
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2784,f2536,f1844,f31496]) ).
fof(f31496,plain,
( spl0_751
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f2784,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_255 ),
inference(resolution,[],[f2537,f1845]) ).
fof(f31494,plain,
( spl0_750
| ~ spl0_174
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2780,f2536,f1835,f31492]) ).
fof(f31492,plain,
( spl0_750
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f2780,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_255 ),
inference(resolution,[],[f2537,f1836]) ).
fof(f31490,plain,
( spl0_749
| ~ spl0_177
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2779,f2536,f1848,f31488]) ).
fof(f31488,plain,
( spl0_749
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f2779,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_255 ),
inference(resolution,[],[f2537,f1849]) ).
fof(f31486,plain,
( spl0_748
| ~ spl0_175
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2745,f2528,f1839,f31484]) ).
fof(f31484,plain,
( spl0_748
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f2745,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_253 ),
inference(resolution,[],[f2529,f1840]) ).
fof(f31482,plain,
( spl0_747
| ~ spl0_176
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2744,f2528,f1844,f31480]) ).
fof(f31480,plain,
( spl0_747
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) = X1
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f2744,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) = X1
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_253 ),
inference(resolution,[],[f2529,f1845]) ).
fof(f31478,plain,
( spl0_746
| ~ spl0_177
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2739,f2528,f1848,f31476]) ).
fof(f31476,plain,
( spl0_746
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f2739,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_253 ),
inference(resolution,[],[f2529,f1849]) ).
fof(f31443,plain,
( spl0_745
| ~ spl0_181
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2632,f2495,f1864,f31441]) ).
fof(f31441,plain,
( spl0_745
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f2632,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_247 ),
inference(resolution,[],[f2496,f1865]) ).
fof(f31439,plain,
( spl0_744
| ~ spl0_182
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2631,f2495,f1868,f31437]) ).
fof(f31437,plain,
( spl0_744
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f2631,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_247 ),
inference(resolution,[],[f2496,f1869]) ).
fof(f31435,plain,
( spl0_743
| ~ spl0_180
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2630,f2495,f1860,f31433]) ).
fof(f31433,plain,
( spl0_743
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f2630,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_247 ),
inference(resolution,[],[f2496,f1861]) ).
fof(f31431,plain,
( spl0_742
| ~ spl0_183
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2629,f2495,f1872,f31429]) ).
fof(f31429,plain,
( spl0_742
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f2629,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_247 ),
inference(resolution,[],[f2496,f1873]) ).
fof(f31427,plain,
( spl0_741
| ~ spl0_181
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2600,f2487,f1864,f31425]) ).
fof(f31425,plain,
( spl0_741
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f2600,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_245 ),
inference(resolution,[],[f2488,f1865]) ).
fof(f31423,plain,
( spl0_740
| ~ spl0_182
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2599,f2487,f1868,f31421]) ).
fof(f31421,plain,
( spl0_740
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f2599,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_245 ),
inference(resolution,[],[f2488,f1869]) ).
fof(f31419,plain,
( spl0_739
| ~ spl0_183
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2597,f2487,f1872,f31417]) ).
fof(f31417,plain,
( spl0_739
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f2597,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_245 ),
inference(resolution,[],[f2488,f1873]) ).
fof(f31415,plain,
( spl0_738
| ~ spl0_151
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2170,f2029,f1672,f31413]) ).
fof(f31413,plain,
( spl0_738
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f2170,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3))
| ~ spl0_151
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1673]) ).
fof(f31411,plain,
( spl0_737
| ~ spl0_175
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2131,f2005,f1839,f31409]) ).
fof(f31409,plain,
( spl0_737
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f2131,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) )
| ~ spl0_175
| ~ spl0_199 ),
inference(resolution,[],[f2006,f1840]) ).
fof(f31407,plain,
( spl0_736
| ~ spl0_176
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2130,f2005,f1844,f31405]) ).
fof(f31405,plain,
( spl0_736
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f2130,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_176
| ~ spl0_199 ),
inference(resolution,[],[f2006,f1845]) ).
fof(f31372,plain,
( spl0_735
| ~ spl0_174
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2127,f2005,f1835,f31370]) ).
fof(f31370,plain,
( spl0_735
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f2127,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| ~ class_Lattices_Olattice(tc_fun(X0,tc_bool)) )
| ~ spl0_174
| ~ spl0_199 ),
inference(resolution,[],[f2006,f1836]) ).
fof(f31368,plain,
( spl0_734
| ~ spl0_177
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2126,f2005,f1848,f31366]) ).
fof(f31366,plain,
( spl0_734
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f2126,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X1,X0)
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_177
| ~ spl0_199 ),
inference(resolution,[],[f2006,f1849]) ).
fof(f31364,plain,
( spl0_733
| ~ spl0_175
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1973,f1888,f1839,f31362]) ).
fof(f31362,plain,
( spl0_733
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X0),X1)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f1973,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X0),X1)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) )
| ~ spl0_175
| ~ spl0_187 ),
inference(resolution,[],[f1889,f1840]) ).
fof(f31360,plain,
( spl0_732
| ~ spl0_176
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1972,f1888,f1844,f31358]) ).
fof(f31358,plain,
( spl0_732
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X0),X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f1972,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X0),X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) )
| ~ spl0_176
| ~ spl0_187 ),
inference(resolution,[],[f1889,f1845]) ).
fof(f31356,plain,
( spl0_731
| ~ spl0_174
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1969,f1888,f1835,f31354]) ).
fof(f31354,plain,
( spl0_731
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X0),X2),X1)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f1969,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X0),X2),X1)
| ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) )
| ~ spl0_174
| ~ spl0_187 ),
inference(resolution,[],[f1889,f1836]) ).
fof(f31352,plain,
( spl0_730
| ~ spl0_177
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1968,f1888,f1848,f31350]) ).
fof(f31350,plain,
( spl0_730
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X0),X2),X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f1968,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X0),X2),X1)
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)) )
| ~ spl0_177
| ~ spl0_187 ),
inference(resolution,[],[f1889,f1849]) ).
fof(f31348,plain,
( spl0_729
| ~ spl0_86
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1737,f1660,f1340,f31346]) ).
fof(f31346,plain,
( spl0_729
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Set_Oinsert(X1,X2),X0))))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X0),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f1737,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Set_Oinsert(X1,X2),X0))))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X0),c_False)) )
| ~ spl0_86
| ~ spl0_148 ),
inference(resolution,[],[f1661,f1341]) ).
fof(f31069,plain,
( spl0_728
| ~ spl0_20
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f13326,f13049,f1057,f31067]) ).
fof(f13049,plain,
( spl0_584
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f13326,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,tc_bool) = c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_bool)
| ~ spl0_20
| ~ spl0_584 ),
inference(resolution,[],[f13050,f1059]) ).
fof(f1059,plain,
( class_Orderings_Oorder(tc_bool)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f1057]) ).
fof(f13050,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_584 ),
inference(avatar_component_clause,[],[f13049]) ).
fof(f30646,plain,
( spl0_727
| ~ spl0_8
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f13325,f13049,f997,f30644]) ).
fof(f997,plain,
( spl0_8
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f13325,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat)
| ~ spl0_8
| ~ spl0_584 ),
inference(resolution,[],[f13050,f999]) ).
fof(f999,plain,
( class_Orderings_Oorder(tc_nat)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f30223,plain,
( spl0_726
| ~ spl0_20
| ~ spl0_583 ),
inference(avatar_split_clause,[],[f13323,f13045,f1057,f30221]) ).
fof(f13045,plain,
( spl0_583
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f13323,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,tc_bool) = c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_bool)
| ~ spl0_20
| ~ spl0_583 ),
inference(resolution,[],[f13046,f1059]) ).
fof(f13046,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_583 ),
inference(avatar_component_clause,[],[f13045]) ).
fof(f29835,plain,
( spl0_725
| ~ spl0_8
| ~ spl0_583 ),
inference(avatar_split_clause,[],[f13322,f13045,f997,f29833]) ).
fof(f13322,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,tc_nat) = c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat)
| ~ spl0_8
| ~ spl0_583 ),
inference(resolution,[],[f13046,f999]) ).
fof(f29489,plain,
( spl0_724
| ~ spl0_65
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f12736,f5543,f1252,f29487]) ).
fof(f29487,plain,
( spl0_724
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X2),X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f5543,plain,
( spl0_407
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X2),X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f12736,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X2),X2,X1)
| ~ spl0_65
| ~ spl0_407 ),
inference(resolution,[],[f5544,f1253]) ).
fof(f5544,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X2),X2,X1)
| ~ spl0_407 ),
inference(avatar_component_clause,[],[f5543]) ).
fof(f29322,plain,
( spl0_723
| ~ spl0_150
| ~ spl0_221
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f9130,f8450,f2097,f1668,f29320]) ).
fof(f29320,plain,
( spl0_723
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X1) = hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f9130,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X1) = hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X0))
| ~ spl0_150
| ~ spl0_221
| ~ spl0_480 ),
inference(forward_demodulation,[],[f9085,f2098]) ).
fof(f9085,plain,
( ! [X2,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X1),tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)) = hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X0))
| ~ spl0_150
| ~ spl0_480 ),
inference(superposition,[],[f8451,f1669]) ).
fof(f29318,plain,
( spl0_722
| ~ spl0_171
| ~ spl0_191
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6155,f5535,f1904,f1792,f29316]) ).
fof(f29316,plain,
( spl0_722
<=> ! [X0,X3,X2,X1] : hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_fequal(X1),X0)) = hAPP(c_fequal(X3),hAPP(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f6155,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_fequal(X1),X0)) = hAPP(c_fequal(X3),hAPP(X2,X0))
| ~ spl0_171
| ~ spl0_191
| ~ spl0_405 ),
inference(forward_demodulation,[],[f6154,f1793]) ).
fof(f6154,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_fequal(X1),X0)) = hAPP(c_Set_Oinsert(hAPP(X2,X0),X3),c_COMBK(c_False,tc_bool,X3))
| ~ spl0_171
| ~ spl0_191
| ~ spl0_405 ),
inference(forward_demodulation,[],[f6046,f1905]) ).
fof(f6046,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Set_Oinsert(hAPP(X2,X0),X3),hAPP(c_Set_Oimage(X2,X1,X3),c_COMBK(c_False,tc_bool,X1))) = hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_fequal(X1),X0))
| ~ spl0_171
| ~ spl0_405 ),
inference(superposition,[],[f5536,f1793]) ).
fof(f29314,plain,
( spl0_721
| ~ spl0_375
| ~ spl0_396 ),
inference(avatar_split_clause,[],[f12733,f5499,f5030,f29312]) ).
fof(f29312,plain,
( spl0_721
<=> ! [X0] : c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) != c_COMBK(c_False,tc_bool,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f5499,plain,
( spl0_396
<=> ! [X0,X1] : c_COMBK(c_False,tc_bool,X1) != hAPP(c_fequal(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f12733,plain,
( ! [X0] : c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) != c_COMBK(c_False,tc_bool,tc_bool)
| ~ spl0_375
| ~ spl0_396 ),
inference(superposition,[],[f5500,f5031]) ).
fof(f5500,plain,
( ! [X0,X1] : c_COMBK(c_False,tc_bool,X1) != hAPP(c_fequal(X1),X0)
| ~ spl0_396 ),
inference(avatar_component_clause,[],[f5499]) ).
fof(f29310,plain,
( spl0_720
| ~ spl0_82
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6119,f5535,f1324,f29308]) ).
fof(f29308,plain,
( spl0_720
<=> ! [X4,X0,X3,X2,X1] : hBOOL(c_in(hAPP(X0,X1),hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f6119,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(c_in(hAPP(X0,X1),hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),X2))
| ~ spl0_82
| ~ spl0_405 ),
inference(superposition,[],[f1325,f5536]) ).
fof(f29306,plain,
( spl0_719
| ~ spl0_122
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f5640,f5467,f1531,f29304]) ).
fof(f29304,plain,
( spl0_719
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)),X3)
| ~ c_Finite__Set_Ofinite(X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f5640,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X0,X2,X3),hAPP(c_Set_Oimage(X1,X4,X2),X5)),X3)
| ~ c_Finite__Set_Ofinite(X5,X4) )
| ~ spl0_122
| ~ spl0_388 ),
inference(superposition,[],[f1532,f5468]) ).
fof(f29189,plain,
( spl0_718
| ~ spl0_24
| ~ spl0_146
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5215,f5042,f1651,f1077,f29187]) ).
fof(f29187,plain,
( spl0_718
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f5215,plain,
( ! [X2,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1))) )
| ~ spl0_146
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1652]) ).
fof(f29185,plain,
( spl0_717
| ~ spl0_57
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4692,f4368,f1218,f29183]) ).
fof(f29183,plain,
( spl0_717
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_fequal(X3),X2,tc_fun(X4,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1218,plain,
( spl0_57
<=> ! [X0,X3] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f4692,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_fequal(X3),X2,tc_fun(X4,tc_bool)),X0)) )
| ~ spl0_57
| ~ spl0_359 ),
inference(resolution,[],[f4369,f1219]) ).
fof(f1219,plain,
( ! [X3,X0] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),X3))
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f29181,plain,
( spl0_716
| ~ spl0_76
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4629,f4352,f1299,f29179]) ).
fof(f29179,plain,
( spl0_716
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1299,plain,
( spl0_76
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f4629,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_76
| ~ spl0_355 ),
inference(resolution,[],[f4353,f1300]) ).
fof(f1300,plain,
( ! [X3,X0] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3))
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1299]) ).
fof(f29177,plain,
( spl0_715
| ~ spl0_76
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4604,f4348,f1299,f29175]) ).
fof(f29175,plain,
( spl0_715
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f4604,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_76
| ~ spl0_354 ),
inference(resolution,[],[f4349,f1300]) ).
fof(f29173,plain,
( spl0_714
| ~ spl0_76
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4431,f4319,f1299,f29171]) ).
fof(f29171,plain,
( spl0_714
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f4431,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_76
| ~ spl0_347 ),
inference(resolution,[],[f4320,f1300]) ).
fof(f29169,plain,
( spl0_713
| ~ spl0_76
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4412,f4315,f1299,f29167]) ).
fof(f29167,plain,
( spl0_713
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f4412,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_76
| ~ spl0_346 ),
inference(resolution,[],[f4316,f1300]) ).
fof(f29165,plain,
( spl0_712
| ~ spl0_171
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4282,f3973,f1792,f29163]) ).
fof(f29163,plain,
( spl0_712
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(X1),X0) != hAPP(c_Set_Oinsert(X2,X1),c_COMBK(c_False,tc_bool,X1))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f3973,plain,
( spl0_340
<=> ! [X2,X0,X1] :
( hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)) != hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f4282,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X1),X0) != hAPP(c_Set_Oinsert(X2,X1),c_COMBK(c_False,tc_bool,X1))
| X0 = X2 )
| ~ spl0_171
| ~ spl0_340 ),
inference(superposition,[],[f3974,f1793]) ).
fof(f3974,plain,
( ! [X2,X0,X1] :
( hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)) != hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))
| X1 = X2 )
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f3973]) ).
fof(f29161,plain,
( spl0_711
| ~ spl0_371
| ~ spl0_396 ),
inference(avatar_split_clause,[],[f12732,f5499,f4832,f29159]) ).
fof(f29159,plain,
( spl0_711
<=> ! [X0] : c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat) != c_COMBK(c_False,tc_bool,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f12732,plain,
( ! [X0] : c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat) != c_COMBK(c_False,tc_bool,tc_nat)
| ~ spl0_371
| ~ spl0_396 ),
inference(superposition,[],[f5500,f4833]) ).
fof(f29157,plain,
( spl0_710
| ~ spl0_175
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4193,f3949,f1839,f29155]) ).
fof(f29155,plain,
( spl0_710
<=> ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X0)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f4193,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X0)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_334 ),
inference(resolution,[],[f3950,f1840]) ).
fof(f29153,plain,
( spl0_709
| ~ spl0_176
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4192,f3949,f1844,f29151]) ).
fof(f29151,plain,
( spl0_709
<=> ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f4192,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_334 ),
inference(resolution,[],[f3950,f1845]) ).
fof(f29149,plain,
( spl0_708
| ~ spl0_207
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3750,f3408,f2037,f29147]) ).
fof(f29147,plain,
( spl0_708
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f3750,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)) = X1
| ~ spl0_207
| ~ spl0_310 ),
inference(resolution,[],[f3409,f2038]) ).
fof(f29145,plain,
( spl0_707
| ~ spl0_207
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3717,f3404,f2037,f29143]) ).
fof(f29143,plain,
( spl0_707
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f3717,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X0,tc_bool)),X2)),X1) = X1
| ~ spl0_207
| ~ spl0_309 ),
inference(resolution,[],[f3405,f2038]) ).
fof(f29141,plain,
( spl0_706
| ~ spl0_107
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3706,f3400,f1442,f29139]) ).
fof(f29139,plain,
( spl0_706
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f3706,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1443]) ).
fof(f29137,plain,
( spl0_705
| ~ spl0_105
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3688,f3400,f1433,f29135]) ).
fof(f29135,plain,
( spl0_705
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),c_Orderings_Obot__class_Obot(X1)))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f3688,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),c_Orderings_Obot__class_Obot(X1)))
| ~ class_Orderings_Obot(X1) )
| ~ spl0_105
| ~ spl0_308 ),
inference(resolution,[],[f3401,f1434]) ).
fof(f29133,plain,
( spl0_704
| ~ spl0_107
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3576,f3372,f1442,f29131]) ).
fof(f29131,plain,
( spl0_704
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f3576,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = X0
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) )
| ~ spl0_107
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1443]) ).
fof(f29129,plain,
( spl0_703
| ~ spl0_105
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3559,f3372,f1433,f29127]) ).
fof(f29127,plain,
( spl0_703
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X1))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f3559,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X1))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_301 ),
inference(resolution,[],[f3373,f1434]) ).
fof(f29125,plain,
( spl0_702
| ~ spl0_107
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3548,f3368,f1442,f29123]) ).
fof(f29123,plain,
( spl0_702
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f3548,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1443]) ).
fof(f29121,plain,
( spl0_701
| ~ spl0_105
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3531,f3368,f1433,f29119]) ).
fof(f29119,plain,
( spl0_701
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f3531,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) )
| ~ spl0_105
| ~ spl0_300 ),
inference(resolution,[],[f3369,f1434]) ).
fof(f29117,plain,
( spl0_700
| ~ spl0_363
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11680,f5030,f4384,f29115]) ).
fof(f29115,plain,
( spl0_700
<=> ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f4384,plain,
( spl0_363
<=> ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f11680,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)) = X0
| ~ spl0_363
| ~ spl0_375 ),
inference(superposition,[],[f4385,f5031]) ).
fof(f4385,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f4384]) ).
fof(f29113,plain,
( spl0_699
| ~ spl0_12
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3226,f2980,f1017,f29111]) ).
fof(f29111,plain,
( spl0_699
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X2,tc_bool,X0),X0,tc_bool) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f3226,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X2,tc_bool,X0),X0,tc_bool) = X2 )
| ~ spl0_12
| ~ spl0_283 ),
inference(resolution,[],[f2981,f1019]) ).
fof(f29109,plain,
( spl0_698
| ~ spl0_12
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3224,f2976,f1017,f29107]) ).
fof(f29107,plain,
( spl0_698
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_bool,X0),X0,tc_bool) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f3224,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_bool,X0),X0,tc_bool) = X2 )
| ~ spl0_12
| ~ spl0_282 ),
inference(resolution,[],[f2977,f1019]) ).
fof(f29105,plain,
( spl0_697
| ~ spl0_238
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3182,f2944,f2299,f29103]) ).
fof(f29103,plain,
( spl0_697
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2),X3,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f3182,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2),X3,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X0) )
| ~ spl0_238
| ~ spl0_274 ),
inference(resolution,[],[f2945,f2300]) ).
fof(f29101,plain,
( spl0_696
| ~ spl0_237
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3181,f2944,f2295,f29099]) ).
fof(f29099,plain,
( spl0_696
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2),X3,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f3181,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2),X3,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X0) )
| ~ spl0_237
| ~ spl0_274 ),
inference(resolution,[],[f2945,f2296]) ).
fof(f29097,plain,
( spl0_695
| ~ spl0_238
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3156,f2940,f2299,f29095]) ).
fof(f29095,plain,
( spl0_695
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f3156,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X1),X2) )
| ~ spl0_238
| ~ spl0_273 ),
inference(resolution,[],[f2941,f2300]) ).
fof(f29093,plain,
( spl0_694
| ~ spl0_237
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3155,f2940,f2295,f29091]) ).
fof(f29091,plain,
( spl0_694
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f3155,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1),X3),X2) )
| ~ spl0_237
| ~ spl0_273 ),
inference(resolution,[],[f2941,f2296]) ).
fof(f29089,plain,
( spl0_693
| ~ spl0_238
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3122,f2936,f2299,f29087]) ).
fof(f29087,plain,
( spl0_693
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f3122,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X1))
| ~ spl0_238
| ~ spl0_272 ),
inference(resolution,[],[f2937,f2300]) ).
fof(f29085,plain,
( spl0_692
| ~ spl0_237
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2879,f2572,f2295,f29083]) ).
fof(f29083,plain,
( spl0_692
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_Set_Oinsert(X1,X0),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f2879,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_Set_Oinsert(X1,X0),X2)))
| ~ spl0_237
| ~ spl0_264 ),
inference(superposition,[],[f2296,f2573]) ).
fof(f29081,plain,
( spl0_691
| ~ spl0_79
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f2821,f2548,f1311,f29079]) ).
fof(f29079,plain,
( spl0_691
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f2821,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X0)) )
| ~ spl0_79
| ~ spl0_258 ),
inference(resolution,[],[f2549,f1312]) ).
fof(f29077,plain,
( spl0_690
| ~ spl0_79
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f2812,f2544,f1311,f29075]) ).
fof(f29075,plain,
( spl0_690
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f2812,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),X0)) )
| ~ spl0_79
| ~ spl0_257 ),
inference(resolution,[],[f2545,f1312]) ).
fof(f29073,plain,
( spl0_689
| ~ spl0_370
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11679,f5030,f4515,f29071]) ).
fof(f29071,plain,
( spl0_689
<=> ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f4515,plain,
( spl0_370
<=> ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f11679,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)) = X0
| ~ spl0_370
| ~ spl0_375 ),
inference(superposition,[],[f4516,f5031]) ).
fof(f4516,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f4515]) ).
fof(f29069,plain,
( spl0_688
| ~ spl0_80
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2733,f2524,f1315,f29067]) ).
fof(f29067,plain,
( spl0_688
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| X0 = X3
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f2733,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| X0 = X3
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X2),X1),X0)) )
| ~ spl0_80
| ~ spl0_252 ),
inference(resolution,[],[f2525,f1316]) ).
fof(f29065,plain,
( spl0_687
| ~ spl0_79
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2702,f2520,f1311,f29063]) ).
fof(f29063,plain,
( spl0_687
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(c_Set_Oimage(X3,X2,X4),X1),hAPP(X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f2702,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(c_Set_Oimage(X3,X2,X4),X1),hAPP(X3,X0))) )
| ~ spl0_79
| ~ spl0_251 ),
inference(resolution,[],[f2521,f1312]) ).
fof(f29061,plain,
( spl0_686
| ~ spl0_181
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2394,f2291,f1864,f29059]) ).
fof(f29059,plain,
( spl0_686
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f2394,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1865]) ).
fof(f29057,plain,
( spl0_685
| ~ spl0_182
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2393,f2291,f1868,f29055]) ).
fof(f29055,plain,
( spl0_685
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f2393,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1869]) ).
fof(f29053,plain,
( spl0_684
| ~ spl0_180
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2392,f2291,f1860,f29051]) ).
fof(f29051,plain,
( spl0_684
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f2392,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1861]) ).
fof(f29049,plain,
( spl0_683
| ~ spl0_183
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2391,f2291,f1872,f29047]) ).
fof(f29047,plain,
( spl0_683
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f2391,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1873]) ).
fof(f29045,plain,
( spl0_682
| ~ spl0_175
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2388,f2291,f1839,f29043]) ).
fof(f29043,plain,
( spl0_682
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f2388,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1840]) ).
fof(f29041,plain,
( spl0_681
| ~ spl0_176
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2387,f2291,f1844,f29039]) ).
fof(f29039,plain,
( spl0_681
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f2387,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1845]) ).
fof(f29037,plain,
( spl0_680
| ~ spl0_174
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2383,f2291,f1835,f29035]) ).
fof(f29035,plain,
( spl0_680
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f2383,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1836]) ).
fof(f29033,plain,
( spl0_679
| ~ spl0_177
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2382,f2291,f1848,f29031]) ).
fof(f29031,plain,
( spl0_679
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f2382,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1849]) ).
fof(f29028,plain,
( spl0_678
| ~ spl0_181
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2374,f2287,f1864,f29026]) ).
fof(f29026,plain,
( spl0_678
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f2374,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_181
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1865]) ).
fof(f29024,plain,
( spl0_677
| ~ spl0_182
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2373,f2287,f1868,f29022]) ).
fof(f29022,plain,
( spl0_677
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f2373,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_182
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1869]) ).
fof(f29020,plain,
( spl0_676
| ~ spl0_180
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2372,f2287,f1860,f29018]) ).
fof(f29018,plain,
( spl0_676
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f2372,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_180
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1861]) ).
fof(f29016,plain,
( spl0_675
| ~ spl0_183
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2371,f2287,f1872,f29014]) ).
fof(f29014,plain,
( spl0_675
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f2371,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_183
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1873]) ).
fof(f29012,plain,
( spl0_674
| ~ spl0_175
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2368,f2287,f1839,f29010]) ).
fof(f29010,plain,
( spl0_674
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f2368,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_175
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1840]) ).
fof(f29008,plain,
( spl0_673
| ~ spl0_176
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2367,f2287,f1844,f29006]) ).
fof(f29006,plain,
( spl0_673
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f2367,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_176
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1845]) ).
fof(f29004,plain,
( spl0_672
| ~ spl0_174
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2363,f2287,f1835,f29002]) ).
fof(f29002,plain,
( spl0_672
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f2363,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_174
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1836]) ).
fof(f29000,plain,
( spl0_671
| ~ spl0_177
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2362,f2287,f1848,f28998]) ).
fof(f28998,plain,
( spl0_671
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f2362,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_177
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1849]) ).
fof(f28996,plain,
( spl0_670
| ~ spl0_230
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2358,f2283,f2267,f28994]) ).
fof(f28994,plain,
( spl0_670
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f2358,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) )
| ~ spl0_230
| ~ spl0_234 ),
inference(duplicate_literal_removal,[],[f2353]) ).
fof(f2353,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) )
| ~ spl0_230
| ~ spl0_234 ),
inference(resolution,[],[f2284,f2268]) ).
fof(f28992,plain,
( spl0_669
| ~ spl0_70
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2174,f2029,f1273,f28990]) ).
fof(f28990,plain,
( spl0_669
<=> ! [X4,X0,X5,X2,X1] : hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f2174,plain,
( ! [X2,X0,X1,X4,X5] : hBOOL(c_in(X0,hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))),X5))
| ~ spl0_70
| ~ spl0_205 ),
inference(superposition,[],[f2030,f1274]) ).
fof(f28987,plain,
( spl0_668
| ~ spl0_35
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1508,f1446,f1123,f28985]) ).
fof(f28985,plain,
( spl0_668
<=> ! [X2,X0,X1] :
( c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,tc_fun(X1,X2),tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1446,plain,
( spl0_108
<=> ! [X0,X60] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X60,X0,X0),X0) = X60 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1508,plain,
( ! [X2,X0,X1] :
( c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,tc_fun(X1,X2),tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_35
| ~ spl0_108 ),
inference(resolution,[],[f1447,f1124]) ).
fof(f1447,plain,
( ! [X0,X60] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X60,X0,X0),X0) = X60 )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1446]) ).
fof(f28755,plain,
( spl0_667
| ~ spl0_375
| ~ spl0_646 ),
inference(avatar_split_clause,[],[f28657,f28613,f5030,f28752]) ).
fof(f28752,plain,
( spl0_667
<=> c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f28613,plain,
( spl0_646
<=> ! [X0] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_fequal(X0),c_False)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f28657,plain,
( c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_bool))
| ~ spl0_375
| ~ spl0_646 ),
inference(superposition,[],[f28614,f5031]) ).
fof(f28614,plain,
( ! [X0] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_fequal(X0),c_False))
| ~ spl0_646 ),
inference(avatar_component_clause,[],[f28613]) ).
fof(f28713,plain,
( spl0_666
| ~ spl0_371
| ~ spl0_646 ),
inference(avatar_split_clause,[],[f28656,f28613,f4832,f28710]) ).
fof(f28710,plain,
( spl0_666
<=> c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f28656,plain,
( c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_nat))
| ~ spl0_371
| ~ spl0_646 ),
inference(superposition,[],[f28614,f4833]) ).
fof(f28708,plain,
( spl0_665
| ~ spl0_66
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f7200,f6752,f1256,f28706]) ).
fof(f28706,plain,
( spl0_665
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f7200,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_Set_Oinsert(X0,X1),X3)),X0))
| ~ spl0_66
| ~ spl0_442 ),
inference(superposition,[],[f1257,f6753]) ).
fof(f28704,plain,
( spl0_664
| ~ spl0_119
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6122,f5535,f1510,f28702]) ).
fof(f28702,plain,
( spl0_664
<=> ! [X4,X0,X3,X2,X1] : c_COMBK(c_False,tc_bool,X2) != hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f6122,plain,
( ! [X2,X3,X0,X1,X4] : c_COMBK(c_False,tc_bool,X2) != hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4))
| ~ spl0_119
| ~ spl0_405 ),
inference(superposition,[],[f1511,f5536]) ).
fof(f28700,plain,
( spl0_663
| ~ spl0_66
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f6118,f5535,f1256,f28698]) ).
fof(f28698,plain,
( spl0_663
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),hAPP(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f6118,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X3,X2),hAPP(c_Set_Oinsert(X1,X3),X4)),hAPP(X0,X1)))
| ~ spl0_66
| ~ spl0_405 ),
inference(superposition,[],[f1257,f5536]) ).
fof(f28696,plain,
( spl0_662
| ~ spl0_151
| ~ spl0_171
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f5089,f5022,f1792,f1672,f28694]) ).
fof(f28694,plain,
( spl0_662
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f5089,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X1) )
| ~ spl0_151
| ~ spl0_171
| ~ spl0_373 ),
inference(forward_demodulation,[],[f5081,f1673]) ).
fof(f5081,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X0)),X1)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1)),X1) )
| ~ spl0_171
| ~ spl0_373 ),
inference(superposition,[],[f5023,f1793]) ).
fof(f28678,plain,
( ~ spl0_24
| spl0_661
| ~ spl0_167
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4043,f3920,f1776,f28676,f1077]) ).
fof(f28676,plain,
( spl0_661
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f4043,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X2)),X2))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_167
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1777]) ).
fof(f28674,plain,
( spl0_660
| ~ spl0_150
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3192,f2948,f1668,f28672]) ).
fof(f28670,plain,
( spl0_659
| ~ spl0_207
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3171,f2944,f2037,f28668]) ).
fof(f28668,plain,
( spl0_659
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f3171,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X1,X2) )
| ~ spl0_207
| ~ spl0_274 ),
inference(resolution,[],[f2945,f2038]) ).
fof(f28666,plain,
( spl0_658
| ~ spl0_207
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3145,f2940,f2037,f28664]) ).
fof(f28664,plain,
( spl0_658
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f3145,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X3),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2) )
| ~ spl0_207
| ~ spl0_273 ),
inference(resolution,[],[f2941,f2038]) ).
fof(f28662,plain,
( spl0_657
| ~ spl0_213
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2877,f2572,f2064,f28660]) ).
fof(f28660,plain,
( spl0_657
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f2877,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X1),X3)) )
| ~ spl0_213
| ~ spl0_264 ),
inference(superposition,[],[f2065,f2573]) ).
fof(f28655,plain,
( spl0_656
| ~ spl0_80
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f2468,f2315,f1315,f28653]) ).
fof(f28653,plain,
( spl0_656
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2468,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1),X0)) )
| ~ spl0_80
| ~ spl0_242 ),
inference(resolution,[],[f2316,f1316]) ).
fof(f28651,plain,
( spl0_655
| ~ spl0_80
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2463,f2311,f1315,f28649]) ).
fof(f28649,plain,
( spl0_655
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2463,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3),X0)) )
| ~ spl0_80
| ~ spl0_241 ),
inference(resolution,[],[f2312,f1316]) ).
fof(f28647,plain,
( spl0_654
| ~ spl0_42
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1595,f1563,f1151,f28645]) ).
fof(f28645,plain,
( spl0_654
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(tc_fun(X0,X1)),X2) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f1151,plain,
( spl0_42
<=> ! [X80,X79] :
( ~ class_Orderings_Oorder(X80)
| class_Orderings_Oorder(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1563,plain,
( spl0_130
<=> ! [X0,X1] :
( hAPP(c_fequal(X0),X1) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1595,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(tc_fun(X0,X1)),X2) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_42
| ~ spl0_130 ),
inference(resolution,[],[f1564,f1152]) ).
fof(f1152,plain,
( ! [X80,X79] :
( class_Orderings_Oorder(tc_fun(X79,X80))
| ~ class_Orderings_Oorder(X80) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f1564,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| hAPP(c_fequal(X0),X1) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X0) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1563]) ).
fof(f28643,plain,
( spl0_653
| ~ spl0_35
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1592,f1559,f1123,f28641]) ).
fof(f28641,plain,
( spl0_653
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f1559,plain,
( spl0_129
<=> ! [X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_fequal(X0),X1)) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1592,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_35
| ~ spl0_129 ),
inference(resolution,[],[f1560,f1124]) ).
fof(f1560,plain,
( ! [X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_fequal(X0),X1)) = X1 )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f28639,plain,
( spl0_652
| ~ spl0_35
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1590,f1555,f1123,f28637]) ).
fof(f28637,plain,
( spl0_652
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f1555,plain,
( spl0_128
<=> ! [X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_fequal(X0),X1)) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1590,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_35
| ~ spl0_128 ),
inference(resolution,[],[f1556,f1124]) ).
fof(f1556,plain,
( ! [X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_fequal(X0),X1)) = X1 )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1555]) ).
fof(f28635,plain,
( spl0_651
| ~ spl0_44
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1586,f1551,f1159,f28633]) ).
fof(f28633,plain,
( spl0_651
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,X1))),v_x)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1159,plain,
( spl0_44
<=> ! [X80,X79] :
( ~ class_Orderings_Obot(X80)
| class_Orderings_Obot(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1551,plain,
( spl0_127
<=> ! [X7] :
( ~ class_Orderings_Obot(X7)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X7)),v_x) = c_Orderings_Obot__class_Obot(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1586,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,X1))),v_x)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_44
| ~ spl0_127 ),
inference(resolution,[],[f1552,f1160]) ).
fof(f1160,plain,
( ! [X80,X79] :
( class_Orderings_Obot(tc_fun(X79,X80))
| ~ class_Orderings_Obot(X80) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f1552,plain,
( ! [X7] :
( ~ class_Orderings_Obot(X7)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X7)),v_x) = c_Orderings_Obot__class_Obot(X7) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1551]) ).
fof(f28631,plain,
( spl0_650
| ~ spl0_43
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1583,f1543,f1155,f28629]) ).
fof(f28629,plain,
( spl0_650
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_fun(X0,X1))),v_x)
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f1155,plain,
( spl0_43
<=> ! [X80,X79] :
( ~ class_Orderings_Otop(X80)
| class_Orderings_Otop(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1543,plain,
( spl0_125
<=> ! [X7] :
( ~ class_Orderings_Otop(X7)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X7)),v_x) = c_Orderings_Otop__class_Otop(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1583,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_fun(X0,X1))),v_x)
| ~ class_Orderings_Otop(X1) )
| ~ spl0_43
| ~ spl0_125 ),
inference(resolution,[],[f1544,f1156]) ).
fof(f1156,plain,
( ! [X80,X79] :
( class_Orderings_Otop(tc_fun(X79,X80))
| ~ class_Orderings_Otop(X80) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f1544,plain,
( ! [X7] :
( ~ class_Orderings_Otop(X7)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X7)),v_x) = c_Orderings_Otop__class_Otop(X7) )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1543]) ).
fof(f28627,plain,
( spl0_649
| ~ spl0_39
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1577,f1539,f1139,f28625]) ).
fof(f28625,plain,
( spl0_649
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f1539,plain,
( spl0_124
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Obot__class_Obot(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1577,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_39
| ~ spl0_124 ),
inference(resolution,[],[f1540,f1140]) ).
fof(f1540,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Obot__class_Obot(X0)) = X3 )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1539]) ).
fof(f28623,plain,
( spl0_648
| ~ spl0_39
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1575,f1535,f1139,f28621]) ).
fof(f28621,plain,
( spl0_648
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f1535,plain,
( spl0_123
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1575,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_39
| ~ spl0_123 ),
inference(resolution,[],[f1536,f1140]) ).
fof(f1536,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X3) = X3 )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1535]) ).
fof(f28619,plain,
( spl0_647
| ~ spl0_39
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1573,f1527,f1139,f28617]) ).
fof(f28617,plain,
( spl0_647
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f1527,plain,
( spl0_121
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Otop__class_Otop(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1573,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_39
| ~ spl0_121 ),
inference(resolution,[],[f1528,f1140]) ).
fof(f1528,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Otop__class_Otop(X0)) = X3 )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1527]) ).
fof(f28615,plain,
( spl0_646
| ~ spl0_57
| ~ spl0_622 ),
inference(avatar_split_clause,[],[f28438,f14633,f1218,f28613]) ).
fof(f14633,plain,
( spl0_622
<=> ! [X0,X1] :
( c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_fequal(X1),X0)) = X0
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X0),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f28438,plain,
( ! [X0] : c_False = c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_fequal(X0),c_False))
| ~ spl0_57
| ~ spl0_622 ),
inference(resolution,[],[f14634,f1219]) ).
fof(f14634,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X0),c_False))
| c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_fequal(X1),X0)) = X0 )
| ~ spl0_622 ),
inference(avatar_component_clause,[],[f14633]) ).
fof(f28611,plain,
( spl0_645
| ~ spl0_39
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1571,f1523,f1139,f28609]) ).
fof(f28609,plain,
( spl0_645
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1523,plain,
( spl0_120
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1571,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_39
| ~ spl0_120 ),
inference(resolution,[],[f1524,f1140]) ).
fof(f1524,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X3) = X3 )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1523]) ).
fof(f28430,plain,
( spl0_644
| ~ spl0_150
| ~ spl0_169
| ~ spl0_171
| ~ spl0_275
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f8809,f8434,f2948,f1792,f1784,f1668,f28428]) ).
fof(f28428,plain,
( spl0_644
<=> ! [X0,X3,X2,X1] : hAPP(X2,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X1),X0),X2,X1,tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f8809,plain,
( ! [X2,X3,X0,X1] : hAPP(X2,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X1),X0),X2,X1,tc_fun(X3,tc_bool))
| ~ spl0_150
| ~ spl0_169
| ~ spl0_171
| ~ spl0_275
| ~ spl0_476 ),
inference(forward_demodulation,[],[f8808,f1785]) ).
fof(f8808,plain,
( ! [X2,X3,X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X1),X0),X2,X1,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X2,X0)),c_COMBK(c_False,tc_bool,X3))
| ~ spl0_150
| ~ spl0_171
| ~ spl0_275
| ~ spl0_476 ),
inference(forward_demodulation,[],[f8672,f3192]) ).
fof(f8672,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X2,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X1),X2,X1,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X1),X0),X2,X1,tc_fun(X3,tc_bool))
| ~ spl0_171
| ~ spl0_476 ),
inference(superposition,[],[f8435,f1793]) ).
fof(f28417,plain,
( ~ spl0_24
| spl0_643
| ~ spl0_146
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4052,f3920,f1651,f28415,f1077]) ).
fof(f28415,plain,
( spl0_643
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f4052,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_146
| ~ spl0_327 ),
inference(resolution,[],[f3921,f1652]) ).
fof(f28413,plain,
( spl0_642
| ~ spl0_107
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3282,f3004,f1442,f28411]) ).
fof(f28411,plain,
( spl0_642
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f3282,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1443]) ).
fof(f28409,plain,
( spl0_641
| ~ spl0_105
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3266,f3004,f1433,f28407]) ).
fof(f28407,plain,
( spl0_641
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f3266,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1434]) ).
fof(f28405,plain,
( spl0_640
| ~ spl0_107
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3256,f3000,f1442,f28403]) ).
fof(f28403,plain,
( spl0_640
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f3256,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1443]) ).
fof(f28401,plain,
( ~ spl0_639
| spl0_56
| ~ spl0_86
| ~ spl0_194
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f6402,f3137,f1922,f1340,f1213,f28398]) ).
fof(f28398,plain,
( spl0_639
<=> hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f1922,plain,
( spl0_194
<=> ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_False) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f6402,plain,
( hBOOL(c_False)
| ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))
| ~ spl0_86
| ~ spl0_194
| ~ spl0_295 ),
inference(forward_demodulation,[],[f6386,f1923]) ).
fof(f1923,plain,
( ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_False)
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f1922]) ).
fof(f6386,plain,
( ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))
| hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_False))
| ~ spl0_86
| ~ spl0_295 ),
inference(superposition,[],[f1341,f3138]) ).
fof(f28396,plain,
( spl0_638
| ~ spl0_105
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3240,f3000,f1433,f28394]) ).
fof(f28394,plain,
( spl0_638
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f3240,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1434]) ).
fof(f27533,plain,
( ~ spl0_16
| spl0_636
| ~ spl0_637
| ~ spl0_186
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2423,f2001,f1884,f27530,f27527,f1037]) ).
fof(f1037,plain,
( spl0_16
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f27527,plain,
( spl0_636
<=> ! [X0] : c_False = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f27530,plain,
( spl0_637
<=> c_False = c_Orderings_Otop__class_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f2001,plain,
( spl0_198
<=> ! [X11,X0,X12] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X12
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2423,plain,
( ! [X0] :
( c_False != c_Orderings_Otop__class_Otop(tc_bool)
| c_False = X0
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_186
| ~ spl0_198 ),
inference(inner_rewriting,[],[f2413]) ).
fof(f2413,plain,
( ! [X0] :
( c_False != c_Orderings_Otop__class_Otop(tc_bool)
| c_Orderings_Otop__class_Otop(tc_bool) = X0
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_186
| ~ spl0_198 ),
inference(superposition,[],[f2002,f1885]) ).
fof(f2002,plain,
( ! [X0,X11,X12] :
( c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X11),X12)
| c_Orderings_Otop__class_Otop(X0) = X12
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2001]) ).
fof(f26987,plain,
( ~ spl0_7
| spl0_635
| ~ spl0_114
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1917,f1835,f1476,f26985,f992]) ).
fof(f26985,plain,
( spl0_635
<=> ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1476,plain,
( spl0_114
<=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1917,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X0),X0))
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_114
| ~ spl0_174 ),
inference(superposition,[],[f1836,f1477]) ).
fof(f1477,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X0) = X0
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1476]) ).
fof(f17584,plain,
( spl0_634
| ~ spl0_114
| ~ spl0_619 ),
inference(avatar_split_clause,[],[f13711,f13677,f1476,f17582]) ).
fof(f17582,plain,
( spl0_634
<=> ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f13677,plain,
( spl0_619
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f13711,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),X0))
| ~ spl0_114
| ~ spl0_619 ),
inference(superposition,[],[f13678,f1477]) ).
fof(f13678,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(X0,X1)))
| ~ spl0_619 ),
inference(avatar_component_clause,[],[f13677]) ).
fof(f17466,plain,
( ~ spl0_200
| ~ spl0_631 ),
inference(avatar_contradiction_clause,[],[f17465]) ).
fof(f17465,plain,
( $false
| ~ spl0_200
| ~ spl0_631 ),
inference(resolution,[],[f2010,f17423]) ).
fof(f17423,plain,
( ! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,X0,t_a)
| ~ spl0_631 ),
inference(avatar_component_clause,[],[f17422]) ).
fof(f17422,plain,
( spl0_631
<=> ! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f2010,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X0,X1)
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2009]) ).
fof(f2009,plain,
( spl0_200
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f17446,plain,
( ~ spl0_436
| ~ spl0_632 ),
inference(avatar_contradiction_clause,[],[f17445]) ).
fof(f17445,plain,
( $false
| ~ spl0_436
| ~ spl0_632 ),
inference(resolution,[],[f6729,f17431]) ).
fof(f17431,plain,
( ! [X2] : ~ hBOOL(X2)
| ~ spl0_632 ),
inference(avatar_component_clause,[],[f17430]) ).
fof(f17430,plain,
( spl0_632
<=> ! [X2] : ~ hBOOL(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f6729,plain,
( hBOOL(c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_436 ),
inference(avatar_component_clause,[],[f6727]) ).
fof(f6727,plain,
( spl0_436
<=> hBOOL(c_Orderings_Otop__class_Otop(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f17436,plain,
( spl0_633
| ~ spl0_12
| ~ spl0_630 ),
inference(avatar_split_clause,[],[f15298,f14664,f1017,f17434]) ).
fof(f17434,plain,
( spl0_633
<=> ! [X0] : class_Complete__Lattice_Ocomplete__lattice(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f15298,plain,
( ! [X0] : class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ spl0_12
| ~ spl0_630 ),
inference(superposition,[],[f1019,f14665]) ).
fof(f14665,plain,
( ! [X3,X4] : X3 = X4
| ~ spl0_630 ),
inference(avatar_component_clause,[],[f14664]) ).
fof(f17432,plain,
( spl0_632
| ~ spl0_77
| ~ spl0_630 ),
inference(avatar_split_clause,[],[f14803,f14664,f1303,f17430]) ).
fof(f14803,plain,
( ! [X2] : ~ hBOOL(X2)
| ~ spl0_77
| ~ spl0_630 ),
inference(superposition,[],[f1304,f14665]) ).
fof(f17424,plain,
( spl0_631
| spl0_49
| ~ spl0_630 ),
inference(avatar_split_clause,[],[f15255,f14664,f1182,f17422]) ).
fof(f15255,plain,
( ! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,X0,t_a)
| spl0_49
| ~ spl0_630 ),
inference(superposition,[],[f1184,f14665]) ).
fof(f14666,plain,
( spl0_629
| spl0_630
| ~ spl0_70
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3108,f2920,f1273,f14664,f14661]) ).
fof(f14661,plain,
( spl0_629
<=> ! [X5,X0,X6,X2,X1] : ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f3108,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( X3 = X4
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_70
| ~ spl0_269 ),
inference(trivial_inequality_removal,[],[f3107]) ).
fof(f3107,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( X0 != X0
| X3 = X4
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_70
| ~ spl0_269 ),
inference(forward_demodulation,[],[f3063,f1274]) ).
fof(f3063,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_COMBK(X0,X1,X2),X4) != X0
| X3 = X4
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_70
| ~ spl0_269 ),
inference(superposition,[],[f2921,f1274]) ).
fof(f14659,plain,
( spl0_628
| ~ spl0_207
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2837,f2552,f2037,f14657]) ).
fof(f14657,plain,
( spl0_628
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X2,tc_bool)),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f2837,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X2,tc_bool)),X3),X1)) )
| ~ spl0_207
| ~ spl0_259 ),
inference(resolution,[],[f2553,f2038]) ).
fof(f14655,plain,
( spl0_627
| ~ spl0_107
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2796,f2536,f1442,f14653]) ).
fof(f14653,plain,
( spl0_627
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f2796,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_255 ),
inference(resolution,[],[f2537,f1443]) ).
fof(f14651,plain,
( spl0_626
| ~ spl0_107
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2756,f2528,f1442,f14649]) ).
fof(f14649,plain,
( spl0_626
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f2756,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_253 ),
inference(resolution,[],[f2529,f1443]) ).
fof(f14647,plain,
( spl0_625
| ~ spl0_105
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2621,f2495,f1433,f14645]) ).
fof(f14645,plain,
( spl0_625
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f2621,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_247 ),
inference(resolution,[],[f2496,f1434]) ).
fof(f14643,plain,
( spl0_624
| ~ spl0_105
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2589,f2487,f1433,f14641]) ).
fof(f14641,plain,
( spl0_624
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f2589,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_245 ),
inference(resolution,[],[f2488,f1434]) ).
fof(f14639,plain,
( spl0_623
| ~ spl0_79
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2157,f2029,f1311,f14637]) ).
fof(f14637,plain,
( spl0_623
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),hAPP(X0,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f2157,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_Set_Oimage(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),hAPP(X0,X3)))
| ~ spl0_79
| ~ spl0_205 ),
inference(resolution,[],[f2030,f1312]) ).
fof(f14635,plain,
( spl0_622
| ~ spl0_87
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1514,f1455,f1344,f14633]) ).
fof(f1514,plain,
( ! [X0,X1] :
( c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(hAPP(c_fequal(X1),X0)) = X0
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X0),c_False)) )
| ~ spl0_87
| ~ spl0_110 ),
inference(resolution,[],[f1456,f1345]) ).
fof(f14631,plain,
( spl0_621
| ~ spl0_70
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1470,f1375,f1273,f14629]) ).
fof(f14629,plain,
( spl0_621
<=> ! [X2,X4,X0,X5,X3,X1] : c_COMBK(X0,X1,X2) = c_Fun_Ofun__upd(c_COMBK(X0,X1,X2),X3,X0,X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f1470,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_COMBK(X0,X1,X2) = c_Fun_Ofun__upd(c_COMBK(X0,X1,X2),X3,X0,X4,X5)
| ~ spl0_70
| ~ spl0_91 ),
inference(superposition,[],[f1376,f1274]) ).
fof(f14155,plain,
( spl0_620
| ~ spl0_375
| ~ spl0_599 ),
inference(avatar_split_clause,[],[f13623,f13524,f5030,f14153]) ).
fof(f14153,plain,
( spl0_620
<=> ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f13524,plain,
( spl0_599
<=> ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f13623,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool)
| ~ spl0_375
| ~ spl0_599 ),
inference(superposition,[],[f13525,f5031]) ).
fof(f13525,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ spl0_599 ),
inference(avatar_component_clause,[],[f13524]) ).
fof(f13679,plain,
( spl0_619
| ~ spl0_24
| ~ spl0_83
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5185,f5042,f1328,f1077,f13677]) ).
fof(f5185,plain,
( ! [X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(X0,X1))) )
| ~ spl0_83
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1329]) ).
fof(f13675,plain,
( spl0_618
| ~ spl0_167
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3180,f2944,f1776,f13673]) ).
fof(f13673,plain,
( spl0_618
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X2),X3,X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f3180,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X2),X3,X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X1) )
| ~ spl0_167
| ~ spl0_274 ),
inference(resolution,[],[f2945,f1777]) ).
fof(f13671,plain,
( spl0_617
| ~ spl0_167
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3120,f2936,f1776,f13669]) ).
fof(f13669,plain,
( spl0_617
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(X0,hAPP(c_Set_Oinsert(X1,X2),hAPP(c_Set_Oinsert(X0,X2),X3)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f3120,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,hAPP(c_Set_Oinsert(X1,X2),hAPP(c_Set_Oinsert(X0,X2),X3)),X2))
| ~ spl0_167
| ~ spl0_272 ),
inference(resolution,[],[f2937,f1777]) ).
fof(f13667,plain,
( spl0_616
| ~ spl0_371
| ~ spl0_599 ),
inference(avatar_split_clause,[],[f13622,f13524,f4832,f13665]) ).
fof(f13665,plain,
( spl0_616
<=> ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f13622,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat)
| ~ spl0_371
| ~ spl0_599 ),
inference(superposition,[],[f13525,f4833]) ).
fof(f13663,plain,
( spl0_615
| ~ spl0_105
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2782,f2536,f1433,f13661]) ).
fof(f13661,plain,
( spl0_615
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f2782,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_255 ),
inference(resolution,[],[f2537,f1434]) ).
fof(f13659,plain,
( spl0_614
| ~ spl0_105
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2742,f2528,f1433,f13657]) ).
fof(f2742,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_253 ),
inference(resolution,[],[f2529,f1434]) ).
fof(f13655,plain,
( spl0_613
| ~ spl0_239
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2642,f2499,f2303,f13653]) ).
fof(f13653,plain,
( spl0_613
<=> ! [X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X3)
| c_Fun_Oinj__on(X2,X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f2642,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X3)
| c_Fun_Oinj__on(X2,X1,X0,X3) )
| ~ spl0_239
| ~ spl0_248 ),
inference(superposition,[],[f2500,f2304]) ).
fof(f13651,plain,
( spl0_612
| ~ spl0_107
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2635,f2495,f1442,f13649]) ).
fof(f13649,plain,
( spl0_612
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f2635,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_247 ),
inference(resolution,[],[f2496,f1443]) ).
fof(f13647,plain,
( spl0_611
| ~ spl0_107
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2603,f2487,f1442,f13645]) ).
fof(f13645,plain,
( spl0_611
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2603,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_245 ),
inference(resolution,[],[f2488,f1443]) ).
fof(f13643,plain,
( spl0_610
| ~ spl0_28
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2244,f2105,f1094,f13641]) ).
fof(f13641,plain,
( spl0_610
<=> ! [X0,X1] : hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = hAPP(c_fequal(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f1094,plain,
( spl0_28
<=> ! [X29,X0] : c_Collect(X29,X0) = X29 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f2105,plain,
( spl0_223
<=> ! [X0,X1] : c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = hAPP(c_fequal(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2244,plain,
( ! [X0,X1] : hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = hAPP(c_fequal(X0),X1)
| ~ spl0_28
| ~ spl0_223 ),
inference(superposition,[],[f2106,f1095]) ).
fof(f1095,plain,
( ! [X29,X0] : c_Collect(X29,X0) = X29
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1094]) ).
fof(f2106,plain,
( ! [X0,X1] : c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = hAPP(c_fequal(X0),X1)
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2105]) ).
fof(f13639,plain,
( spl0_609
| ~ spl0_13
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2186,f2041,f1022,f13637]) ).
fof(f13637,plain,
( spl0_609
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2186,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0)
| ~ spl0_13
| ~ spl0_208 ),
inference(resolution,[],[f2042,f1024]) ).
fof(f13635,plain,
( spl0_608
| ~ spl0_2
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2185,f2041,f967,f13633]) ).
fof(f2185,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X0)
| ~ spl0_2
| ~ spl0_208 ),
inference(resolution,[],[f2042,f969]) ).
fof(f13631,plain,
( spl0_607
| ~ spl0_14
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2151,f2021,f1027,f13629]) ).
fof(f13629,plain,
( spl0_607
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f2151,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)
| ~ spl0_14
| ~ spl0_203 ),
inference(resolution,[],[f2022,f1029]) ).
fof(f13627,plain,
( spl0_606
| ~ spl0_3
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2150,f2021,f972,f13625]) ).
fof(f2150,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X0)
| ~ spl0_3
| ~ spl0_203 ),
inference(resolution,[],[f2022,f974]) ).
fof(f13620,plain,
( spl0_605
| ~ spl0_19
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2117,f1993,f1052,f13618]) ).
fof(f13618,plain,
( spl0_605
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f2117,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)) = X0
| ~ spl0_19
| ~ spl0_196 ),
inference(resolution,[],[f1994,f1054]) ).
fof(f13616,plain,
( spl0_604
| ~ spl0_7
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2116,f1993,f992,f13614]) ).
fof(f2116,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1)) = X0
| ~ spl0_7
| ~ spl0_196 ),
inference(resolution,[],[f1994,f994]) ).
fof(f13612,plain,
( spl0_603
| ~ spl0_19
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2114,f1989,f1052,f13610]) ).
fof(f13610,plain,
( spl0_603
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f2114,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)) = X0
| ~ spl0_19
| ~ spl0_195 ),
inference(resolution,[],[f1990,f1054]) ).
fof(f13608,plain,
( spl0_602
| ~ spl0_7
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2113,f1989,f992,f13606]) ).
fof(f13606,plain,
( spl0_602
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f2113,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1)) = X0
| ~ spl0_7
| ~ spl0_195 ),
inference(resolution,[],[f1990,f994]) ).
fof(f13604,plain,
( spl0_601
| ~ spl0_79
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1956,f1876,f1311,f13602]) ).
fof(f13602,plain,
( spl0_601
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f1956,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X2),X1),X0)) )
| ~ spl0_79
| ~ spl0_184 ),
inference(resolution,[],[f1877,f1312]) ).
fof(f13600,plain,
( spl0_600
| spl0_56
| ~ spl0_86
| ~ spl0_169
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1819,f1788,f1784,f1340,f1213,f13598]) ).
fof(f13598,plain,
( spl0_600
<=> ! [X0] : ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f1819,plain,
( ! [X0] :
( hBOOL(c_False)
| ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)))) )
| ~ spl0_86
| ~ spl0_169
| ~ spl0_170 ),
inference(forward_demodulation,[],[f1818,f1785]) ).
fof(f1818,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_False),c_COMBK(c_False,tc_bool,X0)))
| ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)))) )
| ~ spl0_86
| ~ spl0_170 ),
inference(forward_demodulation,[],[f1815,f341]) ).
fof(f341,axiom,
! [X0,X11,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f1815,plain,
( ! [X0] :
( ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))))
| hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_False)) )
| ~ spl0_86
| ~ spl0_170 ),
inference(superposition,[],[f1341,f1789]) ).
fof(f13526,plain,
( spl0_599
| ~ spl0_47
| ~ spl0_590 ),
inference(avatar_split_clause,[],[f13417,f13345,f1171,f13524]) ).
fof(f13345,plain,
( spl0_590
<=> ! [X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_fequal(X1),X0),X1)
| ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f13417,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ spl0_47
| ~ spl0_590 ),
inference(resolution,[],[f13346,f1172]) ).
fof(f13346,plain,
( ! [X0,X1] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X1)
| c_Finite__Set_Ofinite(hAPP(c_fequal(X1),X0),X1) )
| ~ spl0_590 ),
inference(avatar_component_clause,[],[f13345]) ).
fof(f13410,plain,
( spl0_598
| ~ spl0_66
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3823,f3420,f1256,f13408]) ).
fof(f3823,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X2,X1),hAPP(c_Set_Oinsert(X0,X1),X3)),X0))
| ~ spl0_66
| ~ spl0_313 ),
inference(superposition,[],[f1257,f3421]) ).
fof(f13375,plain,
( spl0_597
| ~ spl0_155
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3173,f2944,f1690,f13373]) ).
fof(f13373,plain,
( spl0_597
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X2)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f3173,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X2)),X1,X2) )
| ~ spl0_155
| ~ spl0_274 ),
inference(resolution,[],[f2945,f1691]) ).
fof(f13371,plain,
( spl0_596
| ~ spl0_187
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2406,f2299,f1888,f13369]) ).
fof(f13369,plain,
( spl0_596
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2),X2,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f2406,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2),X2,X0)
| ~ spl0_187
| ~ spl0_238 ),
inference(resolution,[],[f2300,f1889]) ).
fof(f13367,plain,
( spl0_595
| ~ spl0_187
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2399,f2295,f1888,f13365]) ).
fof(f13365,plain,
( spl0_595
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2),X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2399,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1),X2),X1,X0)
| ~ spl0_187
| ~ spl0_237 ),
inference(resolution,[],[f2296,f1889]) ).
fof(f13363,plain,
( spl0_594
| ~ spl0_107
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2395,f2291,f1442,f13361]) ).
fof(f13361,plain,
( spl0_594
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f2395,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1443]) ).
fof(f13359,plain,
( spl0_593
| ~ spl0_105
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2385,f2291,f1433,f13357]) ).
fof(f13357,plain,
( spl0_593
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f2385,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_236 ),
inference(resolution,[],[f2292,f1434]) ).
fof(f13355,plain,
( spl0_592
| ~ spl0_107
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2375,f2287,f1442,f13353]) ).
fof(f13353,plain,
( spl0_592
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f2375,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_107
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1443]) ).
fof(f13351,plain,
( spl0_591
| ~ spl0_105
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2365,f2287,f1433,f13349]) ).
fof(f13349,plain,
( spl0_591
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2365,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_105
| ~ spl0_235 ),
inference(resolution,[],[f2288,f1434]) ).
fof(f13347,plain,
( spl0_590
| ~ spl0_97
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1824,f1792,f1401,f13345]) ).
fof(f1824,plain,
( ! [X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_fequal(X1),X0),X1)
| ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X1),X1) )
| ~ spl0_97
| ~ spl0_171 ),
inference(superposition,[],[f1402,f1793]) ).
fof(f13343,plain,
( spl0_589
| ~ spl0_65
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1748,f1694,f1252,f13341]) ).
fof(f13341,plain,
( spl0_589
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSKIP,X2,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f1748,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSKIP,X2,X1)),X1)
| ~ spl0_65
| ~ spl0_156 ),
inference(resolution,[],[f1695,f1253]) ).
fof(f13339,plain,
( spl0_588
| ~ spl0_36
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1491,f1409,f1127,f13337]) ).
fof(f1409,plain,
( spl0_99
<=> ! [X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1491,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_36
| ~ spl0_99 ),
inference(resolution,[],[f1410,f1128]) ).
fof(f1410,plain,
( ! [X3,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X3) = X3 )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1409]) ).
fof(f13335,plain,
( spl0_587
| ~ spl0_114
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f13084,f13053,f1476,f13333]) ).
fof(f13053,plain,
( spl0_585
<=> ! [X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_False),hAPP(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f13084,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_False),X0))
| ~ spl0_114
| ~ spl0_585 ),
inference(superposition,[],[f13054,f1477]) ).
fof(f13054,plain,
( ! [X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_False),hAPP(X2,X1)))
| ~ spl0_585 ),
inference(avatar_component_clause,[],[f13053]) ).
fof(f13331,plain,
( spl0_586
| ~ spl0_37
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1474,f1383,f1131,f13329]) ).
fof(f1383,plain,
( spl0_93
<=> ! [X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1474,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_37
| ~ spl0_93 ),
inference(resolution,[],[f1384,f1132]) ).
fof(f1384,plain,
( ! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X3) = X3 )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f13055,plain,
( ~ spl0_24
| spl0_585
| ~ spl0_70
| ~ spl0_155
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5220,f5042,f1690,f1273,f13053,f1077]) ).
fof(f5220,plain,
( ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_False),hAPP(X2,X1)))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_70
| ~ spl0_155
| ~ spl0_378 ),
inference(forward_demodulation,[],[f5192,f1274]) ).
fof(f5192,plain,
( ! [X2,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(c_COMBK(c_False,tc_bool,X0),X1)),hAPP(X2,X1))) )
| ~ spl0_155
| ~ spl0_378 ),
inference(resolution,[],[f5043,f1691]) ).
fof(f13051,plain,
( spl0_584
| ~ spl0_84
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3285,f3004,f1332,f13049]) ).
fof(f3285,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_84
| ~ spl0_289 ),
inference(duplicate_literal_removal,[],[f3262]) ).
fof(f3262,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_84
| ~ spl0_289 ),
inference(resolution,[],[f3005,f1333]) ).
fof(f13047,plain,
( spl0_583
| ~ spl0_84
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3259,f3000,f1332,f13045]) ).
fof(f3259,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_84
| ~ spl0_288 ),
inference(duplicate_literal_removal,[],[f3236]) ).
fof(f3236,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_84
| ~ spl0_288 ),
inference(resolution,[],[f3001,f1333]) ).
fof(f13043,plain,
( spl0_582
| ~ spl0_187
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f2181,f2037,f1888,f13041]) ).
fof(f2181,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X1)
| ~ spl0_187
| ~ spl0_207 ),
inference(resolution,[],[f2038,f1889]) ).
fof(f13038,plain,
( spl0_581
| ~ spl0_80
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1730,f1643,f1315,f13036]) ).
fof(f13036,plain,
( spl0_581
<=> ! [X2,X0,X1] :
( hAPP(c_Set_Oinsert(X0,X1),X2) = X2
| ~ hBOOL(hAPP(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1730,plain,
( ! [X2,X0,X1] :
( hAPP(c_Set_Oinsert(X0,X1),X2) = X2
| ~ hBOOL(hAPP(X2,X0)) )
| ~ spl0_80
| ~ spl0_144 ),
inference(resolution,[],[f1644,f1316]) ).
fof(f12858,plain,
( spl0_580
| ~ spl0_26
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2325,f2259,f1086,f12856]) ).
fof(f12856,plain,
( spl0_580
<=> ! [X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X0,X1,X2,X3)
| c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2325,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Fun_Oinj__on(X0,X1,X2,X3)
| c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X3) )
| ~ spl0_26
| ~ spl0_228 ),
inference(resolution,[],[f2260,f1087]) ).
fof(f12854,plain,
( spl0_579
| ~ spl0_12
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1750,f1703,f1017,f12851]) ).
fof(f1750,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(c_False,tc_bool,tc_bool))
| ~ spl0_12
| ~ spl0_158 ),
inference(resolution,[],[f1704,f1019]) ).
fof(f12849,plain,
( spl0_578
| ~ spl0_12
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1727,f1639,f1017,f12846]) ).
fof(f12846,plain,
( spl0_578
<=> c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1727,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)))
| ~ spl0_12
| ~ spl0_143 ),
inference(resolution,[],[f1640,f1019]) ).
fof(f12844,plain,
( spl0_577
| ~ spl0_16
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1718,f1619,f1037,f12842]) ).
fof(f12842,plain,
( spl0_577
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1718,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0)
| ~ spl0_16
| ~ spl0_138 ),
inference(resolution,[],[f1620,f1039]) ).
fof(f1039,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f1037]) ).
fof(f12839,plain,
( spl0_576
| ~ spl0_16
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1716,f1610,f1037,f12837]) ).
fof(f12837,plain,
( spl0_576
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f1716,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_16
| ~ spl0_136 ),
inference(resolution,[],[f1611,f1039]) ).
fof(f12619,plain,
spl0_575,
inference(avatar_split_clause,[],[f216,f12617]) ).
fof(f12617,plain,
( spl0_575
<=> ! [X18,X11,X0,X12,X8,X7] :
( ~ c_Fun_Oinj__on(X8,X18,X0,X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X8,X0,X7),X11),tc_fun(X7,tc_bool)),hAPP(c_Set_Oimage(X8,X0,X7),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f216,axiom,
! [X0,X11,X18,X8,X7,X12] :
( ~ c_Fun_Oinj__on(X8,X18,X0,X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X8,X0,X7),X11),tc_fun(X7,tc_bool)),hAPP(c_Set_Oimage(X8,X0,X7),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
fof(f12596,plain,
( spl0_574
| ~ spl0_244
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11665,f5030,f2328,f12594]) ).
fof(f12594,plain,
( spl0_574
<=> ! [X0] : hBOOL(c_in(X0,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f11665,plain,
( ! [X0] : hBOOL(c_in(X0,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool))
| ~ spl0_244
| ~ spl0_375 ),
inference(superposition,[],[f2329,f5031]) ).
fof(f12592,plain,
( spl0_573
| ~ spl0_28
| ~ spl0_223
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f12588,f12585,f2105,f1094,f12590]) ).
fof(f12590,plain,
( spl0_573
<=> ! [X5,X13,X29,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X5,c_COMBK(hAPP(X30,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f12585,plain,
( spl0_572
<=> ! [X5,X13,X29,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X5,c_COMBK(hAPP(X30,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f12588,plain,
( ! [X29,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X5,c_COMBK(hAPP(X30,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a) )
| ~ spl0_28
| ~ spl0_223
| ~ spl0_572 ),
inference(forward_demodulation,[],[f12586,f2244]) ).
fof(f12586,plain,
( ! [X29,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X5,c_COMBK(hAPP(X30,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a) )
| ~ spl0_572 ),
inference(avatar_component_clause,[],[f12585]) ).
fof(f12587,plain,
spl0_572,
inference(avatar_split_clause,[],[f815,f12585]) ).
fof(f815,plain,
! [X29,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X5,c_COMBK(hAPP(X30,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a) ),
inference(forward_demodulation,[],[f814,f686]) ).
fof(f686,plain,
! [X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),
inference(forward_demodulation,[],[f685,f665]) ).
fof(f665,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,X0),
inference(forward_demodulation,[],[f592,f272]) ).
fof(f272,axiom,
! [X29,X0] : c_Collect(X29,X0) = X29,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f592,axiom,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__def_0) ).
fof(f685,plain,
! [X0,X1] : hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = hAPP(c_fequal(X0),X1),
inference(forward_demodulation,[],[f542,f272]) ).
fof(f542,axiom,
! [X0,X1] : hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Collect(hAPP(c_fequal(X0),X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
fof(f814,plain,
! [X29,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X5,c_COMBK(hAPP(X30,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a) ),
inference(forward_demodulation,[],[f813,f665]) ).
fof(f813,plain,
! [X29,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X5,c_COMBK(hAPP(X30,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f812,f686]) ).
fof(f812,plain,
! [X29,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X5,c_COMBK(hAPP(X30,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f575,f665]) ).
fof(f575,axiom,
! [X29,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X5,c_COMBK(hAPP(X30,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_1) ).
fof(f12579,plain,
spl0_571,
inference(avatar_split_clause,[],[f933,f12577]) ).
fof(f12577,plain,
( spl0_571
<=> ! [X5,X29,X0,X13,X6,X2,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X6,X30,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OCond(X2,X5,X6),X30,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X30,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f933,plain,
! [X2,X0,X29,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X6,X30,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OCond(X2,X5,X6),X30,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X30,X0)),X0) ),
inference(forward_demodulation,[],[f932,f686]) ).
fof(f932,plain,
! [X2,X29,X0,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X6,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OCond(X2,X5,X6),X30,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X30,X0)),X0) ),
inference(forward_demodulation,[],[f931,f665]) ).
fof(f931,plain,
! [X2,X0,X29,X6,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OCond(X2,X5,X6),X30,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X30,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X6,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f930,f686]) ).
fof(f930,plain,
! [X2,X29,X0,X6,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OCond(X2,X5,X6),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X30,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X6,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f929,f665]) ).
fof(f929,plain,
! [X2,X0,X29,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X30,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OCond(X2,X5,X6),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X6,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f928,f686]) ).
fof(f928,plain,
! [X2,X29,X0,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OCond(X2,X5,X6),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X6,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f538,f665]) ).
fof(f538,axiom,
! [X2,X29,X0,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OCond(X2,X5,X6),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X6,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OIf_0) ).
fof(f12567,plain,
spl0_570,
inference(avatar_split_clause,[],[f957,f12565]) ).
fof(f12565,plain,
( spl0_570
<=> ! [X5,X3,X13,X29,X74,X25,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f957,plain,
! [X3,X29,X5,X25,X13,X30,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25))) ),
inference(forward_demodulation,[],[f956,f686]) ).
fof(f956,plain,
! [X3,X29,X5,X25,X13,X30,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25))) ),
inference(forward_demodulation,[],[f955,f665]) ).
fof(f955,plain,
! [X3,X29,X5,X25,X13,X74,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f954,f686]) ).
fof(f954,plain,
! [X3,X29,X5,X25,X13,X74,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f576,f665]) ).
fof(f576,axiom,
! [X3,X29,X5,X25,X74,X13,X30] :
( ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_1) ).
fof(f12563,plain,
spl0_569,
inference(avatar_split_clause,[],[f953,f12561]) ).
fof(f12561,plain,
( spl0_569
<=> ! [X5,X3,X13,X29,X74,X25,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f953,plain,
! [X3,X29,X5,X25,X13,X30,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25))) ),
inference(forward_demodulation,[],[f952,f686]) ).
fof(f952,plain,
! [X3,X29,X5,X25,X13,X30,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25))) ),
inference(forward_demodulation,[],[f951,f665]) ).
fof(f951,plain,
! [X3,X29,X5,X25,X13,X74,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f950,f686]) ).
fof(f950,plain,
! [X3,X29,X5,X25,X13,X74,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f578,f665]) ).
fof(f578,axiom,
! [X3,X29,X5,X25,X74,X13,X30] :
( ~ hBOOL(hAPP(hAPP(X3,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5)))
| hBOOL(hAPP(hAPP(X25,X74),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
fof(f12512,plain,
( spl0_568
| ~ spl0_226
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11664,f5030,f2251,f12510]) ).
fof(f12510,plain,
( spl0_568
<=> ! [X0] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f2251,plain,
( spl0_226
<=> ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X1),X0),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f11664,plain,
( ! [X0] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0
| ~ spl0_226
| ~ spl0_375 ),
inference(superposition,[],[f2252,f5031]) ).
fof(f2252,plain,
( ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X1),X0),X1) = X0
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2251]) ).
fof(f12479,plain,
spl0_567,
inference(avatar_split_clause,[],[f943,f12477]) ).
fof(f12477,plain,
( spl0_567
<=> ! [X11,X0,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3))),X12))
| hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f943,plain,
! [X3,X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3))),X12))
| hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
inference(forward_demodulation,[],[f942,f686]) ).
fof(f942,plain,
! [X3,X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)))),X12))
| hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
inference(forward_demodulation,[],[f301,f665]) ).
fof(f301,axiom,
! [X3,X0,X11,X12] :
( hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
fof(f12475,plain,
spl0_566,
inference(avatar_split_clause,[],[f10,f12473]) ).
fof(f12473,plain,
( spl0_566
<=> ! [X5,X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f10,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).
fof(f12471,plain,
spl0_565,
inference(avatar_split_clause,[],[f9,f12469]) ).
fof(f12469,plain,
( spl0_565
<=> ! [X2,X6,X0,X5,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f9,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).
fof(f12463,plain,
spl0_564,
inference(avatar_split_clause,[],[f949,f12461]) ).
fof(f12461,plain,
( spl0_564
<=> ! [X5,X74,X13,X75,X29,X76,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X76,X74),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75)))
| hBOOL(hAPP(hAPP(X75,X74),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f949,plain,
! [X74,X29,X76,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X76,X74),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75)))
| hBOOL(hAPP(hAPP(X75,X74),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75))) ),
inference(forward_demodulation,[],[f948,f686]) ).
fof(f948,plain,
! [X74,X29,X76,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X76,X74),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75)))
| hBOOL(hAPP(hAPP(X75,X74),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75))) ),
inference(forward_demodulation,[],[f947,f665]) ).
fof(f947,plain,
! [X30,X29,X76,X5,X13,X74,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X76,X74),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75)))
| hBOOL(hAPP(hAPP(X75,X74),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f946,f686]) ).
fof(f946,plain,
! [X30,X29,X76,X5,X13,X74,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X76,X74),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75)))
| hBOOL(hAPP(hAPP(X75,X74),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f577,f665]) ).
fof(f577,axiom,
! [X13,X29,X76,X5,X74,X30,X75] :
( ~ hBOOL(hAPP(hAPP(X76,X74),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75)))
| hBOOL(hAPP(hAPP(X75,X74),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_1) ).
fof(f12388,plain,
spl0_563,
inference(avatar_split_clause,[],[f311,f12386]) ).
fof(f12386,plain,
( spl0_563
<=> ! [X18,X11,X0,X12,X3,X7] :
( ~ hBOOL(c_in(X3,X18,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_prod(X7,X0),tc_bool)),c_Product__Type_OSigma(X11,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0)),c_Product__Type_OSigma(X12,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f311,axiom,
! [X3,X0,X11,X18,X7,X12] :
( ~ hBOOL(c_in(X3,X18,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_prod(X7,X0),tc_bool)),c_Product__Type_OSigma(X11,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0)),c_Product__Type_OSigma(X12,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
fof(f12384,plain,
spl0_562,
inference(avatar_split_clause,[],[f310,f12382]) ).
fof(f12382,plain,
( spl0_562
<=> ! [X18,X11,X0,X12,X3,X7] :
( ~ hBOOL(c_in(X3,X18,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_prod(X7,X0),tc_bool)),c_Product__Type_OSigma(X11,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0)),c_Product__Type_OSigma(X12,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f310,axiom,
! [X3,X0,X11,X18,X7,X12] :
( ~ hBOOL(c_in(X3,X18,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_prod(X7,X0),tc_bool)),c_Product__Type_OSigma(X11,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0)),c_Product__Type_OSigma(X12,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
fof(f12380,plain,
( spl0_561
| ~ spl0_153
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11659,f5030,f1681,f12378]) ).
fof(f12378,plain,
( spl0_561
<=> ! [X0] : c_Set_Ocontents(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f1681,plain,
( spl0_153
<=> ! [X0,X3] : c_Set_Ocontents(hAPP(c_fequal(X0),X3),X0) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f11659,plain,
( ! [X0] : c_Set_Ocontents(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0
| ~ spl0_153
| ~ spl0_375 ),
inference(superposition,[],[f1682,f5031]) ).
fof(f1682,plain,
( ! [X3,X0] : c_Set_Ocontents(hAPP(c_fequal(X0),X3),X0) = X3
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1681]) ).
fof(f12359,plain,
spl0_560,
inference(avatar_split_clause,[],[f783,f12357]) ).
fof(f12357,plain,
( spl0_560
<=> ! [X18,X11,X0,X12,X7] :
( c_COMBK(c_False,tc_bool,X7) = X18
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X12,X7,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f783,plain,
! [X0,X11,X18,X7,X12] :
( c_COMBK(c_False,tc_bool,X7) = X18
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X12,X7,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f212,f665]) ).
fof(f212,axiom,
! [X0,X11,X18,X7,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X18
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X12,X7,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I3_J_1) ).
fof(f12210,plain,
spl0_559,
inference(avatar_split_clause,[],[f939,f12208]) ).
fof(f12208,plain,
( spl0_559
<=> ! [X11,X0,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3))),X12))
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f939,plain,
! [X3,X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3))),X12))
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
inference(forward_demodulation,[],[f938,f686]) ).
fof(f938,plain,
! [X3,X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)))),X12))
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
inference(forward_demodulation,[],[f315,f665]) ).
fof(f315,axiom,
! [X3,X0,X11,X12] :
( ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
fof(f12206,plain,
spl0_558,
inference(avatar_split_clause,[],[f937,f12204]) ).
fof(f937,plain,
! [X3,X0,X11,X12] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3))),X12))
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
inference(forward_demodulation,[],[f936,f686]) ).
fof(f936,plain,
! [X3,X0,X11,X12] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)))),X12))
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
inference(forward_demodulation,[],[f314,f665]) ).
fof(f314,axiom,
! [X3,X0,X11,X12] :
( ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
fof(f12202,plain,
spl0_557,
inference(avatar_split_clause,[],[f463,f12200]) ).
fof(f12200,plain,
( spl0_557
<=> ! [X18,X11,X53,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X53))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X18),X53))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f463,axiom,
! [X0,X11,X18,X53,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X53))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X18),X53))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
fof(f12134,plain,
( spl0_556
| ~ spl0_64
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11656,f5030,f1248,f12132]) ).
fof(f12132,plain,
( spl0_556
<=> ! [X0] : c_The(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f1248,plain,
( spl0_64
<=> ! [X0,X3] : c_The(hAPP(c_fequal(X0),X3),X0) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f11656,plain,
( ! [X0] : c_The(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0
| ~ spl0_64
| ~ spl0_375 ),
inference(superposition,[],[f1249,f5031]) ).
fof(f1249,plain,
( ! [X3,X0] : c_The(hAPP(c_fequal(X0),X3),X0) = X3
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1248]) ).
fof(f12112,plain,
spl0_555,
inference(avatar_split_clause,[],[f921,f12110]) ).
fof(f12110,plain,
( spl0_555
<=> ! [X5,X3,X13,X29,X25,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f921,plain,
! [X3,X29,X5,X25,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25))) ),
inference(forward_demodulation,[],[f920,f686]) ).
fof(f920,plain,
! [X3,X29,X5,X25,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25))) ),
inference(forward_demodulation,[],[f919,f665]) ).
fof(f919,plain,
! [X3,X29,X5,X25,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f918,f686]) ).
fof(f918,plain,
! [X3,X29,X5,X25,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f580,f665]) ).
fof(f580,axiom,
! [X3,X29,X5,X25,X30,X13] :
( ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X13,X29,X30,X5,X3,X25)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
fof(f12108,plain,
spl0_554,
inference(avatar_split_clause,[],[f917,f12106]) ).
fof(f12106,plain,
( spl0_554
<=> ! [X5,X3,X13,X29,X25,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f917,plain,
! [X3,X29,X5,X25,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25))) ),
inference(forward_demodulation,[],[f916,f686]) ).
fof(f916,plain,
! [X3,X29,X5,X25,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25))) ),
inference(forward_demodulation,[],[f915,f665]) ).
fof(f915,plain,
! [X3,X29,X5,X25,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f914,f686]) ).
fof(f914,plain,
! [X3,X29,X5,X25,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f585,f665]) ).
fof(f585,axiom,
! [X3,X29,X5,X25,X30,X13] :
( ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X13,X29,X30,X5,X3,X25)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X25,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_2) ).
fof(f12104,plain,
spl0_553,
inference(avatar_split_clause,[],[f781,f12102]) ).
fof(f12102,plain,
( spl0_553
<=> ! [X18,X11,X0,X12,X7] :
( c_COMBK(c_False,tc_bool,X7) = X18
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,c_COMBB(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X12,X7,tc_fun(X0,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f781,plain,
! [X0,X11,X18,X7,X12] :
( c_COMBK(c_False,tc_bool,X7) = X18
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,c_COMBB(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X12,X7,tc_fun(X0,tc_bool))) ),
inference(forward_demodulation,[],[f309,f665]) ).
fof(f309,axiom,
! [X0,X11,X18,X7,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X18
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,c_COMBB(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X12,X7,tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_1) ).
fof(f12037,plain,
spl0_552,
inference(avatar_split_clause,[],[f440,f12035]) ).
fof(f12035,plain,
( spl0_552
<=> ! [X18,X11,X53,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X53),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),hAPP(c_HOL_Ominus__class_Ominus(X18,tc_fun(X0,tc_bool)),X53))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f440,axiom,
! [X0,X11,X18,X53,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X53),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),hAPP(c_HOL_Ominus__class_Ominus(X18,tc_fun(X0,tc_bool)),X53))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
fof(f11972,plain,
spl0_551,
inference(avatar_split_clause,[],[f927,f11970]) ).
fof(f927,plain,
! [X31,X0,X29,X6,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X5,X6),X31,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X30,X6,X31,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,X0)),X0) ),
inference(forward_demodulation,[],[f926,f686]) ).
fof(f926,plain,
! [X31,X29,X0,X6,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X5,X6),X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X30,X6,X31,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,X0)),X0) ),
inference(forward_demodulation,[],[f925,f665]) ).
fof(f925,plain,
! [X31,X0,X29,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X30,X6,X31,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X5,X6),X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f924,f686]) ).
fof(f924,plain,
! [X31,X0,X29,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,X6,X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X5,X6),X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f923,f665]) ).
fof(f923,plain,
! [X31,X0,X29,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,X6,X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X5,X6),X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f922,f686]) ).
fof(f922,plain,
! [X31,X29,X0,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,X6,X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X5,X6),X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f595,f665]) ).
fof(f595,axiom,
! [X31,X29,X0,X6,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,X6,X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X5,X6),X31,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comp_0) ).
fof(f11968,plain,
spl0_550,
inference(avatar_split_clause,[],[f913,f11966]) ).
fof(f913,plain,
! [X29,X76,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75))) ),
inference(forward_demodulation,[],[f912,f686]) ).
fof(f912,plain,
! [X29,X76,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75))) ),
inference(forward_demodulation,[],[f911,f665]) ).
fof(f911,plain,
! [X29,X76,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f910,f686]) ).
fof(f910,plain,
! [X29,X76,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f583,f665]) ).
fof(f583,axiom,
! [X29,X76,X5,X30,X13,X75] :
( hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X76,X30,X75)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_0) ).
fof(f11964,plain,
spl0_549,
inference(avatar_split_clause,[],[f909,f11962]) ).
fof(f11962,plain,
( spl0_549
<=> ! [X5,X13,X75,X29,X76,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f909,plain,
! [X29,X76,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75))) ),
inference(forward_demodulation,[],[f908,f686]) ).
fof(f908,plain,
! [X29,X76,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75))) ),
inference(forward_demodulation,[],[f907,f665]) ).
fof(f907,plain,
! [X29,X76,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f906,f686]) ).
fof(f906,plain,
! [X29,X76,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f587,f665]) ).
fof(f587,axiom,
! [X29,X76,X5,X30,X13,X75] :
( ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X76,X30,X75)),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X76,X30,X75)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_2) ).
fof(f11960,plain,
spl0_548,
inference(avatar_split_clause,[],[f823,f11958]) ).
fof(f11958,plain,
( spl0_548
<=> ! [X0,X13,X29,X73,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),X13),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f823,plain,
! [X29,X73,X0,X30,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),X13),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0)),X0) ),
inference(forward_demodulation,[],[f822,f686]) ).
fof(f822,plain,
! [X29,X73,X0,X30,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),X13),hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0)),X0) ),
inference(forward_demodulation,[],[f821,f665]) ).
fof(f821,plain,
! [X0,X29,X73,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),X13),hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f820,f686]) ).
fof(f820,plain,
! [X29,X73,X0,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),X13),hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f536,f665]) ).
fof(f536,axiom,
! [X29,X73,X0,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),X13),hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BodyN_0) ).
fof(f11956,plain,
spl0_547,
inference(avatar_split_clause,[],[f217,f11954]) ).
fof(f11954,plain,
( spl0_547
<=> ! [X11,X0,X12,X8,X7] :
( ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X8,X0,X7),X11),tc_fun(X7,tc_bool)),hAPP(c_Set_Oimage(X8,X0,X7),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f217,axiom,
! [X0,X11,X8,X7,X12] :
( ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X8,X0,X7),X11),tc_fun(X7,tc_bool)),hAPP(c_Set_Oimage(X8,X0,X7),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
fof(f11952,plain,
spl0_546,
inference(avatar_split_clause,[],[f177,f11950]) ).
fof(f11950,plain,
( spl0_546
<=> ! [X6,X0,X5,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f177,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).
fof(f11942,plain,
( spl0_545
| ~ spl0_57
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f11655,f5030,f1218,f11940]) ).
fof(f11940,plain,
( spl0_545
<=> ! [X0] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f11655,plain,
( ! [X0] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X0))
| ~ spl0_57
| ~ spl0_375 ),
inference(superposition,[],[f1219,f5031]) ).
fof(f11938,plain,
spl0_544,
inference(avatar_split_clause,[],[f831,f11936]) ).
fof(f11936,plain,
( spl0_544
<=> ! [X5,X0,X13,X29,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f831,plain,
! [X2,X0,X29,X5,X13] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0)),X0) ),
inference(forward_demodulation,[],[f830,f686]) ).
fof(f830,plain,
! [X2,X29,X0,X5,X13] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0)),X0) ),
inference(forward_demodulation,[],[f829,f665]) ).
fof(f829,plain,
! [X2,X0,X29,X5,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f828,f686]) ).
fof(f828,plain,
! [X2,X29,X0,X5,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f535,f665]) ).
fof(f535,axiom,
! [X2,X29,X0,X5,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Loop_0) ).
fof(f11934,plain,
spl0_543,
inference(avatar_split_clause,[],[f827,f11932]) ).
fof(f11932,plain,
( spl0_543
<=> ! [X5,X0,X13,X29,X2] :
( c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f827,plain,
! [X2,X0,X29,X5,X13] :
( c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0)),X0) ),
inference(forward_demodulation,[],[f826,f686]) ).
fof(f826,plain,
! [X2,X29,X0,X5,X13] :
( c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0)),X0) ),
inference(forward_demodulation,[],[f825,f665]) ).
fof(f825,plain,
! [X2,X0,X29,X5,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f824,f686]) ).
fof(f824,plain,
! [X2,X29,X0,X5,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f365,f665]) ).
fof(f365,axiom,
! [X2,X29,X0,X5,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X29,X2,X0),X5,X29,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__valids(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OWhile(X2,X5),c_Hoare__Mirabelle_Opeek__and(X29,c_Fun_Ocomp(c_Not,X2,tc_bool,tc_bool,tc_Com_Ostate),X0),X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Loop__sound__lemma_0) ).
fof(f11729,plain,
spl0_542,
inference(avatar_split_clause,[],[f960,f11727]) ).
fof(f11727,plain,
( spl0_542
<=> ! [X11,X0,X3,X25] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X25,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X11,X0),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f960,plain,
! [X3,X0,X11,X25] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X25,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X11,X0),X0))) ),
inference(forward_demodulation,[],[f664,f665]) ).
fof(f664,plain,
! [X3,X0,X11,X25] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X25,X11,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X11
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X11,X0),X0))) ),
inference(definition_unfolding,[],[f103,f263]) ).
fof(f263,axiom,
! [X0,X11,X8] : c_Finite__Set_Ofold1(X8,X11,X0) = c_The(c_Finite__Set_Ofold1Set(X8,X11,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__def_0) ).
fof(f103,axiom,
! [X3,X0,X11,X25] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X25,X11,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X11
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X11,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).
fof(f11725,plain,
spl0_541,
inference(avatar_split_clause,[],[f779,f11723]) ).
fof(f11723,plain,
( spl0_541
<=> ! [X18,X0,X12,X1,X7] :
( c_COMBK(c_False,tc_bool,X7) = X18
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,c_COMBB(c_Set_Oinsert(X1,X0),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X12,X7,tc_fun(X0,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f779,plain,
! [X0,X18,X1,X7,X12] :
( c_COMBK(c_False,tc_bool,X7) = X18
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,c_COMBB(c_Set_Oinsert(X1,X0),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X12,X7,tc_fun(X0,tc_bool))) ),
inference(forward_demodulation,[],[f208,f665]) ).
fof(f208,axiom,
! [X0,X18,X1,X7,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X18
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,c_COMBB(c_Set_Oinsert(X1,X0),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X12,X7,tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I1_J_1) ).
fof(f11654,plain,
spl0_540,
inference(avatar_split_clause,[],[f759,f11652]) ).
fof(f11652,plain,
( spl0_540
<=> ! [X4,X11,X0,X3,X8,X7] :
( hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X8,X3,X4,X7,X0),X7,X0),X11) = hAPP(c_Set_Oinsert(X4,X0),hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X7,tc_bool)),hAPP(c_fequal(X7),X3))))
| ~ hBOOL(c_in(X3,X11,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f759,plain,
! [X3,X0,X11,X8,X7,X4] :
( hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X8,X3,X4,X7,X0),X7,X0),X11) = hAPP(c_Set_Oinsert(X4,X0),hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X7,tc_bool)),hAPP(c_fequal(X7),X3))))
| ~ hBOOL(c_in(X3,X11,X7)) ),
inference(forward_demodulation,[],[f758,f686]) ).
fof(f758,plain,
! [X3,X0,X11,X8,X7,X4] :
( hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X8,X3,X4,X7,X0),X7,X0),X11) = hAPP(c_Set_Oinsert(X4,X0),hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X7,tc_bool)),hAPP(c_Set_Oinsert(X3,X7),c_COMBK(c_False,tc_bool,X7)))))
| ~ hBOOL(c_in(X3,X11,X7)) ),
inference(forward_demodulation,[],[f300,f665]) ).
fof(f300,axiom,
! [X3,X0,X11,X8,X7,X4] :
( ~ hBOOL(c_in(X3,X11,X7))
| hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X8,X3,X4,X7,X0),X7,X0),X11) = hAPP(c_Set_Oinsert(X4,X0),hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X7,tc_bool)),hAPP(c_Set_Oinsert(X3,X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
fof(f11650,plain,
spl0_539,
inference(avatar_split_clause,[],[f245,f11648]) ).
fof(f11648,plain,
( spl0_539
<=> ! [X11,X0,X12,X8,X7] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X8,X7,X0),X11),tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X12))),hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X7,tc_bool)),X12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f245,axiom,
! [X0,X11,X8,X7,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X8,X7,X0),X11),tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X12))),hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X7,tc_bool)),X12)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
fof(f11646,plain,
spl0_538,
inference(avatar_split_clause,[],[f215,f11644]) ).
fof(f11644,plain,
( spl0_538
<=> ! [X11,X0,X12,X8,X7] :
( ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),hAPP(c_Set_Oimage(X8,X0,X7),X11)),hAPP(c_Set_Oimage(X8,X0,X7),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f215,axiom,
! [X0,X11,X8,X7,X12] :
( ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),hAPP(c_Set_Oimage(X8,X0,X7),X11)),hAPP(c_Set_Oimage(X8,X0,X7),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
fof(f11642,plain,
spl0_537,
inference(avatar_split_clause,[],[f124,f11640]) ).
fof(f11640,plain,
( spl0_537
<=> ! [X11,X0,X12,X28,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28,X11,X7,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X11,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f124,axiom,
! [X28,X0,X11,X7,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28,X11,X7,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X11,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__INT__distrib_0) ).
fof(f11059,plain,
spl0_536,
inference(avatar_split_clause,[],[f884,f11057]) ).
fof(f884,plain,
! [X0,X11,X1,X8,X7] :
( hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))),X7))
| ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) ),
inference(forward_demodulation,[],[f883,f686]) ).
fof(f883,plain,
! [X0,X11,X1,X8,X7] :
( hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)))),X7))
| ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) ),
inference(forward_demodulation,[],[f299,f665]) ).
fof(f299,axiom,
! [X0,X11,X1,X8,X7] :
( ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7)
| hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
fof(f11055,plain,
spl0_535,
inference(avatar_split_clause,[],[f508,f11053]) ).
fof(f508,axiom,
! [X0,X11,X44,X7,X12] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X7,tc_bool)),X11),X12),X44,X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X44,X7,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X44,X7,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
fof(f11051,plain,
spl0_534,
inference(avatar_split_clause,[],[f336,f11049]) ).
fof(f336,axiom,
! [X0,X11,X18,X12] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),tc_fun(X0,tc_bool)),X18) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X18)),hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
fof(f11047,plain,
spl0_533,
inference(avatar_split_clause,[],[f206,f11045]) ).
fof(f11045,plain,
( spl0_533
<=> ! [X24,X20,X0,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X23),X24))
| c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X20,X23,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23,X24,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f206,axiom,
! [X0,X24,X23,X20] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X23),X24))
| c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X20,X23,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23,X24,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I22_J_0) ).
fof(f11043,plain,
spl0_532,
inference(avatar_split_clause,[],[f205,f11041]) ).
fof(f11041,plain,
( spl0_532
<=> ! [X24,X20,X0,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X23),X24))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X20,X23,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f205,axiom,
! [X0,X24,X23,X20] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X23),X24))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X20,X23,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).
fof(f11039,plain,
spl0_531,
inference(avatar_split_clause,[],[f202,f11037]) ).
fof(f11037,plain,
( spl0_531
<=> ! [X24,X11,X0,X12,X1,X7] :
( ~ hBOOL(c_in(X24,X11,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBB(c_Set_Oinsert(X1,X7),X12,tc_fun(X7,tc_bool),tc_fun(X7,tc_bool),X0),X0,tc_fun(X7,tc_bool)) = hAPP(c_Set_Oinsert(X1,X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f202,axiom,
! [X0,X11,X1,X7,X24,X12] :
( ~ hBOOL(c_in(X24,X11,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBB(c_Set_Oinsert(X1,X7),X12,tc_fun(X7,tc_bool),tc_fun(X7,tc_bool),X0),X0,tc_fun(X7,tc_bool)) = hAPP(c_Set_Oinsert(X1,X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert__distrib_0) ).
fof(f11035,plain,
spl0_530,
inference(avatar_split_clause,[],[f100,f11033]) ).
fof(f11033,plain,
( spl0_530
<=> ! [X24,X20,X0,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X23),X24))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X20,X23,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X23,X24,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(X20,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f100,axiom,
! [X0,X24,X23,X20] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X23),X24))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X20,X23,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X23,X24,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(X20,X24,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
fof(f11031,plain,
spl0_529,
inference(avatar_split_clause,[],[f99,f11029]) ).
fof(f11029,plain,
( spl0_529
<=> ! [X24,X20,X0,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X23),X24))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X23,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23,X24,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f99,axiom,
! [X0,X24,X23,X20] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X23),X24))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X23,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23,X24,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X24,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I20_J_0) ).
fof(f10606,plain,
spl0_528,
inference(avatar_split_clause,[],[f905,f10604]) ).
fof(f905,plain,
! [X29,X76,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76))) ),
inference(forward_demodulation,[],[f904,f686]) ).
fof(f904,plain,
! [X29,X76,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76))) ),
inference(forward_demodulation,[],[f903,f665]) ).
fof(f903,plain,
! [X29,X76,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f902,f686]) ).
fof(f902,plain,
! [X29,X76,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f584,f665]) ).
fof(f584,axiom,
! [X29,X76,X5,X13,X30] :
( hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_0) ).
fof(f10602,plain,
spl0_527,
inference(avatar_split_clause,[],[f901,f10600]) ).
fof(f901,plain,
! [X29,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| hBOOL(hAPP(hAPP(X75,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75))) ),
inference(forward_demodulation,[],[f900,f686]) ).
fof(f900,plain,
! [X29,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| hBOOL(hAPP(hAPP(X75,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75))) ),
inference(forward_demodulation,[],[f899,f665]) ).
fof(f899,plain,
! [X29,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| hBOOL(hAPP(hAPP(X75,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f898,f686]) ).
fof(f898,plain,
! [X29,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X75,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f582,f665]) ).
fof(f582,axiom,
! [X29,X5,X30,X13,X75] :
( hBOOL(hAPP(hAPP(X75,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_0) ).
fof(f10591,plain,
spl0_526,
inference(avatar_split_clause,[],[f897,f10589]) ).
fof(f897,plain,
! [X29,X76,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X76,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76))) ),
inference(forward_demodulation,[],[f896,f686]) ).
fof(f896,plain,
! [X29,X76,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X76,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76))) ),
inference(forward_demodulation,[],[f895,f665]) ).
fof(f895,plain,
! [X29,X76,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X76,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f894,f686]) ).
fof(f894,plain,
! [X29,X76,X5,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X76,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f586,f665]) ).
fof(f586,axiom,
! [X29,X76,X5,X13,X30] :
( ~ hBOOL(hAPP(hAPP(X76,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X76)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X76)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X76,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_1) ).
fof(f10587,plain,
spl0_525,
inference(avatar_split_clause,[],[f893,f10585]) ).
fof(f893,plain,
! [X29,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75))) ),
inference(forward_demodulation,[],[f892,f686]) ).
fof(f892,plain,
! [X29,X5,X13,X30,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75))) ),
inference(forward_demodulation,[],[f891,f665]) ).
fof(f891,plain,
! [X29,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f890,f686]) ).
fof(f890,plain,
! [X29,X5,X13,X30,X75] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f588,f665]) ).
fof(f588,axiom,
! [X29,X5,X30,X13,X75] :
( ~ hBOOL(hAPP(hAPP(X30,v_sko__Hoare__Mirabelle__Xconseq2__1(X30,X75)),v_sko__Hoare__Mirabelle__Xconseq2__2(X30,X75)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X75,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_1) ).
fof(f10583,plain,
spl0_524,
inference(avatar_split_clause,[],[f238,f10581]) ).
fof(f10581,plain,
( spl0_524
<=> ! [X18,X11,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f238,axiom,
! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
fof(f10579,plain,
spl0_523,
inference(avatar_split_clause,[],[f219,f10577]) ).
fof(f10577,plain,
( spl0_523
<=> ! [X18,X11,X0,X12,X7] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,X12,X7,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,c_COMBB(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f219,axiom,
! [X0,X11,X18,X7,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,X12,X7,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,c_COMBB(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I7_J_0) ).
fof(f10575,plain,
spl0_522,
inference(avatar_split_clause,[],[f93,f10573]) ).
fof(f93,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
fof(f10571,plain,
spl0_521,
inference(avatar_split_clause,[],[f92,f10569]) ).
fof(f92,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
fof(f10512,plain,
spl0_520,
inference(avatar_split_clause,[],[f510,f10510]) ).
fof(f510,axiom,
! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X18,tc_fun(X0,tc_bool)),X11)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
fof(f10338,plain,
spl0_519,
inference(avatar_split_clause,[],[f876,f10336]) ).
fof(f10336,plain,
( spl0_519
<=> ! [X4,X11,X0,X3,X10,X8,X7] :
( ~ c_Finite__Set_Ofold__graph(X8,X10,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X4,X0,X7)
| ~ hBOOL(c_in(X3,X11,X0))
| c_Finite__Set_Ofold__graph(X8,X10,X11,hAPP(hAPP(X8,X3),X4),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f876,plain,
! [X3,X10,X0,X11,X8,X7,X4] :
( ~ c_Finite__Set_Ofold__graph(X8,X10,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X4,X0,X7)
| ~ hBOOL(c_in(X3,X11,X0))
| c_Finite__Set_Ofold__graph(X8,X10,X11,hAPP(hAPP(X8,X3),X4),X0,X7) ),
inference(forward_demodulation,[],[f875,f686]) ).
fof(f875,plain,
! [X3,X10,X0,X11,X8,X7,X4] :
( ~ c_Finite__Set_Ofold__graph(X8,X10,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0))),X4,X0,X7)
| ~ hBOOL(c_in(X3,X11,X0))
| c_Finite__Set_Ofold__graph(X8,X10,X11,hAPP(hAPP(X8,X3),X4),X0,X7) ),
inference(forward_demodulation,[],[f318,f665]) ).
fof(f318,axiom,
! [X3,X10,X0,X11,X8,X7,X4] :
( ~ hBOOL(c_in(X3,X11,X0))
| c_Finite__Set_Ofold__graph(X8,X10,X11,hAPP(hAPP(X8,X3),X4),X0,X7)
| ~ c_Finite__Set_Ofold__graph(X8,X10,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X4,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
fof(f10334,plain,
spl0_518,
inference(avatar_split_clause,[],[f874,f10332]) ).
fof(f10332,plain,
( spl0_518
<=> ! [X4,X11,X0,X3,X10,X8,X7] :
( ~ c_Nitpick_Ofold__graph_H(X8,X10,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X4,X0,X7)
| ~ hBOOL(c_in(X3,X11,X0))
| c_Nitpick_Ofold__graph_H(X8,X10,X11,hAPP(hAPP(X8,X3),X4),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f874,plain,
! [X3,X10,X0,X11,X8,X7,X4] :
( ~ c_Nitpick_Ofold__graph_H(X8,X10,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X4,X0,X7)
| ~ hBOOL(c_in(X3,X11,X0))
| c_Nitpick_Ofold__graph_H(X8,X10,X11,hAPP(hAPP(X8,X3),X4),X0,X7) ),
inference(forward_demodulation,[],[f873,f686]) ).
fof(f873,plain,
! [X3,X10,X0,X11,X8,X7,X4] :
( ~ c_Nitpick_Ofold__graph_H(X8,X10,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0))),X4,X0,X7)
| ~ hBOOL(c_in(X3,X11,X0))
| c_Nitpick_Ofold__graph_H(X8,X10,X11,hAPP(hAPP(X8,X3),X4),X0,X7) ),
inference(forward_demodulation,[],[f313,f665]) ).
fof(f313,axiom,
! [X3,X10,X0,X11,X8,X7,X4] :
( ~ hBOOL(c_in(X3,X11,X0))
| c_Nitpick_Ofold__graph_H(X8,X10,X11,hAPP(hAPP(X8,X3),X4),X0,X7)
| ~ c_Nitpick_Ofold__graph_H(X8,X10,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X4,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
fof(f10330,plain,
spl0_517,
inference(avatar_split_clause,[],[f515,f10328]) ).
fof(f515,axiom,
! [X0,X11,X8,X7,X12] : hAPP(c_Set_Oimage(X8,X7,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X7,tc_bool)),X11),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X11)),hAPP(c_Set_Oimage(X8,X7,X0),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
fof(f10326,plain,
spl0_516,
inference(avatar_split_clause,[],[f201,f10324]) ).
fof(f10324,plain,
( spl0_516
<=> ! [X11,X0,X12,X3] :
( hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f201,axiom,
! [X3,X0,X11,X12] :
( hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
fof(f10322,plain,
spl0_515,
inference(avatar_split_clause,[],[f200,f10320]) ).
fof(f10320,plain,
( spl0_515
<=> ! [X11,X0,X12,X3] :
( hBOOL(c_in(X3,X12,X0))
| hBOOL(c_in(X3,X11,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f200,axiom,
! [X3,X0,X11,X12] :
( hBOOL(c_in(X3,X12,X0))
| hBOOL(c_in(X3,X11,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
fof(f10318,plain,
spl0_514,
inference(avatar_split_clause,[],[f110,f10316]) ).
fof(f10316,plain,
( spl0_514
<=> ! [X17,X11,X0,X12,X8,X7] : hAPP(c_Set_Oimage(X8,X7,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X17,tc_fun(X7,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBB(c_Set_Oimage(X8,X7,X0),X12,tc_fun(X7,tc_bool),tc_fun(X0,tc_bool),X17),X17,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f110,axiom,
! [X0,X11,X8,X7,X17,X12] : hAPP(c_Set_Oimage(X8,X7,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X17,tc_fun(X7,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBB(c_Set_Oimage(X8,X7,X0),X12,tc_fun(X7,tc_bool),tc_fun(X0,tc_bool),X17),X17,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__UN_0) ).
fof(f9546,plain,
spl0_513,
inference(avatar_split_clause,[],[f959,f9544]) ).
fof(f9544,plain,
( spl0_513
<=> ! [X0,X44,X51] :
( c_COMBK(c_False,tc_bool,X0) = X44
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X51,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X44),X51))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMax(X44,X0)),c_Finite__Set_Olinorder__class_OMax(X51,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f959,plain,
! [X51,X0,X44] :
( c_COMBK(c_False,tc_bool,X0) = X44
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X51,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X44),X51))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMax(X44,X0)),c_Finite__Set_Olinorder__class_OMax(X51,X0))) ),
inference(forward_demodulation,[],[f304,f665]) ).
fof(f304,axiom,
! [X51,X0,X44] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X51,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X44
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X44),X51))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMax(X44,X0)),c_Finite__Set_Olinorder__class_OMax(X51,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).
fof(f9542,plain,
spl0_512,
inference(avatar_split_clause,[],[f958,f9540]) ).
fof(f9540,plain,
( spl0_512
<=> ! [X0,X44,X51] :
( c_COMBK(c_False,tc_bool,X0) = X44
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X51,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X44),X51))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X51,X0)),c_Finite__Set_Olinorder__class_OMin(X44,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f958,plain,
! [X51,X0,X44] :
( c_COMBK(c_False,tc_bool,X0) = X44
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X51,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X44),X51))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X51,X0)),c_Finite__Set_Olinorder__class_OMin(X44,X0))) ),
inference(forward_demodulation,[],[f305,f665]) ).
fof(f305,axiom,
! [X51,X0,X44] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X51,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X44
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X44),X51))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X51,X0)),c_Finite__Set_Olinorder__class_OMin(X44,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
fof(f9538,plain,
spl0_511,
inference(avatar_split_clause,[],[f421,f9536]) ).
fof(f9536,plain,
( spl0_511
<=> ! [X6,X0,X5,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f421,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
fof(f9534,plain,
spl0_510,
inference(avatar_split_clause,[],[f420,f9532]) ).
fof(f9532,plain,
( spl0_510
<=> ! [X5,X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f420,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
fof(f9530,plain,
( spl0_509
| ~ spl0_161
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7884,f4832,f1741,f9528]) ).
fof(f9528,plain,
( spl0_509
<=> ! [X0] : c_Finite__Set_Olinorder__class_OMax(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f1741,plain,
( spl0_161
<=> ! [X0] : c_Finite__Set_Olinorder__class_OMax(hAPP(c_fequal(tc_nat),X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f7884,plain,
( ! [X0] : c_Finite__Set_Olinorder__class_OMax(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0
| ~ spl0_161
| ~ spl0_371 ),
inference(superposition,[],[f1742,f4833]) ).
fof(f1742,plain,
( ! [X0] : c_Finite__Set_Olinorder__class_OMax(hAPP(c_fequal(tc_nat),X0),tc_nat) = X0
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1741]) ).
fof(f9526,plain,
spl0_508,
inference(avatar_split_clause,[],[f419,f9524]) ).
fof(f9524,plain,
( spl0_508
<=> ! [X2,X6,X0,X5,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f419,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
fof(f9522,plain,
spl0_507,
inference(avatar_split_clause,[],[f363,f9520]) ).
fof(f363,axiom,
! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),X18))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
fof(f9518,plain,
spl0_506,
inference(avatar_split_clause,[],[f362,f9516]) ).
fof(f362,axiom,
! [X0,X11,X18,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
fof(f9514,plain,
spl0_505,
inference(avatar_split_clause,[],[f287,f9512]) ).
fof(f287,axiom,
! [X3,X28,X0,X11,X7,X12] :
( ~ hBOOL(c_in(X3,X28,X7))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X11,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28,X11,X7,tc_fun(X0,tc_bool))),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
fof(f9510,plain,
spl0_504,
inference(avatar_split_clause,[],[f285,f9508]) ).
fof(f9508,plain,
( spl0_504
<=> ! [X26,X11,X0,X12,X28,X7] :
( ~ hBOOL(c_in(X26,X28,X7))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(X11,X26)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28,X11,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f285,axiom,
! [X28,X0,X11,X26,X7,X12] :
( ~ hBOOL(c_in(X26,X28,X7))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(X11,X26)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28,X11,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__subset__iff_0) ).
fof(f9506,plain,
spl0_503,
inference(avatar_split_clause,[],[f244,f9504]) ).
fof(f244,axiom,
! [X0,X11,X18,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
fof(f9502,plain,
spl0_502,
inference(avatar_split_clause,[],[f243,f9500]) ).
fof(f243,axiom,
! [X0,X11,X18,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
fof(f9498,plain,
spl0_501,
inference(avatar_split_clause,[],[f98,f9496]) ).
fof(f9496,plain,
( spl0_501
<=> ! [X5,X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f98,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).
fof(f9494,plain,
spl0_500,
inference(avatar_split_clause,[],[f96,f9492]) ).
fof(f9492,plain,
( spl0_500
<=> ! [X6,X0,X5,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f96,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).
fof(f9490,plain,
spl0_499,
inference(avatar_split_clause,[],[f95,f9488]) ).
fof(f9488,plain,
( spl0_499
<=> ! [X5,X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f95,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).
fof(f9486,plain,
( spl0_498
| ~ spl0_166
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7883,f4832,f1772,f9484]) ).
fof(f9484,plain,
( spl0_498
<=> ! [X0] : c_Finite__Set_Olinorder__class_OMin(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f1772,plain,
( spl0_166
<=> ! [X0] : c_Finite__Set_Olinorder__class_OMin(hAPP(c_fequal(tc_nat),X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f7883,plain,
( ! [X0] : c_Finite__Set_Olinorder__class_OMin(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0
| ~ spl0_166
| ~ spl0_371 ),
inference(superposition,[],[f1773,f4833]) ).
fof(f1773,plain,
( ! [X0] : c_Finite__Set_Olinorder__class_OMin(hAPP(c_fequal(tc_nat),X0),tc_nat) = X0
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f9482,plain,
spl0_497,
inference(avatar_split_clause,[],[f91,f9480]) ).
fof(f9480,plain,
( spl0_497
<=> ! [X6,X0,X5,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f91,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).
fof(f9478,plain,
spl0_496,
inference(avatar_split_clause,[],[f90,f9476]) ).
fof(f9476,plain,
( spl0_496
<=> ! [X5,X0,X6,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f90,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).
fof(f9341,plain,
spl0_495,
inference(avatar_split_clause,[],[f791,f9339]) ).
fof(f791,plain,
! [X0,X11,X1,X8,X7] :
( ~ hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))),X7))
| ~ c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) ),
inference(forward_demodulation,[],[f790,f686]) ).
fof(f790,plain,
! [X0,X11,X1,X8,X7] :
( ~ hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)))),X7))
| ~ c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) ),
inference(forward_demodulation,[],[f298,f665]) ).
fof(f298,axiom,
! [X0,X11,X1,X8,X7] :
( ~ c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7)
| ~ hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
fof(f9337,plain,
( spl0_494
| ~ spl0_244
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7875,f4832,f2328,f9335]) ).
fof(f9335,plain,
( spl0_494
<=> ! [X0] : hBOOL(c_in(X0,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f7875,plain,
( ! [X0] : hBOOL(c_in(X0,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat))
| ~ spl0_244
| ~ spl0_371 ),
inference(superposition,[],[f2329,f4833]) ).
fof(f9333,plain,
spl0_493,
inference(avatar_split_clause,[],[f144,f9331]) ).
fof(f9331,plain,
( spl0_493
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X10),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f144,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X10),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f9329,plain,
spl0_492,
inference(avatar_split_clause,[],[f143,f9327]) ).
fof(f9327,plain,
( spl0_492
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f143,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f9325,plain,
spl0_491,
inference(avatar_split_clause,[],[f129,f9323]) ).
fof(f9323,plain,
( spl0_491
<=> ! [X0,X11,X8] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| ~ c_Fun_Oinj__on(X8,X11,X0,X0)
| hAPP(c_Set_Oimage(X8,X0,X0),X11) = X11
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X0,X0),X11)),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f129,axiom,
! [X0,X11,X8] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| ~ c_Fun_Oinj__on(X8,X11,X0,X0)
| hAPP(c_Set_Oimage(X8,X0,X0),X11) = X11
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X0,X0),X11)),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
fof(f9321,plain,
spl0_490,
inference(avatar_split_clause,[],[f118,f9319]) ).
fof(f9319,plain,
( spl0_490
<=> ! [X18,X0,X12,X1,X7] : hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,X12,X7,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,c_COMBB(c_Set_Oinsert(X1,X0),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f118,axiom,
! [X0,X1,X18,X7,X12] : hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,X12,X7,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,c_COMBB(c_Set_Oinsert(X1,X0),X12,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I5_J_0) ).
fof(f9317,plain,
spl0_489,
inference(avatar_split_clause,[],[f45,f9315]) ).
fof(f9315,plain,
( spl0_489
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f45,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f9313,plain,
spl0_488,
inference(avatar_split_clause,[],[f44,f9311]) ).
fof(f9311,plain,
( spl0_488
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X10),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f44,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X10),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f9236,plain,
spl0_487,
inference(avatar_split_clause,[],[f294,f9234]) ).
fof(f9234,plain,
( spl0_487
<=> ! [X11,X19,X0,X28,X7] :
( ~ hBOOL(c_in(X19,X28,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28,X11,X0,tc_fun(X7,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X7,tc_bool)),hAPP(X11,X19)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28,X11,X0,tc_fun(X7,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f294,axiom,
! [X28,X0,X11,X19,X7] :
( ~ hBOOL(c_in(X19,X28,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28,X11,X0,tc_fun(X7,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X7,tc_bool)),hAPP(X11,X19)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28,X11,X0,tc_fun(X7,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
fof(f9232,plain,
( spl0_486
| ~ spl0_226
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7874,f4832,f2251,f9230]) ).
fof(f9230,plain,
( spl0_486
<=> ! [X0] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f7874,plain,
( ! [X0] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0
| ~ spl0_226
| ~ spl0_371 ),
inference(superposition,[],[f2252,f4833]) ).
fof(f9228,plain,
spl0_485,
inference(avatar_split_clause,[],[f269,f9226]) ).
fof(f9226,plain,
( spl0_485
<=> ! [X18,X11,X0,X12,X3,X7] :
( X11 = X12
| ~ hBOOL(c_in(X3,X18,X0))
| c_Product__Type_OSigma(X11,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0) != c_Product__Type_OSigma(X12,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f269,axiom,
! [X3,X0,X11,X18,X7,X12] :
( X11 = X12
| ~ hBOOL(c_in(X3,X18,X0))
| c_Product__Type_OSigma(X11,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0) != c_Product__Type_OSigma(X12,c_COMBK(X18,tc_fun(X0,tc_bool),X7),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
fof(f9224,plain,
spl0_484,
inference(avatar_split_clause,[],[f15,f9222]) ).
fof(f15,axiom,
! [X0,X8,X9,X7] :
( ~ class_HOL_Oord(X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X8),X9))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X7)),X8),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X9),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
fof(f8638,plain,
( spl0_483
| ~ spl0_153
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7869,f4832,f1681,f8636]) ).
fof(f8636,plain,
( spl0_483
<=> ! [X0] : c_Set_Ocontents(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f7869,plain,
( ! [X0] : c_Set_Ocontents(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0
| ~ spl0_153
| ~ spl0_371 ),
inference(superposition,[],[f1682,f4833]) ).
fof(f8460,plain,
spl0_482,
inference(avatar_split_clause,[],[f819,f8458]) ).
fof(f8458,plain,
( spl0_482
<=> ! [X0,X13,X29,X73,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f819,plain,
! [X0,X29,X73,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0)),X0) ),
inference(forward_demodulation,[],[f818,f686]) ).
fof(f818,plain,
! [X29,X73,X0,X13,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0)),X0) ),
inference(forward_demodulation,[],[f817,f665]) ).
fof(f817,plain,
! [X0,X29,X73,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f816,f686]) ).
fof(f816,plain,
! [X29,X73,X0,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f537,f665]) ).
fof(f537,axiom,
! [X29,X73,X0,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OBODY(X73),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Option_Othe(c_Com_Obody(X73),tc_Com_Ocom),X30,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__Body_0) ).
fof(f8456,plain,
spl0_481,
inference(avatar_split_clause,[],[f724,f8454]) ).
fof(f724,plain,
! [X0,X11,X1,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),tc_fun(X0,tc_bool)),X12),
inference(forward_demodulation,[],[f723,f686]) ).
fof(f723,plain,
! [X0,X11,X1,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))),tc_fun(X0,tc_bool)),X12),
inference(forward_demodulation,[],[f555,f665]) ).
fof(f555,axiom,
! [X0,X11,X1,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
fof(f8452,plain,
spl0_480,
inference(avatar_split_clause,[],[f722,f8450]) ).
fof(f722,plain,
! [X0,X11,X1,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),
inference(forward_demodulation,[],[f721,f686]) ).
fof(f721,plain,
! [X0,X11,X1,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))),
inference(forward_demodulation,[],[f556,f665]) ).
fof(f556,axiom,
! [X0,X11,X1,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
fof(f8448,plain,
spl0_479,
inference(avatar_split_clause,[],[f514,f8446]) ).
fof(f514,axiom,
! [X3,X0,X11,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X3),X11))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X3)),hAPP(c_Set_Oimage(X8,X7,X0),X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
fof(f8444,plain,
spl0_478,
inference(avatar_split_clause,[],[f507,f8442]) ).
fof(f8442,plain,
( spl0_478
<=> ! [X58,X21,X3,X0,X56,X8,X9,X62,X17,X7,X61] :
( hAPP(X8,hAPP(X9,X3)) != hAPP(X56,hAPP(X61,X21))
| hAPP(c_Fun_Ocomp(X8,X9,X7,X0,X17),X3) = hAPP(c_Fun_Ocomp(X56,X61,X58,X0,X62),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f507,axiom,
! [X21,X3,X58,X0,X56,X8,X9,X7,X62,X17,X61] :
( hAPP(X8,hAPP(X9,X3)) != hAPP(X56,hAPP(X61,X21))
| hAPP(c_Fun_Ocomp(X8,X9,X7,X0,X17),X3) = hAPP(c_Fun_Ocomp(X56,X61,X58,X0,X62),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
fof(f8440,plain,
( spl0_477
| ~ spl0_64
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7866,f4832,f1248,f8438]) ).
fof(f8438,plain,
( spl0_477
<=> ! [X0] : c_The(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f7866,plain,
( ! [X0] : c_The(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),tc_nat) = X0
| ~ spl0_64
| ~ spl0_371 ),
inference(superposition,[],[f1249,f4833]) ).
fof(f8436,plain,
spl0_476,
inference(avatar_split_clause,[],[f456,f8434]) ).
fof(f456,axiom,
! [X0,X11,X1,X7,X12] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(X1,X7),X11),X12,X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X12,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
fof(f8432,plain,
spl0_475,
inference(avatar_split_clause,[],[f356,f8430]) ).
fof(f8430,plain,
( spl0_475
<=> ! [X11,X0,X12,X3] :
( hBOOL(c_in(X3,X12,X0))
| hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),X12) = hAPP(c_Set_Oinsert(X3,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f356,axiom,
! [X3,X0,X11,X12] :
( hBOOL(c_in(X3,X12,X0))
| hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),X12) = hAPP(c_Set_Oinsert(X3,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
fof(f8428,plain,
spl0_474,
inference(avatar_split_clause,[],[f306,f8426]) ).
fof(f8426,plain,
( spl0_474
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_Ocomplete__lattice(c_Complete__Lattice_OSup__class_OSup(X0),c_Complete__Lattice_OInf__class_OInf(X0),c_COMBC(c_lessequals(X0),X0,X0,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X0),X0,X0,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0),c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),c_Orderings_Obot__class_Obot(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f306,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_Ocomplete__lattice(c_Complete__Lattice_OSup__class_OSup(X0),c_Complete__Lattice_OInf__class_OInf(X0),c_COMBC(c_lessequals(X0),X0,X0,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X0),X0,X0,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0),c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),c_Orderings_Obot__class_Obot(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__complete__lattice_0) ).
fof(f8424,plain,
spl0_473,
inference(avatar_split_clause,[],[f230,f8422]) ).
fof(f8422,plain,
( spl0_473
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f230,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
fof(f8420,plain,
spl0_472,
inference(avatar_split_clause,[],[f227,f8418]) ).
fof(f8418,plain,
( spl0_472
<=> ! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| c_Complete__Lattice_Ocomplete__lattice(X32,X33,c_COMBC(X34,X0,X0,tc_bool),c_COMBC(X35,X0,X0,tc_bool),X36,X37,X38,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f227,axiom,
! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| c_Complete__Lattice_Ocomplete__lattice(X32,X33,c_COMBC(X34,X0,X0,tc_bool),c_COMBC(X35,X0,X0,tc_bool),X36,X37,X38,X39,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
fof(f8416,plain,
spl0_471,
inference(avatar_split_clause,[],[f180,f8414]) ).
fof(f180,axiom,
! [X0,X8,X7,X17,X15,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X17)
| ~ c_Fun_Oinj__on(X8,X12,X0,X7)
| c_Finite__Set_Osetsum(X15,hAPP(c_Set_Oimage(X8,X0,X7),X12),X7,X17) = c_Finite__Set_Osetsum(c_Fun_Ocomp(X15,X8,X7,X17,X0),X12,X0,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__reindex_0) ).
fof(f8412,plain,
spl0_470,
inference(avatar_split_clause,[],[f108,f8410]) ).
fof(f8410,plain,
( spl0_470
<=> ! [X11,X0,X12,X8,X7] :
( X11 = X12
| ~ c_Fun_Oinj__on(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0,X7)
| hAPP(c_Set_Oimage(X8,X0,X7),X11) != hAPP(c_Set_Oimage(X8,X0,X7),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f108,axiom,
! [X0,X11,X8,X7,X12] :
( X11 = X12
| ~ c_Fun_Oinj__on(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0,X7)
| hAPP(c_Set_Oimage(X8,X0,X7),X11) != hAPP(c_Set_Oimage(X8,X0,X7),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
fof(f8408,plain,
spl0_469,
inference(avatar_split_clause,[],[f38,f8406]) ).
fof(f8406,plain,
( spl0_469
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f38,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
fof(f7955,plain,
spl0_468,
inference(avatar_split_clause,[],[f492,f7953]) ).
fof(f492,axiom,
! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f7951,plain,
( spl0_467
| ~ spl0_57
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f7865,f4832,f1218,f7949]) ).
fof(f7949,plain,
( spl0_467
<=> ! [X0] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f7865,plain,
( ! [X0] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat),X0))
| ~ spl0_57
| ~ spl0_371 ),
inference(superposition,[],[f1219,f4833]) ).
fof(f7947,plain,
spl0_466,
inference(avatar_split_clause,[],[f470,f7945]) ).
fof(f470,axiom,
! [X3,X0,X11,X12] :
( ~ hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X11)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f7943,plain,
spl0_465,
inference(avatar_split_clause,[],[f328,f7941]) ).
fof(f7941,plain,
( spl0_465
<=> ! [X11,X0,X12,X3] :
( hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f328,axiom,
! [X3,X0,X11,X12] :
( hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
fof(f7939,plain,
spl0_464,
inference(avatar_split_clause,[],[f146,f7937]) ).
fof(f7937,plain,
( spl0_464
<=> ! [X18,X11,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X12),X18))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f146,axiom,
! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X12),X18))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
fof(f7935,plain,
spl0_463,
inference(avatar_split_clause,[],[f120,f7933]) ).
fof(f7933,plain,
( spl0_463
<=> ! [X17,X11,X0,X12,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_Set_Oimage(X8,X17,X7),X11),X12,X7,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBB(X12,X8,X7,tc_fun(X0,tc_bool),X17),X17,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f120,axiom,
! [X0,X11,X8,X7,X17,X12] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_Set_Oimage(X8,X17,X7),X11),X12,X7,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBB(X12,X8,X7,tc_fun(X0,tc_bool),X17),X17,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I10_J_0) ).
fof(f7931,plain,
spl0_462,
inference(avatar_split_clause,[],[f111,f7929]) ).
fof(f7929,plain,
( spl0_462
<=> ! [X17,X11,X0,X12,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X8,X17,X7),X11),X12,X7,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBB(X12,X8,X7,tc_fun(X0,tc_bool),X17),X17,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f111,axiom,
! [X0,X11,X8,X7,X17,X12] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X8,X17,X7),X11),X12,X7,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBB(X12,X8,X7,tc_fun(X0,tc_bool),X17),X17,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).
fof(f7927,plain,
spl0_461,
inference(avatar_split_clause,[],[f104,f7925]) ).
fof(f104,axiom,
! [X0,X26,X27,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X26),X27))
| hAPP(c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X26,X23,X0),tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X26,X27,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(X27,X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).
fof(f7923,plain,
spl0_460,
inference(avatar_split_clause,[],[f89,f7921]) ).
fof(f7921,plain,
( spl0_460
<=> ! [X11,X0,X12,X3] :
( ~ hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f89,axiom,
! [X3,X0,X11,X12] :
( ~ hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
fof(f7919,plain,
spl0_459,
inference(avatar_split_clause,[],[f88,f7917]) ).
fof(f7917,plain,
( spl0_459
<=> ! [X11,X0,X12,X3] :
( ~ hBOOL(c_in(X3,X12,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f88,axiom,
! [X3,X0,X11,X12] :
( ~ hBOOL(c_in(X3,X12,X0))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
fof(f7915,plain,
spl0_458,
inference(avatar_split_clause,[],[f87,f7913]) ).
fof(f87,axiom,
! [X3,X10,X0,X11,X8,X7,X4] :
( hBOOL(c_in(X3,X11,X0))
| ~ c_Finite__Set_Ofold__graph(X8,X10,X11,X4,X0,X7)
| c_Finite__Set_Ofold__graph(X8,X10,hAPP(c_Set_Oinsert(X3,X0),X11),hAPP(hAPP(X8,X3),X4),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
fof(f7911,plain,
spl0_457,
inference(avatar_split_clause,[],[f56,f7909]) ).
fof(f56,axiom,
! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X12),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
fof(f7864,plain,
spl0_456,
inference(avatar_split_clause,[],[f55,f7862]) ).
fof(f55,axiom,
! [X0,X11,X18,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
fof(f7529,plain,
spl0_455,
inference(avatar_split_clause,[],[f811,f7527]) ).
fof(f811,plain,
! [X29,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5))) ),
inference(forward_demodulation,[],[f810,f686]) ).
fof(f810,plain,
! [X29,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5))) ),
inference(forward_demodulation,[],[f589,f665]) ).
fof(f589,axiom,
! [X29,X5,X13,X30] :
( hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xescape__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xescape__2(X13,X29,X30,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_0) ).
fof(f7506,plain,
spl0_454,
inference(avatar_split_clause,[],[f809,f7504]) ).
fof(f809,plain,
! [X29,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5))) ),
inference(forward_demodulation,[],[f808,f686]) ).
fof(f808,plain,
! [X29,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5))) ),
inference(forward_demodulation,[],[f579,f665]) ).
fof(f579,axiom,
! [X29,X5,X13,X30] :
( hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X13,X29,X30,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
fof(f7502,plain,
spl0_453,
inference(avatar_split_clause,[],[f807,f7500]) ).
fof(f807,plain,
! [X29,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5))) ),
inference(forward_demodulation,[],[f806,f686]) ).
fof(f806,plain,
! [X29,X5,X13,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5))) ),
inference(forward_demodulation,[],[f581,f665]) ).
fof(f581,axiom,
! [X29,X5,X13,X30] :
( hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X13,X29,X30,X5)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X13,X29,X30,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X5,X30,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_0) ).
fof(f7498,plain,
spl0_452,
inference(avatar_split_clause,[],[f799,f7496]) ).
fof(f7496,plain,
( spl0_452
<=> ! [X2,X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(hAPP(X36,X1),X2) = hAPP(X32,hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f799,plain,
! [X2,X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(hAPP(X36,X1),X2) = hAPP(X32,hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f798,f686]) ).
fof(f798,plain,
! [X2,X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(hAPP(X36,X1),X2) = hAPP(X32,hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f554,f665]) ).
fof(f554,axiom,
! [X2,X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| hAPP(X32,hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) = hAPP(hAPP(X36,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
fof(f7494,plain,
spl0_451,
inference(avatar_split_clause,[],[f797,f7492]) ).
fof(f7492,plain,
( spl0_451
<=> ! [X2,X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(hAPP(X37,X1),X2) = hAPP(X33,hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f797,plain,
! [X2,X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(hAPP(X37,X1),X2) = hAPP(X33,hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f796,f686]) ).
fof(f796,plain,
! [X2,X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(hAPP(X37,X1),X2) = hAPP(X33,hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f553,f665]) ).
fof(f553,axiom,
! [X2,X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| hAPP(X33,hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) = hAPP(hAPP(X37,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
fof(f7490,plain,
spl0_450,
inference(avatar_split_clause,[],[f402,f7488]) ).
fof(f402,axiom,
! [X0,X18,X1,X53] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X18),X53))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X18)),hAPP(c_Set_Oinsert(X1,X0),X53))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f7486,plain,
spl0_449,
inference(avatar_split_clause,[],[f259,f7484]) ).
fof(f259,axiom,
! [X3,X0,X11,X8,X7,X12] :
( ~ hBOOL(c_in(X3,X11,X7))
| hBOOL(c_in(hAPP(X8,X3),X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oimage(X8,X7,X0),X11)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f7482,plain,
spl0_448,
inference(avatar_split_clause,[],[f131,f7480]) ).
fof(f131,axiom,
! [X2,X0,X1,X6,X7,X5,X23] :
( X1 = X5
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X23,X1,X2,X0,X7),X5,X6,X0,X7) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X23,X5,X6,X0,X7),X1,X2,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
fof(f6774,plain,
spl0_447,
inference(avatar_split_clause,[],[f870,f6772]) ).
fof(f6772,plain,
( spl0_447
<=> ! [X11,X0,X12,X3,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool)) != c_COMBK(c_False,tc_bool,X0)
| hAPP(X12,X3) = c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X3,X11,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f870,plain,
! [X3,X0,X11,X7,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool)) != c_COMBK(c_False,tc_bool,X0)
| hAPP(X12,X3) = c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X3,X11,X7)) ),
inference(forward_demodulation,[],[f869,f665]) ).
fof(f869,plain,
! [X3,X0,X11,X7,X12] :
( hAPP(X12,X3) = c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X3,X11,X7))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f433,f665]) ).
fof(f433,axiom,
! [X3,X0,X11,X7,X12] :
( ~ hBOOL(c_in(X3,X11,X7))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X12,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
fof(f6770,plain,
spl0_446,
inference(avatar_split_clause,[],[f763,f6768]) ).
fof(f763,plain,
! [X0,X11,X1,X8] :
( c_Finite__Set_Osetsum(X8,X11,X0,tc_nat) = c_Finite__Set_Osetsum(X8,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X0,tc_nat)
| hBOOL(c_in(X1,X11,X0)) ),
inference(forward_demodulation,[],[f762,f686]) ).
fof(f762,plain,
! [X0,X11,X1,X8] :
( c_Finite__Set_Osetsum(X8,X11,X0,tc_nat) = c_Finite__Set_Osetsum(X8,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))),X0,tc_nat)
| hBOOL(c_in(X1,X11,X0)) ),
inference(forward_demodulation,[],[f317,f665]) ).
fof(f317,axiom,
! [X0,X11,X1,X8] :
( hBOOL(c_in(X1,X11,X0))
| c_Finite__Set_Osetsum(X8,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X0,tc_nat) = c_Finite__Set_Osetsum(X8,X11,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
fof(f6766,plain,
spl0_445,
inference(avatar_split_clause,[],[f483,f6764]) ).
fof(f483,axiom,
! [X0,X11,X18,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f6762,plain,
spl0_444,
inference(avatar_split_clause,[],[f482,f6760]) ).
fof(f482,axiom,
! [X0,X11,X18,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f6758,plain,
spl0_443,
inference(avatar_split_clause,[],[f411,f6756]) ).
fof(f6754,plain,
spl0_442,
inference(avatar_split_clause,[],[f410,f6752]) ).
fof(f410,axiom,
! [X0,X11,X1,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X1,X0),X12)) = hAPP(c_Set_Oinsert(X1,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
fof(f6750,plain,
spl0_441,
inference(avatar_split_clause,[],[f407,f6748]) ).
fof(f6748,plain,
( spl0_441
<=> ! [X38,X39,X0,X36,X1,X37,X11,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| hAPP(X32,hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(X36,X1),hAPP(X32,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f407,axiom,
! [X38,X39,X0,X36,X11,X1,X37,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| hAPP(X32,hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(X36,X1),hAPP(X32,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
fof(f6746,plain,
spl0_440,
inference(avatar_split_clause,[],[f406,f6744]) ).
fof(f6744,plain,
( spl0_440
<=> ! [X38,X39,X0,X36,X1,X37,X11,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| hAPP(X33,hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(X37,X1),hAPP(X33,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f406,axiom,
! [X38,X39,X0,X36,X11,X1,X37,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| hAPP(X33,hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(X37,X1),hAPP(X33,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
fof(f6742,plain,
spl0_439,
inference(avatar_split_clause,[],[f338,f6740]) ).
fof(f6740,plain,
( spl0_439
<=> ! [X11,X0,X12,X3,X7] :
( ~ hBOOL(c_in(X3,X11,X7))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(X12,X3)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f338,axiom,
! [X3,X0,X11,X7,X12] :
( ~ hBOOL(c_in(X3,X11,X7))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(X12,X3)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_0) ).
fof(f6738,plain,
spl0_438,
inference(avatar_split_clause,[],[f242,f6736]) ).
fof(f6736,plain,
( spl0_438
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f242,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f6734,plain,
spl0_437,
inference(avatar_split_clause,[],[f241,f6732]) ).
fof(f6732,plain,
( spl0_437
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f241,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f6730,plain,
( spl0_436
| ~ spl0_52
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f6671,f4278,f1195,f6727]) ).
fof(f1195,plain,
( spl0_52
<=> ! [X0,X3] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f6671,plain,
( hBOOL(c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_52
| ~ spl0_345 ),
inference(superposition,[],[f1196,f4280]) ).
fof(f1196,plain,
( ! [X3,X0] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3))
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f6725,plain,
spl0_435,
inference(avatar_split_clause,[],[f240,f6723]) ).
fof(f240,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f6721,plain,
spl0_434,
inference(avatar_split_clause,[],[f239,f6719]) ).
fof(f239,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f6717,plain,
spl0_433,
inference(avatar_split_clause,[],[f204,f6715]) ).
fof(f204,axiom,
! [X0,X11,X1,X8,X7] :
( hBOOL(c_in(X1,X11,X0))
| ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| ~ hBOOL(c_in(hAPP(X8,X1),hAPP(c_Set_Oimage(X8,X0,X7),X11),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
fof(f6713,plain,
spl0_432,
inference(avatar_split_clause,[],[f163,f6711]) ).
fof(f163,axiom,
! [X3,X0,X11,X8,X7,X4] :
( X3 = X4
| ~ hBOOL(c_in(X4,X11,X0))
| ~ hBOOL(c_in(X3,X11,X0))
| ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| hAPP(X8,X3) != hAPP(X8,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
fof(f6709,plain,
spl0_431,
inference(avatar_split_clause,[],[f159,f6707]) ).
fof(f159,axiom,
! [X3,X0,X8,X9,X7,X4,X17] : c_Fun_Ocomp(X8,c_Fun_Ofun__upd(X9,X3,X4,X0,X17),X17,X7,X0) = c_Fun_Ofun__upd(c_Fun_Ocomp(X8,X9,X17,X7,X0),X3,hAPP(X8,X4),X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__comp_0) ).
fof(f6705,plain,
spl0_430,
inference(avatar_split_clause,[],[f128,f6703]) ).
fof(f6703,plain,
( spl0_430
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f128,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f6701,plain,
spl0_429,
inference(avatar_split_clause,[],[f127,f6699]) ).
fof(f6699,plain,
( spl0_429
<=> ! [X4,X0,X3,X10] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f127,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f6697,plain,
spl0_428,
inference(avatar_split_clause,[],[f126,f6695]) ).
fof(f126,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f6693,plain,
spl0_427,
inference(avatar_split_clause,[],[f116,f6691]) ).
fof(f6691,plain,
( spl0_427
<=> ! [X17,X11,X0,X9,X8,X7] :
( ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| ~ c_Fun_Oinj__on(X9,hAPP(c_Set_Oimage(X8,X0,X7),X11),X7,X17)
| c_Fun_Oinj__on(c_Fun_Ocomp(X9,X8,X7,X17,X0),X11,X0,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f116,axiom,
! [X0,X11,X8,X9,X7,X17] :
( ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| ~ c_Fun_Oinj__on(X9,hAPP(c_Set_Oimage(X8,X0,X7),X11),X7,X17)
| c_Fun_Oinj__on(c_Fun_Ocomp(X9,X8,X7,X17,X0),X11,X0,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).
fof(f6689,plain,
spl0_426,
inference(avatar_split_clause,[],[f43,f6687]) ).
fof(f43,axiom,
! [X3,X0,X11,X8,X7,X4] :
( ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| hBOOL(c_in(X4,hAPP(c_Set_Oimage(X8,X0,X7),X11),X7))
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X8,X3,X4,X0,X7),X11,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
fof(f6670,plain,
spl0_425,
inference(avatar_split_clause,[],[f25,f6668]) ).
fof(f25,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X10) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f6442,plain,
spl0_424,
inference(avatar_split_clause,[],[f889,f6440]) ).
fof(f6440,plain,
( spl0_424
<=> ! [X0,X11,X3] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_fequal(X0),X3)))
| hAPP(c_fequal(X0),X3) = X11
| c_COMBK(c_False,tc_bool,X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f889,plain,
! [X3,X0,X11] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_fequal(X0),X3)))
| hAPP(c_fequal(X0),X3) = X11
| c_COMBK(c_False,tc_bool,X0) = X11 ),
inference(forward_demodulation,[],[f888,f686]) ).
fof(f888,plain,
! [X3,X0,X11] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0))))
| hAPP(c_fequal(X0),X3) = X11
| c_COMBK(c_False,tc_bool,X0) = X11 ),
inference(forward_demodulation,[],[f887,f665]) ).
fof(f887,plain,
! [X3,X0,X11] :
( hAPP(c_fequal(X0),X3) = X11
| c_COMBK(c_False,tc_bool,X0) = X11
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
inference(forward_demodulation,[],[f886,f686]) ).
fof(f886,plain,
! [X3,X0,X11] :
( hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)) = X11
| c_COMBK(c_False,tc_bool,X0) = X11
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
inference(forward_demodulation,[],[f885,f665]) ).
fof(f885,plain,
! [X3,X0,X11] :
( c_COMBK(c_False,tc_bool,X0) = X11
| hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X11
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
inference(forward_demodulation,[],[f543,f665]) ).
fof(f543,axiom,
! [X3,X0,X11] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X11
| hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X11
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f6438,plain,
spl0_423,
inference(avatar_split_clause,[],[f506,f6436]) ).
fof(f6436,plain,
( spl0_423
<=> ! [X2,X58,X0,X1,X54,X6,X7,X17,X5] :
( hAPP(X1,hAPP(X2,X54)) = hAPP(X5,hAPP(X6,X54))
| c_Fun_Ocomp(X1,X2,X17,X7,X0) != c_Fun_Ocomp(X5,X6,X58,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f506,axiom,
! [X2,X58,X0,X1,X54,X6,X7,X17,X5] :
( hAPP(X1,hAPP(X2,X54)) = hAPP(X5,hAPP(X6,X54))
| c_Fun_Ocomp(X1,X2,X17,X7,X0) != c_Fun_Ocomp(X5,X6,X58,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
fof(f6434,plain,
spl0_422,
inference(avatar_split_clause,[],[f425,f6432]) ).
fof(f425,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
fof(f6430,plain,
spl0_421,
inference(avatar_split_clause,[],[f417,f6428]) ).
fof(f6428,plain,
( spl0_421
<=> ! [X11,X0,X12,X3] :
( X11 = X12
| hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| hAPP(c_Set_Oinsert(X3,X0),X11) != hAPP(c_Set_Oinsert(X3,X0),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f417,axiom,
! [X3,X0,X11,X12] :
( X11 = X12
| hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(X3,X12,X0))
| hAPP(c_Set_Oinsert(X3,X0),X11) != hAPP(c_Set_Oinsert(X3,X0),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f6426,plain,
spl0_420,
inference(avatar_split_clause,[],[f348,f6424]) ).
fof(f348,axiom,
! [X0,X11,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f6422,plain,
spl0_419,
inference(avatar_split_clause,[],[f326,f6420]) ).
fof(f326,axiom,
! [X3,X0,X11,X8,X7] :
( ~ hBOOL(c_in(X3,X11,X0))
| hAPP(c_Set_Oimage(X8,X0,X7),X11) = hAPP(c_Set_Oinsert(hAPP(X8,X3),X7),hAPP(c_Set_Oimage(X8,X0,X7),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
fof(f6418,plain,
spl0_418,
inference(avatar_split_clause,[],[f266,f6416]) ).
fof(f266,axiom,
! [X3,X0,X11,X12] :
( ~ hBOOL(c_in(X3,X12,X0))
| hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
fof(f6414,plain,
spl0_417,
inference(avatar_split_clause,[],[f113,f6412]) ).
fof(f6412,plain,
( spl0_417
<=> ! [X11,X0,X12,X8,X7] :
( X11 = X12
| ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hAPP(c_Set_Oimage(X8,X0,X7),X11) != hAPP(c_Set_Oimage(X8,X0,X7),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f113,axiom,
! [X0,X11,X8,X7,X12] :
( X11 = X12
| ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hAPP(c_Set_Oimage(X8,X0,X7),X11) != hAPP(c_Set_Oimage(X8,X0,X7),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
fof(f6410,plain,
spl0_416,
inference(avatar_split_clause,[],[f97,f6408]) ).
fof(f6408,plain,
( spl0_416
<=> ! [X5,X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f97,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).
fof(f5986,plain,
( spl0_415
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2483,f2319,f5984]) ).
fof(f5984,plain,
( spl0_415
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f2483,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243 ),
inference(factoring,[],[f2320]) ).
fof(f5744,plain,
( spl0_414
| ~ spl0_146
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2138,f2005,f1651,f5742]) ).
fof(f5742,plain,
( spl0_414
<=> ! [X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f2138,plain,
( ! [X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) )
| ~ spl0_146
| ~ spl0_199 ),
inference(resolution,[],[f2006,f1652]) ).
fof(f5569,plain,
spl0_413,
inference(avatar_split_clause,[],[f860,f5567]) ).
fof(f5567,plain,
( spl0_413
<=> ! [X5,X0,X6,X2,X1] :
( hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_fequal(X0),X6))
| X2 = X6
| X2 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f860,plain,
! [X2,X0,X1,X6,X5] :
( hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_fequal(X0),X6))
| X2 = X6
| X2 = X5 ),
inference(forward_demodulation,[],[f859,f686]) ).
fof(f859,plain,
! [X2,X0,X1,X6,X5] :
( hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_fequal(X0),X6))
| X2 = X6
| X2 = X5 ),
inference(forward_demodulation,[],[f858,f686]) ).
fof(f858,plain,
! [X2,X0,X1,X6,X5] :
( hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X6,X0),c_COMBK(c_False,tc_bool,X0)))
| X2 = X6
| X2 = X5 ),
inference(forward_demodulation,[],[f604,f665]) ).
fof(f604,axiom,
! [X2,X0,X1,X6,X5] :
( X2 = X6
| X2 = X5
| hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X6,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
fof(f5565,plain,
spl0_412,
inference(avatar_split_clause,[],[f857,f5563]) ).
fof(f5563,plain,
( spl0_412
<=> ! [X5,X0,X6,X2,X1] :
( hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_fequal(X0),X6))
| X1 = X5
| X1 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f857,plain,
! [X2,X0,X1,X6,X5] :
( hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_fequal(X0),X6))
| X1 = X5
| X1 = X6 ),
inference(forward_demodulation,[],[f856,f686]) ).
fof(f856,plain,
! [X2,X0,X1,X6,X5] :
( hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_fequal(X0),X6))
| X1 = X5
| X1 = X6 ),
inference(forward_demodulation,[],[f855,f686]) ).
fof(f855,plain,
! [X2,X0,X1,X6,X5] :
( hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X6,X0),c_COMBK(c_False,tc_bool,X0)))
| X1 = X5
| X1 = X6 ),
inference(forward_demodulation,[],[f607,f665]) ).
fof(f607,axiom,
! [X2,X0,X1,X6,X5] :
( X1 = X5
| X1 = X6
| hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X6,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
fof(f5561,plain,
spl0_411,
inference(avatar_split_clause,[],[f663,f5559]) ).
fof(f663,plain,
! [X0,X11,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X1,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X11,X0),X0)),X1)) ),
inference(definition_unfolding,[],[f83,f263]) ).
fof(f83,axiom,
! [X0,X11,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X1,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X11,X0)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).
fof(f5557,plain,
spl0_410,
inference(avatar_split_clause,[],[f485,f5555]) ).
fof(f485,axiom,
! [X3,X10,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f5553,plain,
spl0_409,
inference(avatar_split_clause,[],[f484,f5551]) ).
fof(f484,axiom,
! [X3,X10,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X10),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X10),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f5549,plain,
spl0_408,
inference(avatar_split_clause,[],[f472,f5547]) ).
fof(f472,axiom,
! [X0,X59,X8,X9,X7,X17] : hAPP(c_Set_Oimage(c_Fun_Ocomp(X8,X9,X17,X0,X7),X7,X0),X59) = hAPP(c_Set_Oimage(X8,X17,X0),hAPP(c_Set_Oimage(X9,X7,X17),X59)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
fof(f5545,plain,
( spl0_407
| ~ spl0_167
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1974,f1888,f1776,f5543]) ).
fof(f1974,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(X0,tc_Hoare__Mirabelle_Otriple(X1)),X2),X2,X1)
| ~ spl0_167
| ~ spl0_187 ),
inference(resolution,[],[f1889,f1777]) ).
fof(f5541,plain,
spl0_406,
inference(avatar_split_clause,[],[f466,f5539]) ).
fof(f466,axiom,
! [X58,X0,X8,X9,X7,X17,X15] : c_Fun_Ocomp(X8,c_Fun_Ocomp(X9,X15,X58,X17,X0),X17,X7,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X8,X9,X17,X7,X58),X15,X58,X7,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
fof(f5537,plain,
spl0_405,
inference(avatar_split_clause,[],[f405,f5535]) ).
fof(f405,axiom,
! [X0,X1,X8,X7,X12] : hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_Set_Oinsert(X1,X7),X12)) = hAPP(c_Set_Oinsert(hAPP(X8,X1),X0),hAPP(c_Set_Oimage(X8,X7,X0),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f5533,plain,
spl0_404,
inference(avatar_split_clause,[],[f340,f5531]) ).
fof(f5531,plain,
( spl0_404
<=> ! [X38,X3,X39,X0,X36,X37,X11,X34,X35,X32,X33] :
( ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(X34,X3),hAPP(X32,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f340,axiom,
! [X38,X3,X39,X0,X11,X36,X37,X34,X35,X32,X33] :
( ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(X34,X3),hAPP(X32,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
fof(f5529,plain,
spl0_403,
inference(avatar_split_clause,[],[f339,f5527]) ).
fof(f5527,plain,
( spl0_403
<=> ! [X38,X3,X39,X0,X11,X36,X37,X34,X35,X32,X33] :
( ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(X34,hAPP(X33,X11)),X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f339,axiom,
! [X38,X3,X39,X0,X11,X36,X37,X34,X35,X32,X33] :
( ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(X34,hAPP(X33,X11)),X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
fof(f5525,plain,
spl0_402,
inference(avatar_split_clause,[],[f334,f5523]) ).
fof(f334,axiom,
! [X0,X11,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
fof(f5521,plain,
spl0_401,
inference(avatar_split_clause,[],[f333,f5519]) ).
fof(f333,axiom,
! [X0,X11,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X12,tc_fun(X0,tc_bool)),X11)),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
fof(f5517,plain,
spl0_400,
inference(avatar_split_clause,[],[f331,f5515]) ).
fof(f331,axiom,
! [X2,X3,X0,X11,X7,X12] :
( ~ hBOOL(c_in(X3,X11,X7))
| ~ hBOOL(c_in(X2,hAPP(X12,X3),X0))
| hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X7,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).
fof(f5513,plain,
spl0_399,
inference(avatar_split_clause,[],[f289,f5511]) ).
fof(f289,axiom,
! [X2,X0,X11,X1,X7,X12] :
( ~ hBOOL(c_in(X1,X11,X7))
| hBOOL(c_in(X2,hAPP(X12,X1),X0))
| ~ hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X7,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__D_0) ).
fof(f5509,plain,
spl0_398,
inference(avatar_split_clause,[],[f257,f5507]) ).
fof(f257,axiom,
! [X8,X9,X7] :
( ~ class_Lattices_Olattice(X7)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X7)),X8),X9),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7),hAPP(X8,v_x)),hAPP(X9,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
fof(f5505,plain,
spl0_397,
inference(avatar_split_clause,[],[f225,f5503]) ).
fof(f5503,plain,
( spl0_397
<=> ! [X11,X0,X8,X3,X1] :
( hBOOL(c_in(X1,X11,X0))
| ~ c_Finite__Set_Ofold__graph(X8,X1,X11,X3,X0,X0)
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f225,axiom,
! [X3,X0,X11,X1,X8] :
( hBOOL(c_in(X1,X11,X0))
| ~ c_Finite__Set_Ofold__graph(X8,X1,X11,X3,X0,X0)
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set_Ointros_0) ).
fof(f5501,plain,
( spl0_396
| ~ spl0_119
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1826,f1792,f1510,f5499]) ).
fof(f1826,plain,
( ! [X0,X1] : c_COMBK(c_False,tc_bool,X1) != hAPP(c_fequal(X1),X0)
| ~ spl0_119
| ~ spl0_171 ),
inference(superposition,[],[f1511,f1793]) ).
fof(f5497,plain,
spl0_395,
inference(avatar_split_clause,[],[f148,f5495]) ).
fof(f148,axiom,
! [X3,X10,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f5493,plain,
spl0_394,
inference(avatar_split_clause,[],[f145,f5491]) ).
fof(f5491,plain,
( spl0_394
<=> ! [X4,X0,X3,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X10))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f145,axiom,
! [X3,X10,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X10))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f5489,plain,
spl0_393,
inference(avatar_split_clause,[],[f94,f5487]) ).
fof(f94,axiom,
! [X3,X0,X11,X8,X7,X4] :
( hBOOL(c_in(X3,X11,X7))
| hAPP(c_Set_Oimage(X8,X7,X0),X11) = hAPP(c_Set_Oimage(c_Fun_Ofun__upd(X8,X3,X4,X7,X0),X7,X0),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
fof(f5485,plain,
spl0_392,
inference(avatar_split_clause,[],[f59,f5483]) ).
fof(f59,axiom,
! [X3,X10,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f5481,plain,
spl0_391,
inference(avatar_split_clause,[],[f58,f5479]) ).
fof(f58,axiom,
! [X3,X10,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f5477,plain,
spl0_390,
inference(avatar_split_clause,[],[f52,f5475]) ).
fof(f52,axiom,
! [X3,X10,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f5473,plain,
spl0_389,
inference(avatar_split_clause,[],[f51,f5471]) ).
fof(f51,axiom,
! [X3,X10,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X10),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X10),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f5469,plain,
spl0_388,
inference(avatar_split_clause,[],[f46,f5467]) ).
fof(f46,axiom,
! [X0,X11,X8,X9,X7,X17] : hAPP(c_Set_Oimage(X8,X7,X0),hAPP(c_Set_Oimage(X9,X17,X7),X11)) = hAPP(c_Set_Oimage(c_COMBB(X8,X9,X7,X0,X17),X17,X0),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
fof(f5465,plain,
spl0_387,
inference(avatar_split_clause,[],[f17,f5463]) ).
fof(f17,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f5419,plain,
( spl0_386
| ~ spl0_12
| ~ spl0_137
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1754,f1707,f1614,f1017,f5416]) ).
fof(f1614,plain,
( spl0_137
<=> c_False = c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1754,plain,
( c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_COMBK(c_False,tc_bool,tc_bool))
| ~ spl0_12
| ~ spl0_137
| ~ spl0_159 ),
inference(forward_demodulation,[],[f1752,f1616]) ).
fof(f1616,plain,
( c_False = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1614]) ).
fof(f1752,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_COMBK(c_False,tc_bool,tc_bool))
| ~ spl0_12
| ~ spl0_159 ),
inference(resolution,[],[f1708,f1019]) ).
fof(f5078,plain,
( spl0_385
| ~ spl0_12
| ~ spl0_137
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1735,f1647,f1614,f1017,f5075]) ).
fof(f5075,plain,
( spl0_385
<=> c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f1735,plain,
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)))
| ~ spl0_12
| ~ spl0_137
| ~ spl0_145 ),
inference(forward_demodulation,[],[f1733,f1616]) ).
fof(f1733,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)))
| ~ spl0_12
| ~ spl0_145 ),
inference(resolution,[],[f1648,f1019]) ).
fof(f5068,plain,
spl0_384,
inference(avatar_split_clause,[],[f837,f5066]) ).
fof(f837,plain,
! [X0,X24,X20] :
( c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X20,X0),c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X24,X0))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24)) ),
inference(forward_demodulation,[],[f836,f673]) ).
fof(f673,plain,
! [X0,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X12) = X12,
inference(forward_demodulation,[],[f387,f665]) ).
fof(f387,axiom,
! [X0,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f836,plain,
! [X0,X24,X20] :
( c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X20,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X24,X0)))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24)) ),
inference(forward_demodulation,[],[f835,f665]) ).
fof(f835,plain,
! [X0,X24,X20] :
( c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X20,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X24,X0)))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24)) ),
inference(forward_demodulation,[],[f302,f411]) ).
fof(f302,axiom,
! [X0,X24,X20] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24))
| c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X20,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X20,X24,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I5_J_0) ).
fof(f5064,plain,
spl0_383,
inference(avatar_split_clause,[],[f834,f5062]) ).
fof(f834,plain,
! [X0,X24,X20] :
( c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X24,X0),c_SetInterval_Oord__class_OatLeastLessThan(X20,X24,X0))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24)) ),
inference(forward_demodulation,[],[f833,f672]) ).
fof(f672,plain,
! [X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_COMBK(c_False,tc_bool,X0)) = X11,
inference(forward_demodulation,[],[f386,f665]) ).
fof(f386,axiom,
! [X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f833,plain,
! [X0,X24,X20] :
( c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X24,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X20,X24,X0)),c_COMBK(c_False,tc_bool,X0)))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24)) ),
inference(forward_demodulation,[],[f832,f665]) ).
fof(f832,plain,
! [X0,X24,X20] :
( c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(c_Set_Oinsert(X24,X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X20,X24,X0)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24)) ),
inference(forward_demodulation,[],[f303,f410]) ).
fof(f303,axiom,
! [X0,X24,X20] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X24))
| c_SetInterval_Oord__class_OatLeastAtMost(X20,X24,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X20,X24,X0)),hAPP(c_Set_Oinsert(X24,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).
fof(f5060,plain,
spl0_382,
inference(avatar_split_clause,[],[f435,f5058]) ).
fof(f435,axiom,
! [X0,X11,X1,X7,X12] :
( ~ hBOOL(c_in(X1,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X0,tc_fun(X7,tc_bool))),hAPP(X12,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__lower_0) ).
fof(f5056,plain,
spl0_381,
inference(avatar_split_clause,[],[f430,f5054]) ).
fof(f430,axiom,
! [X0,X11,X5,X12] :
( hBOOL(c_in(X5,X12,X0))
| hBOOL(c_in(X5,X11,X0))
| ~ hBOOL(c_in(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f5052,plain,
spl0_380,
inference(avatar_split_clause,[],[f413,f5050]) ).
fof(f413,axiom,
! [X3,X0,X11,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X11)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
fof(f5048,plain,
spl0_379,
inference(avatar_split_clause,[],[f412,f5046]) ).
fof(f412,axiom,
! [X2,X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oinsert(X2,X0),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
fof(f5044,plain,
spl0_378,
inference(avatar_split_clause,[],[f364,f5042]) ).
fof(f364,axiom,
! [X3,X0,X8,X9,X7] :
( ~ class_HOL_Oord(X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X8),X9))
| hBOOL(hAPP(hAPP(c_lessequals(X7),hAPP(X8,X3)),hAPP(X9,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f5040,plain,
spl0_377,
inference(avatar_split_clause,[],[f265,f5038]) ).
fof(f265,axiom,
! [X0,X11,X1,X7,X12] :
( ~ hBOOL(c_in(X1,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),hAPP(X12,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
fof(f5036,plain,
spl0_376,
inference(avatar_split_clause,[],[f181,f5034]) ).
fof(f5034,plain,
( spl0_376
<=> ! [X0,X11,X8] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Fun_Oinj__on(X8,X11,X0,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oimage(X8,X0,X0),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f181,axiom,
! [X0,X11,X8] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Fun_Oinj__on(X8,X11,X0,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(c_Set_Oimage(X8,X0,X0),X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
fof(f5032,plain,
( spl0_375
| ~ spl0_20
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1594,f1563,f1057,f5030]) ).
fof(f1594,plain,
( ! [X0] : hAPP(c_fequal(tc_bool),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)
| ~ spl0_20
| ~ spl0_130 ),
inference(resolution,[],[f1564,f1059]) ).
fof(f5028,plain,
spl0_374,
inference(avatar_split_clause,[],[f115,f5026]) ).
fof(f115,axiom,
! [X0,X11,X1,X12] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
fof(f5024,plain,
spl0_373,
inference(avatar_split_clause,[],[f114,f5022]) ).
fof(f114,axiom,
! [X0,X11,X1,X12] :
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),X12)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
fof(f5020,plain,
spl0_372,
inference(avatar_split_clause,[],[f101,f5018]) ).
fof(f5018,plain,
( spl0_372
<=> ! [X11,X0,X12,X3,X7] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X3,X11,X0))
| c_Finite__Set_Ofinite(hAPP(X12,X3),X7)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f101,axiom,
! [X3,X0,X11,X7,X12] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X3,X11,X0))
| c_Finite__Set_Ofinite(hAPP(X12,X3),X7)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UN_0) ).
fof(f4834,plain,
( spl0_371
| ~ spl0_8
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1593,f1563,f997,f4832]) ).
fof(f1593,plain,
( ! [X0] : hAPP(c_fequal(tc_nat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_8
| ~ spl0_130 ),
inference(resolution,[],[f1564,f999]) ).
fof(f4517,plain,
( spl0_370
| ~ spl0_12
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1591,f1559,f1017,f4515]) ).
fof(f1591,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0
| ~ spl0_12
| ~ spl0_129 ),
inference(resolution,[],[f1560,f1019]) ).
fof(f4411,plain,
spl0_369,
inference(avatar_split_clause,[],[f868,f4409]) ).
fof(f868,plain,
! [X0,X69,X60,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X60),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0) ),
inference(forward_demodulation,[],[f867,f686]) ).
fof(f867,plain,
! [X0,X69,X60,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0) ),
inference(forward_demodulation,[],[f596,f665]) ).
fof(f596,axiom,
! [X0,X69,X60,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
fof(f4407,plain,
spl0_368,
inference(avatar_split_clause,[],[f761,f4405]) ).
fof(f761,plain,
! [X3,X0,X11] :
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)) = X11
| hBOOL(c_in(X3,X11,X0)) ),
inference(forward_demodulation,[],[f760,f686]) ).
fof(f760,plain,
! [X3,X0,X11] :
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0))) = X11
| hBOOL(c_in(X3,X11,X0)) ),
inference(forward_demodulation,[],[f401,f665]) ).
fof(f401,axiom,
! [X3,X0,X11] :
( hBOOL(c_in(X3,X11,X0))
| hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X3,X0),X11),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
fof(f4402,plain,
spl0_367,
inference(avatar_split_clause,[],[f709,f4400]) ).
fof(f4400,plain,
( spl0_367
<=> ! [X0,X12,X1] : hAPP(c_Set_Oinsert(X1,X0),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1)),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f709,plain,
! [X0,X1,X12] : hAPP(c_Set_Oinsert(X1,X0),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1)),X12),
inference(forward_demodulation,[],[f337,f272]) ).
fof(f337,axiom,
! [X0,X1,X12] : hAPP(c_Set_Oinsert(X1,X0),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
fof(f4398,plain,
spl0_366,
inference(avatar_split_clause,[],[f497,f4396]) ).
fof(f4396,plain,
( spl0_366
<=> ! [X11,X0,X7,X12,X2,X1] :
( ~ hBOOL(c_in(X1,X11,X0))
| hBOOL(hAPP(hAPP(X12,X1),X2))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X0,tc_fun(X7,tc_bool)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f497,axiom,
! [X2,X0,X11,X1,X7,X12] :
( ~ hBOOL(c_in(X1,X11,X0))
| hBOOL(hAPP(hAPP(X12,X1),X2))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X12,X0,tc_fun(X7,tc_bool)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__D_0) ).
fof(f4394,plain,
spl0_365,
inference(avatar_split_clause,[],[f481,f4392]) ).
fof(f481,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
fof(f4390,plain,
spl0_364,
inference(avatar_split_clause,[],[f479,f4388]) ).
fof(f479,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f4386,plain,
( spl0_363
| ~ spl0_12
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1589,f1555,f1017,f4384]) ).
fof(f1589,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0
| ~ spl0_12
| ~ spl0_128 ),
inference(resolution,[],[f1556,f1019]) ).
fof(f4382,plain,
spl0_362,
inference(avatar_split_clause,[],[f478,f4380]) ).
fof(f478,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f4378,plain,
spl0_361,
inference(avatar_split_clause,[],[f476,f4376]) ).
fof(f476,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
fof(f4374,plain,
spl0_360,
inference(avatar_split_clause,[],[f444,f4372]) ).
fof(f444,axiom,
! [X0,X11,X12] :
( X11 = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
fof(f4370,plain,
spl0_359,
inference(avatar_split_clause,[],[f352,f4368]) ).
fof(f352,axiom,
! [X2,X3,X0,X11,X7,X12] :
( ~ hBOOL(c_in(X3,X11,X0))
| ~ hBOOL(hAPP(hAPP(X12,X3),X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X12,X0,tc_fun(X7,tc_bool)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
fof(f4366,plain,
spl0_358,
inference(avatar_split_clause,[],[f335,f4364]) ).
fof(f335,axiom,
! [X11,X7,X12] :
( ~ class_HOL_Ominus(X7)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(t_a,X7)),X12),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X11,v_x),X7),hAPP(X12,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
fof(f4362,plain,
spl0_357,
inference(avatar_split_clause,[],[f324,f4360]) ).
fof(f324,axiom,
! [X0,X11,X5,X12] :
( ~ hBOOL(c_in(X5,X11,X0))
| hBOOL(c_in(X5,X12,X0))
| hBOOL(c_in(X5,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
fof(f4358,plain,
spl0_356,
inference(avatar_split_clause,[],[f249,f4356]) ).
fof(f4356,plain,
( spl0_356
<=> ! [X11,X0,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),tc_fun(X0,tc_bool)),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f249,axiom,
! [X0,X11,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),tc_fun(X0,tc_bool)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f4354,plain,
spl0_355,
inference(avatar_split_clause,[],[f185,f4352]) ).
fof(f185,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
fof(f4350,plain,
spl0_354,
inference(avatar_split_clause,[],[f184,f4348]) ).
fof(f184,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
fof(f4346,plain,
spl0_353,
inference(avatar_split_clause,[],[f174,f4344]) ).
fof(f174,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
fof(f4342,plain,
( spl0_352
| ~ spl0_9
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1584,f1551,f1002,f4339]) ).
fof(f4339,plain,
( spl0_352
<=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_nat)),v_x) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f1584,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_nat)),v_x) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_9
| ~ spl0_127 ),
inference(resolution,[],[f1552,f1004]) ).
fof(f4337,plain,
spl0_351,
inference(avatar_split_clause,[],[f173,f4335]) ).
fof(f173,axiom,
! [X3,X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f4333,plain,
spl0_350,
inference(avatar_split_clause,[],[f172,f4331]) ).
fof(f172,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f4329,plain,
spl0_349,
inference(avatar_split_clause,[],[f171,f4327]) ).
fof(f171,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f4325,plain,
spl0_348,
inference(avatar_split_clause,[],[f71,f4323]) ).
fof(f71,axiom,
! [X0,X11,X12] :
( X11 = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
fof(f4321,plain,
spl0_347,
inference(avatar_split_clause,[],[f2,f4319]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
fof(f4317,plain,
spl0_346,
inference(avatar_split_clause,[],[f1,f4315]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
fof(f4281,plain,
( spl0_345
| ~ spl0_21
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1582,f1543,f1062,f4278]) ).
fof(f1062,plain,
( spl0_21
<=> class_Orderings_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1582,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x)
| ~ spl0_21
| ~ spl0_125 ),
inference(resolution,[],[f1544,f1064]) ).
fof(f1064,plain,
( class_Orderings_Otop(tc_bool)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f3991,plain,
spl0_344,
inference(avatar_split_clause,[],[f778,f3989]) ).
fof(f778,plain,
! [X0,X11,X7,X5] :
( hAPP(c_Set_Oimage(c_COMBK(X5,X0,X7),X7,X0),X11) = hAPP(c_fequal(X0),X5)
| c_COMBK(c_False,tc_bool,X7) = X11 ),
inference(forward_demodulation,[],[f777,f686]) ).
fof(f777,plain,
! [X0,X11,X7,X5] :
( hAPP(c_Set_Oimage(c_COMBK(X5,X0,X7),X7,X0),X11) = hAPP(c_Set_Oinsert(X5,X0),c_COMBK(c_False,tc_bool,X0))
| c_COMBK(c_False,tc_bool,X7) = X11 ),
inference(forward_demodulation,[],[f776,f665]) ).
fof(f776,plain,
! [X0,X11,X7,X5] :
( c_COMBK(c_False,tc_bool,X7) = X11
| hAPP(c_Set_Oimage(c_COMBK(X5,X0,X7),X7,X0),X11) = hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
inference(forward_demodulation,[],[f591,f665]) ).
fof(f591,axiom,
! [X0,X11,X7,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X11
| hAPP(c_Set_Oimage(c_COMBK(X5,X0,X7),X7,X0),X11) = hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
fof(f3987,plain,
spl0_343,
inference(avatar_split_clause,[],[f775,f3985]) ).
fof(f775,plain,
! [X0,X11,X7,X5] :
( c_COMBK(c_False,tc_bool,X7) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(X5,tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = X5 ),
inference(forward_demodulation,[],[f573,f665]) ).
fof(f573,axiom,
! [X0,X11,X7,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(X5,tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_1) ).
fof(f3983,plain,
( spl0_342
| ~ spl0_137
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f3939,f3936,f1614,f3981]) ).
fof(f3981,plain,
( spl0_342
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_False) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f3936,plain,
( spl0_331
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f3939,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_False) = X0
| ~ spl0_137
| ~ spl0_331 ),
inference(forward_demodulation,[],[f3937,f1616]) ).
fof(f3937,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) = X0
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f3936]) ).
fof(f3979,plain,
spl0_341,
inference(avatar_split_clause,[],[f774,f3977]) ).
fof(f3977,plain,
( spl0_341
<=> ! [X11,X0,X5,X7] :
( c_COMBK(c_False,tc_bool,X7) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBK(X5,tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f774,plain,
! [X0,X11,X7,X5] :
( c_COMBK(c_False,tc_bool,X7) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBK(X5,tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = X5 ),
inference(forward_demodulation,[],[f572,f665]) ).
fof(f572,axiom,
! [X0,X11,X7,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBK(X5,tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_1) ).
fof(f3975,plain,
spl0_340,
inference(avatar_split_clause,[],[f746,f3973]) ).
fof(f746,plain,
! [X2,X0,X1] :
( hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)) != hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))
| X1 = X2 ),
inference(forward_demodulation,[],[f616,f665]) ).
fof(f616,axiom,
! [X2,X0,X1] :
( X1 = X2
| hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) != hAPP(c_Set_Oinsert(X2,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f3971,plain,
spl0_339,
inference(avatar_split_clause,[],[f738,f3969]) ).
fof(f738,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f737,f686]) ).
fof(f737,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f399,f665]) ).
fof(f399,axiom,
! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
fof(f3967,plain,
spl0_338,
inference(avatar_split_clause,[],[f736,f3965]) ).
fof(f736,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_fequal(X0),X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f735,f686]) ).
fof(f735,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_COMBK(c_False,tc_bool,X0))))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f218,f665]) ).
fof(f218,axiom,
! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X2,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
fof(f3963,plain,
spl0_337,
inference(avatar_split_clause,[],[f714,f3961]) ).
fof(f714,plain,
! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(c_Set_Oinsert(X1,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))),
inference(forward_demodulation,[],[f713,f686]) ).
fof(f713,plain,
! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(c_Set_Oinsert(X1,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)))),
inference(forward_demodulation,[],[f563,f665]) ).
fof(f563,axiom,
! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(c_Set_Oinsert(X1,X0),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
fof(f3959,plain,
spl0_336,
inference(avatar_split_clause,[],[f704,f3957]) ).
fof(f3957,plain,
( spl0_336
<=> ! [X0,X11,X7] : c_COMBK(c_False,tc_bool,tc_prod(X0,X7)) = c_Product__Type_OSigma(X11,c_COMBK(c_COMBK(c_False,tc_bool,X7),tc_fun(X7,tc_bool),X0),X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f704,plain,
! [X0,X11,X7] : c_COMBK(c_False,tc_bool,tc_prod(X0,X7)) = c_Product__Type_OSigma(X11,c_COMBK(c_COMBK(c_False,tc_bool,X7),tc_fun(X7,tc_bool),X0),X0,X7),
inference(forward_demodulation,[],[f703,f665]) ).
fof(f703,plain,
! [X0,X11,X7] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X7),tc_bool)) = c_Product__Type_OSigma(X11,c_COMBK(c_COMBK(c_False,tc_bool,X7),tc_fun(X7,tc_bool),X0),X0,X7),
inference(forward_demodulation,[],[f519,f665]) ).
fof(f519,axiom,
! [X0,X11,X7] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X7),tc_bool)) = c_Product__Type_OSigma(X11,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),tc_fun(X7,tc_bool),X0),X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).
fof(f3955,plain,
spl0_335,
inference(avatar_split_clause,[],[f700,f3953]) ).
fof(f3953,plain,
( spl0_335
<=> ! [X0,X11,X7] : c_COMBK(c_False,tc_bool,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f700,plain,
! [X0,X11,X7] : c_COMBK(c_False,tc_bool,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f571,f665]) ).
fof(f571,axiom,
! [X0,X11,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool),X7),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
fof(f3951,plain,
spl0_334,
inference(avatar_split_clause,[],[f503,f3949]) ).
fof(f503,axiom,
! [X0,X11,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X8,X11)),X11))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Inductive_Ocomplete__lattice__class_Olfp(X8,X0)),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lfp__lowerbound_0) ).
fof(f3947,plain,
spl0_333,
inference(avatar_split_clause,[],[f434,f3945]) ).
fof(f434,axiom,
! [X0,X11,X44,X26,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| ~ hBOOL(c_in(X26,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X7),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X44,X0,X7)),hAPP(X44,X26))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
fof(f3943,plain,
spl0_332,
inference(avatar_split_clause,[],[f350,f3941]) ).
fof(f3941,plain,
( spl0_332
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f350,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f3938,plain,
( spl0_331
| ~ spl0_16
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1576,f1539,f1037,f3936]) ).
fof(f1576,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) = X0
| ~ spl0_16
| ~ spl0_124 ),
inference(resolution,[],[f1540,f1039]) ).
fof(f3934,plain,
spl0_330,
inference(avatar_split_clause,[],[f349,f3932]) ).
fof(f349,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f3930,plain,
spl0_329,
inference(avatar_split_clause,[],[f276,f3928]) ).
fof(f276,axiom,
! [X0,X11,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
fof(f3926,plain,
spl0_328,
inference(avatar_split_clause,[],[f264,f3924]) ).
fof(f264,axiom,
! [X0,X11,X44,X26,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| ~ hBOOL(c_in(X26,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X7),hAPP(X44,X26)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,X44,X0,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
fof(f3922,plain,
spl0_327,
inference(avatar_split_clause,[],[f157,f3920]) ).
fof(f157,axiom,
! [X0,X8,X9,X7] :
( ~ class_HOL_Oord(X7)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X7)),X8),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X9),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
fof(f3918,plain,
spl0_326,
inference(avatar_split_clause,[],[f125,f3916]) ).
fof(f125,axiom,
! [X0,X11,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),X11)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
fof(f3914,plain,
spl0_325,
inference(avatar_split_clause,[],[f117,f3912]) ).
fof(f117,axiom,
! [X0,X11,X8,X9,X7,X17] :
( ~ c_Fun_Oinj__on(c_Fun_Ocomp(X9,X8,X17,X7,X0),X11,X0,X7)
| c_Fun_Oinj__on(X9,hAPP(c_Set_Oimage(X8,X0,X17),X11),X17,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).
fof(f3910,plain,
spl0_324,
inference(avatar_split_clause,[],[f107,f3908]) ).
fof(f107,axiom,
! [X0,X11,X8,X7,X12] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(X12,X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X12),hAPP(c_Set_Oimage(X8,X0,X7),X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
fof(f3906,plain,
spl0_323,
inference(avatar_split_clause,[],[f48,f3904]) ).
fof(f3904,plain,
( spl0_323
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f48,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f3902,plain,
spl0_322,
inference(avatar_split_clause,[],[f47,f3900]) ).
fof(f47,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f3898,plain,
spl0_321,
inference(avatar_split_clause,[],[f27,f3896]) ).
fof(f27,axiom,
! [X0,X8,X9,X7] :
( ~ class_HOL_Oord(X7)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,X7)),X8),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X7)),X8),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
fof(f3669,plain,
( ~ spl0_320
| spl0_56
| ~ spl0_86
| ~ spl0_132
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3457,f3396,f1579,f1340,f1213,f3666]) ).
fof(f3666,plain,
( spl0_320
<=> hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_False))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f1579,plain,
( spl0_132
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f3396,plain,
( spl0_307
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_False),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f3457,plain,
( hBOOL(c_False)
| ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_False)))
| ~ spl0_86
| ~ spl0_132
| ~ spl0_307 ),
inference(forward_demodulation,[],[f3449,f1580]) ).
fof(f1580,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1579]) ).
fof(f3449,plain,
( ~ hBOOL(c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_False)))
| hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_False),c_False))
| ~ spl0_86
| ~ spl0_307 ),
inference(superposition,[],[f1341,f3397]) ).
fof(f3397,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_False),X0) = X0
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f3396]) ).
fof(f3468,plain,
spl0_319,
inference(avatar_split_clause,[],[f773,f3466]) ).
fof(f773,plain,
! [X0,X11,X12] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X11 ),
inference(forward_demodulation,[],[f772,f665]) ).
fof(f772,plain,
! [X0,X11,X12] :
( c_COMBK(c_False,tc_bool,X0) = X11
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) ),
inference(forward_demodulation,[],[f395,f665]) ).
fof(f395,axiom,
! [X0,X11,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X11
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f3464,plain,
spl0_318,
inference(avatar_split_clause,[],[f771,f3462]) ).
fof(f771,plain,
! [X0,X11,X12] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X12 ),
inference(forward_demodulation,[],[f770,f665]) ).
fof(f770,plain,
! [X0,X11,X12] :
( c_COMBK(c_False,tc_bool,X0) = X12
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) ),
inference(forward_demodulation,[],[f394,f665]) ).
fof(f394,axiom,
! [X0,X11,X12] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X12
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f3441,plain,
spl0_317,
inference(avatar_split_clause,[],[f754,f3439]) ).
fof(f754,plain,
! [X3,X0,X11,X7,X5] :
( hAPP(c_Set_Oimage(c_COMBK(X5,X7,X0),X0,X7),X11) = hAPP(c_fequal(X7),X5)
| ~ hBOOL(c_in(X3,X11,X0)) ),
inference(forward_demodulation,[],[f753,f686]) ).
fof(f753,plain,
! [X3,X0,X11,X7,X5] :
( hAPP(c_Set_Oimage(c_COMBK(X5,X7,X0),X0,X7),X11) = hAPP(c_Set_Oinsert(X5,X7),c_COMBK(c_False,tc_bool,X7))
| ~ hBOOL(c_in(X3,X11,X0)) ),
inference(forward_demodulation,[],[f539,f665]) ).
fof(f539,axiom,
! [X3,X0,X11,X7,X5] :
( ~ hBOOL(c_in(X3,X11,X0))
| hAPP(c_Set_Oimage(c_COMBK(X5,X7,X0),X0,X7),X11) = hAPP(c_Set_Oinsert(X5,X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
fof(f3436,plain,
spl0_316,
inference(avatar_split_clause,[],[f712,f3434]) ).
fof(f3434,plain,
( spl0_316
<=> ! [X0,X12,X1,X7] : hAPP(c_fequal(X0),X1) = hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f712,plain,
! [X0,X1,X7,X12] : hAPP(c_fequal(X0),X1) = hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool))),
inference(forward_demodulation,[],[f711,f686]) ).
fof(f711,plain,
! [X0,X1,X7,X12] : hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)) = hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool))),
inference(forward_demodulation,[],[f710,f665]) ).
fof(f710,plain,
! [X0,X1,X7,X12] : hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool))),
inference(forward_demodulation,[],[f549,f665]) ).
fof(f549,axiom,
! [X0,X1,X7,X12] : hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = hAPP(c_Set_Oinsert(X1,X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X12,X7,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
fof(f3431,plain,
spl0_315,
inference(avatar_split_clause,[],[f698,f3429]) ).
fof(f3429,plain,
( spl0_315
<=> ! [X11,X0,X12,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X11,X7,tc_fun(X0,tc_bool))),X12) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f698,plain,
! [X0,X11,X7,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X11,X7,tc_fun(X0,tc_bool))),X12) = X12,
inference(forward_demodulation,[],[f436,f665]) ).
fof(f436,axiom,
! [X0,X11,X7,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X11,X7,tc_fun(X0,tc_bool))),X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
fof(f3426,plain,
spl0_314,
inference(avatar_split_clause,[],[f697,f3424]) ).
fof(f3424,plain,
( spl0_314
<=> ! [X11,X0,X12,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool))) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f697,plain,
! [X0,X11,X7,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool))) = X11,
inference(forward_demodulation,[],[f437,f665]) ).
fof(f437,axiom,
! [X0,X11,X7,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X12,X7,tc_fun(X0,tc_bool))) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
fof(f3422,plain,
spl0_313,
inference(avatar_split_clause,[],[f613,f3420]) ).
fof(f613,axiom,
! [X3,X0,X11,X4] : hAPP(c_Set_Oinsert(X3,X0),hAPP(c_Set_Oinsert(X4,X0),X11)) = hAPP(c_Set_Oinsert(X4,X0),hAPP(c_Set_Oinsert(X3,X0),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f3418,plain,
spl0_312,
inference(avatar_split_clause,[],[f487,f3416]) ).
fof(f487,axiom,
! [X0,X11,X5,X12] :
( ~ hBOOL(c_in(X5,X11,X0))
| hBOOL(c_in(X5,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
fof(f3414,plain,
spl0_311,
inference(avatar_split_clause,[],[f454,f3412]) ).
fof(f454,axiom,
! [X0,X11,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) != X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f3410,plain,
spl0_310,
inference(avatar_split_clause,[],[f453,f3408]) ).
fof(f453,axiom,
! [X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X11))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f3406,plain,
spl0_309,
inference(avatar_split_clause,[],[f452,f3404]) ).
fof(f452,axiom,
! [X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f3402,plain,
spl0_308,
inference(avatar_split_clause,[],[f448,f3400]) ).
fof(f448,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f3398,plain,
( spl0_307
| ~ spl0_137
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3350,f3347,f1614,f3396]) ).
fof(f3347,plain,
( spl0_297
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f3350,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_False),X0) = X0
| ~ spl0_137
| ~ spl0_297 ),
inference(forward_demodulation,[],[f3348,f1616]) ).
fof(f3348,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) = X0
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f3347]) ).
fof(f3394,plain,
spl0_306,
inference(avatar_split_clause,[],[f427,f3392]) ).
fof(f427,axiom,
! [X3,X0,X11,X12] :
( hBOOL(hAPP(X12,X3))
| hBOOL(hAPP(X11,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f3390,plain,
spl0_305,
inference(avatar_split_clause,[],[f222,f3388]) ).
fof(f222,axiom,
! [X3,X0,X11] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Olinorder__class_OMin(X11,X0)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).
fof(f3386,plain,
spl0_304,
inference(avatar_split_clause,[],[f221,f3384]) ).
fof(f221,axiom,
! [X3,X0,X11] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Finite__Set_Olinorder__class_OMax(X11,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).
fof(f3382,plain,
spl0_303,
inference(avatar_split_clause,[],[f147,f3380]) ).
fof(f147,axiom,
! [X0,X11,X5,X12] :
( ~ hBOOL(c_in(X5,X11,X0))
| hBOOL(c_in(X5,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
fof(f3378,plain,
spl0_302,
inference(avatar_split_clause,[],[f106,f3376]) ).
fof(f106,axiom,
! [X3,X28,X0,X11,X7] :
( ~ hBOOL(c_in(X3,X28,X0))
| ~ c_Finite__Set_Ofinite(hAPP(X11,X3),X7)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28,X11,X0,tc_fun(X7,tc_bool)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__INT_0) ).
fof(f3374,plain,
spl0_301,
inference(avatar_split_clause,[],[f78,f3372]) ).
fof(f78,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f3370,plain,
spl0_300,
inference(avatar_split_clause,[],[f69,f3368]) ).
fof(f69,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
fof(f3366,plain,
spl0_299,
inference(avatar_split_clause,[],[f53,f3364]) ).
fof(f53,axiom,
! [X0,X11,X8,X7,X12] :
( ~ c_Fun_Oinj__on(X8,X12,X0,X7)
| c_Fun_Oinj__on(X8,X11,X0,X7)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
fof(f3362,plain,
spl0_298,
inference(avatar_split_clause,[],[f4,f3360]) ).
fof(f3360,plain,
( spl0_298
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f4,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f3349,plain,
( spl0_297
| ~ spl0_16
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1574,f1535,f1037,f3347]) ).
fof(f1574,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) = X0
| ~ spl0_16
| ~ spl0_123 ),
inference(resolution,[],[f1536,f1039]) ).
fof(f3231,plain,
( spl0_296
| ~ spl0_16
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1572,f1527,f1037,f3229]) ).
fof(f3229,plain,
( spl0_296
<=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f1572,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) = X0
| ~ spl0_16
| ~ spl0_121 ),
inference(resolution,[],[f1528,f1039]) ).
fof(f3139,plain,
( spl0_295
| ~ spl0_16
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1570,f1523,f1037,f3137]) ).
fof(f1570,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) = X0
| ~ spl0_16
| ~ spl0_120 ),
inference(resolution,[],[f1524,f1039]) ).
fof(f3026,plain,
spl0_294,
inference(avatar_split_clause,[],[f935,f3024]) ).
fof(f935,plain,
! [X0,X11] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X11,X0),X11,X0)) ),
inference(forward_demodulation,[],[f223,f665]) ).
fof(f223,axiom,
! [X0,X11] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X11
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X11,X0),X11,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).
fof(f3022,plain,
spl0_293,
inference(avatar_split_clause,[],[f934,f3020]) ).
fof(f934,plain,
! [X0,X11] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X11,X0),X11,X0)) ),
inference(forward_demodulation,[],[f224,f665]) ).
fof(f224,axiom,
! [X0,X11] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X11
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X11,X0),X11,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).
fof(f3018,plain,
spl0_292,
inference(avatar_split_clause,[],[f853,f3016]) ).
fof(f853,plain,
! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ),
inference(forward_demodulation,[],[f458,f665]) ).
fof(f458,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
fof(f3014,plain,
spl0_291,
inference(avatar_split_clause,[],[f851,f3012]) ).
fof(f851,plain,
! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2)) ),
inference(forward_demodulation,[],[f176,f665]) ).
fof(f176,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
fof(f3010,plain,
spl0_290,
inference(avatar_split_clause,[],[f849,f3008]) ).
fof(f849,plain,
! [X0,X19,X20] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X19),X20)) ),
inference(forward_demodulation,[],[f62,f665]) ).
fof(f62,axiom,
! [X0,X19,X20] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X19),X20))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_1) ).
fof(f3006,plain,
spl0_289,
inference(avatar_split_clause,[],[f848,f3004]) ).
fof(f848,plain,
! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ),
inference(forward_demodulation,[],[f86,f665]) ).
fof(f86,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
fof(f3002,plain,
spl0_288,
inference(avatar_split_clause,[],[f847,f3000]) ).
fof(f847,plain,
! [X0,X19,X20] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X19)) ),
inference(forward_demodulation,[],[f85,f665]) ).
fof(f85,axiom,
! [X0,X19,X20] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X20),X19))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty_0) ).
fof(f2998,plain,
spl0_287,
inference(avatar_split_clause,[],[f845,f2996]) ).
fof(f2996,plain,
( spl0_287
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f845,plain,
! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ),
inference(forward_demodulation,[],[f459,f665]) ).
fof(f459,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
fof(f2994,plain,
spl0_286,
inference(avatar_split_clause,[],[f844,f2992]) ).
fof(f844,plain,
! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ),
inference(forward_demodulation,[],[f105,f665]) ).
fof(f105,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).
fof(f2990,plain,
spl0_285,
inference(avatar_split_clause,[],[f842,f2988]) ).
fof(f2988,plain,
( spl0_285
<=> ! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f842,plain,
! [X2,X0,X1] :
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2)) ),
inference(forward_demodulation,[],[f175,f665]) ).
fof(f175,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
fof(f2986,plain,
spl0_284,
inference(avatar_split_clause,[],[f840,f2984]) ).
fof(f2984,plain,
( spl0_284
<=> ! [X20,X0,X19] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X19),X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f840,plain,
! [X0,X19,X20] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X19),X20)) ),
inference(forward_demodulation,[],[f139,f665]) ).
fof(f139,axiom,
! [X0,X19,X20] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X19),X20))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X19,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_0) ).
fof(f2982,plain,
spl0_283,
inference(avatar_split_clause,[],[f839,f2980]) ).
fof(f839,plain,
! [X0,X11,X44,X7] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(X44,X7,X0),X0,X7) = X44 ),
inference(forward_demodulation,[],[f570,f665]) ).
fof(f570,axiom,
! [X0,X11,X44,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,c_COMBK(X44,X7,X0),X0,X7) = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).
fof(f2978,plain,
spl0_282,
inference(avatar_split_clause,[],[f838,f2976]) ).
fof(f838,plain,
! [X0,X11,X44,X7] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBK(X44,X7,X0),X0,X7) = X44 ),
inference(forward_demodulation,[],[f568,f665]) ).
fof(f568,axiom,
! [X0,X11,X44,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X7)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X11
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBK(X44,X7,X0),X0,X7) = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__const_0) ).
fof(f2974,plain,
spl0_281,
inference(avatar_split_clause,[],[f795,f2972]) ).
fof(f2972,plain,
( spl0_281
<=> ! [X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(X33,hAPP(c_fequal(X0),X1)) = X1
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f795,plain,
! [X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(X33,hAPP(c_fequal(X0),X1)) = X1
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f794,f686]) ).
fof(f794,plain,
! [X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(X33,hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))) = X1
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f545,f665]) ).
fof(f545,axiom,
! [X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| hAPP(X33,hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
fof(f2970,plain,
( spl0_280
| ~ spl0_65
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f2924,f2556,f1252,f2968]) ).
fof(f2968,plain,
( spl0_280
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2556,plain,
( spl0_260
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2924,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1,X0)
| ~ spl0_65
| ~ spl0_260 ),
inference(resolution,[],[f2557,f1253]) ).
fof(f2557,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1,X0)
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f2556]) ).
fof(f2966,plain,
spl0_279,
inference(avatar_split_clause,[],[f793,f2964]) ).
fof(f2964,plain,
( spl0_279
<=> ! [X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(X32,hAPP(c_fequal(X0),X1)) = X1
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f793,plain,
! [X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(X32,hAPP(c_fequal(X0),X1)) = X1
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f792,f686]) ).
fof(f792,plain,
! [X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( hAPP(X32,hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))) = X1
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f546,f665]) ).
fof(f546,axiom,
! [X38,X39,X0,X36,X1,X37,X34,X35,X32,X33] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0)
| hAPP(X32,hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
fof(f2962,plain,
spl0_278,
inference(avatar_split_clause,[],[f786,f2960]) ).
fof(f2960,plain,
( spl0_278
<=> ! [X38,X33,X32,X0,X34,X36,X35,X39,X37] :
( hAPP(X32,c_COMBK(c_False,tc_bool,X0)) = X39
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f786,plain,
! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( hAPP(X32,c_COMBK(c_False,tc_bool,X0)) = X39
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f374,f665]) ).
fof(f374,axiom,
! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( hAPP(X32,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X39
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
fof(f2958,plain,
spl0_277,
inference(avatar_split_clause,[],[f785,f2956]) ).
fof(f2956,plain,
( spl0_277
<=> ! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( hAPP(X33,c_COMBK(c_False,tc_bool,X0)) = X38
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f785,plain,
! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( hAPP(X33,c_COMBK(c_False,tc_bool,X0)) = X38
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
inference(forward_demodulation,[],[f373,f665]) ).
fof(f373,axiom,
! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( hAPP(X33,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X38
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
fof(f2954,plain,
spl0_276,
inference(avatar_split_clause,[],[f769,f2952]) ).
fof(f769,plain,
! [X0,X11] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),c_COMBK(c_False,tc_bool,X0)))
| c_COMBK(c_False,tc_bool,X0) = X11 ),
inference(forward_demodulation,[],[f768,f665]) ).
fof(f768,plain,
! [X0,X11] :
( c_COMBK(c_False,tc_bool,X0) = X11
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
inference(forward_demodulation,[],[f381,f665]) ).
fof(f381,axiom,
! [X0,X11] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X11
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f2950,plain,
spl0_275,
inference(avatar_split_clause,[],[f694,f2948]) ).
fof(f694,plain,
! [X0,X11,X7,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool))) = X11,
inference(forward_demodulation,[],[f254,f665]) ).
fof(f254,axiom,
! [X0,X11,X7,X12] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X12,X7,tc_fun(X0,tc_bool))) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
fof(f2946,plain,
spl0_274,
inference(avatar_split_clause,[],[f528,f2944]) ).
fof(f528,axiom,
! [X0,X71,X69,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X71,X69,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X71),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_thin_0) ).
fof(f2942,plain,
spl0_273,
inference(avatar_split_clause,[],[f527,f2940]) ).
fof(f527,axiom,
! [X70,X0,X69,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X70,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X69),X70)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weaken_0) ).
fof(f2938,plain,
spl0_272,
inference(avatar_split_clause,[],[f325,f2936]) ).
fof(f325,axiom,
! [X3,X0,X11,X12] :
( hBOOL(c_in(X3,X12,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X3,X0),X11)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f2934,plain,
spl0_271,
inference(avatar_split_clause,[],[f268,f2932]) ).
fof(f2932,plain,
( spl0_271
<=> ! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( hAPP(X33,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X39
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f268,axiom,
! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( hAPP(X33,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X39
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).
fof(f2930,plain,
spl0_270,
inference(avatar_split_clause,[],[f267,f2928]) ).
fof(f2928,plain,
( spl0_270
<=> ! [X38,X33,X32,X0,X34,X36,X35,X39,X37] :
( hAPP(X32,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X38
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f267,axiom,
! [X38,X39,X0,X36,X37,X34,X35,X32,X33] :
( hAPP(X32,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X38
| ~ c_Complete__Lattice_Ocomplete__lattice(X33,X32,X34,X35,X37,X36,X39,X38,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
fof(f2922,plain,
spl0_269,
inference(avatar_split_clause,[],[f130,f2920]) ).
fof(f130,axiom,
! [X3,X0,X8,X7,X4] :
( X3 = X4
| hAPP(X8,X3) != hAPP(X8,X4)
| ~ c_Fun_Oinj__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
fof(f2918,plain,
spl0_268,
inference(avatar_split_clause,[],[f26,f2916]) ).
fof(f26,axiom,
! [X0,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
fof(f2914,plain,
spl0_267,
inference(avatar_split_clause,[],[f20,f2912]) ).
fof(f20,axiom,
! [X3,X10,X0,X8,X7,X4] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X8,X3,X4,X0,X7),X3,X10,X0,X7) = c_Fun_Ofun__upd(X8,X3,X10,X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
fof(f2582,plain,
spl0_266,
inference(avatar_split_clause,[],[f789,f2580]) ).
fof(f789,plain,
! [X0,X69,X60,X13] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X60),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0) ),
inference(forward_demodulation,[],[f788,f686]) ).
fof(f788,plain,
! [X0,X69,X60,X13] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0) ),
inference(forward_demodulation,[],[f617,f665]) ).
fof(f617,axiom,
! [X0,X69,X60,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).
fof(f2578,plain,
spl0_265,
inference(avatar_split_clause,[],[f765,f2576]) ).
fof(f765,plain,
! [X0,X11,X8,X7] :
( hAPP(c_Set_Oimage(X8,X7,X0),X11) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X7) = X11 ),
inference(forward_demodulation,[],[f764,f665]) ).
fof(f764,plain,
! [X0,X11,X8,X7] :
( c_COMBK(c_False,tc_bool,X7) = X11
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Set_Oimage(X8,X7,X0),X11) ),
inference(forward_demodulation,[],[f391,f665]) ).
fof(f391,axiom,
! [X0,X11,X8,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X11
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Set_Oimage(X8,X7,X0),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
fof(f2574,plain,
spl0_264,
inference(avatar_split_clause,[],[f708,f2572]) ).
fof(f708,plain,
! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X11),
inference(forward_demodulation,[],[f707,f686]) ).
fof(f707,plain,
! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))),X11),
inference(forward_demodulation,[],[f566,f665]) ).
fof(f566,axiom,
! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
fof(f2570,plain,
spl0_263,
inference(avatar_split_clause,[],[f526,f2568]) ).
fof(f2568,plain,
( spl0_263
<=> ! [X48,X68,X0,X64,X67,X7] : hAPP(hAPP(hAPP(X64,X67),X48),X68) = c_Hoare__Mirabelle_Otriple_Otriple__case(X64,c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X7),X7,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f526,axiom,
! [X48,X0,X68,X7,X67,X64] : hAPP(hAPP(hAPP(X64,X67),X48),X68) = c_Hoare__Mirabelle_Otriple_Otriple__case(X64,c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X7),X7,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Ocases_0) ).
fof(f2566,plain,
spl0_262,
inference(avatar_split_clause,[],[f525,f2564]) ).
fof(f2564,plain,
( spl0_262
<=> ! [X48,X68,X0,X64,X67,X7] : hAPP(hAPP(hAPP(X64,X67),X48),X68) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X64,c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X7),X7,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f525,axiom,
! [X48,X0,X68,X7,X67,X64] : hAPP(hAPP(hAPP(X64,X67),X48),X68) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X64,c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X7),X7,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Orecs_0) ).
fof(f2562,plain,
spl0_261,
inference(avatar_split_clause,[],[f516,f2560]) ).
fof(f516,axiom,
! [X3,X0,X11] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
fof(f2558,plain,
( spl0_260
| ~ spl0_146
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1980,f1888,f1651,f2556]) ).
fof(f1980,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X1,X0)
| ~ spl0_146
| ~ spl0_187 ),
inference(resolution,[],[f1889,f1652]) ).
fof(f2554,plain,
spl0_259,
inference(avatar_split_clause,[],[f493,f2552]) ).
fof(f493,axiom,
! [X3,X29,X0,X30] :
( ~ hBOOL(hAPP(X29,X3))
| hBOOL(hAPP(X30,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X29),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
fof(f2550,plain,
spl0_258,
inference(avatar_split_clause,[],[f475,f2548]) ).
fof(f475,axiom,
! [X0,X11,X5,X12] :
( ~ hBOOL(c_in(X5,X11,X0))
| hBOOL(c_in(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f2546,plain,
spl0_257,
inference(avatar_split_clause,[],[f474,f2544]) ).
fof(f474,axiom,
! [X0,X11,X5,X12] :
( ~ hBOOL(c_in(X5,X12,X0))
| hBOOL(c_in(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f2542,plain,
spl0_256,
inference(avatar_split_clause,[],[f457,f2540]) ).
fof(f457,axiom,
! [X3,X0,X11] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X11)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
fof(f2538,plain,
spl0_255,
inference(avatar_split_clause,[],[f451,f2536]) ).
fof(f451,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f2534,plain,
spl0_254,
inference(avatar_split_clause,[],[f450,f2532]) ).
fof(f2532,plain,
( spl0_254
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f450,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f2530,plain,
spl0_253,
inference(avatar_split_clause,[],[f449,f2528]) ).
fof(f449,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f2526,plain,
spl0_252,
inference(avatar_split_clause,[],[f408,f2524]) ).
fof(f408,axiom,
! [X2,X0,X11,X1] :
( X1 = X2
| hBOOL(c_in(X1,X11,X0))
| ~ hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X2,X0),X11),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f2522,plain,
spl0_251,
inference(avatar_split_clause,[],[f361,f2520]) ).
fof(f361,axiom,
! [X3,X0,X11,X8,X7] :
( ~ hBOOL(c_in(X3,X11,X0))
| hBOOL(c_in(hAPP(X8,X3),hAPP(c_Set_Oimage(X8,X0,X7),X11),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
fof(f2518,plain,
spl0_250,
inference(avatar_split_clause,[],[f341,f2516]) ).
fof(f2505,plain,
spl0_249,
inference(avatar_split_clause,[],[f183,f2503]) ).
fof(f183,axiom,
! [X0,X11,X8,X7,X12] :
( c_Fun_Oinj__on(X8,X11,X0,X7)
| ~ c_Fun_Oinj__on(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
fof(f2501,plain,
spl0_248,
inference(avatar_split_clause,[],[f182,f2499]) ).
fof(f182,axiom,
! [X0,X11,X8,X7,X12] :
( c_Fun_Oinj__on(X8,X12,X0,X7)
| ~ c_Fun_Oinj__on(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
fof(f2497,plain,
spl0_247,
inference(avatar_split_clause,[],[f166,f2495]) ).
fof(f166,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f2493,plain,
spl0_246,
inference(avatar_split_clause,[],[f165,f2491]) ).
fof(f2491,plain,
( spl0_246
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f165,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f2489,plain,
spl0_245,
inference(avatar_split_clause,[],[f164,f2487]) ).
fof(f164,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f2330,plain,
( spl0_244
| ~ spl0_82
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1823,f1792,f1324,f2328]) ).
fof(f1823,plain,
( ! [X0,X1] : hBOOL(c_in(X0,hAPP(c_fequal(X1),X0),X1))
| ~ spl0_82
| ~ spl0_171 ),
inference(superposition,[],[f1325,f1793]) ).
fof(f2321,plain,
spl0_243,
inference(avatar_split_clause,[],[f518,f2319]) ).
fof(f518,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2317,plain,
spl0_242,
inference(avatar_split_clause,[],[f286,f2315]) ).
fof(f286,axiom,
! [X0,X11,X5,X12] :
( ~ hBOOL(c_in(X5,X12,X0))
| ~ hBOOL(c_in(X5,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f2313,plain,
spl0_241,
inference(avatar_split_clause,[],[f284,f2311]) ).
fof(f284,axiom,
! [X0,X11,X5,X12] :
( hBOOL(c_in(X5,X11,X0))
| ~ hBOOL(c_in(X5,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f2309,plain,
spl0_240,
inference(avatar_split_clause,[],[f280,f2307]) ).
fof(f280,axiom,
! [X0,X11] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
fof(f2305,plain,
spl0_239,
inference(avatar_split_clause,[],[f279,f2303]) ).
fof(f279,axiom,
! [X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
fof(f2301,plain,
spl0_238,
inference(avatar_split_clause,[],[f237,f2299]) ).
fof(f237,axiom,
! [X0,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f2297,plain,
spl0_237,
inference(avatar_split_clause,[],[f236,f2295]) ).
fof(f236,axiom,
! [X0,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f2293,plain,
spl0_236,
inference(avatar_split_clause,[],[f158,f2291]) ).
fof(f158,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f2289,plain,
spl0_235,
inference(avatar_split_clause,[],[f153,f2287]) ).
fof(f153,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f2285,plain,
spl0_234,
inference(avatar_split_clause,[],[f150,f2283]) ).
fof(f150,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f2281,plain,
spl0_233,
inference(avatar_split_clause,[],[f137,f2279]) ).
fof(f137,axiom,
! [X0,X11,X8,X7,X12] :
( ~ c_Fun_Oinj__on(X8,X11,X0,X7)
| c_Fun_Oinj__on(X8,hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
fof(f2277,plain,
spl0_232,
inference(avatar_split_clause,[],[f132,f2275]) ).
fof(f132,axiom,
! [X0,X14,X13] :
( ~ c_Finite__Set_Ofinite(X14,X0)
| ~ c_Finite__Set_Ofinite(X13,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X13),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
fof(f2273,plain,
spl0_231,
inference(avatar_split_clause,[],[f81,f2271]) ).
fof(f81,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f2269,plain,
spl0_230,
inference(avatar_split_clause,[],[f80,f2267]) ).
fof(f80,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2265,plain,
spl0_229,
inference(avatar_split_clause,[],[f79,f2263]) ).
fof(f79,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2261,plain,
spl0_228,
inference(avatar_split_clause,[],[f68,f2259]) ).
fof(f68,axiom,
! [X0,X11,X8,X7] :
( c_Finite__Set_Ofinite(X11,X7)
| ~ c_Fun_Oinj__on(X8,X11,X7,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X8,X7,X0),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
fof(f2257,plain,
spl0_227,
inference(avatar_split_clause,[],[f29,f2255]) ).
fof(f29,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2253,plain,
( spl0_226
| ~ spl0_110
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1749,f1699,f1455,f2251]) ).
fof(f1699,plain,
( spl0_157
<=> ! [X0,X3] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X3),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1749,plain,
( ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X1),X0),X1) = X0
| ~ spl0_110
| ~ spl0_157 ),
inference(resolution,[],[f1700,f1456]) ).
fof(f1700,plain,
( ! [X3,X0] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X3),X0)))
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1699]) ).
fof(f2249,plain,
spl0_225,
inference(avatar_split_clause,[],[f28,f2247]) ).
fof(f28,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2111,plain,
spl0_224,
inference(avatar_split_clause,[],[f805,f2109]) ).
fof(f2109,plain,
( spl0_224
<=> ! [X4,X0,X3] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X3),X0) = X4
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f805,plain,
! [X3,X0,X4] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X3),X0) = X4
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X3),X4)) ),
inference(forward_demodulation,[],[f804,f686]) ).
fof(f804,plain,
! [X3,X0,X4] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0) = X4
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X3),X4)) ),
inference(forward_demodulation,[],[f803,f665]) ).
fof(f803,plain,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X0),X3),X4))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X4 ),
inference(forward_demodulation,[],[f802,f686]) ).
fof(f802,plain,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X4))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X4 ),
inference(forward_demodulation,[],[f559,f665]) ).
fof(f559,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X4))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
fof(f2107,plain,
spl0_223,
inference(avatar_split_clause,[],[f696,f2105]) ).
fof(f696,plain,
! [X0,X1] : c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = hAPP(c_fequal(X0),X1),
inference(forward_demodulation,[],[f695,f686]) ).
fof(f695,plain,
! [X0,X1] : c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),
inference(forward_demodulation,[],[f397,f665]) ).
fof(f397,axiom,
! [X0,X1] : hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
fof(f2103,plain,
spl0_222,
inference(avatar_split_clause,[],[f688,f2101]) ).
fof(f2101,plain,
( spl0_222
<=> ! [X0,X12,X7] : c_COMBK(c_False,tc_bool,tc_prod(X0,X7)) = c_Product__Type_OSigma(c_COMBK(c_False,tc_bool,X0),X12,X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f688,plain,
! [X0,X7,X12] : c_COMBK(c_False,tc_bool,tc_prod(X0,X7)) = c_Product__Type_OSigma(c_COMBK(c_False,tc_bool,X0),X12,X0,X7),
inference(forward_demodulation,[],[f687,f665]) ).
fof(f687,plain,
! [X0,X7,X12] : c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X12,X0,X7) = c_COMBK(c_False,tc_bool,tc_prod(X0,X7)),
inference(forward_demodulation,[],[f347,f665]) ).
fof(f347,axiom,
! [X0,X7,X12] : c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X12,X0,X7) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X7),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).
fof(f2099,plain,
spl0_221,
inference(avatar_split_clause,[],[f684,f2097]) ).
fof(f684,plain,
! [X0,X11] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool)),X11),
inference(forward_demodulation,[],[f385,f665]) ).
fof(f385,axiom,
! [X0,X11] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f2095,plain,
( spl0_220
| ~ spl0_65
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2053,f2009,f1252,f2093]) ).
fof(f2093,plain,
( spl0_220
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2053,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,X0,X1)
| ~ spl0_65
| ~ spl0_200 ),
inference(resolution,[],[f2010,f1253]) ).
fof(f2091,plain,
spl0_219,
inference(avatar_split_clause,[],[f683,f2089]) ).
fof(f683,plain,
! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = c_COMBK(c_False,tc_bool,X0),
inference(forward_demodulation,[],[f462,f665]) ).
fof(f462,axiom,
! [X0,X11] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
fof(f2087,plain,
spl0_218,
inference(avatar_split_clause,[],[f682,f2085]) ).
fof(f2085,plain,
( spl0_218
<=> ! [X0,X12,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f682,plain,
! [X0,X7,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_COMBK(c_False,tc_bool,X7),X12,X7,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f468,f665]) ).
fof(f468,axiom,
! [X0,X7,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X12,X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__empty_0) ).
fof(f2083,plain,
( spl0_217
| ~ spl0_171
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2079,f2076,f1792,f2081]) ).
fof(f2076,plain,
( spl0_216
<=> ! [X0,X1,X8] : c_The(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2079,plain,
( ! [X0,X1,X8] : c_The(c_Finite__Set_Ofold1Set(X8,hAPP(c_fequal(X0),X1),X0),X0) = X1
| ~ spl0_171
| ~ spl0_216 ),
inference(forward_demodulation,[],[f2077,f1793]) ).
fof(f2077,plain,
( ! [X0,X1,X8] : c_The(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),X0),X0) = X1
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f2076]) ).
fof(f2078,plain,
spl0_216,
inference(avatar_split_clause,[],[f674,f2076]) ).
fof(f674,plain,
! [X0,X1,X8] : c_The(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),X0),X0) = X1,
inference(forward_demodulation,[],[f662,f665]) ).
fof(f662,plain,
! [X0,X1,X8] : c_The(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0),X0) = X1,
inference(definition_unfolding,[],[f561,f263]) ).
fof(f561,axiom,
! [X0,X1,X8] : c_Finite__Set_Ofold1(X8,hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
fof(f2074,plain,
spl0_215,
inference(avatar_split_clause,[],[f611,f2072]) ).
fof(f611,axiom,
! [X3,X0,X11] : hAPP(c_Set_Oinsert(X3,X0),X11) = hAPP(c_Set_Oinsert(X3,X0),hAPP(c_Set_Oinsert(X3,X0),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f2070,plain,
spl0_214,
inference(avatar_split_clause,[],[f610,f2068]) ).
fof(f610,axiom,
! [X3,X0,X11,X4] :
( X3 = X4
| hBOOL(hAPP(X11,X3))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X4,X0),X11),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f2066,plain,
spl0_213,
inference(avatar_split_clause,[],[f429,f2064]) ).
fof(f429,axiom,
! [X3,X0,X11,X12] :
( ~ hBOOL(hAPP(X11,X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f2062,plain,
spl0_212,
inference(avatar_split_clause,[],[f428,f2060]) ).
fof(f428,axiom,
! [X3,X0,X11,X12] :
( ~ hBOOL(hAPP(X12,X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X12),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f2058,plain,
spl0_211,
inference(avatar_split_clause,[],[f370,f2056]) ).
fof(f2056,plain,
( spl0_211
<=> ! [X11,X0,X12] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X12
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f370,axiom,
! [X0,X11,X12] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X12
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f2051,plain,
spl0_210,
inference(avatar_split_clause,[],[f369,f2049]) ).
fof(f2049,plain,
( spl0_210
<=> ! [X12,X0,X11] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X11
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f369,axiom,
! [X0,X11,X12] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X11
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f2047,plain,
spl0_209,
inference(avatar_split_clause,[],[f343,f2045]) ).
fof(f2045,plain,
( spl0_209
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f343,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f2043,plain,
spl0_208,
inference(avatar_split_clause,[],[f342,f2041]) ).
fof(f342,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f2039,plain,
spl0_207,
inference(avatar_split_clause,[],[f320,f2037]) ).
fof(f320,axiom,
! [X0,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12)),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f2035,plain,
spl0_206,
inference(avatar_split_clause,[],[f251,f2033]) ).
fof(f251,axiom,
! [X31,X29,X0,X7,X17,X30] : hAPP(hAPP(c_COMBC(X29,X7,X17,X0),X30),X31) = hAPP(hAPP(X29,X31),X30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
fof(f2031,plain,
spl0_205,
inference(avatar_split_clause,[],[f248,f2029]) ).
fof(f248,axiom,
! [X3,X0,X8,X7] : hBOOL(c_in(hAPP(X8,X3),hAPP(c_Set_Oimage(X8,X7,X0),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool))),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
fof(f2027,plain,
spl0_204,
inference(avatar_split_clause,[],[f168,f2025]) ).
fof(f2025,plain,
( spl0_204
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f168,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f2023,plain,
spl0_203,
inference(avatar_split_clause,[],[f167,f2021]) ).
fof(f167,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f2019,plain,
spl0_202,
inference(avatar_split_clause,[],[f135,f2017]) ).
fof(f135,axiom,
! [X0,X11,X12] :
( ~ c_Finite__Set_Ofinite(X12,X0)
| c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
fof(f2015,plain,
spl0_201,
inference(avatar_split_clause,[],[f65,f2013]) ).
fof(f65,axiom,
! [X3,X10,X0,X8,X7,X4] :
( X3 = X10
| hAPP(X8,X10) = hAPP(c_Fun_Ofun__upd(X8,X3,X4,X0,X7),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
fof(f2011,plain,
( spl0_200
| ~ spl0_83
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1965,f1888,f1328,f2009]) ).
fof(f1965,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X0,X1)
| ~ spl0_83
| ~ spl0_187 ),
inference(resolution,[],[f1889,f1329]) ).
fof(f2007,plain,
spl0_199,
inference(avatar_split_clause,[],[f54,f2005]) ).
fof(f54,axiom,
! [X0,X11,X12] :
( ~ c_Finite__Set_Ofinite(X12,X0)
| c_Finite__Set_Ofinite(X11,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
fof(f2003,plain,
spl0_198,
inference(avatar_split_clause,[],[f22,f2001]) ).
fof(f22,axiom,
! [X0,X11,X12] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X12
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
fof(f1999,plain,
spl0_197,
inference(avatar_split_clause,[],[f21,f1997]) ).
fof(f1997,plain,
( spl0_197
<=> ! [X12,X0,X11] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X11
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f21,axiom,
! [X0,X11,X12] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X11
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
fof(f1995,plain,
spl0_196,
inference(avatar_split_clause,[],[f11,f1993]) ).
fof(f11,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f1991,plain,
spl0_195,
inference(avatar_split_clause,[],[f3,f1989]) ).
fof(f3,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f1924,plain,
( spl0_194
| ~ spl0_16
| ~ spl0_135
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1715,f1614,f1606,f1037,f1922]) ).
fof(f1715,plain,
( ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_False)
| ~ spl0_16
| ~ spl0_135
| ~ spl0_137 ),
inference(forward_demodulation,[],[f1713,f1616]) ).
fof(f1713,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool))
| ~ spl0_16
| ~ spl0_135 ),
inference(resolution,[],[f1607,f1039]) ).
fof(f1915,plain,
( spl0_193
| ~ spl0_171
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1911,f1908,f1792,f1913]) ).
fof(f1908,plain,
( spl0_192
<=> ! [X0,X8,X3] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1911,plain,
( ! [X3,X0,X8] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_fequal(X0),X3),X0),X3))
| ~ spl0_171
| ~ spl0_192 ),
inference(forward_demodulation,[],[f1909,f1793]) ).
fof(f1909,plain,
( ! [X3,X0,X8] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0),X3))
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f1908]) ).
fof(f1910,plain,
spl0_192,
inference(avatar_split_clause,[],[f681,f1908]) ).
fof(f681,plain,
! [X3,X0,X8] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0),X3)),
inference(forward_demodulation,[],[f550,f665]) ).
fof(f550,axiom,
! [X3,X0,X8] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
fof(f1906,plain,
spl0_191,
inference(avatar_split_clause,[],[f676,f1904]) ).
fof(f676,plain,
! [X0,X8,X7] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_Set_Oimage(X8,X7,X0),c_COMBK(c_False,tc_bool,X7)),
inference(forward_demodulation,[],[f675,f665]) ).
fof(f675,plain,
! [X0,X8,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Set_Oimage(X8,X7,X0),c_COMBK(c_False,tc_bool,X7)),
inference(forward_demodulation,[],[f392,f665]) ).
fof(f392,axiom,
! [X0,X8,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Set_Oimage(X8,X7,X0),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
fof(f1902,plain,
spl0_190,
inference(avatar_split_clause,[],[f603,f1900]) ).
fof(f1900,plain,
( spl0_190
<=> ! [X48,X0,X77,X78,X67,X46,X68] :
( X67 = X77
| c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X77,X46,X78,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f603,axiom,
! [X48,X0,X46,X78,X68,X77,X67] :
( X67 = X77
| c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X77,X46,X78,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
fof(f1898,plain,
spl0_189,
inference(avatar_split_clause,[],[f602,f1896]) ).
fof(f1896,plain,
( spl0_189
<=> ! [X48,X77,X0,X78,X67,X46,X68] :
( X46 = X48
| c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X77,X46,X78,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f602,axiom,
! [X48,X46,X0,X78,X68,X77,X67] :
( X46 = X48
| c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X77,X46,X78,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
fof(f1894,plain,
spl0_188,
inference(avatar_split_clause,[],[f601,f1892]) ).
fof(f1892,plain,
( spl0_188
<=> ! [X48,X77,X0,X78,X67,X46,X68] :
( X68 = X78
| c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X77,X46,X78,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f601,axiom,
! [X48,X0,X46,X78,X68,X77,X67] :
( X68 = X78
| c_Hoare__Mirabelle_Otriple_Otriple(X67,X48,X68,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X77,X46,X78,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
fof(f1890,plain,
spl0_187,
inference(avatar_split_clause,[],[f530,f1888]) ).
fof(f530,axiom,
! [X0,X69,X13] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X69),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).
fof(f1886,plain,
( spl0_186
| ~ spl0_16
| ~ spl0_134
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1712,f1614,f1602,f1037,f1884]) ).
fof(f1712,plain,
( ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),X0)
| ~ spl0_16
| ~ spl0_134
| ~ spl0_137 ),
inference(forward_demodulation,[],[f1710,f1616]) ).
fof(f1710,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0)
| ~ spl0_16
| ~ spl0_134 ),
inference(resolution,[],[f1603,f1039]) ).
fof(f1882,plain,
spl0_185,
inference(avatar_split_clause,[],[f424,f1880]) ).
fof(f424,axiom,
! [X2,X0,X1,X54,X7,X17] : hAPP(X1,hAPP(X2,X54)) = hAPP(c_Fun_Ocomp(X1,X2,X17,X7,X0),X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
fof(f1878,plain,
spl0_184,
inference(avatar_split_clause,[],[f404,f1876]) ).
fof(f404,axiom,
! [X2,X0,X1,X12] :
( ~ hBOOL(c_in(X1,X12,X0))
| hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X2,X0),X12),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
fof(f1874,plain,
spl0_183,
inference(avatar_split_clause,[],[f233,f1872]) ).
fof(f233,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1870,plain,
spl0_182,
inference(avatar_split_clause,[],[f232,f1868]) ).
fof(f232,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1866,plain,
spl0_181,
inference(avatar_split_clause,[],[f229,f1864]) ).
fof(f229,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f1862,plain,
spl0_180,
inference(avatar_split_clause,[],[f228,f1860]) ).
fof(f228,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f1858,plain,
spl0_179,
inference(avatar_split_clause,[],[f196,f1856]) ).
fof(f196,axiom,
! [X0,X11,X1,X8,X7] :
( c_Fun_Oinj__on(X8,X11,X0,X7)
| ~ c_Fun_Oinj__on(X8,hAPP(c_Set_Oinsert(X1,X0),X11),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
fof(f1854,plain,
spl0_178,
inference(avatar_split_clause,[],[f149,f1852]) ).
fof(f149,axiom,
! [X31,X29,X0,X7,X17,X30] : hAPP(c_COMBB(X29,X30,X7,X0,X17),X31) = hAPP(X29,hAPP(X30,X31)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
fof(f1850,plain,
spl0_177,
inference(avatar_split_clause,[],[f42,f1848]) ).
fof(f42,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f1846,plain,
spl0_176,
inference(avatar_split_clause,[],[f41,f1844]) ).
fof(f41,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f1841,plain,
spl0_175,
inference(avatar_split_clause,[],[f37,f1839]) ).
fof(f37,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f1837,plain,
spl0_174,
inference(avatar_split_clause,[],[f36,f1835]) ).
fof(f36,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f1802,plain,
spl0_173,
inference(avatar_split_clause,[],[f745,f1800]) ).
fof(f745,plain,
! [X2,X0,X1,X8] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_fequal(X0),X1),X0),X2))
| X1 = X2 ),
inference(forward_demodulation,[],[f744,f686]) ).
fof(f744,plain,
! [X2,X0,X1,X8] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),X0),X2))
| X1 = X2 ),
inference(forward_demodulation,[],[f557,f665]) ).
fof(f557,axiom,
! [X2,X0,X1,X8] :
( X1 = X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
fof(f1798,plain,
spl0_172,
inference(avatar_split_clause,[],[f741,f1796]) ).
fof(f1796,plain,
( spl0_172
<=> ! [X10,X0,X3,X8,X7] :
( ~ c_Finite__Set_Ofold__graph(X8,X10,c_COMBK(c_False,tc_bool,X0),X3,X0,X7)
| X3 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f741,plain,
! [X3,X10,X0,X8,X7] :
( ~ c_Finite__Set_Ofold__graph(X8,X10,c_COMBK(c_False,tc_bool,X0),X3,X0,X7)
| X3 = X10 ),
inference(forward_demodulation,[],[f190,f665]) ).
fof(f190,axiom,
! [X3,X10,X0,X8,X7] :
( X3 = X10
| ~ c_Finite__Set_Ofold__graph(X8,X10,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
fof(f1794,plain,
spl0_171,
inference(avatar_split_clause,[],[f686,f1792]) ).
fof(f1790,plain,
spl0_170,
inference(avatar_split_clause,[],[f673,f1788]) ).
fof(f1786,plain,
spl0_169,
inference(avatar_split_clause,[],[f672,f1784]) ).
fof(f1782,plain,
spl0_168,
inference(avatar_split_clause,[],[f597,f1780]) ).
fof(f597,axiom,
! [X0,X69,X60,X13] :
( c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(X60,tc_Hoare__Mirabelle_Otriple(X0)),X69),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
fof(f1778,plain,
spl0_167,
inference(avatar_split_clause,[],[f409,f1776]) ).
fof(f409,axiom,
! [X0,X1,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(c_Set_Oinsert(X1,X0),X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f1774,plain,
( spl0_166
| ~ spl0_6
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1516,f1463,f987,f1772]) ).
fof(f1463,plain,
( spl0_112
<=> ! [X0,X1] :
( c_Finite__Set_Olinorder__class_OMin(hAPP(c_fequal(X0),X1),X0) = X1
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1516,plain,
( ! [X0] : c_Finite__Set_Olinorder__class_OMin(hAPP(c_fequal(tc_nat),X0),tc_nat) = X0
| ~ spl0_6
| ~ spl0_112 ),
inference(resolution,[],[f1464,f989]) ).
fof(f989,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f987]) ).
fof(f1464,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMin(hAPP(c_fequal(X0),X1),X0) = X1 )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1463]) ).
fof(f1770,plain,
spl0_165,
inference(avatar_split_clause,[],[f288,f1768]) ).
fof(f288,axiom,
! [X8,X7,X17,X5] : hAPP(c_Fun_Ocomp(c_COMBK(X5,X7,X17),X8,X17,X7,t_a),v_x) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
fof(f1766,plain,
spl0_164,
inference(avatar_split_clause,[],[f179,f1764]) ).
fof(f179,axiom,
! [X3,X0,X8,X7,X4] :
( hAPP(X8,X3) = X4
| c_Fun_Ofun__upd(X8,X3,X4,X0,X7) != X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
fof(f1762,plain,
spl0_163,
inference(avatar_split_clause,[],[f24,f1760]) ).
fof(f24,axiom,
! [X0,X14,X13] :
( c_Finite__Set_Ofinite(X14,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X13),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
fof(f1758,plain,
spl0_162,
inference(avatar_split_clause,[],[f23,f1756]) ).
fof(f23,axiom,
! [X0,X14,X13] :
( c_Finite__Set_Ofinite(X13,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X13),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
fof(f1743,plain,
( spl0_161
| ~ spl0_6
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1515,f1459,f987,f1741]) ).
fof(f1459,plain,
( spl0_111
<=> ! [X0,X1] :
( c_Finite__Set_Olinorder__class_OMax(hAPP(c_fequal(X0),X1),X0) = X1
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1515,plain,
( ! [X0] : c_Finite__Set_Olinorder__class_OMax(hAPP(c_fequal(tc_nat),X0),tc_nat) = X0
| ~ spl0_6
| ~ spl0_111 ),
inference(resolution,[],[f1460,f989]) ).
fof(f1460,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(hAPP(c_fequal(X0),X1),X0) = X1 )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1459]) ).
fof(f1724,plain,
( spl0_160
| ~ spl0_12
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1507,f1446,f1017,f1722]) ).
fof(f1507,plain,
( ! [X0] : c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X0,tc_bool,tc_bool),tc_bool) = X0
| ~ spl0_12
| ~ spl0_108 ),
inference(resolution,[],[f1447,f1019]) ).
fof(f1709,plain,
spl0_159,
inference(avatar_split_clause,[],[f730,f1707]) ).
fof(f730,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_COMBK(c_False,tc_bool,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f541,f665]) ).
fof(f541,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
fof(f1705,plain,
spl0_158,
inference(avatar_split_clause,[],[f729,f1703]) ).
fof(f729,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_COMBK(c_False,tc_bool,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f471,f665]) ).
fof(f471,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
fof(f1701,plain,
spl0_157,
inference(avatar_split_clause,[],[f706,f1699]) ).
fof(f706,plain,
! [X3,X0] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X3),X0))),
inference(forward_demodulation,[],[f705,f686]) ).
fof(f705,plain,
! [X3,X0] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0))),
inference(forward_demodulation,[],[f548,f665]) ).
fof(f548,axiom,
! [X3,X0] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
fof(f1696,plain,
spl0_156,
inference(avatar_split_clause,[],[f693,f1694]) ).
fof(f693,plain,
! [X0,X29,X13] : c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSKIP,X29,X0)),X0),
inference(forward_demodulation,[],[f692,f686]) ).
fof(f692,plain,
! [X29,X0,X13] : c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSKIP,X29,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0),
inference(forward_demodulation,[],[f594,f665]) ).
fof(f594,axiom,
! [X29,X0,X13] : c_Hoare__Mirabelle_Ohoare__derivs(X13,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSKIP,X29,X0),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
fof(f1692,plain,
spl0_155,
inference(avatar_split_clause,[],[f671,f1690]) ).
fof(f671,plain,
! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X11)),
inference(forward_demodulation,[],[f390,f665]) ).
fof(f390,axiom,
! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f1687,plain,
spl0_154,
inference(avatar_split_clause,[],[f670,f1685]) ).
fof(f1685,plain,
( spl0_154
<=> ! [X0,X3] : c_The(hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f670,plain,
! [X3,X0] : c_The(hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0) = X3,
inference(forward_demodulation,[],[f552,f665]) ).
fof(f552,axiom,
! [X3,X0] : c_The(hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
fof(f1683,plain,
( spl0_153
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1679,f1676,f1681]) ).
fof(f1676,plain,
( spl0_152
<=> ! [X0,X3] : c_Set_Ocontents(hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1679,plain,
( ! [X3,X0] : c_Set_Ocontents(hAPP(c_fequal(X0),X3),X0) = X3
| ~ spl0_152 ),
inference(forward_demodulation,[],[f1677,f686]) ).
fof(f1677,plain,
( ! [X3,X0] : c_Set_Ocontents(hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0) = X3
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1676]) ).
fof(f1678,plain,
spl0_152,
inference(avatar_split_clause,[],[f669,f1676]) ).
fof(f669,plain,
! [X3,X0] : c_Set_Ocontents(hAPP(c_Set_Oinsert(X3,X0),c_COMBK(c_False,tc_bool,X0)),X0) = X3,
inference(forward_demodulation,[],[f558,f665]) ).
fof(f558,axiom,
! [X3,X0] : c_Set_Ocontents(hAPP(c_Set_Oinsert(X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__eq_0) ).
fof(f1674,plain,
spl0_151,
inference(avatar_split_clause,[],[f668,f1672]) ).
fof(f668,plain,
! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)) = X11,
inference(forward_demodulation,[],[f389,f665]) ).
fof(f389,axiom,
! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f1670,plain,
spl0_150,
inference(avatar_split_clause,[],[f667,f1668]) ).
fof(f667,plain,
! [X0,X11] : hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X11) = c_COMBK(c_False,tc_bool,X0),
inference(forward_demodulation,[],[f388,f665]) ).
fof(f388,axiom,
! [X0,X11] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f1666,plain,
spl0_149,
inference(avatar_split_clause,[],[f666,f1664]) ).
fof(f666,plain,
! [X0,X11] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),c_COMBK(c_False,tc_bool,X0))),
inference(forward_demodulation,[],[f188,f665]) ).
fof(f188,axiom,
! [X0,X11] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
fof(f1662,plain,
spl0_148,
inference(avatar_split_clause,[],[f618,f1660]) ).
fof(f618,axiom,
! [X3,X0,X11,X4] :
( ~ hBOOL(hAPP(X11,X3))
| hBOOL(hAPP(hAPP(c_Set_Oinsert(X4,X0),X11),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f1657,plain,
spl0_147,
inference(avatar_split_clause,[],[f599,f1655]) ).
fof(f599,axiom,
! [X0,X71,X69,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X71,X69,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X71,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
fof(f1653,plain,
spl0_146,
inference(avatar_split_clause,[],[f464,f1651]) ).
fof(f464,axiom,
! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
fof(f1649,plain,
spl0_145,
inference(avatar_split_clause,[],[f441,f1647]) ).
fof(f441,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
fof(f1645,plain,
spl0_144,
inference(avatar_split_clause,[],[f418,f1643]) ).
fof(f418,axiom,
! [X0,X11,X1] :
( ~ hBOOL(c_in(X1,X11,X0))
| hAPP(c_Set_Oinsert(X1,X0),X11) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f1641,plain,
spl0_143,
inference(avatar_split_clause,[],[f357,f1639]) ).
fof(f357,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
fof(f1637,plain,
spl0_142,
inference(avatar_split_clause,[],[f297,f1635]) ).
fof(f1635,plain,
( spl0_142
<=> ! [X41,X40,X50,X49,X45,X47] :
( X45 = X47
| c_Com_Ocom_OCond(X45,X49,X50) != c_Com_Ocom_OCond(X47,X40,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f297,axiom,
! [X50,X40,X41,X49,X47,X45] :
( X45 = X47
| c_Com_Ocom_OCond(X45,X49,X50) != c_Com_Ocom_OCond(X47,X40,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
fof(f1633,plain,
spl0_141,
inference(avatar_split_clause,[],[f296,f1631]) ).
fof(f1631,plain,
( spl0_141
<=> ! [X41,X47,X40,X50,X45,X49] :
( X40 = X49
| c_Com_Ocom_OCond(X45,X49,X50) != c_Com_Ocom_OCond(X47,X40,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f296,axiom,
! [X50,X40,X41,X49,X47,X45] :
( X40 = X49
| c_Com_Ocom_OCond(X45,X49,X50) != c_Com_Ocom_OCond(X47,X40,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
fof(f1629,plain,
spl0_140,
inference(avatar_split_clause,[],[f295,f1627]) ).
fof(f1627,plain,
( spl0_140
<=> ! [X41,X40,X50,X45,X49,X47] :
( X41 = X50
| c_Com_Ocom_OCond(X45,X49,X50) != c_Com_Ocom_OCond(X47,X40,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f295,axiom,
! [X50,X40,X41,X49,X47,X45] :
( X41 = X50
| c_Com_Ocom_OCond(X45,X49,X50) != c_Com_Ocom_OCond(X47,X40,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
fof(f1625,plain,
spl0_139,
inference(avatar_split_clause,[],[f292,f1623]) ).
fof(f1623,plain,
( spl0_139
<=> ! [X0,X1] : c_The(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f292,axiom,
! [X0,X1] : c_The(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__eq__trivial_0) ).
fof(f1621,plain,
spl0_138,
inference(avatar_split_clause,[],[f278,f1619]) ).
fof(f278,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
fof(f1617,plain,
( spl0_137
| ~ spl0_22
| ~ spl0_70
| ~ spl0_88
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1588,f1551,f1348,f1273,f1067,f1614]) ).
fof(f1067,plain,
( spl0_22
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1348,plain,
( spl0_88
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1588,plain,
( c_False = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_22
| ~ spl0_70
| ~ spl0_88
| ~ spl0_127 ),
inference(forward_demodulation,[],[f1587,f1274]) ).
fof(f1587,plain,
( hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_22
| ~ spl0_88
| ~ spl0_127 ),
inference(forward_demodulation,[],[f1585,f1349]) ).
fof(f1349,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,X0)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1348]) ).
fof(f1585,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_22
| ~ spl0_127 ),
inference(resolution,[],[f1552,f1069]) ).
fof(f1069,plain,
( class_Orderings_Obot(tc_bool)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1067]) ).
fof(f1612,plain,
spl0_136,
inference(avatar_split_clause,[],[f277,f1610]) ).
fof(f277,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Otop__class_Otop(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
fof(f1608,plain,
spl0_135,
inference(avatar_split_clause,[],[f187,f1606]) ).
fof(f187,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Obot__class_Obot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f1604,plain,
spl0_134,
inference(avatar_split_clause,[],[f186,f1602]) ).
fof(f186,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f1600,plain,
spl0_133,
inference(avatar_split_clause,[],[f138,f1598]) ).
fof(f138,axiom,
! [X0,X11,X12] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
fof(f1581,plain,
( spl0_132
| ~ spl0_13
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1490,f1409,f1022,f1579]) ).
fof(f1490,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0
| ~ spl0_13
| ~ spl0_99 ),
inference(resolution,[],[f1410,f1024]) ).
fof(f1569,plain,
spl0_131,
inference(avatar_split_clause,[],[f743,f1567]) ).
fof(f743,plain,
! [X2,X0,X1] :
( ~ hBOOL(c_in(X2,hAPP(c_fequal(X0),X1),X0))
| X1 = X2 ),
inference(forward_demodulation,[],[f742,f686]) ).
fof(f742,plain,
! [X2,X0,X1] :
( ~ hBOOL(c_in(X2,hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),X0))
| X1 = X2 ),
inference(forward_demodulation,[],[f560,f665]) ).
fof(f560,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(c_in(X2,hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f1565,plain,
spl0_130,
inference(avatar_split_clause,[],[f740,f1563]) ).
fof(f740,plain,
! [X0,X1] :
( hAPP(c_fequal(X0),X1) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(forward_demodulation,[],[f739,f686]) ).
fof(f739,plain,
! [X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X0) = hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))
| ~ class_Orderings_Oorder(X0) ),
inference(forward_demodulation,[],[f564,f665]) ).
fof(f564,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
fof(f1561,plain,
spl0_129,
inference(avatar_split_clause,[],[f734,f1559]) ).
fof(f734,plain,
! [X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_fequal(X0),X1)) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f733,f686]) ).
fof(f733,plain,
! [X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f567,f665]) ).
fof(f567,axiom,
! [X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
fof(f1557,plain,
spl0_128,
inference(avatar_split_clause,[],[f732,f1555]) ).
fof(f732,plain,
! [X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_fequal(X0),X1)) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f731,f686]) ).
fof(f731,plain,
! [X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0))) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f547,f665]) ).
fof(f547,axiom,
! [X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
fof(f1553,plain,
spl0_127,
inference(avatar_split_clause,[],[f540,f1551]) ).
fof(f540,axiom,
! [X7] :
( ~ class_Orderings_Obot(X7)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X7)),v_x) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
fof(f1549,plain,
( spl0_126
| ~ spl0_2
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1489,f1409,f967,f1547]) ).
fof(f1547,plain,
( spl0_126
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1489,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X0) = X0
| ~ spl0_2
| ~ spl0_99 ),
inference(resolution,[],[f1410,f969]) ).
fof(f1545,plain,
spl0_125,
inference(avatar_split_clause,[],[f443,f1543]) ).
fof(f443,axiom,
! [X7] :
( ~ class_Orderings_Otop(X7)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X7)),v_x) = c_Orderings_Otop__class_Otop(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
fof(f1541,plain,
spl0_124,
inference(avatar_split_clause,[],[f367,f1539]) ).
fof(f367,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Obot__class_Obot(X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1537,plain,
spl0_123,
inference(avatar_split_clause,[],[f366,f1535]) ).
fof(f366,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1533,plain,
spl0_122,
inference(avatar_split_clause,[],[f30,f1531]) ).
fof(f30,axiom,
! [X0,X7,X14,X15] :
( ~ c_Finite__Set_Ofinite(X14,X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X15,X0,X7),X14),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
fof(f1529,plain,
spl0_121,
inference(avatar_split_clause,[],[f19,f1527]) ).
fof(f19,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Otop__class_Otop(X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
fof(f1525,plain,
spl0_120,
inference(avatar_split_clause,[],[f18,f1523]) ).
fof(f18,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
fof(f1512,plain,
( spl0_119
| ~ spl0_88
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1453,f1450,f1348,f1510]) ).
fof(f1450,plain,
( spl0_109
<=> ! [X0,X11,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Set_Oinsert(X1,X0),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1453,plain,
( ! [X0,X11,X1] : hAPP(c_Set_Oinsert(X1,X0),X11) != c_COMBK(c_False,tc_bool,X0)
| ~ spl0_88
| ~ spl0_109 ),
inference(forward_demodulation,[],[f1451,f1349]) ).
fof(f1451,plain,
( ! [X0,X11,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Set_Oinsert(X1,X0),X11)
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1450]) ).
fof(f1506,plain,
( spl0_118
| ~ spl0_88
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1440,f1437,f1348,f1504]) ).
fof(f1437,plain,
( spl0_106
<=> ! [X0,X8,X3] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1440,plain,
( ! [X3,X0,X8] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,c_COMBK(c_False,tc_bool,X0),X0),X3))
| ~ spl0_88
| ~ spl0_106 ),
inference(forward_demodulation,[],[f1438,f1349]) ).
fof(f1438,plain,
( ! [X3,X0,X8] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X3))
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1437]) ).
fof(f1499,plain,
( spl0_117
| ~ spl0_14
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1473,f1383,f1027,f1497]) ).
fof(f1497,plain,
( spl0_117
<=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1473,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0
| ~ spl0_14
| ~ spl0_93 ),
inference(resolution,[],[f1384,f1029]) ).
fof(f1486,plain,
( spl0_116
| ~ spl0_88
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1399,f1396,f1348,f1484]) ).
fof(f1396,plain,
( spl0_96
<=> ! [X0,X7,X8,X10] : c_Nitpick_Ofold__graph_H(X8,X10,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X10,X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1399,plain,
( ! [X10,X0,X8,X7] : c_Nitpick_Ofold__graph_H(X8,X10,c_COMBK(c_False,tc_bool,X0),X10,X0,X7)
| ~ spl0_88
| ~ spl0_96 ),
inference(forward_demodulation,[],[f1397,f1349]) ).
fof(f1397,plain,
( ! [X10,X0,X8,X7] : c_Nitpick_Ofold__graph_H(X8,X10,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X10,X0,X7)
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1396]) ).
fof(f1482,plain,
( spl0_115
| ~ spl0_88
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1394,f1391,f1348,f1480]) ).
fof(f1391,plain,
( spl0_95
<=> ! [X0,X7,X8,X10] : c_Finite__Set_Ofold__graph(X8,X10,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X10,X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1394,plain,
( ! [X10,X0,X8,X7] : c_Finite__Set_Ofold__graph(X8,X10,c_COMBK(c_False,tc_bool,X0),X10,X0,X7)
| ~ spl0_88
| ~ spl0_95 ),
inference(forward_demodulation,[],[f1392,f1349]) ).
fof(f1392,plain,
( ! [X10,X0,X8,X7] : c_Finite__Set_Ofold__graph(X8,X10,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X10,X0,X7)
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1391]) ).
fof(f1478,plain,
( spl0_114
| ~ spl0_3
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1472,f1383,f972,f1476]) ).
fof(f1472,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X0) = X0
| ~ spl0_3
| ~ spl0_93 ),
inference(resolution,[],[f1384,f974]) ).
fof(f1469,plain,
spl0_113,
inference(avatar_split_clause,[],[f749,f1467]) ).
fof(f749,plain,
! [X3,X0,X29] :
( c_COMBK(c_False,tc_bool,X0) != X29
| ~ hBOOL(hAPP(X29,X3)) ),
inference(forward_demodulation,[],[f748,f665]) ).
fof(f748,plain,
! [X3,X0,X29] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X29
| ~ hBOOL(hAPP(X29,X3)) ),
inference(forward_demodulation,[],[f382,f272]) ).
fof(f382,axiom,
! [X3,X29,X0] :
( ~ hBOOL(hAPP(X29,X3))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Collect(X29,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
fof(f1465,plain,
spl0_112,
inference(avatar_split_clause,[],[f728,f1463]) ).
fof(f728,plain,
! [X0,X1] :
( c_Finite__Set_Olinorder__class_OMin(hAPP(c_fequal(X0),X1),X0) = X1
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f727,f686]) ).
fof(f727,plain,
! [X0,X1] :
( c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),X0) = X1
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f551,f665]) ).
fof(f551,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
fof(f1461,plain,
spl0_111,
inference(avatar_split_clause,[],[f726,f1459]) ).
fof(f726,plain,
! [X0,X1] :
( c_Finite__Set_Olinorder__class_OMax(hAPP(c_fequal(X0),X1),X0) = X1
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f725,f686]) ).
fof(f725,plain,
! [X0,X1] :
( c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(X1,X0),c_COMBK(c_False,tc_bool,X0)),X0) = X1
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f562,f665]) ).
fof(f562,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
fof(f1457,plain,
spl0_110,
inference(avatar_split_clause,[],[f661,f1455]) ).
fof(f661,axiom,
! [X82,X0,X81] :
( X81 = X82
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X81),X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1452,plain,
spl0_109,
inference(avatar_split_clause,[],[f612,f1450]) ).
fof(f612,axiom,
! [X0,X11,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Set_Oinsert(X1,X0),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
fof(f1448,plain,
spl0_108,
inference(avatar_split_clause,[],[f521,f1446]) ).
fof(f521,axiom,
! [X0,X60] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(X60,X0,X0),X0) = X60 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lfp__const_0) ).
fof(f1444,plain,
spl0_107,
inference(avatar_split_clause,[],[f465,f1442]) ).
fof(f465,axiom,
! [X3,X0] :
( ~ class_Orderings_Otop(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Orderings_Otop__class_Otop(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
fof(f1439,plain,
spl0_106,
inference(avatar_split_clause,[],[f383,f1437]) ).
fof(f383,axiom,
! [X3,X0,X8] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
fof(f1435,plain,
spl0_105,
inference(avatar_split_clause,[],[f368,f1433]) ).
fof(f368,axiom,
! [X3,X0] :
( ~ class_Orderings_Obot(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1431,plain,
spl0_104,
inference(avatar_split_clause,[],[f346,f1429]) ).
fof(f1429,plain,
( spl0_104
<=> ! [X45,X48,X46,X47] :
( X46 = X48
| c_Com_Ocom_OWhile(X45,X46) != c_Com_Ocom_OWhile(X47,X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f346,axiom,
! [X48,X46,X47,X45] :
( X46 = X48
| c_Com_Ocom_OWhile(X45,X46) != c_Com_Ocom_OWhile(X47,X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
fof(f1427,plain,
spl0_103,
inference(avatar_split_clause,[],[f345,f1425]) ).
fof(f1425,plain,
( spl0_103
<=> ! [X48,X47,X46,X45] :
( X45 = X47
| c_Com_Ocom_OWhile(X45,X46) != c_Com_Ocom_OWhile(X47,X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f345,axiom,
! [X48,X46,X47,X45] :
( X45 = X47
| c_Com_Ocom_OWhile(X45,X46) != c_Com_Ocom_OWhile(X47,X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
fof(f1423,plain,
spl0_102,
inference(avatar_split_clause,[],[f274,f1421]) ).
fof(f1421,plain,
( spl0_102
<=> ! [X41,X40,X50,X49] :
( X40 = X49
| c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OSemi(X49,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f274,axiom,
! [X50,X40,X41,X49] :
( X40 = X49
| c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OSemi(X49,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
fof(f1419,plain,
spl0_101,
inference(avatar_split_clause,[],[f273,f1417]) ).
fof(f1417,plain,
( spl0_101
<=> ! [X41,X50,X40,X49] :
( X41 = X50
| c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OSemi(X49,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f273,axiom,
! [X50,X40,X41,X49] :
( X41 = X50
| c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OSemi(X49,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
fof(f1415,plain,
spl0_100,
inference(avatar_split_clause,[],[f256,f1413]) ).
fof(f256,axiom,
! [X0,X11] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X11) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f1411,plain,
spl0_99,
inference(avatar_split_clause,[],[f255,f1409]) ).
fof(f255,axiom,
! [X3,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f1407,plain,
spl0_98,
inference(avatar_split_clause,[],[f195,f1405]) ).
fof(f195,axiom,
! [X0,X11,X1] :
( c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
fof(f1403,plain,
spl0_97,
inference(avatar_split_clause,[],[f194,f1401]) ).
fof(f194,axiom,
! [X0,X11,X1] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(X1,X0),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
fof(f1398,plain,
spl0_96,
inference(avatar_split_clause,[],[f193,f1396]) ).
fof(f193,axiom,
! [X10,X0,X8,X7] : c_Nitpick_Ofold__graph_H(X8,X10,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X10,X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
fof(f1393,plain,
spl0_95,
inference(avatar_split_clause,[],[f192,f1391]) ).
fof(f192,axiom,
! [X10,X0,X8,X7] : c_Finite__Set_Ofold__graph(X8,X10,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X10,X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
fof(f1389,plain,
spl0_94,
inference(avatar_split_clause,[],[f142,f1387]) ).
fof(f142,axiom,
! [X3,X10,X0,X11,X8,X7] :
( c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofold__graph(X8,X10,X11,X3,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
fof(f1385,plain,
spl0_93,
inference(avatar_split_clause,[],[f50,f1383]) ).
fof(f50,axiom,
! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f1381,plain,
spl0_92,
inference(avatar_split_clause,[],[f34,f1379]) ).
fof(f34,axiom,
! [X3,X0,X8,X16,X4] : hAPP(c_Fun_Ofun__upd(X8,X3,X4,X0,X16),X3) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
fof(f1377,plain,
spl0_91,
inference(avatar_split_clause,[],[f31,f1375]) ).
fof(f31,axiom,
! [X3,X0,X8,X7] : c_Fun_Ofun__upd(X8,X3,hAPP(X8,X3),X7,X0) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
fof(f1363,plain,
( spl0_90
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f1322,f1319,f1361]) ).
fof(f1361,plain,
( spl0_90
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1319,plain,
( spl0_81
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1322,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_COMBK(c_False,tc_bool,X0)
| ~ spl0_81 ),
inference(forward_demodulation,[],[f1320,f665]) ).
fof(f1320,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1319]) ).
fof(f1355,plain,
spl0_89,
inference(avatar_split_clause,[],[f680,f1352]) ).
fof(f1352,plain,
( spl0_89
<=> c_False = c_in(v_x,c_COMBK(c_False,tc_bool,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f680,plain,
c_False = c_in(v_x,c_COMBK(c_False,tc_bool,t_a),t_a),
inference(forward_demodulation,[],[f679,f658]) ).
fof(f658,axiom,
! [X29,X0,X7,X30] : hAPP(c_COMBK(X29,X0,X7),X30) = X29,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBK__def_0) ).
fof(f679,plain,
hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = c_in(v_x,c_COMBK(c_False,tc_bool,t_a),t_a),
inference(forward_demodulation,[],[f455,f665]) ).
fof(f455,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
fof(f1350,plain,
spl0_88,
inference(avatar_split_clause,[],[f665,f1348]) ).
fof(f1346,plain,
spl0_87,
inference(avatar_split_clause,[],[f533,f1344]) ).
fof(f533,axiom,
! [X29] :
( ~ hBOOL(hAPP(X29,c_False))
| hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Set__Xex__bool__eq__1__1(X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__bool__eq_2) ).
fof(f1342,plain,
spl0_86,
inference(avatar_split_clause,[],[f531,f1340]) ).
fof(f531,axiom,
! [X29] :
( hBOOL(hAPP(X29,c_False))
| ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Set__Xall__bool__eq__1__1(X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_all__bool__eq_1) ).
fof(f1338,plain,
spl0_85,
inference(avatar_split_clause,[],[f495,f1336]) ).
fof(f495,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1334,plain,
spl0_84,
inference(avatar_split_clause,[],[f494,f1332]) ).
fof(f494,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1330,plain,
spl0_83,
inference(avatar_split_clause,[],[f491,f1328]) ).
fof(f491,axiom,
! [X0,X11] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
fof(f1326,plain,
spl0_82,
inference(avatar_split_clause,[],[f416,f1324]) ).
fof(f416,axiom,
! [X3,X0,X12] : hBOOL(c_in(X3,hAPP(c_Set_Oinsert(X3,X0),X12),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f1321,plain,
spl0_81,
inference(avatar_split_clause,[],[f384,f1319]) ).
fof(f384,axiom,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
fof(f1317,plain,
spl0_80,
inference(avatar_split_clause,[],[f253,f1315]) ).
fof(f253,axiom,
! [X3,X0,X43] :
( ~ hBOOL(hAPP(X43,X3))
| hBOOL(c_in(X3,X43,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1313,plain,
spl0_79,
inference(avatar_split_clause,[],[f252,f1311]) ).
fof(f252,axiom,
! [X3,X0,X43] :
( hBOOL(hAPP(X43,X3))
| ~ hBOOL(c_in(X3,X43,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1309,plain,
( spl0_78
| ~ spl0_65
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f1289,f1286,f1252,f1307]) ).
fof(f1307,plain,
( spl0_78
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1286,plain,
( spl0_73
<=> ! [X13,X0] : c_Hoare__Mirabelle_Ohoare__derivs(X13,c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1289,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X1)),X1)
| ~ spl0_65
| ~ spl0_73 ),
inference(resolution,[],[f1287,f1253]) ).
fof(f1287,plain,
( ! [X0,X13] : c_Hoare__Mirabelle_Ohoare__derivs(X13,c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1286]) ).
fof(f1305,plain,
spl0_77,
inference(avatar_split_clause,[],[f16,f1303]) ).
fof(f16,axiom,
! [X3,X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
fof(f1301,plain,
spl0_76,
inference(avatar_split_clause,[],[f14,f1299]) ).
fof(f14,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1297,plain,
spl0_75,
inference(avatar_split_clause,[],[f13,f1295]) ).
fof(f1295,plain,
( spl0_75
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f13,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1293,plain,
spl0_74,
inference(avatar_split_clause,[],[f12,f1291]) ).
fof(f1291,plain,
( spl0_74
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f12,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1288,plain,
( spl0_73
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1263,f1260,f1286]) ).
fof(f1260,plain,
( spl0_67
<=> ! [X13,X0] : c_Hoare__Mirabelle_Ohoare__derivs(X13,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1263,plain,
( ! [X0,X13] : c_Hoare__Mirabelle_Ohoare__derivs(X13,c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ spl0_67 ),
inference(forward_demodulation,[],[f1261,f665]) ).
fof(f1261,plain,
( ! [X0,X13] : c_Hoare__Mirabelle_Ohoare__derivs(X13,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1260]) ).
fof(f1284,plain,
( spl0_72
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f1242,f1239,f1282]) ).
fof(f1239,plain,
( spl0_62
<=> ! [X5,X0] : ~ hBOOL(c_in(X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1242,plain,
( ! [X0,X5] : ~ hBOOL(c_in(X5,c_COMBK(c_False,tc_bool,X0),X0))
| ~ spl0_62 ),
inference(forward_demodulation,[],[f1240,f665]) ).
fof(f1240,plain,
( ! [X0,X5] : ~ hBOOL(c_in(X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f1279,plain,
( spl0_71
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f1225,f1222,f1277]) ).
fof(f1222,plain,
( spl0_58
<=> ! [X0,X7,X8] : c_Fun_Oinj__on(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1225,plain,
( ! [X0,X8,X7] : c_Fun_Oinj__on(X8,c_COMBK(c_False,tc_bool,X0),X0,X7)
| ~ spl0_58 ),
inference(forward_demodulation,[],[f1223,f665]) ).
fof(f1223,plain,
( ! [X0,X8,X7] : c_Fun_Oinj__on(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X7)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1222]) ).
fof(f1275,plain,
spl0_70,
inference(avatar_split_clause,[],[f658,f1273]) ).
fof(f1271,plain,
spl0_69,
inference(avatar_split_clause,[],[f626,f1269]) ).
fof(f1269,plain,
( spl0_69
<=> ! [X80,X79] :
( ~ class_Finite__Set_Ofinite_Ofinite(X79)
| ~ class_Finite__Set_Ofinite_Ofinite(X80)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f626,axiom,
! [X80,X79] :
( ~ class_Finite__Set_Ofinite_Ofinite(X79)
| ~ class_Finite__Set_Ofinite_Ofinite(X80)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f1267,plain,
spl0_68,
inference(avatar_split_clause,[],[f620,f1265]) ).
fof(f1265,plain,
( spl0_68
<=> ! [X80,X79] :
( ~ class_Finite__Set_Ofinite_Ofinite(X79)
| ~ class_Finite__Set_Ofinite_Ofinite(X80)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f620,axiom,
! [X80,X79] :
( ~ class_Finite__Set_Ofinite_Ofinite(X79)
| ~ class_Finite__Set_Ofinite_Ofinite(X80)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
fof(f1262,plain,
spl0_67,
inference(avatar_split_clause,[],[f609,f1260]) ).
fof(f609,axiom,
! [X0,X13] : c_Hoare__Mirabelle_Ohoare__derivs(X13,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).
fof(f1258,plain,
spl0_66,
inference(avatar_split_clause,[],[f598,f1256]) ).
fof(f598,axiom,
! [X3,X0,X11] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X3,X0),X11),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f1254,plain,
spl0_65,
inference(avatar_split_clause,[],[f529,f1252]) ).
fof(f529,axiom,
! [X0,X69,X13] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X69,X0)
| c_Hoare__Mirabelle_Ohoare__valids(X13,X69,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__sound_0) ).
fof(f1250,plain,
spl0_64,
inference(avatar_split_clause,[],[f509,f1248]) ).
fof(f509,axiom,
! [X3,X0] : c_The(hAPP(c_fequal(X0),X3),X0) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
fof(f1246,plain,
spl0_63,
inference(avatar_split_clause,[],[f422,f1244]) ).
fof(f422,axiom,
! [X3,X0] : hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f1241,plain,
spl0_62,
inference(avatar_split_clause,[],[f378,f1239]) ).
fof(f378,axiom,
! [X0,X5] : ~ hBOOL(c_in(X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f1237,plain,
spl0_61,
inference(avatar_split_clause,[],[f354,f1235]) ).
fof(f1235,plain,
( spl0_61
<=> ! [X41,X40,X45,X46,X47] : c_Com_Ocom_OWhile(X45,X46) != c_Com_Ocom_OCond(X47,X40,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f354,axiom,
! [X40,X41,X46,X47,X45] : c_Com_Ocom_OWhile(X45,X46) != c_Com_Ocom_OCond(X47,X40,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
fof(f1233,plain,
spl0_60,
inference(avatar_split_clause,[],[f344,f1231]) ).
fof(f1231,plain,
( spl0_60
<=> ! [X52,X42] :
( X42 = X52
| c_Com_Ocom_OBODY(X42) != c_Com_Ocom_OBODY(X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f344,axiom,
! [X52,X42] :
( X42 = X52
| c_Com_Ocom_OBODY(X42) != c_Com_Ocom_OBODY(X52) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
fof(f1229,plain,
spl0_59,
inference(avatar_split_clause,[],[f281,f1227]) ).
fof(f1227,plain,
( spl0_59
<=> ! [X41,X40,X50,X49,X45] : c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OCond(X45,X49,X50) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f281,axiom,
! [X50,X40,X41,X49,X45] : c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OCond(X45,X49,X50),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
fof(f1224,plain,
spl0_58,
inference(avatar_split_clause,[],[f191,f1222]) ).
fof(f191,axiom,
! [X0,X8,X7] : c_Fun_Oinj__on(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
fof(f1220,plain,
spl0_57,
inference(avatar_split_clause,[],[f660,f1218]) ).
fof(f660,axiom,
! [X3,X0] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1216,plain,
( ~ spl0_56
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f1211,f1207,f1213]) ).
fof(f1207,plain,
( spl0_55
<=> ! [X0,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1211,plain,
( ~ hBOOL(c_False)
| ~ spl0_55 ),
inference(forward_demodulation,[],[f1210,f658]) ).
fof(f1210,plain,
( ! [X3,X0] : ~ hBOOL(hAPP(c_COMBK(c_False,tc_bool,X0),X3))
| ~ spl0_55 ),
inference(forward_demodulation,[],[f1208,f665]) ).
fof(f1208,plain,
( ! [X3,X0] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3))
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f1209,plain,
spl0_55,
inference(avatar_split_clause,[],[f608,f1207]) ).
fof(f608,axiom,
! [X3,X0] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f1205,plain,
spl0_54,
inference(avatar_split_clause,[],[f534,f1203]) ).
fof(f1203,plain,
( spl0_54
<=> ! [X0,X64,X72] : c_Product__Type_Obool_Obool__rec(X64,X72,c_False,X0) = X72 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f534,axiom,
! [X72,X0,X64] : c_Product__Type_Obool_Obool__rec(X64,X72,c_False,X0) = X72,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bool_Orecs_I2_J_0) ).
fof(f1201,plain,
spl0_53,
inference(avatar_split_clause,[],[f532,f1199]) ).
fof(f1199,plain,
( spl0_53
<=> ! [X0,X64,X72] : c_Product__Type_Obool_Obool__case(X64,X72,c_False,X0) = X72 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f532,axiom,
! [X72,X0,X64] : c_Product__Type_Obool_Obool__case(X64,X72,c_False,X0) = X72,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bool_Osimps_I4_J_0) ).
fof(f1197,plain,
spl0_52,
inference(avatar_split_clause,[],[f442,f1195]) ).
fof(f442,axiom,
! [X3,X0] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
fof(f1193,plain,
spl0_51,
inference(avatar_split_clause,[],[f432,f1191]) ).
fof(f1191,plain,
( spl0_51
<=> ! [X42,X41,X40,X47] : c_Com_Ocom_OBODY(X42) != c_Com_Ocom_OCond(X47,X40,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f432,axiom,
! [X40,X41,X47,X42] : c_Com_Ocom_OBODY(X42) != c_Com_Ocom_OCond(X47,X40,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
fof(f1189,plain,
spl0_50,
inference(avatar_split_clause,[],[f275,f1187]) ).
fof(f1187,plain,
( spl0_50
<=> ! [X45,X41,X40,X46] : c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OWhile(X45,X46) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f275,axiom,
! [X40,X41,X46,X45] : c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OWhile(X45,X46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
fof(f1185,plain,
( ~ spl0_49
| spl0_48 ),
inference(avatar_split_clause,[],[f1180,f1175,f1182]) ).
fof(f1175,plain,
( spl0_48
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1180,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a)),t_a)
| spl0_48 ),
inference(forward_demodulation,[],[f1179,f686]) ).
fof(f1179,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| spl0_48 ),
inference(forward_demodulation,[],[f1177,f665]) ).
fof(f1177,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| spl0_48 ),
inference(avatar_component_clause,[],[f1175]) ).
fof(f1178,plain,
~ spl0_48,
inference(avatar_split_clause,[],[f619,f1175]) ).
fof(f619,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1173,plain,
( spl0_47
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1109,f1106,f1171]) ).
fof(f1106,plain,
( spl0_31
<=> ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1109,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0)
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1107,f665]) ).
fof(f1107,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1106]) ).
fof(f1169,plain,
spl0_46,
inference(avatar_split_clause,[],[f633,f1167]) ).
fof(f1167,plain,
( spl0_46
<=> ! [X80,X79] :
( ~ class_HOL_Oord(X80)
| class_HOL_Oord(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f633,axiom,
! [X80,X79] :
( ~ class_HOL_Oord(X80)
| class_HOL_Oord(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f1165,plain,
spl0_45,
inference(avatar_split_clause,[],[f632,f1163]) ).
fof(f632,axiom,
! [X80,X79] :
( ~ class_HOL_Ominus(X80)
| class_HOL_Ominus(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
fof(f1161,plain,
spl0_44,
inference(avatar_split_clause,[],[f631,f1159]) ).
fof(f631,axiom,
! [X80,X79] :
( ~ class_Orderings_Obot(X80)
| class_Orderings_Obot(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1157,plain,
spl0_43,
inference(avatar_split_clause,[],[f630,f1155]) ).
fof(f630,axiom,
! [X80,X79] :
( ~ class_Orderings_Otop(X80)
| class_Orderings_Otop(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
fof(f1153,plain,
spl0_42,
inference(avatar_split_clause,[],[f629,f1151]) ).
fof(f629,axiom,
! [X80,X79] :
( ~ class_Orderings_Oorder(X80)
| class_Orderings_Oorder(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1149,plain,
spl0_41,
inference(avatar_split_clause,[],[f628,f1147]) ).
fof(f628,axiom,
! [X80,X79] :
( ~ class_Lattices_Olattice(X80)
| class_Lattices_Olattice(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f1145,plain,
spl0_40,
inference(avatar_split_clause,[],[f627,f1143]) ).
fof(f1143,plain,
( spl0_40
<=> ! [X80,X79] :
( ~ class_Orderings_Opreorder(X80)
| class_Orderings_Opreorder(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f627,axiom,
! [X80,X79] :
( ~ class_Orderings_Opreorder(X80)
| class_Orderings_Opreorder(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1141,plain,
spl0_39,
inference(avatar_split_clause,[],[f625,f1139]) ).
fof(f625,axiom,
! [X80,X79] :
( ~ class_Lattices_Obounded__lattice(X80)
| class_Lattices_Obounded__lattice(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f1137,plain,
spl0_38,
inference(avatar_split_clause,[],[f624,f1135]) ).
fof(f1135,plain,
( spl0_38
<=> ! [X80,X79] :
( ~ class_Lattices_Odistrib__lattice(X80)
| class_Lattices_Odistrib__lattice(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f624,axiom,
! [X80,X79] :
( ~ class_Lattices_Odistrib__lattice(X80)
| class_Lattices_Odistrib__lattice(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f1133,plain,
spl0_37,
inference(avatar_split_clause,[],[f623,f1131]) ).
fof(f623,axiom,
! [X80,X79] :
( ~ class_Lattices_Olattice(X80)
| class_Lattices_Olower__semilattice(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f1129,plain,
spl0_36,
inference(avatar_split_clause,[],[f622,f1127]) ).
fof(f622,axiom,
! [X80,X79] :
( ~ class_Lattices_Olattice(X80)
| class_Lattices_Oupper__semilattice(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f1125,plain,
spl0_35,
inference(avatar_split_clause,[],[f621,f1123]) ).
fof(f621,axiom,
! [X80,X79] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X80)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f1121,plain,
spl0_34,
inference(avatar_split_clause,[],[f504,f1119]) ).
fof(f1119,plain,
( spl0_34
<=> ! [X42,X48,X47] : c_Com_Ocom_OBODY(X42) != c_Com_Ocom_OWhile(X47,X48) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f504,axiom,
! [X48,X47,X42] : c_Com_Ocom_OBODY(X42) != c_Com_Ocom_OWhile(X47,X48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
fof(f1117,plain,
spl0_33,
inference(avatar_split_clause,[],[f319,f1115]) ).
fof(f1115,plain,
( spl0_33
<=> ! [X45,X50,X49] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X45,X49,X50) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f319,axiom,
! [X50,X49,X45] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X45,X49,X50),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
fof(f1113,plain,
spl0_32,
inference(avatar_split_clause,[],[f250,f1111]) ).
fof(f1111,plain,
( spl0_32
<=> ! [X41,X40,X42] : c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OBODY(X42) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f250,axiom,
! [X40,X41,X42] : c_Com_Ocom_OSemi(X40,X41) != c_Com_Ocom_OBODY(X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
fof(f1108,plain,
spl0_31,
inference(avatar_split_clause,[],[f189,f1106]) ).
fof(f189,axiom,
! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
fof(f1104,plain,
spl0_30,
inference(avatar_split_clause,[],[f659,f1102]) ).
fof(f1102,plain,
( spl0_30
<=> ! [X29,X0] : c_COMBI(X29,X0) = X29 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f659,axiom,
! [X29,X0] : c_COMBI(X29,X0) = X29,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBI__def_0) ).
fof(f1100,plain,
spl0_29,
inference(avatar_split_clause,[],[f517,f1098]) ).
fof(f1098,plain,
( spl0_29
<=> ! [X50,X49] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X49,X50) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f517,axiom,
! [X50,X49] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X49,X50),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
fof(f1096,plain,
spl0_28,
inference(avatar_split_clause,[],[f272,f1094]) ).
fof(f1092,plain,
spl0_27,
inference(avatar_split_clause,[],[f270,f1090]) ).
fof(f1090,plain,
( spl0_27
<=> ! [X45,X46] : c_Com_Ocom_OWhile(X45,X46) != c_Com_Ocom_OSKIP ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f270,axiom,
! [X46,X45] : c_Com_Ocom_OWhile(X45,X46) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
fof(f1088,plain,
spl0_26,
inference(avatar_split_clause,[],[f178,f1086]) ).
fof(f178,axiom,
! [X0,X11] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
fof(f1084,plain,
spl0_25,
inference(avatar_split_clause,[],[f505,f1082]) ).
fof(f1082,plain,
( spl0_25
<=> ! [X42] : c_Com_Ocom_OBODY(X42) != c_Com_Ocom_OSKIP ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f505,axiom,
! [X42] : c_Com_Ocom_OBODY(X42) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
fof(f1080,plain,
spl0_24,
inference(avatar_split_clause,[],[f657,f1077]) ).
fof(f657,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f1075,plain,
spl0_23,
inference(avatar_split_clause,[],[f656,f1072]) ).
fof(f656,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
fof(f1070,plain,
spl0_22,
inference(avatar_split_clause,[],[f655,f1067]) ).
fof(f655,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f1065,plain,
spl0_21,
inference(avatar_split_clause,[],[f654,f1062]) ).
fof(f654,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
fof(f1060,plain,
spl0_20,
inference(avatar_split_clause,[],[f653,f1057]) ).
fof(f653,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f1055,plain,
spl0_19,
inference(avatar_split_clause,[],[f652,f1052]) ).
fof(f652,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f1050,plain,
spl0_18,
inference(avatar_split_clause,[],[f651,f1047]) ).
fof(f651,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f1045,plain,
spl0_17,
inference(avatar_split_clause,[],[f650,f1042]) ).
fof(f1042,plain,
( spl0_17
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f650,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f1040,plain,
spl0_16,
inference(avatar_split_clause,[],[f649,f1037]) ).
fof(f649,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f1035,plain,
spl0_15,
inference(avatar_split_clause,[],[f648,f1032]) ).
fof(f1032,plain,
( spl0_15
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f648,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f1030,plain,
spl0_14,
inference(avatar_split_clause,[],[f647,f1027]) ).
fof(f647,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f1025,plain,
spl0_13,
inference(avatar_split_clause,[],[f646,f1022]) ).
fof(f646,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f1020,plain,
spl0_12,
inference(avatar_split_clause,[],[f645,f1017]) ).
fof(f645,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(f1015,plain,
spl0_11,
inference(avatar_split_clause,[],[f644,f1012]) ).
fof(f1012,plain,
( spl0_11
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f644,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
fof(f1010,plain,
spl0_10,
inference(avatar_split_clause,[],[f643,f1007]) ).
fof(f643,axiom,
class_HOL_Ominus(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
fof(f1005,plain,
spl0_9,
inference(avatar_split_clause,[],[f642,f1002]) ).
fof(f642,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f1000,plain,
spl0_8,
inference(avatar_split_clause,[],[f641,f997]) ).
fof(f641,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f995,plain,
spl0_7,
inference(avatar_split_clause,[],[f640,f992]) ).
fof(f640,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f990,plain,
spl0_6,
inference(avatar_split_clause,[],[f639,f987]) ).
fof(f639,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f985,plain,
spl0_5,
inference(avatar_split_clause,[],[f638,f982]) ).
fof(f982,plain,
( spl0_5
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f638,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f980,plain,
spl0_4,
inference(avatar_split_clause,[],[f637,f977]) ).
fof(f977,plain,
( spl0_4
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f637,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f975,plain,
spl0_3,
inference(avatar_split_clause,[],[f636,f972]) ).
fof(f636,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f970,plain,
spl0_2,
inference(avatar_split_clause,[],[f635,f967]) ).
fof(f635,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f965,plain,
spl0_1,
inference(avatar_split_clause,[],[f634,f962]) ).
fof(f962,plain,
( spl0_1
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f634,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV909-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:14:04 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (568)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.41 % (571)WARNING: value z3 for option sas not known
% 0.14/0.41 % (569)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.41 % (570)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.41 % (572)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.41 % (571)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)
% 0.14/0.41 % (573)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.41 % (574)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.41 % (575)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)
% 1.39/0.60 TRYING [1]
% 1.39/0.62 TRYING [2]
% 4.56/1.04 TRYING [1]
% 4.56/1.05 TRYING [3]
% 4.89/1.11 TRYING [2]
% 8.70/1.66 TRYING [1]
% 9.13/1.70 TRYING [2]
% 13.00/2.23 TRYING [3]
% 15.57/2.60 TRYING [3]
% 29.93/4.66 TRYING [4]
% 42.57/6.46 TRYING [4]
% 73.61/10.86 % (573)First to succeed.
% 74.15/10.94 % (573)Refutation found. Thanks to Tanya!
% 74.15/10.94 % SZS status Unsatisfiable for theBenchmark
% 74.15/10.94 % SZS output start Proof for theBenchmark
% See solution above
% 74.15/10.98 % (573)------------------------------
% 74.15/10.98 % (573)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 74.15/10.98 % (573)Termination reason: Refutation
% 74.15/10.98
% 74.15/10.98 % (573)Memory used [KB]: 82263
% 74.15/10.98 % (573)Time elapsed: 10.517 s
% 74.15/10.98 % (573)Instructions burned: 26808 (million)
% 74.15/10.98 % (573)------------------------------
% 74.15/10.98 % (573)------------------------------
% 74.15/10.98 % (568)Success in time 10.575 s
%------------------------------------------------------------------------------