TSTP Solution File: SWV879-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV879-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 May 21 06:37:01 EDT 2024
% Result : Unsatisfiable 21.63s 3.50s
% Output : Refutation 21.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1759
% Syntax : Number of formulae : 3638 ( 854 unt; 0 def)
% Number of atoms : 9782 (1379 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 11110 (4966 ~;5071 |; 0 &)
% (1073 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 1106 (1104 usr;1074 prp; 0-4 aty)
% Number of functors : 50 ( 50 usr; 9 con; 0-5 aty)
% Number of variables : 7295 (7295 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34088,plain,
$false,
inference(avatar_sat_refutation,[],[f1006,f1011,f1016,f1021,f1026,f1031,f1036,f1041,f1046,f1051,f1056,f1061,f1066,f1071,f1076,f1081,f1086,f1091,f1096,f1101,f1106,f1111,f1116,f1121,f1126,f1131,f1136,f1141,f1146,f1151,f1156,f1161,f1166,f1171,f1176,f1181,f1186,f1191,f1197,f1201,f1205,f1209,f1213,f1217,f1221,f1225,f1229,f1233,f1237,f1241,f1245,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1285,f1289,f1293,f1297,f1301,f1305,f1309,f1313,f1317,f1321,f1325,f1329,f1333,f1339,f1343,f1347,f1351,f1355,f1359,f1363,f1367,f1371,f1375,f1384,f1388,f1392,f1396,f1400,f1404,f1408,f1412,f1416,f1420,f1424,f1428,f1432,f1436,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1492,f1496,f1500,f1504,f1508,f1516,f1585,f1602,f1606,f1610,f1614,f1618,f1622,f1626,f1630,f1634,f1638,f1642,f1646,f1650,f1654,f1658,f1662,f1666,f1670,f1674,f1678,f1682,f1689,f1693,f1697,f1701,f1705,f1709,f1713,f1717,f1721,f1726,f1797,f1877,f1881,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f1914,f1918,f1922,f1926,f1930,f1934,f1938,f1942,f1946,f1950,f1954,f1958,f1962,f1966,f1980,f1984,f1988,f1992,f1996,f2000,f2004,f2009,f2014,f2018,f2022,f2026,f2030,f2034,f2178,f2242,f2264,f2268,f2272,f2276,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2313,f2317,f2321,f2331,f2335,f2464,f2468,f2472,f2476,f2480,f2484,f2488,f2492,f2496,f2500,f2504,f2508,f2512,f2516,f2520,f2524,f2528,f2532,f2536,f2540,f2544,f2548,f2552,f2562,f2566,f2570,f2574,f2578,f2582,f2586,f2590,f2610,f2933,f2937,f2941,f2946,f2950,f2954,f2958,f2962,f2966,f2970,f2974,f2978,f2982,f2986,f2994,f2998,f3002,f3006,f3010,f3014,f3018,f3022,f3026,f3030,f3035,f3039,f3043,f3047,f3051,f3055,f3059,f3063,f3067,f3071,f3075,f3080,f3084,f3088,f3093,f3099,f3107,f3241,f3750,f4057,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4117,f4121,f4125,f4129,f4136,f4140,f4144,f4148,f4152,f4156,f4160,f4164,f4168,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4204,f4208,f4212,f4216,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4274,f4278,f4282,f4286,f4290,f4294,f4298,f4302,f4306,f4310,f4314,f4318,f4322,f4326,f4330,f4334,f4338,f4342,f4346,f4354,f4358,f4362,f4366,f4370,f4488,f5102,f5443,f5961,f5965,f5970,f5974,f5978,f5982,f5986,f5990,f5994,f5998,f6002,f6006,f6010,f6020,f6024,f6028,f6032,f6036,f6040,f6044,f6048,f6052,f6056,f6060,f6064,f6068,f6573,f6636,f6640,f6644,f6648,f6677,f6681,f6685,f6689,f6693,f6697,f6701,f6705,f6709,f6713,f6717,f6721,f6725,f6729,f6733,f6737,f6741,f7118,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7256,f7260,f7264,f7268,f7272,f7276,f7280,f7284,f7293,f7297,f7301,f7305,f7309,f7313,f7317,f7321,f7325,f7329,f7338,f7342,f7491,f8012,f8016,f8025,f8029,f8033,f8037,f8041,f8045,f8049,f8053,f8057,f8061,f8065,f8069,f8073,f8077,f8081,f8085,f8089,f8093,f8097,f8101,f8105,f8109,f8113,f8117,f8122,f8127,f8131,f8135,f8139,f8143,f8147,f8151,f8155,f8159,f8163,f8167,f8171,f8175,f8179,f8183,f8187,f8214,f8996,f9364,f9368,f9391,f9395,f9399,f9403,f9407,f9411,f9415,f9419,f9423,f9427,f9431,f9435,f9439,f9443,f9447,f9451,f9455,f9459,f9463,f9467,f9471,f9477,f9481,f9485,f9489,f9493,f9497,f9659,f10130,f10273,f10277,f10281,f10285,f10289,f10293,f10333,f10337,f10341,f10345,f10349,f10353,f10357,f10361,f10365,f10373,f10618,f10622,f10626,f10630,f10634,f10638,f10642,f10647,f10651,f10655,f10659,f10663,f10667,f10671,f10675,f10679,f10683,f10687,f10698,f10702,f10706,f10837,f11179,f11183,f11187,f11191,f11195,f11199,f11203,f11208,f11212,f11216,f11220,f11224,f11228,f11232,f11236,f11732,f11753,f11757,f11761,f11765,f11769,f11773,f11777,f11781,f11785,f11801,f11805,f11809,f11813,f11817,f11989,f12363,f12408,f12412,f12416,f12420,f12424,f12428,f12432,f12436,f12440,f12444,f12448,f12452,f12456,f12460,f12464,f12468,f12472,f12476,f12480,f12484,f12488,f12493,f12497,f12501,f12505,f12509,f12513,f12517,f12521,f12525,f12529,f12533,f12541,f12545,f12549,f12553,f12658,f12965,f13205,f13210,f13214,f13218,f13222,f13226,f13230,f13234,f13238,f13374,f13538,f13542,f13546,f13550,f13554,f13558,f13562,f13566,f14093,f14124,f14128,f14132,f14136,f14140,f14144,f14148,f14152,f14510,f14514,f14518,f14522,f14526,f14530,f14534,f14538,f14542,f14546,f14550,f14554,f14558,f14562,f14569,f15566,f15570,f15574,f15578,f15582,f15644,f15648,f15652,f15656,f15660,f15664,f15668,f15672,f15676,f15680,f15687,f15762,f15854,f15858,f15862,f15870,f15874,f15878,f15882,f15886,f15890,f15894,f15898,f15902,f15906,f15914,f15918,f15922,f15926,f17545,f17549,f17553,f17557,f17561,f17565,f17569,f17573,f17577,f17581,f17585,f17677,f18437,f18482,f18505,f18509,f18514,f18518,f18606,f18695,f18823,f18827,f18831,f18835,f18839,f18843,f18999,f19005,f19009,f19013,f19017,f19036,f19318,f19322,f19326,f19330,f19335,f20074,f20079,f20083,f20087,f20236,f20240,f20359,f20363,f20406,f20410,f20508,f20552,f20579,f20698,f20702,f20768,f20774,f21169,f21173,f21177,f21182,f21186,f21190,f21194,f21198,f21352,f21356,f21360,f21364,f21368,f21372,f21376,f21447,f21676,f21684,f21689,f21729,f21773,f21777,f21790,f21794,f21802,f21806,f22069,f22073,f22266,f22315,f22319,f22323,f22327,f22506,f22510,f22514,f22518,f22523,f22565,f22573,f22577,f22605,f22609,f22613,f22617,f22621,f22625,f22630,f22634,f22638,f22645,f22649,f22653,f22657,f23017,f23163,f23167,f23171,f23175,f23229,f23233,f23237,f23241,f23245,f23250,f23254,f23258,f23263,f23268,f23272,f23277,f23282,f23287,f23292,f23296,f23300,f23304,f23308,f23312,f23368,f23710,f23846,f23852,f23856,f23860,f23864,f23868,f23872,f23876,f23880,f23884,f23888,f23892,f23896,f23900,f23904,f23908,f23916,f23920,f23924,f23930,f24044,f24048,f24806,f24849,f24892,f24896,f24900,f24904,f24908,f24951,f24998,f25012,f25035,f25039,f25059,f25083,f25087,f25091,f25095,f25123,f25147,f25151,f25372,f25415,f25419,f25423,f25427,f25488,f25549,f25553,f25557,f25561,f25599,f25638,f25667,f25875,f25956,f25960,f25964,f25968,f25972,f25976,f25980,f25984,f25988,f25992,f25996,f26000,f26004,f26008,f26012,f26016,f26020,f26024,f26028,f26032,f26053,f26057,f26061,f26065,f26069,f26073,f26077,f26081,f26085,f26089,f26152,f26156,f26160,f26164,f26168,f26172,f26176,f26180,f26184,f26188,f26193,f26197,f26201,f26205,f26209,f26213,f26242,f26246,f26250,f26254,f26260,f26264,f26268,f26272,f26276,f26280,f26284,f26288,f26292,f26296,f26300,f26304,f26308,f26312,f26316,f26320,f26324,f26328,f26332,f26336,f26340,f26389,f26393,f26397,f26401,f26511,f26631,f26742,f26746,f26750,f26754,f26806,f26858,f26862,f26866,f26870,f26874,f26878,f26882,f26886,f27134,f28272,f28850,f29423,f30896,f31045,f31049,f31053,f31057,f31061,f31065,f31069,f31076,f31080,f31084,f31088,f31092,f31096,f31144,f31148,f31152,f31156,f31160,f31164,f31168,f31172,f31176,f31180,f31184,f31188,f31192,f31196,f31200,f31204,f31295,f31299,f31387,f31391,f31395,f31399,f31536,f31540,f31628,f31632,f31636,f31640,f31644,f31648,f31652,f31658,f31662,f31666,f31670,f31707,f31711,f31715,f31719,f31726,f32113,f32902,f33488,f33809,f33813,f33817,f33821,f33825,f33889,f33893,f33897,f33901,f33905,f33909,f33913,f33918,f33981,f33987,f34058,f34062,f34066,f34070,f34074,f34078,f34082,f34086,f34087]) ).
fof(f34087,plain,
( spl0_39
| ~ spl0_201
| ~ spl0_1049 ),
inference(avatar_split_clause,[],[f33846,f32900,f2311,f1194]) ).
fof(f1194,plain,
( spl0_39
<=> hBOOL(hAPP(hAPP(v_P,v_G),c_fequal(hAPP(v_mgt__call,v_x),t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f2311,plain,
( spl0_201
<=> ! [X52,X44] :
( ~ c_lessequals(X52,X44,tc_fun(t_a,tc_bool))
| hBOOL(hAPP(hAPP(v_P,X44),X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f32900,plain,
( spl0_1049
<=> ! [X0] : c_lessequals(c_fequal(hAPP(v_mgt__call,v_x),X0),v_G,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f33846,plain,
( hBOOL(hAPP(hAPP(v_P,v_G),c_fequal(hAPP(v_mgt__call,v_x),t_a)))
| ~ spl0_201
| ~ spl0_1049 ),
inference(resolution,[],[f32901,f2312]) ).
fof(f2312,plain,
( ! [X44,X52] :
( ~ c_lessequals(X52,X44,tc_fun(t_a,tc_bool))
| hBOOL(hAPP(hAPP(v_P,X44),X52)) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2311]) ).
fof(f32901,plain,
( ! [X0] : c_lessequals(c_fequal(hAPP(v_mgt__call,v_x),X0),v_G,tc_fun(X0,tc_bool))
| ~ spl0_1049 ),
inference(avatar_component_clause,[],[f32900]) ).
fof(f34086,plain,
( spl0_1073
| ~ spl0_126
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2907,f2568,f1632,f34084]) ).
fof(f34084,plain,
( spl0_1073
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_HOL_Oord__class_Oless(c_Complete__Lattice_OSup__class_OSup(X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f1632,plain,
( spl0_126
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f2568,plain,
( spl0_231
<=> ! [X6,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f2907,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_HOL_Oord__class_Oless(c_Complete__Lattice_OSup__class_OSup(X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_126
| ~ spl0_231 ),
inference(resolution,[],[f2569,f1633]) ).
fof(f1633,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1632]) ).
fof(f2569,plain,
( ! [X0,X1,X6] :
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0)
| ~ hBOOL(c_in(X1,X6,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2568]) ).
fof(f34082,plain,
( spl0_1072
| ~ spl0_127
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2906,f2568,f1636,f34080]) ).
fof(f34080,plain,
( spl0_1072
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_HOL_Oord__class_Oless(c_Complete__Lattice_OSup__class_OSup(X1,X2),X0,X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f1636,plain,
( spl0_127
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f2906,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_HOL_Oord__class_Oless(c_Complete__Lattice_OSup__class_OSup(X1,X2),X0,X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_127
| ~ spl0_231 ),
inference(resolution,[],[f2569,f1637]) ).
fof(f1637,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1636]) ).
fof(f34078,plain,
( spl0_1071
| ~ spl0_126
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2891,f2564,f1632,f34076]) ).
fof(f34076,plain,
( spl0_1071
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_HOL_Oord__class_Oless(X0,c_Complete__Lattice_OInf__class_OInf(X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f2564,plain,
( spl0_230
<=> ! [X6,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2891,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_HOL_Oord__class_Oless(X0,c_Complete__Lattice_OInf__class_OInf(X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_126
| ~ spl0_230 ),
inference(resolution,[],[f2565,f1633]) ).
fof(f2565,plain,
( ! [X0,X1,X6] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,X0),X1,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2564]) ).
fof(f34074,plain,
( spl0_1070
| ~ spl0_127
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2890,f2564,f1636,f34072]) ).
fof(f34072,plain,
( spl0_1070
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_HOL_Oord__class_Oless(X0,c_Complete__Lattice_OInf__class_OInf(X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f2890,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_HOL_Oord__class_Oless(X0,c_Complete__Lattice_OInf__class_OInf(X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_127
| ~ spl0_230 ),
inference(resolution,[],[f2565,f1637]) ).
fof(f34070,plain,
( spl0_1069
| ~ spl0_98
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2800,f2502,f1438,f34068]) ).
fof(f34068,plain,
( spl0_1069
<=> ! [X0,X1] :
( c_lessequals(c_Suc(X0),X1,tc_nat)
| c_Suc(X1) = c_Suc(X0)
| c_lessequals(c_Suc(X1),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f1438,plain,
( spl0_98
<=> ! [X13,X4] :
( c_lessequals(X4,X13,tc_nat)
| c_lessequals(c_Suc(X13),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f2502,plain,
( spl0_216
<=> ! [X13,X4] :
( c_Suc(X13) = X4
| c_lessequals(X4,X13,tc_nat)
| ~ c_lessequals(X4,c_Suc(X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2800,plain,
( ! [X0,X1] :
( c_lessequals(c_Suc(X0),X1,tc_nat)
| c_Suc(X1) = c_Suc(X0)
| c_lessequals(c_Suc(X1),X0,tc_nat) )
| ~ spl0_98
| ~ spl0_216 ),
inference(resolution,[],[f2503,f1439]) ).
fof(f1439,plain,
( ! [X4,X13] :
( c_lessequals(c_Suc(X13),X4,tc_nat)
| c_lessequals(X4,X13,tc_nat) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f2503,plain,
( ! [X4,X13] :
( ~ c_lessequals(X4,c_Suc(X13),tc_nat)
| c_lessequals(X4,X13,tc_nat)
| c_Suc(X13) = X4 )
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f2502]) ).
fof(f34066,plain,
( spl0_1068
| ~ spl0_93
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2779,f2498,f1418,f34064]) ).
fof(f34064,plain,
( spl0_1068
<=> ! [X0,X1] :
( c_Suc(X1) = c_Suc(X0)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f1418,plain,
( spl0_93
<=> ! [X13,X4] :
( c_lessequals(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f2498,plain,
( spl0_215
<=> ! [X13,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| c_Suc(X4) = X13
| c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2779,plain,
( ! [X0,X1] :
( c_Suc(X1) = c_Suc(X0)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_lessequals(c_Suc(X0),X1,tc_nat) )
| ~ spl0_93
| ~ spl0_215 ),
inference(resolution,[],[f2499,f1419]) ).
fof(f1419,plain,
( ! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat)
| c_lessequals(X4,X13,tc_nat) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1418]) ).
fof(f2499,plain,
( ! [X4,X13] :
( c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat)
| c_Suc(X4) = X13
| ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2498]) ).
fof(f34062,plain,
( spl0_1067
| ~ spl0_99
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2778,f2498,f1442,f34060]) ).
fof(f34060,plain,
( spl0_1067
<=> ! [X0,X1] :
( c_Suc(X1) = c_Suc(X0)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f1442,plain,
( spl0_99
<=> ! [X13,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f2778,plain,
( ! [X0,X1] :
( c_Suc(X1) = c_Suc(X0)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) )
| ~ spl0_99
| ~ spl0_215 ),
inference(resolution,[],[f2499,f1443]) ).
fof(f1443,plain,
( ! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1442]) ).
fof(f34058,plain,
( spl0_1066
| ~ spl0_134
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2661,f2478,f1664,f34056]) ).
fof(f34056,plain,
( spl0_1066
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f1664,plain,
( spl0_134
<=> ! [X13,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f2478,plain,
( spl0_210
<=> ! [X29,X27,X28] :
( ~ c_HOL_Oord__class_Oless(X27,X29,tc_nat)
| ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X27),X28,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f2661,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_134
| ~ spl0_210 ),
inference(resolution,[],[f2479,f1665]) ).
fof(f1665,plain,
( ! [X4,X13] :
( c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1664]) ).
fof(f2479,plain,
( ! [X28,X29,X27] :
( ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat)
| ~ c_HOL_Oord__class_Oless(X27,X29,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X27),X28,tc_nat) )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f2478]) ).
fof(f33987,plain,
( ~ spl0_20
| spl0_1065
| ~ spl0_116
| ~ spl0_166
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2372,f2270,f1940,f1513,f33985,f1098]) ).
fof(f1098,plain,
( spl0_20
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f33985,plain,
( spl0_1065
<=> ! [X2,X0,X1] :
( c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X2),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f1513,plain,
( spl0_116
<=> c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1940,plain,
( spl0_166
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2270,plain,
( spl0_191
<=> ! [X29,X27,X28] :
( ~ c_lessequals(X27,X29,tc_nat)
| ~ c_lessequals(X29,X28,tc_nat)
| c_lessequals(X27,X28,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2372,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X2),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_116
| ~ spl0_166
| ~ spl0_191 ),
inference(forward_demodulation,[],[f2356,f1515]) ).
fof(f1515,plain,
( c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1513]) ).
fof(f2356,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X2),tc_nat)
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_166
| ~ spl0_191 ),
inference(resolution,[],[f2271,f1941]) ).
fof(f1941,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1940]) ).
fof(f2271,plain,
( ! [X28,X29,X27] :
( ~ c_lessequals(X29,X28,tc_nat)
| ~ c_lessequals(X27,X29,tc_nat)
| c_lessequals(X27,X28,tc_nat) )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f2270]) ).
fof(f33981,plain,
( ~ spl0_20
| spl0_1064
| ~ spl0_156
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2365,f2270,f1900,f33979,f1098]) ).
fof(f33979,plain,
( spl0_1064
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
| c_lessequals(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f1900,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f2365,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
| c_lessequals(X0,X2,tc_nat)
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_156
| ~ spl0_191 ),
inference(resolution,[],[f2271,f1901]) ).
fof(f1901,plain,
( ! [X2,X0,X1] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1900]) ).
fof(f33918,plain,
( spl0_1063
| ~ spl0_242
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f33914,f33911,f2943,f33916]) ).
fof(f33916,plain,
( spl0_1063
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X2),tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f2943,plain,
( spl0_242
<=> c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f33911,plain,
( spl0_1062
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f33914,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X2),tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_242
| ~ spl0_1062 ),
inference(forward_demodulation,[],[f33912,f2945]) ).
fof(f2945,plain,
( c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat)
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2943]) ).
fof(f33912,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_1062 ),
inference(avatar_component_clause,[],[f33911]) ).
fof(f33913,plain,
( ~ spl0_20
| spl0_1062
| ~ spl0_155
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2363,f2270,f1896,f33911,f1098]) ).
fof(f1896,plain,
( spl0_155
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f2363,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
| c_lessequals(X0,X1,tc_nat)
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_155
| ~ spl0_191 ),
inference(resolution,[],[f2271,f1897]) ).
fof(f1897,plain,
( ! [X2,X0,X1] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1896]) ).
fof(f33909,plain,
( spl0_1061
| ~ spl0_64
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2249,f2020,f1295,f33907]) ).
fof(f33907,plain,
( spl0_1061
<=> ! [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_1061])]) ).
fof(f1295,plain,
( spl0_64
<=> ! [X55,X56] :
( ~ class_Orderings_Obot(X56)
| class_Orderings_Obot(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f2020,plain,
( spl0_183
<=> ! [X20] :
( ~ class_Orderings_Obot(X20)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X20)),v_x) = c_Orderings_Obot__class_Obot(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f2249,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_64
| ~ spl0_183 ),
inference(resolution,[],[f2021,f1296]) ).
fof(f1296,plain,
( ! [X56,X55] :
( class_Orderings_Obot(tc_fun(X55,X56))
| ~ class_Orderings_Obot(X56) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f2021,plain,
( ! [X20] :
( ~ class_Orderings_Obot(X20)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X20)),v_x) = c_Orderings_Obot__class_Obot(X20) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f2020]) ).
fof(f33905,plain,
( spl0_1060
| ~ spl0_63
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2244,f1994,f1291,f33903]) ).
fof(f33903,plain,
( spl0_1060
<=> ! [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_1060])]) ).
fof(f1291,plain,
( spl0_63
<=> ! [X55,X56] :
( ~ class_Orderings_Otop(X56)
| class_Orderings_Otop(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1994,plain,
( spl0_177
<=> ! [X20] :
( ~ class_Orderings_Otop(X20)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X20)),v_x) = c_Orderings_Otop__class_Otop(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f2244,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_63
| ~ spl0_177 ),
inference(resolution,[],[f1995,f1292]) ).
fof(f1292,plain,
( ! [X56,X55] :
( class_Orderings_Otop(tc_fun(X55,X56))
| ~ class_Orderings_Otop(X56) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1291]) ).
fof(f1995,plain,
( ! [X20] :
( ~ class_Orderings_Otop(X20)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X20)),v_x) = c_Orderings_Otop__class_Otop(X20) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1994]) ).
fof(f33901,plain,
( spl0_1059
| ~ spl0_59
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f2230,f1964,f1275,f33899]) ).
fof(f33899,plain,
( spl0_1059
<=> ! [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_1059])]) ).
fof(f1275,plain,
( spl0_59
<=> ! [X55,X56] :
( ~ class_Lattices_Obounded__lattice(X56)
| class_Lattices_Obounded__lattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1964,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f2230,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_59
| ~ spl0_172 ),
inference(resolution,[],[f1965,f1276]) ).
fof(f1276,plain,
( ! [X56,X55] :
( class_Lattices_Obounded__lattice(tc_fun(X55,X56))
| ~ class_Lattices_Obounded__lattice(X56) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f1965,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1964]) ).
fof(f33897,plain,
( spl0_1058
| ~ spl0_59
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2228,f1960,f1275,f33895]) ).
fof(f33895,plain,
( spl0_1058
<=> ! [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_1058])]) ).
fof(f1960,plain,
( spl0_171
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f2228,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_59
| ~ spl0_171 ),
inference(resolution,[],[f1961,f1276]) ).
fof(f1961,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1 )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1960]) ).
fof(f33893,plain,
( spl0_1057
| ~ spl0_129
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f2154,f1928,f1644,f33891]) ).
fof(f33891,plain,
( spl0_1057
<=> ! [X0,X1] :
( c_Suc(X1) = c_Suc(X0)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f1644,plain,
( spl0_129
<=> ! [X13,X4] :
( ~ c_lessequals(X13,X4,tc_nat)
| c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1928,plain,
( spl0_163
<=> ! [X13,X4] :
( X4 = X13
| ~ c_lessequals(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(X4,X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f2154,plain,
( ! [X0,X1] :
( c_Suc(X1) = c_Suc(X0)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_129
| ~ spl0_163 ),
inference(resolution,[],[f1929,f1645]) ).
fof(f1645,plain,
( ! [X4,X13] :
( c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat)
| ~ c_lessequals(X13,X4,tc_nat) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1644]) ).
fof(f1929,plain,
( ! [X4,X13] :
( ~ c_lessequals(X4,X13,tc_nat)
| X4 = X13
| c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1928]) ).
fof(f33889,plain,
( spl0_1056
| ~ spl0_133
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2068,f1892,f1660,f33887]) ).
fof(f33887,plain,
( spl0_1056
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat)
| c_Suc(X1) = c_Suc(X0)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f1660,plain,
( spl0_133
<=> ! [X13,X4] :
( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1892,plain,
( spl0_154
<=> ! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f2068,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat)
| c_Suc(X1) = c_Suc(X0)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_133
| ~ spl0_154 ),
inference(resolution,[],[f1893,f1661]) ).
fof(f1661,plain,
( ! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat)
| c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1660]) ).
fof(f1893,plain,
( ! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1892]) ).
fof(f33825,plain,
( spl0_1055
| ~ spl0_129
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2053,f1888,f1644,f33823]) ).
fof(f33823,plain,
( spl0_1055
<=> ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat)
| c_Suc(X1) = c_Suc(X0)
| ~ c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f1888,plain,
( spl0_153
<=> ! [X13,X4] :
( X4 = X13
| ~ c_lessequals(X4,X13,tc_nat)
| ~ c_lessequals(X13,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f2053,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat)
| c_Suc(X1) = c_Suc(X0)
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_129
| ~ spl0_153 ),
inference(resolution,[],[f1889,f1645]) ).
fof(f1889,plain,
( ! [X4,X13] :
( ~ c_lessequals(X13,X4,tc_nat)
| ~ c_lessequals(X4,X13,tc_nat)
| X4 = X13 )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1888]) ).
fof(f33821,plain,
( spl0_1054
| ~ spl0_59
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2038,f1879,f1275,f33819]) ).
fof(f33819,plain,
( spl0_1054
<=> ! [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_1054])]) ).
fof(f1879,plain,
( spl0_151
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f2038,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_59
| ~ spl0_151 ),
inference(resolution,[],[f1880,f1276]) ).
fof(f1880,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1 )
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1879]) ).
fof(f33817,plain,
( spl0_1053
| ~ spl0_59
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f2036,f1875,f1275,f33815]) ).
fof(f33815,plain,
( spl0_1053
<=> ! [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_1053])]) ).
fof(f1875,plain,
( spl0_150
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f2036,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_59
| ~ spl0_150 ),
inference(resolution,[],[f1876,f1276]) ).
fof(f1876,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1 )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1875]) ).
fof(f33813,plain,
( spl0_1052
| ~ spl0_57
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1555,f1422,f1267,f33811]) ).
fof(f33811,plain,
( spl0_1052
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_fun(X0,X1))
| c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)) = c_Orderings_Oord__class_Omin(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f1267,plain,
( spl0_57
<=> ! [X55,X56] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Olower__semilattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1422,plain,
( spl0_94
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X0) = c_Orderings_Oord__class_Omin(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1555,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_fun(X0,X1))
| c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)) = c_Orderings_Oord__class_Omin(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_57
| ~ spl0_94 ),
inference(resolution,[],[f1423,f1268]) ).
fof(f1268,plain,
( ! [X56,X55] :
( class_Lattices_Olower__semilattice(tc_fun(X55,X56))
| ~ class_Lattices_Olattice(X56) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1267]) ).
fof(f1423,plain,
( ! [X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X0) = c_Orderings_Oord__class_Omin(X0) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1422]) ).
fof(f33809,plain,
( spl0_1051
| ~ spl0_56
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f1511,f1382,f1263,f33807]) ).
fof(f33807,plain,
( spl0_1051
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_fun(X0,X1))
| c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)) = c_Orderings_Oord__class_Omax(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f1263,plain,
( spl0_56
<=> ! [X55,X56] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Oupper__semilattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1382,plain,
( spl0_84
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X0) = c_Orderings_Oord__class_Omax(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1511,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_fun(X0,X1))
| c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)) = c_Orderings_Oord__class_Omax(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_56
| ~ spl0_84 ),
inference(resolution,[],[f1383,f1264]) ).
fof(f1264,plain,
( ! [X56,X55] :
( class_Lattices_Oupper__semilattice(tc_fun(X55,X56))
| ~ class_Lattices_Olattice(X56) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f1383,plain,
( ! [X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X0) = c_Orderings_Oord__class_Omax(X0) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1382]) ).
fof(f33488,plain,
( spl0_1050
| ~ spl0_959
| ~ spl0_984 ),
inference(avatar_split_clause,[],[f30823,f26868,f26298,f33486]) ).
fof(f33486,plain,
( spl0_1050
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_G,X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f26298,plain,
( spl0_959
<=> ! [X0] : v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f26868,plain,
( spl0_984
<=> ! [X4,X0,X3,X2,X1] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f30823,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_G,X0,X2)
| ~ spl0_959
| ~ spl0_984 ),
inference(superposition,[],[f26869,f26299]) ).
fof(f26299,plain,
( ! [X0] : v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,X0)
| ~ spl0_959 ),
inference(avatar_component_clause,[],[f26298]) ).
fof(f26869,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ spl0_984 ),
inference(avatar_component_clause,[],[f26868]) ).
fof(f32902,plain,
( spl0_1049
| ~ spl0_883
| ~ spl0_959 ),
inference(avatar_split_clause,[],[f26382,f26298,f25145,f32900]) ).
fof(f25145,plain,
( spl0_883
<=> ! [X2,X0,X1] : c_lessequals(c_fequal(X1,X0),c_Set_Oinsert(X1,X2,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f26382,plain,
( ! [X0] : c_lessequals(c_fequal(hAPP(v_mgt__call,v_x),X0),v_G,tc_fun(X0,tc_bool))
| ~ spl0_883
| ~ spl0_959 ),
inference(superposition,[],[f25146,f26299]) ).
fof(f25146,plain,
( ! [X2,X0,X1] : c_lessequals(c_fequal(X1,X0),c_Set_Oinsert(X1,X2,X0),tc_fun(X0,tc_bool))
| ~ spl0_883 ),
inference(avatar_component_clause,[],[f25145]) ).
fof(f32113,plain,
( spl0_1048
| ~ spl0_875
| ~ spl0_959 ),
inference(avatar_split_clause,[],[f26381,f26298,f25033,f32111]) ).
fof(f32111,plain,
( spl0_1048
<=> ! [X0,X1] : hBOOL(c_in(hAPP(v_mgt__call,v_x),c_Set_Oinsert(X1,v_G,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f25033,plain,
( spl0_875
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f26381,plain,
( ! [X0,X1] : hBOOL(c_in(hAPP(v_mgt__call,v_x),c_Set_Oinsert(X1,v_G,X0),X0))
| ~ spl0_875
| ~ spl0_959 ),
inference(superposition,[],[f25034,f26299]) ).
fof(f25034,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3))
| ~ spl0_875 ),
inference(avatar_component_clause,[],[f25033]) ).
fof(f31726,plain,
( spl0_1047
| ~ spl0_173
| ~ spl0_262
| ~ spl0_565 ),
inference(avatar_split_clause,[],[f11642,f11222,f3028,f1978,f31724]) ).
fof(f31724,plain,
( spl0_1047
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X2,X0,X1),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f1978,plain,
( spl0_173
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f3028,plain,
( spl0_262
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f11222,plain,
( spl0_565
<=> ! [X0,X14,X6,X8] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_fequal(X14,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f11642,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X2,X0,X1),tc_fun(X1,tc_bool))
| ~ spl0_173
| ~ spl0_262
| ~ spl0_565 ),
inference(forward_demodulation,[],[f11619,f3029]) ).
fof(f3029,plain,
( ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f3028]) ).
fof(f11619,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X2,X0,X1),tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_fequal(X2,X1),tc_fun(X1,tc_bool))
| ~ spl0_173
| ~ spl0_565 ),
inference(superposition,[],[f11223,f1979]) ).
fof(f1979,plain,
( ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X0,tc_bool))
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1978]) ).
fof(f11223,plain,
( ! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_fequal(X14,X0),tc_fun(X0,tc_bool))
| ~ spl0_565 ),
inference(avatar_component_clause,[],[f11222]) ).
fof(f31719,plain,
( spl0_1046
| ~ spl0_124
| ~ spl0_519 ),
inference(avatar_split_clause,[],[f10380,f10283,f1624,f31717]) ).
fof(f31717,plain,
( spl0_1046
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
| c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f1624,plain,
( spl0_124
<=> ! [X6,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X6) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f10283,plain,
( spl0_519
<=> ! [X6,X0,X8] :
( c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f10380,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
| c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_124
| ~ spl0_519 ),
inference(superposition,[],[f10284,f1625]) ).
fof(f1625,plain,
( ! [X0,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X6) = X6
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1624]) ).
fof(f10284,plain,
( ! [X0,X8,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
| c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_519 ),
inference(avatar_component_clause,[],[f10283]) ).
fof(f31715,plain,
( spl0_1045
| ~ spl0_82
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f9266,f8165,f1369,f31713]) ).
fof(f31713,plain,
( spl0_1045
<=> ! [X4,X0,X3,X2,X1] : hBOOL(c_in(hAPP(X0,X1),c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f1369,plain,
( spl0_82
<=> ! [X0,X1,X8] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X8,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f8165,plain,
( spl0_477
<=> ! [X20,X0,X14,X25,X8] : c_Set_Oimage(X25,c_Set_Oinsert(X14,X8,X20),X20,X0) = c_Set_Oinsert(hAPP(X25,X14),c_Set_Oimage(X25,X8,X20,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f9266,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(c_in(hAPP(X0,X1),c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),X4))
| ~ spl0_82
| ~ spl0_477 ),
inference(superposition,[],[f1370,f8166]) ).
fof(f8166,plain,
( ! [X0,X8,X14,X25,X20] : c_Set_Oimage(X25,c_Set_Oinsert(X14,X8,X20),X20,X0) = c_Set_Oinsert(hAPP(X25,X14),c_Set_Oimage(X25,X8,X20,X0),X0)
| ~ spl0_477 ),
inference(avatar_component_clause,[],[f8165]) ).
fof(f1370,plain,
( ! [X0,X1,X8] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X8,X0),X0))
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1369]) ).
fof(f31711,plain,
( spl0_1044
| ~ spl0_186
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f7784,f7315,f2032,f31709]) ).
fof(f31709,plain,
( spl0_1044
<=> ! [X2,X0,X1] :
( c_fequal(X0,X1) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f2032,plain,
( spl0_186
<=> ! [X0,X14] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_fequal(X14,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f7315,plain,
( spl0_432
<=> ! [X16,X0,X14] :
( X14 = X16
| c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f7784,plain,
( ! [X2,X0,X1] :
( c_fequal(X0,X1) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| X0 = X2 )
| ~ spl0_186
| ~ spl0_432 ),
inference(superposition,[],[f7316,f2033]) ).
fof(f2033,plain,
( ! [X0,X14] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_fequal(X14,X0)
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f2032]) ).
fof(f7316,plain,
( ! [X0,X16,X14] :
( c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
| X14 = X16 )
| ~ spl0_432 ),
inference(avatar_component_clause,[],[f7315]) ).
fof(f31707,plain,
( spl0_1042
| spl0_1043
| ~ spl0_79
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f7693,f7295,f1357,f31705,f31702]) ).
fof(f31702,plain,
( spl0_1042
<=> ! [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_1042])]) ).
fof(f31705,plain,
( spl0_1043
<=> ! [X4,X3] : X3 = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f1357,plain,
( spl0_79
<=> ! [X20,X0,X50,X26] : hAPP(c_COMBK(X26,X0,X20),X50) = X26 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f7295,plain,
( spl0_427
<=> ! [X20,X0,X25,X2,X1] :
( X1 = X2
| hAPP(X25,X1) != hAPP(X25,X2)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f7693,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_79
| ~ spl0_427 ),
inference(trivial_inequality_removal,[],[f7692]) ).
fof(f7692,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_79
| ~ spl0_427 ),
inference(forward_demodulation,[],[f7663,f1358]) ).
fof(f1358,plain,
( ! [X50,X0,X26,X20] : hAPP(c_COMBK(X26,X0,X20),X50) = X26
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1357]) ).
fof(f7663,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_79
| ~ spl0_427 ),
inference(superposition,[],[f7296,f1358]) ).
fof(f7296,plain,
( ! [X2,X0,X1,X25,X20] :
( hAPP(X25,X1) != hAPP(X25,X2)
| X1 = X2
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) )
| ~ spl0_427 ),
inference(avatar_component_clause,[],[f7295]) ).
fof(f31670,plain,
( ~ spl0_19
| spl0_1041
| ~ spl0_44
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f7099,f6711,f1215,f31668,f1093]) ).
fof(f1093,plain,
( spl0_19
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f31668,plain,
( spl0_1041
<=> ! [X0] :
( ~ c_Finite__Set_Ofinite(X0,tc_nat)
| ~ hBOOL(c_in(c_Suc(hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),X0)),X0,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f1215,plain,
( spl0_44
<=> ! [X13] : ~ c_lessequals(c_Suc(X13),X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f6711,plain,
( spl0_402
<=> ! [X6,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_lessequals(X1,hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f7099,plain,
( ! [X0] :
( ~ c_Finite__Set_Ofinite(X0,tc_nat)
| ~ hBOOL(c_in(c_Suc(hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),X0)),X0,tc_nat))
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_44
| ~ spl0_402 ),
inference(resolution,[],[f6712,f1216]) ).
fof(f1216,plain,
( ! [X13] : ~ c_lessequals(c_Suc(X13),X13,tc_nat)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f6712,plain,
( ! [X0,X1,X6] :
( c_lessequals(X1,hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f6711]) ).
fof(f31666,plain,
( spl0_1040
| ~ spl0_358
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f6493,f6026,f4368,f31664]) ).
fof(f31664,plain,
( spl0_1040
<=> ! [X2,X0,X1] :
( c_Set_Oinsert(X1,X2,X0) != X2
| c_lessequals(c_fequal(X1,X0),X2,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f4368,plain,
( spl0_358
<=> ! [X6,X0,X14] : c_Set_Oinsert(X14,X6,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_fequal(X14,X0)),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f6026,plain,
( spl0_377
<=> ! [X6,X0,X8] :
( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) != X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f6493,plain,
( ! [X2,X0,X1] :
( c_Set_Oinsert(X1,X2,X0) != X2
| c_lessequals(c_fequal(X1,X0),X2,tc_fun(X0,tc_bool)) )
| ~ spl0_358
| ~ spl0_377 ),
inference(superposition,[],[f6027,f4369]) ).
fof(f4369,plain,
( ! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_fequal(X14,X0)),X6)
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f4368]) ).
fof(f6027,plain,
( ! [X0,X8,X6] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) != X8
| c_lessequals(X6,X8,tc_fun(X0,tc_bool)) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f6026]) ).
fof(f31662,plain,
( spl0_1039
| ~ spl0_52
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f6259,f5988,f1247,f31660]) ).
fof(f31660,plain,
( spl0_1039
<=> ! [X2,X0,X1,X3] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
| ~ class_Orderings_Oorder(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f1247,plain,
( spl0_52
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f5988,plain,
( spl0_369
<=> ! [X20,X0,X25,X21,X1] :
( ~ class_HOL_Oord(X20)
| ~ c_lessequals(X25,X21,tc_fun(X0,X20))
| c_lessequals(hAPP(X25,X1),hAPP(X21,X1),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f6259,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
| ~ class_Orderings_Oorder(tc_fun(X3,X0)) )
| ~ spl0_52
| ~ spl0_369 ),
inference(resolution,[],[f5989,f1248]) ).
fof(f1248,plain,
( ! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f5989,plain,
( ! [X21,X0,X1,X25,X20] :
( ~ c_lessequals(X25,X21,tc_fun(X0,X20))
| ~ class_HOL_Oord(X20)
| c_lessequals(hAPP(X25,X1),hAPP(X21,X1),X20) )
| ~ spl0_369 ),
inference(avatar_component_clause,[],[f5988]) ).
fof(f31658,plain,
( spl0_1038
| ~ spl0_53
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f6258,f5988,f1251,f31656]) ).
fof(f31656,plain,
( spl0_1038
<=> ! [X2,X0,X1,X3] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
| ~ class_Orderings_Opreorder(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f1251,plain,
( spl0_53
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f6258,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
| ~ class_Orderings_Opreorder(tc_fun(X3,X0)) )
| ~ spl0_53
| ~ spl0_369 ),
inference(resolution,[],[f5989,f1252]) ).
fof(f1252,plain,
( ! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f31652,plain,
( spl0_1037
| ~ spl0_109
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5422,f4276,f1482,f31650]) ).
fof(f31650,plain,
( spl0_1037
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f1482,plain,
( spl0_109
<=> ! [X0,X1,X51] :
( ~ hBOOL(hAPP(X51,X1))
| hBOOL(c_in(X1,X51,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f4276,plain,
( spl0_336
<=> ! [X15,X0,X6,X8] :
( ~ hBOOL(c_in(X15,X8,X0))
| ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f5422,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X0)) )
| ~ spl0_109
| ~ spl0_336 ),
inference(resolution,[],[f4277,f1483]) ).
fof(f1483,plain,
( ! [X51,X0,X1] :
( hBOOL(c_in(X1,X51,X0))
| ~ hBOOL(hAPP(X51,X1)) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1482]) ).
fof(f4277,plain,
( ! [X0,X8,X6,X15] :
( ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X15,X8,X0)) )
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f4276]) ).
fof(f31648,plain,
( spl0_1036
| ~ spl0_109
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5417,f4272,f1482,f31646]) ).
fof(f31646,plain,
( spl0_1036
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f4272,plain,
( spl0_335
<=> ! [X15,X0,X6,X8] :
( hBOOL(c_in(X15,X6,X0))
| ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f5417,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X0)) )
| ~ spl0_109
| ~ spl0_335 ),
inference(resolution,[],[f4273,f1483]) ).
fof(f4273,plain,
( ! [X0,X8,X6,X15] :
( ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0))
| hBOOL(c_in(X15,X6,X0)) )
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f4272]) ).
fof(f31644,plain,
( spl0_1035
| ~ spl0_68
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f5017,f4178,f1311,f31642]) ).
fof(f31642,plain,
( spl0_1035
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f1311,plain,
( spl0_68
<=> ! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f4178,plain,
( spl0_312
<=> ! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X16,X14,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f5017,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68
| ~ spl0_312 ),
inference(resolution,[],[f4179,f1312]) ).
fof(f1312,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f1311]) ).
fof(f4179,plain,
( ! [X0,X16,X14] :
( ~ c_lessequals(X16,X14,X0)
| ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) )
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f4178]) ).
fof(f31640,plain,
( spl0_1034
| ~ spl0_70
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f5000,f4178,f1319,f31638]) ).
fof(f31638,plain,
( spl0_1034
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f1319,plain,
( spl0_70
<=> ! [X0,X1] :
( ~ class_Orderings_Otop(X0)
| c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f5000,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_312 ),
inference(resolution,[],[f4179,f1320]) ).
fof(f1320,plain,
( ! [X0,X1] :
( c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1319]) ).
fof(f31636,plain,
( spl0_1033
| ~ spl0_68
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f4970,f4170,f1311,f31634]) ).
fof(f31634,plain,
( spl0_1033
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f4170,plain,
( spl0_310
<=> ! [X0,X28,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X3,X28,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f4970,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68
| ~ spl0_310 ),
inference(resolution,[],[f4171,f1312]) ).
fof(f4171,plain,
( ! [X3,X28,X0] :
( ~ c_lessequals(X3,X28,X0)
| ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f4170]) ).
fof(f31632,plain,
( spl0_1032
| ~ spl0_70
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f4953,f4170,f1319,f31630]) ).
fof(f31630,plain,
( spl0_1032
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f4953,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_310 ),
inference(resolution,[],[f4171,f1320]) ).
fof(f31628,plain,
( spl0_1031
| ~ spl0_112
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4046,f3086,f1494,f31626]) ).
fof(f31626,plain,
( spl0_1031
<=> ! [X2,X4,X0,X3,X1] : hBOOL(c_in(X2,c_Set_Oimage(c_Finite__Set_Ofold1(X0,X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1494,plain,
( spl0_112
<=> ! [X25,X0,X14] : hAPP(c_Finite__Set_Ofold1(X25,X0),c_fequal(X14,X0)) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f3086,plain,
( spl0_276
<=> ! [X20,X0,X25,X1] : hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f4046,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(c_in(X2,c_Set_Oimage(c_Finite__Set_Ofold1(X0,X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4))
| ~ spl0_112
| ~ spl0_276 ),
inference(superposition,[],[f3087,f1495]) ).
fof(f1495,plain,
( ! [X0,X14,X25] : hAPP(c_Finite__Set_Ofold1(X25,X0),c_fequal(X14,X0)) = X14
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1494]) ).
fof(f3087,plain,
( ! [X0,X1,X25,X20] : hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0),X0))
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f31540,plain,
( ~ spl0_14
| spl0_1030
| ~ spl0_77
| ~ spl0_116
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3879,f3053,f1513,f1349,f31538,f1068]) ).
fof(f1068,plain,
( spl0_14
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f31538,plain,
( spl0_1030
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = X1
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f1349,plain,
( spl0_77
<=> ! [X13,X4] :
( c_lessequals(X4,X13,tc_nat)
| c_lessequals(X13,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f3053,plain,
( spl0_268
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f3879,plain,
( ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = X1
| ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_77
| ~ spl0_116
| ~ spl0_268 ),
inference(forward_demodulation,[],[f3840,f1515]) ).
fof(f3840,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1) = X1
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_77
| ~ spl0_268 ),
inference(resolution,[],[f3054,f1350]) ).
fof(f1350,plain,
( ! [X4,X13] :
( c_lessequals(X4,X13,tc_nat)
| c_lessequals(X13,X4,tc_nat) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1349]) ).
fof(f3054,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 )
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f3053]) ).
fof(f31536,plain,
( spl0_1029
| ~ spl0_70
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3853,f3053,f1319,f31534]) ).
fof(f31534,plain,
( spl0_1029
<=> ! [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_1029])]) ).
fof(f3853,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_70
| ~ spl0_268 ),
inference(resolution,[],[f3054,f1320]) ).
fof(f31399,plain,
( ~ spl0_14
| spl0_1028
| ~ spl0_77
| ~ spl0_116
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3818,f3045,f1513,f1349,f31397,f1068]) ).
fof(f31397,plain,
( spl0_1028
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = X0
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f3045,plain,
( spl0_266
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f3818,plain,
( ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = X0
| ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_77
| ~ spl0_116
| ~ spl0_266 ),
inference(forward_demodulation,[],[f3779,f1515]) ).
fof(f3779,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1) = X0
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_77
| ~ spl0_266 ),
inference(resolution,[],[f3046,f1350]) ).
fof(f3046,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1 )
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f3045]) ).
fof(f31395,plain,
( spl0_1027
| ~ spl0_70
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3792,f3045,f1319,f31393]) ).
fof(f31393,plain,
( spl0_1027
<=> ! [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_1027])]) ).
fof(f3792,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_70
| ~ spl0_266 ),
inference(resolution,[],[f3046,f1320]) ).
fof(f31391,plain,
( spl0_1026
| ~ spl0_201
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3752,f3041,f2311,f31389]) ).
fof(f31389,plain,
( spl0_1026
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),c_Set_Oimage(X1,c_Set_Ovimage(X1,X0,X2,t_a),X2,t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f3041,plain,
( spl0_265
<=> ! [X20,X0,X6,X25] : c_lessequals(c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f3752,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),c_Set_Oimage(X1,c_Set_Ovimage(X1,X0,X2,t_a),X2,t_a)))
| ~ spl0_201
| ~ spl0_265 ),
inference(resolution,[],[f3042,f2312]) ).
fof(f3042,plain,
( ! [X0,X6,X25,X20] : c_lessequals(c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0),X6,tc_fun(X0,tc_bool))
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f3041]) ).
fof(f31387,plain,
( spl0_1025
| ~ spl0_200
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3751,f3041,f2307,f31385]) ).
fof(f31385,plain,
( spl0_1025
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,X1,X2,X3),X2,X3),X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f2307,plain,
( spl0_200
<=> ! [X6,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(X6,X0)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f3751,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,X1,X2,X3),X2,X3),X3)
| ~ c_Finite__Set_Ofinite(X1,X3) )
| ~ spl0_200
| ~ spl0_265 ),
inference(resolution,[],[f3042,f2308]) ).
fof(f2308,plain,
( ! [X0,X8,X6] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2307]) ).
fof(f31299,plain,
( ~ spl0_15
| spl0_1024
| ~ spl0_77
| ~ spl0_242
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3669,f3008,f2943,f1349,f31297,f1073]) ).
fof(f1073,plain,
( spl0_15
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f31297,plain,
( spl0_1024
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = X1
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f3008,plain,
( spl0_257
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f3669,plain,
( ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = X1
| ~ class_Lattices_Olower__semilattice(tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_77
| ~ spl0_242
| ~ spl0_257 ),
inference(forward_demodulation,[],[f3632,f2945]) ).
fof(f3632,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_nat)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = X1
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_77
| ~ spl0_257 ),
inference(resolution,[],[f3009,f1350]) ).
fof(f3009,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2 )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f3008]) ).
fof(f31295,plain,
( spl0_1023
| ~ spl0_68
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3660,f3008,f1311,f31293]) ).
fof(f31293,plain,
( spl0_1023
<=> ! [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_1023])]) ).
fof(f3660,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_68
| ~ spl0_257 ),
inference(resolution,[],[f3009,f1312]) ).
fof(f31204,plain,
( ~ spl0_15
| spl0_1022
| ~ spl0_77
| ~ spl0_242
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3611,f3000,f2943,f1349,f31202,f1073]) ).
fof(f31202,plain,
( spl0_1022
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = X0
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f3000,plain,
( spl0_255
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f3611,plain,
( ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = X0
| ~ class_Lattices_Olower__semilattice(tc_nat)
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_77
| ~ spl0_242
| ~ spl0_255 ),
inference(forward_demodulation,[],[f3574,f2945]) ).
fof(f3574,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_nat)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = X0
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_77
| ~ spl0_255 ),
inference(resolution,[],[f3001,f1350]) ).
fof(f3001,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f3000]) ).
fof(f31200,plain,
( spl0_1021
| ~ spl0_865
| ~ spl0_984 ),
inference(avatar_split_clause,[],[f30824,f26868,f24804,f31198]) ).
fof(f31198,plain,
( spl0_1021
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_U,X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f24804,plain,
( spl0_865
<=> ! [X0] : v_U = c_Set_Oinsert(v_x,v_U,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f30824,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_U,X0,X2)
| ~ spl0_865
| ~ spl0_984 ),
inference(superposition,[],[f26869,f24805]) ).
fof(f24805,plain,
( ! [X0] : v_U = c_Set_Oinsert(v_x,v_U,X0)
| ~ spl0_865 ),
inference(avatar_component_clause,[],[f24804]) ).
fof(f31196,plain,
( spl0_1020
| ~ spl0_68
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3602,f3000,f1311,f31194]) ).
fof(f31194,plain,
( spl0_1020
<=> ! [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_1020])]) ).
fof(f3602,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_68
| ~ spl0_255 ),
inference(resolution,[],[f3001,f1312]) ).
fof(f31192,plain,
( spl0_1019
| ~ spl0_140
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3536,f2992,f1691,f31190]) ).
fof(f31190,plain,
( spl0_1019
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1691,plain,
( spl0_140
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f2992,plain,
( spl0_253
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f3536,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
| c_lessequals(X1,X2,X0) )
| ~ spl0_140
| ~ spl0_253 ),
inference(duplicate_literal_removal,[],[f3497]) ).
fof(f3497,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_140
| ~ spl0_253 ),
inference(resolution,[],[f2993,f1692]) ).
fof(f1692,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1691]) ).
fof(f2993,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2 )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2992]) ).
fof(f31188,plain,
( spl0_1018
| ~ spl0_125
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3534,f2992,f1628,f31186]) ).
fof(f31186,plain,
( spl0_1018
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f1628,plain,
( spl0_125
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f3534,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
| c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_125
| ~ spl0_253 ),
inference(duplicate_literal_removal,[],[f3499]) ).
fof(f3499,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_125
| ~ spl0_253 ),
inference(resolution,[],[f2993,f1629]) ).
fof(f1629,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1628]) ).
fof(f31184,plain,
( spl0_1017
| ~ spl0_68
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3523,f2992,f1311,f31182]) ).
fof(f31182,plain,
( spl0_1017
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f3523,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68
| ~ spl0_253 ),
inference(resolution,[],[f2993,f1312]) ).
fof(f31180,plain,
( spl0_1016
| ~ spl0_140
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3488,f2980,f1691,f31178]) ).
fof(f31178,plain,
( spl0_1016
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f2980,plain,
( spl0_251
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f3488,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
| c_lessequals(X2,X1,X0) )
| ~ spl0_140
| ~ spl0_251 ),
inference(duplicate_literal_removal,[],[f3449]) ).
fof(f3449,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_140
| ~ spl0_251 ),
inference(resolution,[],[f2981,f1692]) ).
fof(f2981,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1 )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2980]) ).
fof(f31176,plain,
( spl0_1015
| ~ spl0_125
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3486,f2980,f1628,f31174]) ).
fof(f31174,plain,
( spl0_1015
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f3486,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
| c_HOL_Oord__class_Oless(X2,X1,X0) )
| ~ spl0_125
| ~ spl0_251 ),
inference(duplicate_literal_removal,[],[f3451]) ).
fof(f3451,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_125
| ~ spl0_251 ),
inference(resolution,[],[f2981,f1629]) ).
fof(f31172,plain,
( spl0_1014
| ~ spl0_68
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3475,f2980,f1311,f31170]) ).
fof(f31170,plain,
( spl0_1014
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Obot__class_Obot(X0)),X1)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f3475,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Obot__class_Obot(X0)),X1)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68
| ~ spl0_251 ),
inference(resolution,[],[f2981,f1312]) ).
fof(f31168,plain,
( spl0_1013
| ~ spl0_140
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3440,f2976,f1691,f31166]) ).
fof(f31166,plain,
( spl0_1013
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f2976,plain,
( spl0_250
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f3440,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
| c_lessequals(X1,X2,X0) )
| ~ spl0_140
| ~ spl0_250 ),
inference(duplicate_literal_removal,[],[f3401]) ).
fof(f3401,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_140
| ~ spl0_250 ),
inference(resolution,[],[f2977,f1692]) ).
fof(f2977,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1 )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2976]) ).
fof(f31164,plain,
( spl0_1012
| ~ spl0_125
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3438,f2976,f1628,f31162]) ).
fof(f31162,plain,
( spl0_1012
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f3438,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
| c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_125
| ~ spl0_250 ),
inference(duplicate_literal_removal,[],[f3403]) ).
fof(f3403,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_125
| ~ spl0_250 ),
inference(resolution,[],[f2977,f1629]) ).
fof(f31160,plain,
( spl0_1011
| ~ spl0_70
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3412,f2976,f1319,f31158]) ).
fof(f31158,plain,
( spl0_1011
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),c_Orderings_Otop__class_Otop(X0)),X1)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f3412,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),c_Orderings_Otop__class_Otop(X0)),X1)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_250 ),
inference(resolution,[],[f2977,f1320]) ).
fof(f31156,plain,
( spl0_1010
| ~ spl0_865
| ~ spl0_983 ),
inference(avatar_split_clause,[],[f30716,f26864,f24804,f31154]) ).
fof(f31154,plain,
( spl0_1010
<=> ! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oimage(X1,v_U,X0,X2),hAPP(X1,v_x))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f26864,plain,
( spl0_983
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),hAPP(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f30716,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oimage(X1,v_U,X0,X2),hAPP(X1,v_x)))
| ~ spl0_865
| ~ spl0_983 ),
inference(superposition,[],[f26865,f24805]) ).
fof(f26865,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),hAPP(X0,X1)))
| ~ spl0_983 ),
inference(avatar_component_clause,[],[f26864]) ).
fof(f31152,plain,
( spl0_1009
| ~ spl0_140
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3392,f2968,f1691,f31150]) ).
fof(f31150,plain,
( spl0_1009
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f2968,plain,
( spl0_248
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3392,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
| c_lessequals(X2,X1,X0) )
| ~ spl0_140
| ~ spl0_248 ),
inference(duplicate_literal_removal,[],[f3353]) ).
fof(f3353,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_140
| ~ spl0_248 ),
inference(resolution,[],[f2969,f1692]) ).
fof(f2969,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2 )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2968]) ).
fof(f31148,plain,
( spl0_1008
| ~ spl0_125
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3390,f2968,f1628,f31146]) ).
fof(f31146,plain,
( spl0_1008
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f3390,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
| c_HOL_Oord__class_Oless(X2,X1,X0) )
| ~ spl0_125
| ~ spl0_248 ),
inference(duplicate_literal_removal,[],[f3355]) ).
fof(f3355,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_125
| ~ spl0_248 ),
inference(resolution,[],[f2969,f1629]) ).
fof(f31144,plain,
( spl0_1007
| ~ spl0_70
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3364,f2968,f1319,f31142]) ).
fof(f31142,plain,
( spl0_1007
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),c_Orderings_Otop__class_Otop(X0))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f3364,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),c_Orderings_Otop__class_Otop(X0))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_248 ),
inference(resolution,[],[f2969,f1320]) ).
fof(f31096,plain,
( ~ spl0_21
| spl0_1006
| ~ spl0_77
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f3160,f2939,f1349,f31094,f1103]) ).
fof(f1103,plain,
( spl0_21
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f31094,plain,
( spl0_1006
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f2939,plain,
( spl0_241
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X19,X2,X0)
| c_HOL_Oord__class_Oless(X19,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f3160,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat) )
| ~ spl0_77
| ~ spl0_241 ),
inference(resolution,[],[f2940,f1350]) ).
fof(f2940,plain,
( ! [X2,X0,X1,X19] :
( ~ c_lessequals(X19,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X19,X1,X0) )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2939]) ).
fof(f31092,plain,
( spl0_1005
| ~ spl0_68
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3141,f2931,f1311,f31090]) ).
fof(f31090,plain,
( spl0_1005
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
| c_lessequals(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f2931,plain,
( spl0_239
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f3141,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
| c_lessequals(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68
| ~ spl0_239 ),
inference(resolution,[],[f2932,f1312]) ).
fof(f2932,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X2,X1,X0) )
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2931]) ).
fof(f31088,plain,
( spl0_1004
| ~ spl0_70
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3126,f2931,f1319,f31086]) ).
fof(f31086,plain,
( spl0_1004
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Otop__class_Otop(X0),X0)
| c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f3126,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Otop__class_Otop(X0),X0)
| c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_239 ),
inference(resolution,[],[f2932,f1320]) ).
fof(f31084,plain,
( spl0_1003
| ~ spl0_79
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2929,f2584,f1357,f31082]) ).
fof(f31082,plain,
( spl0_1003
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(c_in(X3,c_Set_Ovimage(c_COMBK(X0,X1,X2),c_fequal(X0,X4),X5,X4),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f2584,plain,
( spl0_235
<=> ! [X53,X0,X14,X25] : hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(hAPP(X25,X14),X0),X53,X0),X53)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2929,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(c_in(X3,c_Set_Ovimage(c_COMBK(X0,X1,X2),c_fequal(X0,X4),X5,X4),X5))
| ~ spl0_79
| ~ spl0_235 ),
inference(superposition,[],[f2585,f1358]) ).
fof(f2585,plain,
( ! [X0,X14,X53,X25] : hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(hAPP(X25,X14),X0),X53,X0),X53))
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2584]) ).
fof(f31080,plain,
( spl0_1002
| ~ spl0_129
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2799,f2502,f1644,f31078]) ).
fof(f31078,plain,
( spl0_1002
<=> ! [X0,X1] :
( c_lessequals(c_Suc(X0),X1,tc_nat)
| c_Suc(X1) = c_Suc(X0)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f2799,plain,
( ! [X0,X1] :
( c_lessequals(c_Suc(X0),X1,tc_nat)
| c_Suc(X1) = c_Suc(X0)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_129
| ~ spl0_216 ),
inference(resolution,[],[f2503,f1645]) ).
fof(f31076,plain,
( spl0_1001
| ~ spl0_133
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2763,f2498,f1660,f31074]) ).
fof(f31074,plain,
( spl0_1001
<=> ! [X0,X1] :
( c_Suc(X1) = c_Suc(X0)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f2763,plain,
( ! [X0,X1] :
( c_Suc(X1) = c_Suc(X0)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_133
| ~ spl0_215 ),
inference(resolution,[],[f2499,f1661]) ).
fof(f31069,plain,
( spl0_1000
| ~ spl0_89
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2659,f2478,f1402,f31067]) ).
fof(f31067,plain,
( spl0_1000
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f1402,plain,
( spl0_89
<=> ! [X13,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f2659,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_89
| ~ spl0_210 ),
inference(resolution,[],[f2479,f1403]) ).
fof(f1403,plain,
( ! [X4,X13] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1402]) ).
fof(f31065,plain,
( spl0_999
| ~ spl0_92
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2658,f2478,f1414,f31063]) ).
fof(f31063,plain,
( spl0_999
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f1414,plain,
( spl0_92
<=> ! [X13,X4] :
( ~ c_lessequals(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f2658,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) )
| ~ spl0_92
| ~ spl0_210 ),
inference(resolution,[],[f2479,f1415]) ).
fof(f1415,plain,
( ! [X4,X13] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat)
| ~ c_lessequals(X4,X13,tc_nat) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1414]) ).
fof(f31061,plain,
( spl0_998
| ~ spl0_100
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2657,f2478,f1446,f31059]) ).
fof(f31059,plain,
( spl0_998
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f1446,plain,
( spl0_100
<=> ! [X13,X4] :
( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f2657,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
| ~ spl0_100
| ~ spl0_210 ),
inference(resolution,[],[f2479,f1447]) ).
fof(f1447,plain,
( ! [X4,X13] :
( c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat)
| c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1446]) ).
fof(f31057,plain,
( spl0_997
| ~ spl0_129
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2371,f2270,f1644,f31055]) ).
fof(f31055,plain,
( spl0_997
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f2371,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) )
| ~ spl0_129
| ~ spl0_191 ),
inference(resolution,[],[f2271,f1645]) ).
fof(f31053,plain,
( spl0_996
| ~ spl0_62
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1871,f1711,f1287,f31051]) ).
fof(f31051,plain,
( spl0_996
<=> ! [X2,X0,X1] :
( c_fequal(X0,tc_fun(X1,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f1287,plain,
( spl0_62
<=> ! [X55,X56] :
( ~ class_Orderings_Oorder(X56)
| class_Orderings_Oorder(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1711,plain,
( spl0_145
<=> ! [X0,X14] :
( c_fequal(X14,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X14,X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1871,plain,
( ! [X2,X0,X1] :
( c_fequal(X0,tc_fun(X1,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_62
| ~ spl0_145 ),
inference(resolution,[],[f1712,f1288]) ).
fof(f1288,plain,
( ! [X56,X55] :
( class_Orderings_Oorder(tc_fun(X55,X56))
| ~ class_Orderings_Oorder(X56) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f1712,plain,
( ! [X0,X14] :
( ~ class_Orderings_Oorder(X0)
| c_fequal(X14,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X14,X0) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1711]) ).
fof(f31049,plain,
( spl0_995
| ~ spl0_112
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1834,f1680,f1494,f31047]) ).
fof(f31047,plain,
( spl0_995
<=> ! [X4,X0,X3,X2,X1] : c_Finite__Set_Ofold1(X0,X1) = c_Fun_Ofun__upd(c_Finite__Set_Ofold1(X0,X1),c_fequal(X2,X1),X2,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f1680,plain,
( spl0_138
<=> ! [X20,X0,X25,X1] : c_Fun_Ofun__upd(X25,X1,hAPP(X25,X1),X20,X0) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1834,plain,
( ! [X2,X3,X0,X1,X4] : c_Finite__Set_Ofold1(X0,X1) = c_Fun_Ofun__upd(c_Finite__Set_Ofold1(X0,X1),c_fequal(X2,X1),X2,X3,X4)
| ~ spl0_112
| ~ spl0_138 ),
inference(superposition,[],[f1681,f1495]) ).
fof(f1681,plain,
( ! [X0,X1,X25,X20] : c_Fun_Ofun__upd(X25,X1,hAPP(X25,X1),X20,X0) = X25
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1680]) ).
fof(f31045,plain,
( spl0_994
| ~ spl0_79
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1833,f1680,f1357,f31043]) ).
fof(f31043,plain,
( spl0_994
<=> ! [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_994])]) ).
fof(f1833,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_79
| ~ spl0_138 ),
inference(superposition,[],[f1681,f1358]) ).
fof(f30896,plain,
( spl0_993
| ~ spl0_3
| ~ spl0_981 ),
inference(avatar_split_clause,[],[f30690,f26856,f1013,f30893]) ).
fof(f30893,plain,
( spl0_993
<=> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),v_G,t_a,tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f1013,plain,
( spl0_3
<=> v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f26856,plain,
( spl0_981
<=> ! [X0,X3,X2,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f30690,plain,
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),v_G,t_a,tc_Com_Opname)
| ~ spl0_3
| ~ spl0_981 ),
inference(superposition,[],[f26857,f1015]) ).
fof(f1015,plain,
( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1013]) ).
fof(f26857,plain,
( ! [X2,X3,X0,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2)
| ~ spl0_981 ),
inference(avatar_component_clause,[],[f26856]) ).
fof(f29423,plain,
( ~ spl0_37
| spl0_992
| ~ spl0_254
| ~ spl0_908 ),
inference(avatar_split_clause,[],[f26111,f25990,f2996,f29421,f1183]) ).
fof(f1183,plain,
( spl0_37
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f29421,plain,
( spl0_992
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(v_U,c_fequal(v_x,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f2996,plain,
( spl0_254
<=> ! [X20,X0,X25,X21] :
( ~ class_HOL_Oord(X20)
| ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
| ~ c_lessequals(X21,X25,tc_fun(X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f25990,plain,
( spl0_908
<=> ! [X0] : c_lessequals(c_fequal(v_x,X0),v_U,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f26111,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(v_U,c_fequal(v_x,X0),tc_fun(X0,tc_bool))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_254
| ~ spl0_908 ),
inference(resolution,[],[f25991,f2997]) ).
fof(f2997,plain,
( ! [X21,X0,X25,X20] :
( ~ c_lessequals(X21,X25,tc_fun(X0,X20))
| ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
| ~ class_HOL_Oord(X20) )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2996]) ).
fof(f25991,plain,
( ! [X0] : c_lessequals(c_fequal(v_x,X0),v_U,tc_fun(X0,tc_bool))
| ~ spl0_908 ),
inference(avatar_component_clause,[],[f25990]) ).
fof(f28850,plain,
( spl0_991
| ~ spl0_272
| ~ spl0_908 ),
inference(avatar_split_clause,[],[f26091,f25990,f3069,f28848]) ).
fof(f28848,plain,
( spl0_991
<=> ! [X0,X1] :
( hBOOL(hAPP(v_U,X0))
| ~ hBOOL(hAPP(c_fequal(v_x,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f3069,plain,
( spl0_272
<=> ! [X0,X50,X1,X26] :
( ~ hBOOL(hAPP(X26,X1))
| hBOOL(hAPP(X50,X1))
| ~ c_lessequals(X26,X50,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f26091,plain,
( ! [X0,X1] :
( hBOOL(hAPP(v_U,X0))
| ~ hBOOL(hAPP(c_fequal(v_x,X1),X0)) )
| ~ spl0_272
| ~ spl0_908 ),
inference(resolution,[],[f25991,f3070]) ).
fof(f3070,plain,
( ! [X50,X0,X1,X26] :
( ~ c_lessequals(X26,X50,tc_fun(X0,tc_bool))
| hBOOL(hAPP(X50,X1))
| ~ hBOOL(hAPP(X26,X1)) )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f3069]) ).
fof(f28272,plain,
( spl0_990
| ~ spl0_861
| ~ spl0_959 ),
inference(avatar_split_clause,[],[f26379,f26298,f23922,f28270]) ).
fof(f28270,plain,
( spl0_990
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_G,X0),hAPP(v_mgt__call,v_x))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f23922,plain,
( spl0_861
<=> ! [X2,X0,X1,X3] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f26379,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_G,X0),hAPP(v_mgt__call,v_x)))
| ~ spl0_861
| ~ spl0_959 ),
inference(superposition,[],[f23923,f26299]) ).
fof(f23923,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0))
| ~ spl0_861 ),
inference(avatar_component_clause,[],[f23922]) ).
fof(f27134,plain,
( spl0_989
| ~ spl0_82
| ~ spl0_959 ),
inference(avatar_split_clause,[],[f26342,f26298,f1369,f27132]) ).
fof(f27132,plain,
( spl0_989
<=> ! [X0] : hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f26342,plain,
( ! [X0] : hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,X0))
| ~ spl0_82
| ~ spl0_959 ),
inference(superposition,[],[f1370,f26299]) ).
fof(f26886,plain,
( spl0_988
| ~ spl0_173
| ~ spl0_186
| ~ spl0_225
| ~ spl0_400
| ~ spl0_637 ),
inference(avatar_split_clause,[],[f13866,f13548,f6703,f2538,f2032,f1978,f26884]) ).
fof(f26884,plain,
( spl0_988
<=> ! [X0,X3,X2,X1] : hAPP(X2,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_fequal(X0,X1),X2,X1,tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f2538,plain,
( spl0_225
<=> ! [X6,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f6703,plain,
( spl0_400
<=> ! [X20,X0,X6,X8] : c_HOL_Ominus__class_Ominus(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f13548,plain,
( spl0_637
<=> ! [X20,X0,X14,X6,X8] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X14,X6,X20),X8,X20,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X8,X14)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f13866,plain,
( ! [X2,X3,X0,X1] : hAPP(X2,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_fequal(X0,X1),X2,X1,tc_fun(X3,tc_bool))
| ~ spl0_173
| ~ spl0_186
| ~ spl0_225
| ~ spl0_400
| ~ spl0_637 ),
inference(forward_demodulation,[],[f13865,f2539]) ).
fof(f2539,plain,
( ! [X0,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X6
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2538]) ).
fof(f13865,plain,
( ! [X2,X3,X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_fequal(X0,X1),X2,X1,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X2,X0)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
| ~ spl0_173
| ~ spl0_186
| ~ spl0_400
| ~ spl0_637 ),
inference(forward_demodulation,[],[f13766,f6986]) ).
fof(f6986,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,tc_fun(X2,tc_bool))
| ~ spl0_173
| ~ spl0_400 ),
inference(superposition,[],[f6704,f1979]) ).
fof(f6704,plain,
( ! [X0,X8,X6,X20] : c_HOL_Ominus__class_Ominus(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f6703]) ).
fof(f13766,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_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_fequal(X0,X1),X2,X1,tc_fun(X3,tc_bool))
| ~ spl0_186
| ~ spl0_637 ),
inference(superposition,[],[f13549,f2033]) ).
fof(f13549,plain,
( ! [X0,X8,X6,X14,X20] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X14,X6,X20),X8,X20,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X8,X14)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool)))
| ~ spl0_637 ),
inference(avatar_component_clause,[],[f13548]) ).
fof(f26882,plain,
( spl0_987
| ~ spl0_54
| ~ spl0_186
| ~ spl0_262
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f10593,f10355,f3028,f2032,f1255,f26880]) ).
fof(f26880,plain,
( spl0_987
<=> ! [X0,X1] : c_Finite__Set_Ocard(c_fequal(X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f1255,plain,
( spl0_54
<=> ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f10355,plain,
( spl0_528
<=> ! [X6,X0,X1] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0))
| ~ c_Finite__Set_Ofinite(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f10593,plain,
( ! [X0,X1] : c_Finite__Set_Ocard(c_fequal(X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))
| ~ spl0_54
| ~ spl0_186
| ~ spl0_262
| ~ spl0_528 ),
inference(forward_demodulation,[],[f10592,f2033]) ).
fof(f10592,plain,
( ! [X0,X1] : c_Finite__Set_Ocard(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))
| ~ spl0_54
| ~ spl0_262
| ~ spl0_528 ),
inference(forward_demodulation,[],[f10581,f3029]) ).
fof(f10581,plain,
( ! [X0,X1] : c_Finite__Set_Ocard(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_fequal(X0,X1),tc_fun(X1,tc_bool)),X1))
| ~ spl0_54
| ~ spl0_528 ),
inference(resolution,[],[f10356,f1256]) ).
fof(f1256,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1255]) ).
fof(f10356,plain,
( ! [X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0)) )
| ~ spl0_528 ),
inference(avatar_component_clause,[],[f10355]) ).
fof(f26878,plain,
( spl0_986
| ~ spl0_416
| ~ spl0_519 ),
inference(avatar_split_clause,[],[f10389,f10283,f7246,f26876]) ).
fof(f26876,plain,
( spl0_986
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f7246,plain,
( spl0_416
<=> ! [X6,X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f10389,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1
| ~ spl0_416
| ~ spl0_519 ),
inference(trivial_inequality_removal,[],[f10384]) ).
fof(f10384,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_416
| ~ spl0_519 ),
inference(superposition,[],[f10284,f7247]) ).
fof(f7247,plain,
( ! [X0,X8,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)))
| ~ spl0_416 ),
inference(avatar_component_clause,[],[f7246]) ).
fof(f26874,plain,
( spl0_985
| ~ spl0_186
| ~ spl0_233
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f9288,f8165,f2576,f2032,f26872]) ).
fof(f26872,plain,
( spl0_985
<=> ! [X0,X3,X2,X1] : c_Set_Oimage(X2,c_fequal(X0,X1),X1,X3) = c_fequal(hAPP(X2,X0),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f2576,plain,
( spl0_233
<=> ! [X20,X0,X25] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f9288,plain,
( ! [X2,X3,X0,X1] : c_Set_Oimage(X2,c_fequal(X0,X1),X1,X3) = c_fequal(hAPP(X2,X0),X3)
| ~ spl0_186
| ~ spl0_233
| ~ spl0_477 ),
inference(forward_demodulation,[],[f9287,f2033]) ).
fof(f9287,plain,
( ! [X2,X3,X0,X1] : c_Set_Oimage(X2,c_fequal(X0,X1),X1,X3) = c_Set_Oinsert(hAPP(X2,X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ spl0_186
| ~ spl0_233
| ~ spl0_477 ),
inference(forward_demodulation,[],[f9222,f2577]) ).
fof(f2577,plain,
( ! [X0,X25,X20] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0)
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2576]) ).
fof(f9222,plain,
( ! [X2,X3,X0,X1] : c_Set_Oinsert(hAPP(X2,X0),c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X3),X3) = c_Set_Oimage(X2,c_fequal(X0,X1),X1,X3)
| ~ spl0_186
| ~ spl0_477 ),
inference(superposition,[],[f8166,f2033]) ).
fof(f26870,plain,
( spl0_984
| ~ spl0_106
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f9268,f8165,f1470,f26868]) ).
fof(f1470,plain,
( spl0_106
<=> ! [X6,X0,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X14,X6,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f9268,plain,
( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ spl0_106
| ~ spl0_477 ),
inference(superposition,[],[f1471,f8166]) ).
fof(f1471,plain,
( ! [X0,X6,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X14,X6,X0)
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f26866,plain,
( spl0_983
| ~ spl0_72
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f9265,f8165,f1327,f26864]) ).
fof(f1327,plain,
( spl0_72
<=> ! [X6,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,X6,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f9265,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),hAPP(X0,X1)))
| ~ spl0_72
| ~ spl0_477 ),
inference(superposition,[],[f1328,f8166]) ).
fof(f1328,plain,
( ! [X0,X1,X6] : hBOOL(hAPP(c_Set_Oinsert(X1,X6,X0),X1))
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1327]) ).
fof(f26862,plain,
( spl0_982
| ~ spl0_174
| ~ spl0_186
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f9180,f8153,f2032,f1982,f26860]) ).
fof(f26860,plain,
( spl0_982
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,c_fequal(X0,X1),tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f1982,plain,
( spl0_174
<=> ! [X6,X0] : c_HOL_Ominus__class_Ominus(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f8153,plain,
( spl0_474
<=> ! [X0,X14,X6,X8] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f9180,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,c_fequal(X0,X1),tc_fun(X1,tc_bool)),X1) )
| ~ spl0_174
| ~ spl0_186
| ~ spl0_474 ),
inference(forward_demodulation,[],[f9170,f1983]) ).
fof(f1983,plain,
( ! [X0,X6] : c_HOL_Ominus__class_Ominus(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1982]) ).
fof(f9170,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,c_fequal(X0,X1),tc_fun(X1,tc_bool)),X1)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X1) )
| ~ spl0_186
| ~ spl0_474 ),
inference(superposition,[],[f8154,f2033]) ).
fof(f8154,plain,
( ! [X0,X8,X6,X14] :
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_474 ),
inference(avatar_component_clause,[],[f8153]) ).
fof(f26858,plain,
( spl0_981
| ~ spl0_51
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f9020,f8125,f1243,f26856]) ).
fof(f1243,plain,
( spl0_51
<=> ! [X0,X1] : c_lessequals(X1,X1,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f8125,plain,
( spl0_467
<=> ! [X20,X0,X6,X25,X8] :
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X8,X0,X20)
| ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f9020,plain,
( ! [X2,X3,X0,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2)
| ~ spl0_51
| ~ spl0_467 ),
inference(resolution,[],[f8126,f1244]) ).
fof(f1244,plain,
( ! [X0,X1] : c_lessequals(X1,X1,tc_fun(X0,tc_bool))
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1243]) ).
fof(f8126,plain,
( ! [X0,X8,X6,X25,X20] :
( ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X8,X0,X20) )
| ~ spl0_467 ),
inference(avatar_component_clause,[],[f8125]) ).
fof(f26806,plain,
( ~ spl0_19
| spl0_980
| ~ spl0_21
| ~ spl0_42
| ~ spl0_145
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f8008,f7340,f1711,f1207,f1103,f26804,f1093]) ).
fof(f26804,plain,
( spl0_980
<=> ! [X0] : c_fequal(X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f1207,plain,
( spl0_42
<=> ! [X13] : c_lessequals(X13,X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f7340,plain,
( spl0_437
<=> ! [X5,X0,X3] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X3,c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0),X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f8008,plain,
( ! [X0] :
( c_fequal(X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_21
| ~ spl0_42
| ~ spl0_145
| ~ spl0_437 ),
inference(forward_demodulation,[],[f7933,f1869]) ).
fof(f1869,plain,
( ! [X0] : c_fequal(X0,tc_nat) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_21
| ~ spl0_145 ),
inference(resolution,[],[f1712,f1105]) ).
fof(f1105,plain,
( class_Orderings_Oorder(tc_nat)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f7933,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat) )
| ~ spl0_42
| ~ spl0_437 ),
inference(resolution,[],[f7341,f1208]) ).
fof(f1208,plain,
( ! [X13] : c_lessequals(X13,X13,tc_nat)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f7341,plain,
( ! [X3,X0,X5] :
( ~ c_lessequals(X3,X5,X0)
| ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X3,c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0),X0) )
| ~ spl0_437 ),
inference(avatar_component_clause,[],[f7340]) ).
fof(f26754,plain,
( ~ spl0_19
| spl0_979
| ~ spl0_21
| ~ spl0_42
| ~ spl0_145
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f7932,f7336,f1711,f1207,f1103,f26752,f1093]) ).
fof(f26752,plain,
( spl0_979
<=> ! [X0] : c_fequal(X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f7336,plain,
( spl0_436
<=> ! [X5,X0,X3] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X5,c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0),X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f7932,plain,
( ! [X0] :
( c_fequal(X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_21
| ~ spl0_42
| ~ spl0_145
| ~ spl0_436 ),
inference(forward_demodulation,[],[f7857,f1869]) ).
fof(f7857,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat) )
| ~ spl0_42
| ~ spl0_436 ),
inference(resolution,[],[f7337,f1208]) ).
fof(f7337,plain,
( ! [X3,X0,X5] :
( ~ c_lessequals(X3,X5,X0)
| ~ class_Orderings_Olinorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X5,c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0),X0) )
| ~ spl0_436 ),
inference(avatar_component_clause,[],[f7336]) ).
fof(f26750,plain,
( spl0_978
| ~ spl0_80
| ~ spl0_233
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f6542,f6034,f2576,f1361,f26748]) ).
fof(f26748,plain,
( spl0_978
<=> ! [X2,X0] : c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f1361,plain,
( spl0_80
<=> ! [X20,X0,X25] : c_Fun_Oinj__on(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f6034,plain,
( spl0_379
<=> ! [X20,X0,X6,X25] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f6542,plain,
( ! [X2,X0] : c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ spl0_80
| ~ spl0_233
| ~ spl0_379 ),
inference(forward_demodulation,[],[f6539,f2577]) ).
fof(f6539,plain,
( ! [X2,X0,X1] : c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Finite__Set_Ocard(c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X2),X2)
| ~ spl0_80
| ~ spl0_379 ),
inference(resolution,[],[f6035,f1362]) ).
fof(f1362,plain,
( ! [X0,X25,X20] : c_Fun_Oinj__on(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20)
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1361]) ).
fof(f6035,plain,
( ! [X0,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) )
| ~ spl0_379 ),
inference(avatar_component_clause,[],[f6034]) ).
fof(f26746,plain,
( spl0_977
| ~ spl0_106
| ~ spl0_959 ),
inference(avatar_split_clause,[],[f26344,f26298,f1470,f26744]) ).
fof(f26744,plain,
( spl0_977
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != v_G ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f26344,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != v_G
| ~ spl0_106
| ~ spl0_959 ),
inference(superposition,[],[f1471,f26299]) ).
fof(f26742,plain,
( spl0_976
| ~ spl0_105
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f6517,f6030,f1466,f26740]) ).
fof(f26740,plain,
( spl0_976
<=> ! [X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f1466,plain,
( spl0_105
<=> ! [X6,X0] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f6030,plain,
( spl0_378
<=> ! [X20,X0,X6,X25,X8] :
( ~ c_Fun_Oinj__on(X25,X8,X0,X20)
| c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f6517,plain,
( ! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) )
| ~ spl0_105
| ~ spl0_378 ),
inference(resolution,[],[f6031,f1467]) ).
fof(f1467,plain,
( ! [X0,X6] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1466]) ).
fof(f6031,plain,
( ! [X0,X8,X6,X25,X20] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_Fun_Oinj__on(X25,X8,X0,X20) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f6030]) ).
fof(f26631,plain,
( spl0_975
| ~ spl0_37
| ~ spl0_103
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f6293,f5988,f1458,f1183,f26629]) ).
fof(f26629,plain,
( spl0_975
<=> ! [X2,X0,X1] : c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),hAPP(X2,X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f1458,plain,
( spl0_103
<=> ! [X6,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f6293,plain,
( ! [X2,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),hAPP(X2,X1),tc_bool) )
| ~ spl0_103
| ~ spl0_369 ),
inference(resolution,[],[f5989,f1459]) ).
fof(f1459,plain,
( ! [X0,X6] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1458]) ).
fof(f26511,plain,
( spl0_974
| ~ spl0_37
| ~ spl0_104
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f6278,f5988,f1462,f1183,f26509]) ).
fof(f26509,plain,
( spl0_974
<=> ! [X0,X3,X2,X1] : c_lessequals(hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X0,X3),X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f1462,plain,
( spl0_104
<=> ! [X0,X8,X14] : c_lessequals(X8,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f6278,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X0,X3),X1),tc_bool) )
| ~ spl0_104
| ~ spl0_369 ),
inference(resolution,[],[f5989,f1463]) ).
fof(f1463,plain,
( ! [X0,X8,X14] : c_lessequals(X8,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool))
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f26401,plain,
( spl0_973
| ~ spl0_37
| ~ spl0_105
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f6276,f5988,f1466,f1183,f26399]) ).
fof(f26399,plain,
( spl0_973
<=> ! [X2,X0,X1] : c_lessequals(hAPP(X0,X1),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f6276,plain,
( ! [X2,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(X0,X1),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1),tc_bool) )
| ~ spl0_105
| ~ spl0_369 ),
inference(resolution,[],[f5989,f1467]) ).
fof(f26397,plain,
( spl0_972
| ~ spl0_104
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f6135,f5963,f1462,f26395]) ).
fof(f26395,plain,
( spl0_972
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X1,X2,X0)),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f5963,plain,
( spl0_363
<=> ! [X6,X0,X8] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f6135,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X1,X2,X0)),X2) = X2
| ~ spl0_104
| ~ spl0_363 ),
inference(resolution,[],[f5964,f1463]) ).
fof(f5964,plain,
( ! [X0,X8,X6] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X8 )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f5963]) ).
fof(f26393,plain,
( spl0_971
| ~ spl0_104
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f6091,f5959,f1462,f26391]) ).
fof(f26391,plain,
( spl0_971
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),c_Set_Oinsert(X2,X1,X0)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f5959,plain,
( spl0_362
<=> ! [X6,X0,X8] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f6091,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),c_Set_Oinsert(X2,X1,X0)) = X1
| ~ spl0_104
| ~ spl0_362 ),
inference(resolution,[],[f5960,f1463]) ).
fof(f5960,plain,
( ! [X0,X8,X6] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X6 )
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f5959]) ).
fof(f26389,plain,
( spl0_970
| ~ spl0_347
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f5933,f4368,f4320,f26387]) ).
fof(f26387,plain,
( spl0_970
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X0),X3))
| ~ hBOOL(hAPP(c_fequal(X1,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f4320,plain,
( spl0_347
<=> ! [X6,X0,X1,X8] :
( ~ hBOOL(hAPP(X6,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f5933,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X0),X3))
| ~ hBOOL(hAPP(c_fequal(X1,X0),X3)) )
| ~ spl0_347
| ~ spl0_358 ),
inference(superposition,[],[f4321,f4369]) ).
fof(f4321,plain,
( ! [X0,X1,X8,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1))
| ~ hBOOL(hAPP(X6,X1)) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f4320]) ).
fof(f26340,plain,
( spl0_969
| ~ spl0_186
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f5928,f4364,f2032,f26338]) ).
fof(f26338,plain,
( spl0_969
<=> ! [X2,X0,X1] : c_Set_Oinsert(X2,c_fequal(X0,X1),X1) = c_Set_Oinsert(X0,c_fequal(X2,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f4364,plain,
( spl0_357
<=> ! [X0,X6,X2,X1] : c_Set_Oinsert(X1,c_Set_Oinsert(X2,X6,X0),X0) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X6,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f5928,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X2,c_fequal(X0,X1),X1) = c_Set_Oinsert(X0,c_fequal(X2,X1),X1)
| ~ spl0_186
| ~ spl0_357 ),
inference(forward_demodulation,[],[f5888,f2033]) ).
fof(f5888,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X0,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = c_Set_Oinsert(X2,c_fequal(X0,X1),X1)
| ~ spl0_186
| ~ spl0_357 ),
inference(superposition,[],[f4365,f2033]) ).
fof(f4365,plain,
( ! [X2,X0,X1,X6] : c_Set_Oinsert(X1,c_Set_Oinsert(X2,X6,X0),X0) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X6,X0),X0)
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f4364]) ).
fof(f26336,plain,
( spl0_968
| ~ spl0_32
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f5428,f4280,f1158,f26334]) ).
fof(f26334,plain,
( spl0_968
<=> ! [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_968])]) ).
fof(f1158,plain,
( spl0_32
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f4280,plain,
( spl0_337
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f5428,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_32
| ~ spl0_337 ),
inference(resolution,[],[f4281,f1160]) ).
fof(f1160,plain,
( class_Lattices_Olattice(tc_bool)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f4281,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) )
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f4280]) ).
fof(f26332,plain,
( spl0_967
| ~ spl0_48
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5353,f4256,f1231,f26330]) ).
fof(f26330,plain,
( spl0_967
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f1231,plain,
( spl0_48
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f4256,plain,
( spl0_331
<=> ! [X0,X14,X16,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X16,X0)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f5353,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_48
| ~ spl0_331 ),
inference(resolution,[],[f4257,f1232]) ).
fof(f1232,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1231]) ).
fof(f4257,plain,
( ! [X0,X1,X16,X14] :
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0)
| ~ c_HOL_Oord__class_Oless(X1,X16,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f4256]) ).
fof(f26328,plain,
( spl0_966
| ~ spl0_48
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f5321,f4252,f1231,f26326]) ).
fof(f26326,plain,
( spl0_966
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f4252,plain,
( spl0_330
<=> ! [X0,X14,X16,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X14,X0)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f5321,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_48
| ~ spl0_330 ),
inference(resolution,[],[f4253,f1232]) ).
fof(f4253,plain,
( ! [X0,X1,X16,X14] :
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0)
| ~ c_HOL_Oord__class_Oless(X1,X14,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f4252]) ).
fof(f26324,plain,
( spl0_965
| ~ spl0_19
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f5307,f4232,f1093,f26322]) ).
fof(f26322,plain,
( spl0_965
<=> ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f4232,plain,
( spl0_325
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f5307,plain,
( ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X0)
| ~ spl0_19
| ~ spl0_325 ),
inference(resolution,[],[f4233,f1095]) ).
fof(f1095,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f1093]) ).
fof(f4233,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1) )
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f4232]) ).
fof(f26320,plain,
( spl0_964
| ~ spl0_15
| ~ spl0_242
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4896,f4162,f2943,f1073,f26318]) ).
fof(f26318,plain,
( spl0_964
<=> ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f4162,plain,
( spl0_308
<=> ! [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),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f4896,plain,
( ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X0)
| ~ spl0_15
| ~ spl0_242
| ~ spl0_308 ),
inference(forward_demodulation,[],[f4893,f2945]) ).
fof(f4893,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_15
| ~ spl0_308 ),
inference(resolution,[],[f4163,f1075]) ).
fof(f1075,plain,
( class_Lattices_Olower__semilattice(tc_nat)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f4163,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),X2),X1) )
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f4162]) ).
fof(f26316,plain,
( spl0_963
| ~ spl0_27
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4894,f4162,f1133,f26314]) ).
fof(f26314,plain,
( spl0_963
<=> ! [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_963])]) ).
fof(f1133,plain,
( spl0_27
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f4894,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_27
| ~ spl0_308 ),
inference(resolution,[],[f4163,f1135]) ).
fof(f1135,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f1133]) ).
fof(f26312,plain,
( spl0_962
| ~ spl0_9
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f4811,f4138,f1043,f26310]) ).
fof(f26310,plain,
( spl0_962
<=> ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f1043,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f4138,plain,
( spl0_302
<=> ! [X0,X16,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f4811,plain,
( ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)
| ~ spl0_9
| ~ spl0_302 ),
inference(resolution,[],[f4139,f1045]) ).
fof(f1045,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f4139,plain,
( ! [X0,X16,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X14) )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f4138]) ).
fof(f26308,plain,
( spl0_961
| ~ spl0_48
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f4723,f4119,f1231,f26306]) ).
fof(f26306,plain,
( spl0_961
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f4119,plain,
( spl0_298
<=> ! [X0,X14,X16,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X14,X1,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f4723,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_48
| ~ spl0_298 ),
inference(resolution,[],[f4120,f1232]) ).
fof(f4120,plain,
( ! [X0,X1,X16,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0)
| ~ c_HOL_Oord__class_Oless(X14,X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f4119]) ).
fof(f26304,plain,
( spl0_960
| ~ spl0_48
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4687,f4115,f1231,f26302]) ).
fof(f26302,plain,
( spl0_960
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f4115,plain,
( spl0_297
<=> ! [X0,X14,X16,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X16,X1,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f4687,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_48
| ~ spl0_297 ),
inference(resolution,[],[f4116,f1232]) ).
fof(f4116,plain,
( ! [X0,X1,X16,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0)
| ~ c_HOL_Oord__class_Oless(X16,X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f4115]) ).
fof(f26300,plain,
( spl0_959
| ~ spl0_746
| ~ spl0_852 ),
inference(avatar_split_clause,[],[f24438,f23886,f20403,f26298]) ).
fof(f20403,plain,
( spl0_746
<=> hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_x))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f23886,plain,
( spl0_852
<=> ! [X2,X0,X1] :
( c_Set_Oinsert(X0,X1,X2) = X1
| ~ hBOOL(hAPP(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f24438,plain,
( ! [X0] : v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,X0)
| ~ spl0_746
| ~ spl0_852 ),
inference(resolution,[],[f23887,f20405]) ).
fof(f20405,plain,
( hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_x)))
| ~ spl0_746 ),
inference(avatar_component_clause,[],[f20403]) ).
fof(f23887,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X0))
| c_Set_Oinsert(X0,X1,X2) = X1 )
| ~ spl0_852 ),
inference(avatar_component_clause,[],[f23886]) ).
fof(f26296,plain,
( spl0_958
| ~ spl0_20
| ~ spl0_116
| ~ spl0_242
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4682,f4111,f2943,f1513,f1098,f26294]) ).
fof(f26294,plain,
( spl0_958
<=> ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f4111,plain,
( spl0_296
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f4682,plain,
( ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)) = X0
| ~ spl0_20
| ~ spl0_116
| ~ spl0_242
| ~ spl0_296 ),
inference(forward_demodulation,[],[f4681,f2945]) ).
fof(f4681,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)) = X0
| ~ spl0_20
| ~ spl0_116
| ~ spl0_296 ),
inference(forward_demodulation,[],[f4678,f1515]) ).
fof(f4678,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_20
| ~ spl0_296 ),
inference(resolution,[],[f4112,f1100]) ).
fof(f1100,plain,
( class_Lattices_Olattice(tc_nat)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f1098]) ).
fof(f4112,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1 )
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f4111]) ).
fof(f26292,plain,
( spl0_957
| ~ spl0_32
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4679,f4111,f1158,f26290]) ).
fof(f26290,plain,
( spl0_957
<=> ! [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_957])]) ).
fof(f4679,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_32
| ~ spl0_296 ),
inference(resolution,[],[f4112,f1160]) ).
fof(f26288,plain,
( spl0_956
| ~ spl0_20
| ~ spl0_116
| ~ spl0_242
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4677,f4107,f2943,f1513,f1098,f26286]) ).
fof(f26286,plain,
( spl0_956
<=> ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f4107,plain,
( spl0_295
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f4677,plain,
( ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1)) = X0
| ~ spl0_20
| ~ spl0_116
| ~ spl0_242
| ~ spl0_295 ),
inference(forward_demodulation,[],[f4676,f1515]) ).
fof(f4676,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1)) = X0
| ~ spl0_20
| ~ spl0_242
| ~ spl0_295 ),
inference(forward_demodulation,[],[f4673,f2945]) ).
fof(f4673,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_20
| ~ spl0_295 ),
inference(resolution,[],[f4108,f1100]) ).
fof(f4108,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1 )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f4107]) ).
fof(f26284,plain,
( spl0_955
| ~ spl0_32
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4674,f4107,f1158,f26282]) ).
fof(f26282,plain,
( spl0_955
<=> ! [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_955])]) ).
fof(f4674,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_32
| ~ spl0_295 ),
inference(resolution,[],[f4108,f1160]) ).
fof(f26280,plain,
( spl0_954
| ~ spl0_13
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4671,f4099,f1063,f26278]) ).
fof(f26278,plain,
( spl0_954
<=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f1063,plain,
( spl0_13
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f4099,plain,
( spl0_293
<=> ! [X0,X16,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f4671,plain,
( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)
| ~ spl0_13
| ~ spl0_293 ),
inference(resolution,[],[f4100,f1065]) ).
fof(f1065,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f1063]) ).
fof(f4100,plain,
( ! [X0,X16,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f4099]) ).
fof(f26276,plain,
( spl0_953
| ~ spl0_110
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4039,f3086,f1486,f26274]) ).
fof(f26274,plain,
( spl0_953
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),hAPP(X0,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1486,plain,
( spl0_110
<=> ! [X0,X1,X51] :
( hBOOL(hAPP(X51,X1))
| ~ hBOOL(c_in(X1,X51,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f4039,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),hAPP(X0,X3)))
| ~ spl0_110
| ~ spl0_276 ),
inference(resolution,[],[f3087,f1487]) ).
fof(f1487,plain,
( ! [X51,X0,X1] :
( ~ hBOOL(c_in(X1,X51,X0))
| hBOOL(hAPP(X51,X1)) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1486]) ).
fof(f26272,plain,
( spl0_952
| ~ spl0_165
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f4011,f3069,f1936,f26270]) ).
fof(f26270,plain,
( spl0_952
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1936,plain,
( spl0_165
<=> ! [X6,X0,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f4011,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),X1)) )
| ~ spl0_165
| ~ spl0_272 ),
inference(resolution,[],[f3070,f1937]) ).
fof(f1937,plain,
( ! [X0,X8,X6] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1936]) ).
fof(f26268,plain,
( spl0_951
| ~ spl0_68
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3972,f3065,f1311,f26266]) ).
fof(f26266,plain,
( spl0_951
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,X2,X1)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f3065,plain,
( spl0_271
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X19,X0)
| c_lessequals(X1,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f3972,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,X2,X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_68
| ~ spl0_271 ),
inference(resolution,[],[f3066,f1312]) ).
fof(f3066,plain,
( ! [X2,X0,X1,X19] :
( ~ c_lessequals(X2,X19,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X19,X0) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f3065]) ).
fof(f26264,plain,
( spl0_950
| ~ spl0_70
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f3914,f3061,f1319,f26262]) ).
fof(f26262,plain,
( spl0_950
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f3061,plain,
( spl0_270
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X19,X2,X0)
| c_lessequals(X19,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f3914,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_270 ),
inference(resolution,[],[f3062,f1320]) ).
fof(f3062,plain,
( ! [X2,X0,X1,X19] :
( ~ c_lessequals(X19,X2,X0)
| ~ c_lessequals(X2,X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X19,X1,X0) )
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f3061]) ).
fof(f26260,plain,
( spl0_949
| ~ spl0_68
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3868,f3053,f1311,f26258]) ).
fof(f26258,plain,
( spl0_949
<=> ! [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_949])]) ).
fof(f3868,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_68
| ~ spl0_268 ),
inference(resolution,[],[f3054,f1312]) ).
fof(f26254,plain,
( spl0_948
| ~ spl0_68
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3807,f3045,f1311,f26252]) ).
fof(f26252,plain,
( spl0_948
<=> ! [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_948])]) ).
fof(f3807,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_68
| ~ spl0_266 ),
inference(resolution,[],[f3046,f1312]) ).
fof(f26250,plain,
( spl0_947
| ~ spl0_186
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3738,f3037,f2032,f26248]) ).
fof(f26248,plain,
( spl0_947
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_fequal(X0,X1),X2,tc_fun(X1,tc_bool))
| hBOOL(c_in(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f3037,plain,
( spl0_264
<=> ! [X0,X8,X6,X1] :
( hBOOL(c_in(X1,X8,X0))
| ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f3738,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_fequal(X0,X1),X2,tc_fun(X1,tc_bool))
| hBOOL(c_in(X0,X2,X1)) )
| ~ spl0_186
| ~ spl0_264 ),
inference(superposition,[],[f3038,f2033]) ).
fof(f3038,plain,
( ! [X0,X1,X8,X6] :
( ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X8,X0)) )
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f3037]) ).
fof(f26246,plain,
( spl0_946
| ~ spl0_70
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3645,f3008,f1319,f26244]) ).
fof(f26244,plain,
( spl0_946
<=> ! [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_946])]) ).
fof(f3645,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_70
| ~ spl0_257 ),
inference(resolution,[],[f3009,f1320]) ).
fof(f26242,plain,
( spl0_945
| ~ spl0_70
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3587,f3000,f1319,f26240]) ).
fof(f26240,plain,
( spl0_945
<=> ! [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_945])]) ).
fof(f3587,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_70
| ~ spl0_255 ),
inference(resolution,[],[f3001,f1320]) ).
fof(f26213,plain,
( ~ spl0_37
| spl0_944
| ~ spl0_165
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3567,f2996,f1936,f26211,f1183]) ).
fof(f26211,plain,
( spl0_944
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f3567,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_165
| ~ spl0_254 ),
inference(resolution,[],[f2997,f1937]) ).
fof(f26209,plain,
( spl0_943
| ~ spl0_70
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3508,f2992,f1319,f26207]) ).
fof(f26207,plain,
( spl0_943
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f3508,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_253 ),
inference(resolution,[],[f2993,f1320]) ).
fof(f26205,plain,
( spl0_942
| ~ spl0_70
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3460,f2980,f1319,f26203]) ).
fof(f26203,plain,
( spl0_942
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f3460,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_251 ),
inference(resolution,[],[f2981,f1320]) ).
fof(f26201,plain,
( spl0_941
| ~ spl0_68
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3427,f2976,f1311,f26199]) ).
fof(f26199,plain,
( spl0_941
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f3427,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68
| ~ spl0_250 ),
inference(resolution,[],[f2977,f1312]) ).
fof(f26197,plain,
( spl0_940
| ~ spl0_68
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3379,f2968,f1311,f26195]) ).
fof(f26195,plain,
( spl0_940
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f3379,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68
| ~ spl0_248 ),
inference(resolution,[],[f2969,f1312]) ).
fof(f26193,plain,
( spl0_939
| ~ spl0_201
| ~ spl0_908 ),
inference(avatar_split_clause,[],[f26108,f25990,f2311,f26190]) ).
fof(f26190,plain,
( spl0_939
<=> hBOOL(hAPP(hAPP(v_P,v_U),c_fequal(v_x,t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f26108,plain,
( hBOOL(hAPP(hAPP(v_P,v_U),c_fequal(v_x,t_a)))
| ~ spl0_201
| ~ spl0_908 ),
inference(resolution,[],[f25991,f2312]) ).
fof(f26188,plain,
( spl0_938
| ~ spl0_70
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3301,f2956,f1319,f26186]) ).
fof(f26186,plain,
( spl0_938
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f2956,plain,
( spl0_245
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X2,X19,X0)
| c_HOL_Oord__class_Oless(X1,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f3301,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) )
| ~ spl0_70
| ~ spl0_245 ),
inference(resolution,[],[f2957,f1320]) ).
fof(f2957,plain,
( ! [X2,X0,X1,X19] :
( ~ c_lessequals(X2,X19,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X1,X19,X0) )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2956]) ).
fof(f26184,plain,
( spl0_937
| ~ spl0_68
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f3275,f2952,f1311,f26182]) ).
fof(f26182,plain,
( spl0_937
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X2),X1,X2)
| ~ class_Orderings_Obot(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f2952,plain,
( spl0_244
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X19,X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f3275,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X2),X1,X2)
| ~ class_Orderings_Obot(X2) )
| ~ spl0_68
| ~ spl0_244 ),
inference(resolution,[],[f2953,f1312]) ).
fof(f2953,plain,
( ! [X2,X0,X1,X19] :
( ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X19,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X1,X19,X0) )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2952]) ).
fof(f26180,plain,
( spl0_936
| ~ spl0_68
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f3229,f2948,f1311,f26178]) ).
fof(f26178,plain,
( spl0_936
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(X0,X2,X1)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f2948,plain,
( spl0_243
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X19,X2,X0)
| ~ c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X19,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f3229,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(X0,X2,X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_68
| ~ spl0_243 ),
inference(resolution,[],[f2949,f1312]) ).
fof(f2949,plain,
( ! [X2,X0,X1,X19] :
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X19,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X19,X1,X0) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2948]) ).
fof(f26176,plain,
( spl0_935
| ~ spl0_70
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f3214,f2948,f1319,f26174]) ).
fof(f26174,plain,
( spl0_935
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f3214,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) )
| ~ spl0_70
| ~ spl0_243 ),
inference(resolution,[],[f2949,f1320]) ).
fof(f26172,plain,
( spl0_934
| ~ spl0_68
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f3188,f2939,f1311,f26170]) ).
fof(f26170,plain,
( spl0_934
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X2),X1,X2)
| ~ class_Orderings_Obot(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f3188,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X2),X1,X2)
| ~ class_Orderings_Obot(X2) )
| ~ spl0_68
| ~ spl0_241 ),
inference(resolution,[],[f2940,f1312]) ).
fof(f26168,plain,
( spl0_933
| ~ spl0_70
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f3173,f2939,f1319,f26166]) ).
fof(f26166,plain,
( spl0_933
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f3173,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_241 ),
inference(resolution,[],[f2940,f1320]) ).
fof(f26164,plain,
( spl0_932
| ~ spl0_68
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2880,f2560,f1311,f26162]) ).
fof(f26162,plain,
( spl0_932
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f2560,plain,
( spl0_229
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2880,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_68
| ~ spl0_229 ),
inference(resolution,[],[f2561,f1312]) ).
fof(f2561,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2560]) ).
fof(f26160,plain,
( spl0_931
| ~ spl0_70
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2866,f2560,f1319,f26158]) ).
fof(f26158,plain,
( spl0_931
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f2866,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_229 ),
inference(resolution,[],[f2561,f1320]) ).
fof(f26156,plain,
( spl0_930
| ~ spl0_201
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2817,f2522,f2311,f26154]) ).
fof(f26154,plain,
( spl0_930
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f2522,plain,
( spl0_221
<=> ! [X6,X0,X8] : c_lessequals(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f2817,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1)),X1))
| ~ spl0_201
| ~ spl0_221 ),
inference(resolution,[],[f2523,f2312]) ).
fof(f2523,plain,
( ! [X0,X8,X6] : c_lessequals(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool))
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2522]) ).
fof(f26152,plain,
( spl0_929
| ~ spl0_201
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f2810,f2518,f2311,f26150]) ).
fof(f26150,plain,
( spl0_929
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f2518,plain,
( spl0_220
<=> ! [X6,X0,X8] : c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2810,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1)),X0))
| ~ spl0_201
| ~ spl0_220 ),
inference(resolution,[],[f2519,f2312]) ).
fof(f2519,plain,
( ! [X0,X8,X6] : c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool))
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2518]) ).
fof(f26089,plain,
( spl0_928
| ~ spl0_68
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2747,f2494,f1311,f26087]) ).
fof(f26087,plain,
( spl0_928
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f2494,plain,
( spl0_214
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2747,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68
| ~ spl0_214 ),
inference(resolution,[],[f2495,f1312]) ).
fof(f2495,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| X1 = X2
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2494]) ).
fof(f26085,plain,
( spl0_927
| ~ spl0_70
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2733,f2494,f1319,f26083]) ).
fof(f26083,plain,
( spl0_927
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = X0
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f2733,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = X0
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) )
| ~ spl0_70
| ~ spl0_214 ),
inference(resolution,[],[f2495,f1320]) ).
fof(f26081,plain,
( spl0_926
| ~ spl0_68
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2710,f2490,f1311,f26079]) ).
fof(f26079,plain,
( spl0_926
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f2490,plain,
( spl0_213
<=> ! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| X14 = X16
| ~ c_lessequals(X14,X16,X0)
| c_HOL_Oord__class_Oless(X14,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f2710,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_68
| ~ spl0_213 ),
inference(resolution,[],[f2491,f1312]) ).
fof(f2491,plain,
( ! [X0,X16,X14] :
( ~ c_lessequals(X14,X16,X0)
| X14 = X16
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X14,X16,X0) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2490]) ).
fof(f26077,plain,
( spl0_925
| ~ spl0_70
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2696,f2490,f1319,f26075]) ).
fof(f26075,plain,
( spl0_925
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = X0
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f2696,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = X0
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) )
| ~ spl0_70
| ~ spl0_213 ),
inference(resolution,[],[f2491,f1320]) ).
fof(f26073,plain,
( spl0_924
| ~ spl0_201
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2674,f2486,f2311,f26071]) ).
fof(f26071,plain,
( spl0_924
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f2486,plain,
( spl0_212
<=> ! [X6,X0,X8] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2674,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X1),X0)))
| ~ spl0_201
| ~ spl0_212 ),
inference(resolution,[],[f2487,f2312]) ).
fof(f2487,plain,
( ! [X0,X8,X6] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X8,tc_fun(X0,tc_bool))
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2486]) ).
fof(f26069,plain,
( spl0_923
| ~ spl0_201
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2667,f2482,f2311,f26067]) ).
fof(f26067,plain,
( spl0_923
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f2482,plain,
( spl0_211
<=> ! [X6,X0,X8] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2667,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),X1)))
| ~ spl0_201
| ~ spl0_211 ),
inference(resolution,[],[f2483,f2312]) ).
fof(f2483,plain,
( ! [X0,X8,X6] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X6,tc_fun(X0,tc_bool))
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2482]) ).
fof(f26065,plain,
( spl0_922
| ~ spl0_91
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2370,f2270,f1410,f26063]) ).
fof(f26063,plain,
( spl0_922
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f1410,plain,
( spl0_91
<=> ! [X13,X4] :
( ~ c_HOL_Oord__class_Oless(X13,X4,tc_nat)
| c_lessequals(c_Suc(X13),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f2370,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_91
| ~ spl0_191 ),
inference(resolution,[],[f2271,f1411]) ).
fof(f1411,plain,
( ! [X4,X13] :
( c_lessequals(c_Suc(X13),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X4,tc_nat) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1410]) ).
fof(f26061,plain,
( spl0_921
| ~ spl0_98
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2369,f2270,f1438,f26059]) ).
fof(f26059,plain,
( spl0_921
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f2369,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) )
| ~ spl0_98
| ~ spl0_191 ),
inference(resolution,[],[f2271,f1439]) ).
fof(f26057,plain,
( spl0_920
| ~ spl0_87
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2361,f2270,f1394,f26055]) ).
fof(f26055,plain,
( spl0_920
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f1394,plain,
( spl0_87
<=> ! [X13,X4] :
( ~ c_lessequals(X4,X13,tc_nat)
| c_lessequals(X4,c_Suc(X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f2361,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) )
| ~ spl0_87
| ~ spl0_191 ),
inference(resolution,[],[f2271,f1395]) ).
fof(f1395,plain,
( ! [X4,X13] :
( c_lessequals(X4,c_Suc(X13),tc_nat)
| ~ c_lessequals(X4,X13,tc_nat) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1394]) ).
fof(f26053,plain,
( spl0_919
| ~ spl0_126
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2215,f1952,f1632,f26051]) ).
fof(f26051,plain,
( spl0_919
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f1952,plain,
( spl0_169
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f2215,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_169 ),
inference(resolution,[],[f1953,f1633]) ).
fof(f1953,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1952]) ).
fof(f26032,plain,
( spl0_918
| ~ spl0_127
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2214,f1952,f1636,f26030]) ).
fof(f26030,plain,
( spl0_918
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f2214,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_127
| ~ spl0_169 ),
inference(resolution,[],[f1953,f1637]) ).
fof(f26028,plain,
( spl0_917
| ~ spl0_126
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2199,f1948,f1632,f26026]) ).
fof(f26026,plain,
( spl0_917
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f1948,plain,
( spl0_168
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f2199,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_168 ),
inference(resolution,[],[f1949,f1633]) ).
fof(f1949,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1948]) ).
fof(f26024,plain,
( spl0_916
| ~ spl0_127
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2198,f1948,f1636,f26022]) ).
fof(f26022,plain,
( spl0_916
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f2198,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_127
| ~ spl0_168 ),
inference(resolution,[],[f1949,f1637]) ).
fof(f26020,plain,
( spl0_915
| ~ spl0_126
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2183,f1944,f1632,f26018]) ).
fof(f26018,plain,
( spl0_915
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f1944,plain,
( spl0_167
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f2183,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_167 ),
inference(resolution,[],[f1945,f1633]) ).
fof(f1945,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1944]) ).
fof(f26016,plain,
( spl0_914
| ~ spl0_127
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2182,f1944,f1636,f26014]) ).
fof(f26014,plain,
( spl0_914
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f2182,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_127
| ~ spl0_167 ),
inference(resolution,[],[f1945,f1637]) ).
fof(f26012,plain,
( spl0_913
| ~ spl0_126
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2163,f1940,f1632,f26010]) ).
fof(f26010,plain,
( spl0_913
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f2163,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_166 ),
inference(resolution,[],[f1941,f1633]) ).
fof(f26008,plain,
( spl0_912
| ~ spl0_127
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2162,f1940,f1636,f26006]) ).
fof(f26006,plain,
( spl0_912
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f2162,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_127
| ~ spl0_166 ),
inference(resolution,[],[f1941,f1637]) ).
fof(f26004,plain,
( spl0_911
| ~ spl0_126
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2106,f1908,f1632,f26002]) ).
fof(f26002,plain,
( spl0_911
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1908,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f2106,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_158 ),
inference(resolution,[],[f1909,f1633]) ).
fof(f1909,plain,
( ! [X2,X0,X1] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1908]) ).
fof(f26000,plain,
( spl0_910
| ~ spl0_127
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2105,f1908,f1636,f25998]) ).
fof(f25998,plain,
( spl0_910
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f2105,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_127
| ~ spl0_158 ),
inference(resolution,[],[f1909,f1637]) ).
fof(f25996,plain,
( spl0_909
| ~ spl0_126
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2102,f1904,f1632,f25994]) ).
fof(f25994,plain,
( spl0_909
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f1904,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f2102,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_157 ),
inference(resolution,[],[f1905,f1633]) ).
fof(f1905,plain,
( ! [X2,X0,X1] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1904]) ).
fof(f25992,plain,
( spl0_908
| ~ spl0_865
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f25360,f25145,f24804,f25990]) ).
fof(f25360,plain,
( ! [X0] : c_lessequals(c_fequal(v_x,X0),v_U,tc_fun(X0,tc_bool))
| ~ spl0_865
| ~ spl0_883 ),
inference(superposition,[],[f25146,f24805]) ).
fof(f25988,plain,
( spl0_907
| ~ spl0_127
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2101,f1904,f1636,f25986]) ).
fof(f25986,plain,
( spl0_907
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f2101,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_127
| ~ spl0_157 ),
inference(resolution,[],[f1905,f1637]) ).
fof(f25984,plain,
( spl0_906
| ~ spl0_126
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2090,f1900,f1632,f25982]) ).
fof(f25982,plain,
( spl0_906
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f2090,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_156 ),
inference(resolution,[],[f1901,f1633]) ).
fof(f25980,plain,
( spl0_905
| ~ spl0_127
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2089,f1900,f1636,f25978]) ).
fof(f25978,plain,
( spl0_905
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2089,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_127
| ~ spl0_156 ),
inference(resolution,[],[f1901,f1637]) ).
fof(f25976,plain,
( spl0_904
| ~ spl0_126
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2086,f1896,f1632,f25974]) ).
fof(f25974,plain,
( spl0_904
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f2086,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_155 ),
inference(resolution,[],[f1897,f1633]) ).
fof(f25972,plain,
( spl0_903
| ~ spl0_127
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2085,f1896,f1636,f25970]) ).
fof(f25970,plain,
( spl0_903
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f2085,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_127
| ~ spl0_155 ),
inference(resolution,[],[f1897,f1637]) ).
fof(f25968,plain,
( spl0_902
| ~ spl0_93
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2065,f1892,f1418,f25966]) ).
fof(f25966,plain,
( spl0_902
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat)
| c_Suc(X1) = X0
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f2065,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat)
| c_Suc(X1) = X0
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_93
| ~ spl0_154 ),
inference(resolution,[],[f1893,f1419]) ).
fof(f25964,plain,
( spl0_901
| ~ spl0_91
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2052,f1888,f1410,f25962]) ).
fof(f25962,plain,
( spl0_901
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_Suc(X1) = X0
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f2052,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_Suc(X1) = X0
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_91
| ~ spl0_153 ),
inference(resolution,[],[f1889,f1411]) ).
fof(f25960,plain,
( spl0_900
| ~ spl0_55
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f1597,f1506,f1259,f25958]) ).
fof(f25958,plain,
( spl0_900
<=> ! [X2,X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(c_fequal(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f1259,plain,
( spl0_55
<=> ! [X55,X56] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X56)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1506,plain,
( spl0_115
<=> ! [X0,X14] :
( c_Complete__Lattice_OSup__class_OSup(c_fequal(X14,X0),X0) = X14
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1597,plain,
( ! [X2,X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(c_fequal(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_55
| ~ spl0_115 ),
inference(resolution,[],[f1507,f1260]) ).
fof(f1260,plain,
( ! [X56,X55] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X55,X56))
| ~ class_Complete__Lattice_Ocomplete__lattice(X56) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f1507,plain,
( ! [X0,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_fequal(X14,X0),X0) = X14 )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1506]) ).
fof(f25956,plain,
( spl0_899
| ~ spl0_55
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1595,f1502,f1259,f25954]) ).
fof(f25954,plain,
( spl0_899
<=> ! [X2,X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(c_fequal(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f1502,plain,
( spl0_114
<=> ! [X0,X14] :
( c_Complete__Lattice_OInf__class_OInf(c_fequal(X14,X0),X0) = X14
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1595,plain,
( ! [X2,X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(c_fequal(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_55
| ~ spl0_114 ),
inference(resolution,[],[f1503,f1260]) ).
fof(f1503,plain,
( ! [X0,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(c_fequal(X14,X0),X0) = X14 )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1502]) ).
fof(f25875,plain,
( spl0_898
| ~ spl0_865
| ~ spl0_875 ),
inference(avatar_split_clause,[],[f25291,f25033,f24804,f25873]) ).
fof(f25873,plain,
( spl0_898
<=> ! [X0,X1] : hBOOL(c_in(v_x,c_Set_Oinsert(X1,v_U,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f25291,plain,
( ! [X0,X1] : hBOOL(c_in(v_x,c_Set_Oinsert(X1,v_U,X0),X0))
| ~ spl0_865
| ~ spl0_875 ),
inference(superposition,[],[f25034,f24805]) ).
fof(f25667,plain,
( spl0_897
| ~ spl0_104
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f5528,f4308,f1462,f25665]) ).
fof(f25665,plain,
( spl0_897
<=> ! [X0,X3,X2,X1] : c_lessequals(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,X0,X3),X3),tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f4308,plain,
( spl0_344
<=> ! [X6,X0,X1,X8] :
( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f5528,plain,
( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,X0,X3),X3),tc_fun(X3,tc_bool))
| ~ spl0_104
| ~ spl0_344 ),
inference(resolution,[],[f4309,f1463]) ).
fof(f4309,plain,
( ! [X0,X1,X8,X6] :
( ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool)) )
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f4308]) ).
fof(f25638,plain,
( spl0_896
| ~ spl0_21
| ~ spl0_43
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f5035,f4182,f1211,f1103,f25636]) ).
fof(f25636,plain,
( spl0_896
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f1211,plain,
( spl0_43
<=> ! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f4182,plain,
( spl0_313
<=> ! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X16,X14,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f5035,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(c_Suc(X0),X0,tc_nat) )
| ~ spl0_43
| ~ spl0_313 ),
inference(resolution,[],[f4183,f1212]) ).
fof(f1212,plain,
( ! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1211]) ).
fof(f4183,plain,
( ! [X0,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X16,X14,X0)
| ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) )
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f4182]) ).
fof(f25599,plain,
( ~ spl0_19
| spl0_895
| ~ spl0_44
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4518,f4075,f1215,f25597,f1093]) ).
fof(f25597,plain,
( spl0_895
<=> ! [X0,X1] : ~ c_lessequals(c_Suc(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f4075,plain,
( spl0_287
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X19,X1,X0)
| c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f4518,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_44
| ~ spl0_287 ),
inference(resolution,[],[f4076,f1216]) ).
fof(f4076,plain,
( ! [X2,X0,X1,X19] :
( c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0)
| ~ c_lessequals(X19,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f4075]) ).
fof(f25561,plain,
( ~ spl0_19
| spl0_894
| ~ spl0_44
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4470,f4071,f1215,f25559,f1093]) ).
fof(f25559,plain,
( spl0_894
<=> ! [X0,X1] : ~ c_lessequals(c_Suc(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f4071,plain,
( spl0_286
<=> ! [X0,X14,X16,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X16,X0)
| c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f4470,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_44
| ~ spl0_286 ),
inference(resolution,[],[f4072,f1216]) ).
fof(f4072,plain,
( ! [X0,X1,X16,X14] :
( c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X0)
| ~ c_lessequals(X1,X16,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f4071]) ).
fof(f25557,plain,
( spl0_893
| ~ spl0_110
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2920,f2584,f1486,f25555]) ).
fof(f25555,plain,
( spl0_893
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Ovimage(X0,c_fequal(hAPP(X0,X1),X2),X3,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f2920,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Ovimage(X0,c_fequal(hAPP(X0,X1),X2),X3,X2),X1))
| ~ spl0_110
| ~ spl0_235 ),
inference(resolution,[],[f2585,f1487]) ).
fof(f25553,plain,
( spl0_892
| ~ spl0_110
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2914,f2572,f1486,f25551]) ).
fof(f25551,plain,
( spl0_892
<=> ! [X2,X0,X1,X3] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f2572,plain,
( spl0_232
<=> ! [X0,X14,X16,X8] :
( ~ hBOOL(c_in(X14,X8,X0))
| hBOOL(c_in(X14,c_Set_Oinsert(X16,X8,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2914,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X2),X0)) )
| ~ spl0_110
| ~ spl0_232 ),
inference(resolution,[],[f2573,f1487]) ).
fof(f2573,plain,
( ! [X0,X8,X16,X14] :
( hBOOL(c_in(X14,c_Set_Oinsert(X16,X8,X0),X0))
| ~ hBOOL(c_in(X14,X8,X0)) )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2572]) ).
fof(f25549,plain,
( spl0_891
| ~ spl0_77
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2348,f2270,f1349,f25547]) ).
fof(f25547,plain,
( spl0_891
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2348,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) )
| ~ spl0_77
| ~ spl0_191 ),
inference(resolution,[],[f2271,f1350]) ).
fof(f25488,plain,
( spl0_890
| ~ spl0_19
| ~ spl0_86
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2118,f1916,f1390,f1093,f25486]) ).
fof(f25486,plain,
( spl0_890
<=> ! [X0,X1] : c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),c_Suc(X0)),X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f1390,plain,
( spl0_86
<=> ! [X13,X4] :
( c_lessequals(X4,X13,tc_nat)
| ~ c_lessequals(c_Suc(X4),X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1916,plain,
( spl0_160
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f2118,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),c_Suc(X0)),X1),tc_nat) )
| ~ spl0_86
| ~ spl0_160 ),
inference(resolution,[],[f1917,f1391]) ).
fof(f1391,plain,
( ! [X4,X13] :
( ~ c_lessequals(c_Suc(X4),X13,tc_nat)
| c_lessequals(X4,X13,tc_nat) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1390]) ).
fof(f1917,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1916]) ).
fof(f25427,plain,
( spl0_889
| ~ spl0_19
| ~ spl0_86
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2111,f1912,f1390,f1093,f25425]) ).
fof(f25425,plain,
( spl0_889
<=> ! [X0,X1] : c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f1912,plain,
( spl0_159
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f2111,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),c_Suc(X0)),tc_nat) )
| ~ spl0_86
| ~ spl0_159 ),
inference(resolution,[],[f1913,f1391]) ).
fof(f1913,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1912]) ).
fof(f25423,plain,
( spl0_888
| ~ spl0_56
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1831,f1668,f1263,f25421]) ).
fof(f25421,plain,
( spl0_888
<=> ! [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_888])]) ).
fof(f1668,plain,
( spl0_135
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1831,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_56
| ~ spl0_135 ),
inference(resolution,[],[f1669,f1264]) ).
fof(f1669,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X1) = X1 )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1668]) ).
fof(f25419,plain,
( spl0_887
| ~ spl0_861
| ~ spl0_865 ),
inference(avatar_split_clause,[],[f24992,f24804,f23922,f25417]) ).
fof(f25417,plain,
( spl0_887
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_U,X0),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f24992,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_U,X0),v_x))
| ~ spl0_861
| ~ spl0_865 ),
inference(superposition,[],[f23923,f24805]) ).
fof(f25415,plain,
( spl0_886
| ~ spl0_57
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1738,f1620,f1267,f25413]) ).
fof(f25413,plain,
( spl0_886
<=> ! [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_886])]) ).
fof(f1620,plain,
( spl0_123
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1738,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_57
| ~ spl0_123 ),
inference(resolution,[],[f1621,f1268]) ).
fof(f1621,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X1) = X1 )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1620]) ).
fof(f25372,plain,
( spl0_885
| ~ spl0_1
| ~ spl0_749 ),
inference(avatar_split_clause,[],[f20568,f20550,f1003,f25370]) ).
fof(f25370,plain,
( spl0_885
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,tc_Com_Opname)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X0,tc_Com_Opname,X1)),c_Finite__Set_Osetsum(X2,v_U,tc_Com_Opname,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,X1)),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f1003,plain,
( spl0_1
<=> c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f20550,plain,
( spl0_749
<=> ! [X21,X20,X0,X6,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f20568,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,tc_Com_Opname)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X0,tc_Com_Opname,X1)),c_Finite__Set_Osetsum(X2,v_U,tc_Com_Opname,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,X1)),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,X1)) )
| ~ spl0_1
| ~ spl0_749 ),
inference(resolution,[],[f20551,f1005]) ).
fof(f1005,plain,
( c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f20551,plain,
( ! [X21,X0,X8,X6,X20] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20)) )
| ~ spl0_749 ),
inference(avatar_component_clause,[],[f20550]) ).
fof(f25151,plain,
( spl0_884
| ~ spl0_124
| ~ spl0_556 ),
inference(avatar_split_clause,[],[f11260,f11185,f1624,f25149]) ).
fof(f25149,plain,
( spl0_884
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
| ~ hBOOL(c_in(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f11185,plain,
( spl0_556
<=> ! [X0,X8,X6,X1] :
( ~ hBOOL(c_in(X1,X8,X0))
| ~ hBOOL(c_in(X1,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f11260,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
| ~ hBOOL(c_in(X2,X1,X0)) )
| ~ spl0_124
| ~ spl0_556 ),
inference(duplicate_literal_removal,[],[f11249]) ).
fof(f11249,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
| ~ hBOOL(c_in(X2,X1,X0))
| ~ hBOOL(c_in(X2,X1,X0)) )
| ~ spl0_124
| ~ spl0_556 ),
inference(superposition,[],[f11186,f1625]) ).
fof(f11186,plain,
( ! [X0,X1,X8,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
| ~ hBOOL(c_in(X1,X6,X0))
| ~ hBOOL(c_in(X1,X8,X0)) )
| ~ spl0_556 ),
inference(avatar_component_clause,[],[f11185]) ).
fof(f25147,plain,
( spl0_883
| ~ spl0_220
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f5938,f4368,f2518,f25145]) ).
fof(f5938,plain,
( ! [X2,X0,X1] : c_lessequals(c_fequal(X1,X0),c_Set_Oinsert(X1,X2,X0),tc_fun(X0,tc_bool))
| ~ spl0_220
| ~ spl0_358 ),
inference(superposition,[],[f2519,f4369]) ).
fof(f25123,plain,
( ~ spl0_14
| spl0_882
| ~ spl0_40
| ~ spl0_116
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5375,f4256,f1513,f1199,f25121,f1068]) ).
fof(f25121,plain,
( spl0_882
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f1199,plain,
( spl0_40
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f5375,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1),X1,tc_nat)
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_40
| ~ spl0_116
| ~ spl0_331 ),
inference(forward_demodulation,[],[f5349,f1515]) ).
fof(f5349,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1),X1,tc_nat)
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_40
| ~ spl0_331 ),
inference(resolution,[],[f4257,f1200]) ).
fof(f1200,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f25095,plain,
( ~ spl0_14
| spl0_881
| ~ spl0_40
| ~ spl0_116
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f5343,f4252,f1513,f1199,f25093,f1068]) ).
fof(f25093,plain,
( spl0_881
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f5343,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1),X0,tc_nat)
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_40
| ~ spl0_116
| ~ spl0_330 ),
inference(forward_demodulation,[],[f5317,f1515]) ).
fof(f5317,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1),X0,tc_nat)
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_40
| ~ spl0_330 ),
inference(resolution,[],[f4253,f1200]) ).
fof(f25091,plain,
( spl0_880
| ~ spl0_48
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f4810,f4134,f1231,f25089]) ).
fof(f25089,plain,
( spl0_880
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f4134,plain,
( spl0_301
<=> ! [X0,X28,X3] :
( ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X28,X3,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f4810,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_48
| ~ spl0_301 ),
inference(duplicate_literal_removal,[],[f4786]) ).
fof(f4786,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_48
| ~ spl0_301 ),
inference(resolution,[],[f4135,f1232]) ).
fof(f4135,plain,
( ! [X28,X3,X0] :
( c_HOL_Oord__class_Oless(X28,X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f4134]) ).
fof(f25087,plain,
( spl0_879
| ~ spl0_82
| ~ spl0_865 ),
inference(avatar_split_clause,[],[f24956,f24804,f1369,f25085]) ).
fof(f25085,plain,
( spl0_879
<=> ! [X0] : hBOOL(c_in(v_x,v_U,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f24956,plain,
( ! [X0] : hBOOL(c_in(v_x,v_U,X0))
| ~ spl0_82
| ~ spl0_865 ),
inference(superposition,[],[f1370,f24805]) ).
fof(f25083,plain,
( spl0_878
| ~ spl0_48
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f4781,f4123,f1231,f25081]) ).
fof(f25081,plain,
( spl0_878
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f4123,plain,
( spl0_299
<=> ! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X14,X16,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f4781,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_48
| ~ spl0_299 ),
inference(duplicate_literal_removal,[],[f4757]) ).
fof(f4757,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_48
| ~ spl0_299 ),
inference(resolution,[],[f4124,f1232]) ).
fof(f4124,plain,
( ! [X0,X16,X14] :
( c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f4123]) ).
fof(f25059,plain,
( ~ spl0_15
| spl0_877
| ~ spl0_40
| ~ spl0_242
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f4744,f4119,f2943,f1199,f25057,f1073]) ).
fof(f25057,plain,
( spl0_877
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f4744,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1),tc_nat)
| ~ class_Lattices_Olower__semilattice(tc_nat) )
| ~ spl0_40
| ~ spl0_242
| ~ spl0_298 ),
inference(forward_demodulation,[],[f4719,f2945]) ).
fof(f4719,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1),tc_nat)
| ~ class_Lattices_Olower__semilattice(tc_nat) )
| ~ spl0_40
| ~ spl0_298 ),
inference(resolution,[],[f4120,f1200]) ).
fof(f25039,plain,
( ~ spl0_15
| spl0_876
| ~ spl0_40
| ~ spl0_242
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4708,f4115,f2943,f1199,f25037,f1073]) ).
fof(f25037,plain,
( spl0_876
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f4708,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X0),tc_nat)
| ~ class_Lattices_Olower__semilattice(tc_nat) )
| ~ spl0_40
| ~ spl0_242
| ~ spl0_297 ),
inference(forward_demodulation,[],[f4683,f2945]) ).
fof(f4683,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X0),tc_nat)
| ~ class_Lattices_Olower__semilattice(tc_nat) )
| ~ spl0_40
| ~ spl0_297 ),
inference(resolution,[],[f4116,f1200]) ).
fof(f25035,plain,
( spl0_875
| ~ spl0_104
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3736,f3037,f1462,f25033]) ).
fof(f3736,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3))
| ~ spl0_104
| ~ spl0_264 ),
inference(resolution,[],[f3038,f1463]) ).
fof(f25012,plain,
( ~ spl0_37
| spl0_874
| ~ spl0_104
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3555,f2996,f1462,f25010,f1183]) ).
fof(f25010,plain,
( spl0_874
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f3555,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_104
| ~ spl0_254 ),
inference(resolution,[],[f2997,f1463]) ).
fof(f24998,plain,
( ~ spl0_37
| spl0_873
| ~ spl0_105
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3553,f2996,f1466,f24996,f1183]) ).
fof(f24996,plain,
( spl0_873
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f3553,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
| ~ class_HOL_Oord(tc_bool) )
| ~ spl0_105
| ~ spl0_254 ),
inference(resolution,[],[f2997,f1467]) ).
fof(f24951,plain,
( spl0_872
| ~ spl0_165
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2445,f2311,f1936,f24949]) ).
fof(f24949,plain,
( spl0_872
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(t_a,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2445,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(t_a,tc_bool))))
| ~ spl0_165
| ~ spl0_201 ),
inference(resolution,[],[f2312,f1937]) ).
fof(f24908,plain,
( ~ spl0_22
| spl0_871
| ~ spl0_68
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2368,f2270,f1311,f24906,f1108]) ).
fof(f1108,plain,
( spl0_22
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f24906,plain,
( spl0_871
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2368,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat)
| ~ class_Orderings_Obot(tc_nat) )
| ~ spl0_68
| ~ spl0_191 ),
inference(resolution,[],[f2271,f1312]) ).
fof(f24904,plain,
( spl0_870
| ~ spl0_126
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2130,f1924,f1632,f24902]) ).
fof(f24902,plain,
( spl0_870
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f1924,plain,
( spl0_162
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f2130,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1),X0) )
| ~ spl0_126
| ~ spl0_162 ),
inference(duplicate_literal_removal,[],[f2128]) ).
fof(f2128,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_162 ),
inference(resolution,[],[f1925,f1633]) ).
fof(f1925,plain,
( ! [X2,X0,X1] :
( c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1924]) ).
fof(f24900,plain,
( spl0_869
| ~ spl0_126
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2126,f1920,f1632,f24898]) ).
fof(f24898,plain,
( spl0_869
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f1920,plain,
( spl0_161
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2126,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) )
| ~ spl0_126
| ~ spl0_161 ),
inference(duplicate_literal_removal,[],[f2124]) ).
fof(f2124,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_161 ),
inference(resolution,[],[f1921,f1633]) ).
fof(f1921,plain,
( ! [X2,X0,X1] :
( c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1920]) ).
fof(f24896,plain,
( spl0_868
| ~ spl0_126
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2122,f1916,f1632,f24894]) ).
fof(f24894,plain,
( spl0_868
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2122,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X1,X0) )
| ~ spl0_126
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f2120]) ).
fof(f2120,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_160 ),
inference(resolution,[],[f1917,f1633]) ).
fof(f24892,plain,
( spl0_867
| ~ spl0_126
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2115,f1912,f1632,f24890]) ).
fof(f24890,plain,
( spl0_867
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2115,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X2,X0) )
| ~ spl0_126
| ~ spl0_159 ),
inference(duplicate_literal_removal,[],[f2113]) ).
fof(f2113,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_126
| ~ spl0_159 ),
inference(resolution,[],[f1913,f1633]) ).
fof(f24849,plain,
( ~ spl0_22
| spl0_866
| ~ spl0_68
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2050,f1888,f1311,f24847,f1108]) ).
fof(f24847,plain,
( spl0_866
<=> ! [X0] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2050,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X0
| ~ class_Orderings_Obot(tc_nat) )
| ~ spl0_68
| ~ spl0_153 ),
inference(resolution,[],[f1889,f1312]) ).
fof(f24806,plain,
( spl0_865
| ~ spl0_118
| ~ spl0_852 ),
inference(avatar_split_clause,[],[f24436,f23886,f1599,f24804]) ).
fof(f1599,plain,
( spl0_118
<=> hBOOL(hAPP(v_U,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f24436,plain,
( ! [X0] : v_U = c_Set_Oinsert(v_x,v_U,X0)
| ~ spl0_118
| ~ spl0_852 ),
inference(resolution,[],[f23887,f1601]) ).
fof(f1601,plain,
( hBOOL(hAPP(v_U,v_x))
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f24048,plain,
( spl0_864
| ~ spl0_496
| ~ spl0_499 ),
inference(avatar_split_clause,[],[f9862,f9437,f9425,f24046]) ).
fof(f24046,plain,
( spl0_864
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f9425,plain,
( spl0_496
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f9437,plain,
( spl0_499
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f9862,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) )
| ~ spl0_496
| ~ spl0_499 ),
inference(duplicate_literal_removal,[],[f9842]) ).
fof(f9842,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_496
| ~ spl0_499 ),
inference(resolution,[],[f9438,f9426]) ).
fof(f9426,plain,
( ! [X0,X16,X14,X15] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0)
| c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_496 ),
inference(avatar_component_clause,[],[f9425]) ).
fof(f9438,plain,
( ! [X0,X16,X14,X15] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_499 ),
inference(avatar_component_clause,[],[f9437]) ).
fof(f24044,plain,
( spl0_863
| ~ spl0_487
| ~ spl0_488 ),
inference(avatar_split_clause,[],[f9655,f9393,f9389,f24042]) ).
fof(f24042,plain,
( spl0_863
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f9389,plain,
( spl0_487
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X14,X16,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f9393,plain,
( spl0_488
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f9655,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1) )
| ~ spl0_487
| ~ spl0_488 ),
inference(duplicate_literal_removal,[],[f9610]) ).
fof(f9610,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_487
| ~ spl0_488 ),
inference(resolution,[],[f9394,f9390]) ).
fof(f9390,plain,
( ! [X0,X16,X14,X15] :
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0)
| c_lessequals(X14,X16,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f9389]) ).
fof(f9394,plain,
( ! [X0,X16,X14,X15] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0)
| ~ c_lessequals(X14,X16,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_488 ),
inference(avatar_component_clause,[],[f9393]) ).
fof(f23930,plain,
( spl0_862
| ~ spl0_37
| ~ spl0_51
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f6256,f5988,f1243,f1183,f23928]) ).
fof(f23928,plain,
( spl0_862
<=> ! [X0,X1] : c_lessequals(hAPP(X0,X1),hAPP(X0,X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f6256,plain,
( ! [X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(X0,X1),hAPP(X0,X1),tc_bool) )
| ~ spl0_51
| ~ spl0_369 ),
inference(resolution,[],[f5989,f1244]) ).
fof(f23924,plain,
( spl0_861
| ~ spl0_72
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f5898,f4364,f1327,f23922]) ).
fof(f5898,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0))
| ~ spl0_72
| ~ spl0_357 ),
inference(superposition,[],[f1328,f4365]) ).
fof(f23920,plain,
( spl0_860
| ~ spl0_46
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f5885,f4360,f1223,f23918]) ).
fof(f23918,plain,
( spl0_860
<=> ! [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_860])]) ).
fof(f1223,plain,
( spl0_46
<=> ! [X6,X0] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f4360,plain,
( spl0_356
<=> ! [X20,X0,X6,X25] :
( c_Finite__Set_Ofinite(X6,X20)
| ~ c_Fun_Oinj__on(X25,X6,X20,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X25,X6,X20,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f5885,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_46
| ~ spl0_356 ),
inference(resolution,[],[f4361,f1224]) ).
fof(f1224,plain,
( ! [X0,X6] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ class_Finite__Set_Ofinite_Ofinite(X0) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f1223]) ).
fof(f4361,plain,
( ! [X0,X6,X25,X20] :
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(X25,X6,X20,X0),X0)
| ~ c_Fun_Oinj__on(X25,X6,X20,X0)
| c_Finite__Set_Ofinite(X6,X20) )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f4360]) ).
fof(f23916,plain,
( ~ spl0_858
| spl0_859
| ~ spl0_44
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2898,f2568,f1215,f23914,f23910]) ).
fof(f23910,plain,
( spl0_858
<=> class_Complete__Lattice_Ocomplete__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f23914,plain,
( spl0_859
<=> ! [X0] : ~ hBOOL(c_in(c_Suc(c_Complete__Lattice_OSup__class_OSup(X0,tc_nat)),X0,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f2898,plain,
( ! [X0] :
( ~ hBOOL(c_in(c_Suc(c_Complete__Lattice_OSup__class_OSup(X0,tc_nat)),X0,tc_nat))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_nat) )
| ~ spl0_44
| ~ spl0_231 ),
inference(resolution,[],[f2569,f1216]) ).
fof(f23908,plain,
( spl0_857
| ~ spl0_186
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2450,f2329,f2032,f23906]) ).
fof(f23906,plain,
( spl0_857
<=> ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oinsert(X0,c_fequal(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f2329,plain,
( spl0_204
<=> ! [X6,X0,X1] : c_Set_Oinsert(X1,X6,X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X1,X6,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2450,plain,
( ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oinsert(X0,c_fequal(X0,X1),X1)
| ~ spl0_186
| ~ spl0_204 ),
inference(superposition,[],[f2330,f2033]) ).
fof(f2330,plain,
( ! [X0,X1,X6] : c_Set_Oinsert(X1,X6,X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X1,X6,X0),X0)
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2329]) ).
fof(f23904,plain,
( spl0_856
| ~ spl0_29
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2448,f2319,f1143,f23902]) ).
fof(f23902,plain,
( spl0_856
<=> ! [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_856])]) ).
fof(f1143,plain,
( spl0_29
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f2319,plain,
( spl0_203
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2448,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_29
| ~ spl0_203 ),
inference(resolution,[],[f2320,f1145]) ).
fof(f1145,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f2320,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2319]) ).
fof(f23900,plain,
( spl0_855
| ~ spl0_29
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2446,f2315,f1143,f23898]) ).
fof(f23898,plain,
( spl0_855
<=> ! [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_855])]) ).
fof(f2315,plain,
( spl0_202
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2446,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_29
| ~ spl0_202 ),
inference(resolution,[],[f2316,f1145]) ).
fof(f2316,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0)) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2315]) ).
fof(f23896,plain,
( spl0_854
| ~ spl0_29
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2384,f2295,f1143,f23894]) ).
fof(f23894,plain,
( spl0_854
<=> ! [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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f2295,plain,
( spl0_197
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f2384,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_29
| ~ spl0_197 ),
inference(resolution,[],[f2296,f1145]) ).
fof(f2296,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0)) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2295]) ).
fof(f23892,plain,
( spl0_853
| ~ spl0_29
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2382,f2291,f1143,f23890]) ).
fof(f23890,plain,
( spl0_853
<=> ! [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) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f2291,plain,
( spl0_196
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2382,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_29
| ~ spl0_196 ),
inference(resolution,[],[f2292,f1145]) ).
fof(f2292,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f2291]) ).
fof(f23888,plain,
( spl0_852
| ~ spl0_109
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2253,f2028,f1482,f23886]) ).
fof(f2028,plain,
( spl0_185
<=> ! [X6,X0,X14] :
( ~ hBOOL(c_in(X14,X6,X0))
| c_Set_Oinsert(X14,X6,X0) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f2253,plain,
( ! [X2,X0,X1] :
( c_Set_Oinsert(X0,X1,X2) = X1
| ~ hBOOL(hAPP(X1,X0)) )
| ~ spl0_109
| ~ spl0_185 ),
inference(resolution,[],[f2029,f1483]) ).
fof(f2029,plain,
( ! [X0,X6,X14] :
( ~ hBOOL(c_in(X14,X6,X0))
| c_Set_Oinsert(X14,X6,X0) = X6 )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f2028]) ).
fof(f23884,plain,
( spl0_851
| ~ spl0_789
| ~ spl0_809 ),
inference(avatar_split_clause,[],[f23058,f22632,f22317,f23882]) ).
fof(f23882,plain,
( spl0_851
<=> ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_U,tc_Com_Opname,X0),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f22317,plain,
( spl0_789
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),hAPP(X0,v_x))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f22632,plain,
( spl0_809
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f23058,plain,
( ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_U,tc_Com_Opname,X0),v_x))
| ~ spl0_789
| ~ spl0_809 ),
inference(superposition,[],[f22318,f22633]) ).
fof(f22633,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0
| ~ spl0_809 ),
inference(avatar_component_clause,[],[f22632]) ).
fof(f22318,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),hAPP(X0,v_x)))
| ~ spl0_789 ),
inference(avatar_component_clause,[],[f22317]) ).
fof(f23880,plain,
( spl0_850
| ~ spl0_126
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1864,f1691,f1632,f23878]) ).
fof(f23878,plain,
( spl0_850
<=> ! [X2,X0,X1] :
( c_lessequals(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f1864,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X0,X2) )
| ~ spl0_126
| ~ spl0_140 ),
inference(duplicate_literal_removal,[],[f1853]) ).
fof(f1853,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_126
| ~ spl0_140 ),
inference(resolution,[],[f1692,f1633]) ).
fof(f23876,plain,
( spl0_849
| ~ spl0_76
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1823,f1664,f1345,f23874]) ).
fof(f23874,plain,
( spl0_849
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1345,plain,
( spl0_76
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1823,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) )
| ~ spl0_76
| ~ spl0_134 ),
inference(resolution,[],[f1665,f1346]) ).
fof(f1346,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1345]) ).
fof(f23872,plain,
( spl0_848
| ~ spl0_77
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1784,f1640,f1349,f23870]) ).
fof(f23870,plain,
( spl0_848
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f1640,plain,
( spl0_128
<=> ! [X13,X4] :
( c_lessequals(X13,X4,tc_nat)
| ~ c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1784,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) )
| ~ spl0_77
| ~ spl0_128 ),
inference(resolution,[],[f1641,f1350]) ).
fof(f1641,plain,
( ! [X4,X13] :
( ~ c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat)
| c_lessequals(X13,X4,tc_nat) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1640]) ).
fof(f23868,plain,
( spl0_847
| ~ spl0_88
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1581,f1446,f1398,f23866]) ).
fof(f23866,plain,
( spl0_847
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f1398,plain,
( spl0_88
<=> ! [X13,X4] :
( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1581,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) )
| ~ spl0_88
| ~ spl0_100 ),
inference(resolution,[],[f1447,f1399]) ).
fof(f1399,plain,
( ! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat)
| c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1398]) ).
fof(f23864,plain,
( spl0_846
| ~ spl0_87
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1566,f1434,f1394,f23862]) ).
fof(f23862,plain,
( spl0_846
<=> ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(c_Suc(X1),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f1434,plain,
( spl0_97
<=> ! [X13,X4] :
( ~ c_lessequals(X4,X13,tc_nat)
| ~ c_lessequals(c_Suc(X13),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1566,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(c_Suc(X1),X0,tc_nat) )
| ~ spl0_87
| ~ spl0_97 ),
inference(resolution,[],[f1435,f1395]) ).
fof(f1435,plain,
( ! [X4,X13] :
( ~ c_lessequals(c_Suc(X13),X4,tc_nat)
| ~ c_lessequals(X4,X13,tc_nat) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f23860,plain,
( spl0_845
| ~ spl0_87
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1540,f1406,f1394,f23858]) ).
fof(f23858,plain,
( spl0_845
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1406,plain,
( spl0_90
<=> ! [X13,X4] :
( c_HOL_Oord__class_Oless(X13,X4,tc_nat)
| ~ c_lessequals(c_Suc(X13),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1540,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) )
| ~ spl0_87
| ~ spl0_90 ),
inference(resolution,[],[f1407,f1395]) ).
fof(f1407,plain,
( ! [X4,X13] :
( ~ c_lessequals(c_Suc(X13),X4,tc_nat)
| c_HOL_Oord__class_Oless(X13,X4,tc_nat) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1406]) ).
fof(f23856,plain,
( spl0_844
| ~ spl0_88
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f1532,f1402,f1398,f23854]) ).
fof(f23854,plain,
( spl0_844
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f1532,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) )
| ~ spl0_88
| ~ spl0_89 ),
inference(resolution,[],[f1403,f1399]) ).
fof(f23852,plain,
( spl0_843
| ~ spl0_86
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1525,f1394,f1390,f23850]) ).
fof(f23850,plain,
( spl0_843
<=> ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f1525,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) )
| ~ spl0_86
| ~ spl0_87 ),
inference(resolution,[],[f1395,f1391]) ).
fof(f23846,plain,
( spl0_842
| ~ spl0_789
| ~ spl0_808 ),
inference(avatar_split_clause,[],[f23002,f22628,f22317,f23844]) ).
fof(f23844,plain,
( spl0_842
<=> ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),v_x),v_U,tc_Com_Opname,X0),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f22628,plain,
( spl0_808
<=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f23002,plain,
( ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),v_x),v_U,tc_Com_Opname,X0),v_x))
| ~ spl0_789
| ~ spl0_808 ),
inference(superposition,[],[f22318,f22629]) ).
fof(f22629,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0
| ~ spl0_808 ),
inference(avatar_component_clause,[],[f22628]) ).
fof(f23710,plain,
( spl0_841
| ~ spl0_789
| ~ spl0_806 ),
inference(avatar_split_clause,[],[f22949,f22619,f22317,f23708]) ).
fof(f23708,plain,
( spl0_841
<=> ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Orderings_Oord__class_Omax(tc_nat),v_x),v_U,tc_Com_Opname,X0),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f22619,plain,
( spl0_806
<=> ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f22949,plain,
( ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Orderings_Oord__class_Omax(tc_nat),v_x),v_U,tc_Com_Opname,X0),v_x))
| ~ spl0_789
| ~ spl0_806 ),
inference(superposition,[],[f22318,f22620]) ).
fof(f22620,plain,
( ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X0) = X0
| ~ spl0_806 ),
inference(avatar_component_clause,[],[f22619]) ).
fof(f23368,plain,
( spl0_840
| ~ spl0_789
| ~ spl0_805 ),
inference(avatar_split_clause,[],[f22896,f22615,f22317,f23366]) ).
fof(f23366,plain,
( spl0_840
<=> ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Orderings_Oord__class_Omin(tc_nat),v_x),v_U,tc_Com_Opname,X0),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f22615,plain,
( spl0_805
<=> ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f22896,plain,
( ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Orderings_Oord__class_Omin(tc_nat),v_x),v_U,tc_Com_Opname,X0),v_x))
| ~ spl0_789
| ~ spl0_805 ),
inference(superposition,[],[f22318,f22616]) ).
fof(f22616,plain,
( ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X0) = X0
| ~ spl0_805 ),
inference(avatar_component_clause,[],[f22615]) ).
fof(f23312,plain,
( spl0_839
| ~ spl0_46
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3681,f3012,f1223,f23310]) ).
fof(f23310,plain,
( spl0_839
<=> ! [X0,X3,X2,X1] :
( ~ c_Fun_Obij(X0,X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f3012,plain,
( spl0_258
<=> ! [X35,X20,X0,X33] :
( c_Finite__Set_Ofinite(X33,X20)
| ~ c_Fun_Obij(X35,X0,X20)
| ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f3681,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Fun_Obij(X0,X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) )
| ~ spl0_46
| ~ spl0_258 ),
inference(resolution,[],[f3013,f1224]) ).
fof(f3013,plain,
( ! [X0,X35,X33,X20] :
( ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0)
| ~ c_Fun_Obij(X35,X0,X20)
| c_Finite__Set_Ofinite(X33,X20) )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f3012]) ).
fof(f23308,plain,
( spl0_838
| ~ spl0_103
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2443,f2311,f1458,f23306]) ).
fof(f23306,plain,
( spl0_838
<=> ! [X0] : hBOOL(hAPP(hAPP(v_P,X0),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f2443,plain,
( ! [X0] : hBOOL(hAPP(hAPP(v_P,X0),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))
| ~ spl0_103
| ~ spl0_201 ),
inference(resolution,[],[f2312,f1459]) ).
fof(f23304,plain,
( spl0_837
| ~ spl0_104
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2436,f2311,f1462,f23302]) ).
fof(f23302,plain,
( spl0_837
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(X0,X1,t_a)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f2436,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(X0,X1,t_a)),X1))
| ~ spl0_104
| ~ spl0_201 ),
inference(resolution,[],[f2312,f1463]) ).
fof(f23300,plain,
( spl0_836
| ~ spl0_105
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2434,f2311,f1466,f23298]) ).
fof(f23298,plain,
( spl0_836
<=> ! [X0] : hBOOL(hAPP(hAPP(v_P,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f2434,plain,
( ! [X0] : hBOOL(hAPP(hAPP(v_P,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))),X0))
| ~ spl0_105
| ~ spl0_201 ),
inference(resolution,[],[f2312,f1467]) ).
fof(f23296,plain,
( spl0_835
| ~ spl0_105
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2409,f2307,f1466,f23294]) ).
fof(f23294,plain,
( spl0_835
<=> ! [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_835])]) ).
fof(f2409,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_105
| ~ spl0_200 ),
inference(resolution,[],[f2308,f1467]) ).
fof(f23292,plain,
( spl0_834
| ~ spl0_35
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2248,f2020,f1173,f23289]) ).
fof(f23289,plain,
( spl0_834
<=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f1173,plain,
( spl0_35
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f2248,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_35
| ~ spl0_183 ),
inference(resolution,[],[f2021,f1175]) ).
fof(f1175,plain,
( class_Orderings_Obot(tc_bool)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f23287,plain,
( spl0_833
| ~ spl0_22
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2247,f2020,f1108,f23284]) ).
fof(f23284,plain,
( spl0_833
<=> c_Orderings_Obot__class_Obot(tc_nat) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_nat)),v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f2247,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_nat)),v_x)
| ~ spl0_22
| ~ spl0_183 ),
inference(resolution,[],[f2021,f1110]) ).
fof(f1110,plain,
( class_Orderings_Obot(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1108]) ).
fof(f23282,plain,
( spl0_832
| ~ spl0_25
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2245,f1998,f1123,f23279]) ).
fof(f23279,plain,
( spl0_832
<=> c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f1123,plain,
( spl0_25
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1998,plain,
( spl0_178
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f2245,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_25
| ~ spl0_178 ),
inference(resolution,[],[f1999,f1125]) ).
fof(f1125,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f1999,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1998]) ).
fof(f23277,plain,
( spl0_831
| ~ spl0_34
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2243,f1994,f1168,f23274]) ).
fof(f23274,plain,
( spl0_831
<=> 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_831])]) ).
fof(f1168,plain,
( spl0_34
<=> class_Orderings_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f2243,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x)
| ~ spl0_34
| ~ spl0_177 ),
inference(resolution,[],[f1995,f1170]) ).
fof(f1170,plain,
( class_Orderings_Otop(tc_bool)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1168]) ).
fof(f23272,plain,
( spl0_830
| ~ spl0_79
| ~ spl0_789 ),
inference(avatar_split_clause,[],[f22598,f22317,f1357,f23270]) ).
fof(f23270,plain,
( spl0_830
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),v_U,tc_Com_Opname,X3),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f22598,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),v_U,tc_Com_Opname,X3),X0))
| ~ spl0_79
| ~ spl0_789 ),
inference(superposition,[],[f22318,f1358]) ).
fof(f23268,plain,
( spl0_829
| ~ spl0_25
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2237,f1990,f1123,f23265]) ).
fof(f23265,plain,
( spl0_829
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f1990,plain,
( spl0_176
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2237,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_25
| ~ spl0_176 ),
inference(resolution,[],[f1991,f1125]) ).
fof(f1991,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1990]) ).
fof(f23263,plain,
( spl0_828
| ~ spl0_25
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f2235,f1986,f1123,f23260]) ).
fof(f23260,plain,
( spl0_828
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f1986,plain,
( spl0_175
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f2235,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_25
| ~ spl0_175 ),
inference(resolution,[],[f1987,f1125]) ).
fof(f1987,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1986]) ).
fof(f23258,plain,
( spl0_827
| ~ spl0_29
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f2229,f1964,f1143,f23256]) ).
fof(f23256,plain,
( spl0_827
<=> ! [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_827])]) ).
fof(f2229,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) = X0
| ~ spl0_29
| ~ spl0_172 ),
inference(resolution,[],[f1965,f1145]) ).
fof(f23254,plain,
( spl0_826
| ~ spl0_29
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2227,f1960,f1143,f23252]) ).
fof(f23252,plain,
( spl0_826
<=> ! [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_826])]) ).
fof(f2227,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) = X0
| ~ spl0_29
| ~ spl0_171 ),
inference(resolution,[],[f1961,f1145]) ).
fof(f23250,plain,
( spl0_825
| ~ spl0_25
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2155,f1932,f1123,f23247]) ).
fof(f23247,plain,
( spl0_825
<=> c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f1932,plain,
( spl0_164
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f2155,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_25
| ~ spl0_164 ),
inference(resolution,[],[f1933,f1125]) ).
fof(f1933,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1932]) ).
fof(f23245,plain,
( spl0_824
| ~ spl0_29
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2037,f1879,f1143,f23243]) ).
fof(f23243,plain,
( spl0_824
<=> ! [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_824])]) ).
fof(f2037,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) = X0
| ~ spl0_29
| ~ spl0_151 ),
inference(resolution,[],[f1880,f1145]) ).
fof(f23241,plain,
( spl0_823
| ~ spl0_29
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f2035,f1875,f1143,f23239]) ).
fof(f23239,plain,
( spl0_823
<=> ! [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_823])]) ).
fof(f2035,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) = X0
| ~ spl0_29
| ~ spl0_150 ),
inference(resolution,[],[f1876,f1145]) ).
fof(f23237,plain,
( spl0_822
| ~ spl0_68
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1772,f1636,f1311,f23235]) ).
fof(f23235,plain,
( spl0_822
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f1772,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_68
| ~ spl0_127 ),
inference(resolution,[],[f1637,f1312]) ).
fof(f23233,plain,
( spl0_821
| ~ spl0_70
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1767,f1636,f1319,f23231]) ).
fof(f23231,plain,
( spl0_821
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f1767,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_127 ),
inference(resolution,[],[f1637,f1320]) ).
fof(f23229,plain,
( spl0_820
| ~ spl0_68
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1755,f1632,f1311,f23227]) ).
fof(f23227,plain,
( spl0_820
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f1755,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_68
| ~ spl0_126 ),
inference(resolution,[],[f1633,f1312]) ).
fof(f23175,plain,
( spl0_819
| ~ spl0_70
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1750,f1632,f1319,f23173]) ).
fof(f23173,plain,
( spl0_819
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f1750,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_70
| ~ spl0_126 ),
inference(resolution,[],[f1633,f1320]) ).
fof(f23171,plain,
( spl0_818
| ~ spl0_77
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1536,f1406,f1349,f23169]) ).
fof(f23169,plain,
( spl0_818
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f1536,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) )
| ~ spl0_77
| ~ spl0_90 ),
inference(resolution,[],[f1407,f1350]) ).
fof(f23167,plain,
( spl0_817
| ~ spl0_76
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f1531,f1402,f1345,f23165]) ).
fof(f23165,plain,
( spl0_817
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f1531,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) )
| ~ spl0_76
| ~ spl0_89 ),
inference(resolution,[],[f1403,f1346]) ).
fof(f23163,plain,
( spl0_816
| ~ spl0_77
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f1520,f1390,f1349,f23161]) ).
fof(f23161,plain,
( spl0_816
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f1520,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) )
| ~ spl0_77
| ~ spl0_86 ),
inference(resolution,[],[f1391,f1350]) ).
fof(f23017,plain,
( spl0_815
| ~ spl0_82
| ~ spl0_771 ),
inference(avatar_split_clause,[],[f21633,f21374,f1369,f23015]) ).
fof(f23015,plain,
( spl0_815
<=> ! [X0,X1] : hBOOL(c_in(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f21374,plain,
( spl0_771
<=> ! [X0,X1] : c_Set_Oimage(X0,v_U,tc_Com_Opname,X1) = c_Set_Oinsert(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f21633,plain,
( ! [X0,X1] : hBOOL(c_in(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1))
| ~ spl0_82
| ~ spl0_771 ),
inference(superposition,[],[f1370,f21375]) ).
fof(f21375,plain,
( ! [X0,X1] : c_Set_Oimage(X0,v_U,tc_Com_Opname,X1) = c_Set_Oinsert(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1)
| ~ spl0_771 ),
inference(avatar_component_clause,[],[f21374]) ).
fof(f22657,plain,
( spl0_814
| ~ spl0_106
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2257,f2032,f1470,f22655]) ).
fof(f22655,plain,
( spl0_814
<=> ! [X0,X1] : c_fequal(X0,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f2257,plain,
( ! [X0,X1] : c_fequal(X0,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ spl0_106
| ~ spl0_186 ),
inference(superposition,[],[f1471,f2033]) ).
fof(f22653,plain,
( spl0_813
| ~ spl0_33
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1870,f1711,f1163,f22651]) ).
fof(f22651,plain,
( spl0_813
<=> ! [X0] : c_fequal(X0,tc_bool) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f1163,plain,
( spl0_33
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1870,plain,
( ! [X0] : c_fequal(X0,tc_bool) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)
| ~ spl0_33
| ~ spl0_145 ),
inference(resolution,[],[f1712,f1165]) ).
fof(f1165,plain,
( class_Orderings_Oorder(tc_bool)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f22649,plain,
( spl0_812
| ~ spl0_21
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1869,f1711,f1103,f22647]) ).
fof(f22647,plain,
( spl0_812
<=> ! [X0] : c_fequal(X0,tc_nat) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f22645,plain,
( spl0_811
| ~ spl0_19
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1868,f1707,f1093,f22643]) ).
fof(f22643,plain,
( spl0_811
<=> ! [X0] : hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_fequal(X0,tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f1707,plain,
( spl0_144
<=> ! [X0,X14] :
( hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_fequal(X14,X0)) = X14
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1868,plain,
( ! [X0] : hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_fequal(X0,tc_nat)) = X0
| ~ spl0_19
| ~ spl0_144 ),
inference(resolution,[],[f1708,f1095]) ).
fof(f1708,plain,
( ! [X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_fequal(X14,X0)) = X14 )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1707]) ).
fof(f22638,plain,
( spl0_810
| ~ spl0_19
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1867,f1703,f1093,f22636]) ).
fof(f22636,plain,
( spl0_810
<=> ! [X0] : hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_fequal(X0,tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f1703,plain,
( spl0_143
<=> ! [X0,X14] :
( hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_fequal(X14,X0)) = X14
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1867,plain,
( ! [X0] : hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_fequal(X0,tc_nat)) = X0
| ~ spl0_19
| ~ spl0_143 ),
inference(resolution,[],[f1704,f1095]) ).
fof(f1704,plain,
( ! [X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_fequal(X14,X0)) = X14 )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1703]) ).
fof(f22634,plain,
( spl0_809
| ~ spl0_26
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1830,f1668,f1128,f22632]) ).
fof(f1128,plain,
( spl0_26
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1830,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0
| ~ spl0_26
| ~ spl0_135 ),
inference(resolution,[],[f1669,f1130]) ).
fof(f1130,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f22630,plain,
( spl0_808
| ~ spl0_27
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1737,f1620,f1133,f22628]) ).
fof(f1737,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0
| ~ spl0_27
| ~ spl0_123 ),
inference(resolution,[],[f1621,f1135]) ).
fof(f22625,plain,
( spl0_807
| ~ spl0_15
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1736,f1620,f1073,f22623]) ).
fof(f22623,plain,
( spl0_807
<=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f1736,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X0) = X0
| ~ spl0_15
| ~ spl0_123 ),
inference(resolution,[],[f1621,f1075]) ).
fof(f22621,plain,
( spl0_806
| ~ spl0_19
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1727,f1608,f1093,f22619]) ).
fof(f1608,plain,
( spl0_120
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1727,plain,
( ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X0) = X0
| ~ spl0_19
| ~ spl0_120 ),
inference(resolution,[],[f1609,f1095]) ).
fof(f1609,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X1) = X1 )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1608]) ).
fof(f22617,plain,
( spl0_805
| ~ spl0_19
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1722,f1604,f1093,f22615]) ).
fof(f1604,plain,
( spl0_119
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1722,plain,
( ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X0) = X0
| ~ spl0_19
| ~ spl0_119 ),
inference(resolution,[],[f1605,f1095]) ).
fof(f1605,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X1) = X1 )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1604]) ).
fof(f22613,plain,
( spl0_804
| ~ spl0_89
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1573,f1442,f1402,f22611]) ).
fof(f22611,plain,
( spl0_804
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f1573,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_89
| ~ spl0_99 ),
inference(resolution,[],[f1443,f1403]) ).
fof(f22609,plain,
( spl0_803
| ~ spl0_90
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1569,f1438,f1406,f22607]) ).
fof(f22607,plain,
( spl0_803
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f1569,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_90
| ~ spl0_98 ),
inference(resolution,[],[f1439,f1407]) ).
fof(f22605,plain,
( spl0_802
| ~ spl0_91
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1558,f1434,f1410,f22603]) ).
fof(f22603,plain,
( spl0_802
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f1558,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_91
| ~ spl0_97 ),
inference(resolution,[],[f1435,f1411]) ).
fof(f22577,plain,
( ~ spl0_1
| spl0_801
| ~ spl0_2
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f18983,f18841,f1008,f22575,f1003]) ).
fof(f22575,plain,
( spl0_801
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_Finite__Set_Osetsum(X1,v_U,tc_Com_Opname,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X1,v_x)),c_Finite__Set_Osetsum(X1,c_HOL_Ominus__class_Ominus(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f1008,plain,
( spl0_2
<=> hBOOL(c_in(v_x,v_U,tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f18841,plain,
( spl0_726
<=> ! [X20,X0,X14,X6,X25] :
( c_Finite__Set_Osetsum(X25,X6,X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20))
| ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f18983,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Osetsum(X1,v_U,tc_Com_Opname,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X1,v_x)),c_Finite__Set_Osetsum(X1,c_HOL_Ominus__class_Ominus(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,X0)) )
| ~ spl0_2
| ~ spl0_726 ),
inference(resolution,[],[f18842,f1010]) ).
fof(f1010,plain,
( hBOOL(c_in(v_x,v_U,tc_Com_Opname))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f18842,plain,
( ! [X0,X6,X14,X25,X20] :
( ~ hBOOL(c_in(X14,X6,X0))
| ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Osetsum(X25,X6,X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20)) )
| ~ spl0_726 ),
inference(avatar_component_clause,[],[f18841]) ).
fof(f22573,plain,
( spl0_799
| ~ spl0_800
| ~ spl0_1
| ~ spl0_709 ),
inference(avatar_split_clause,[],[f18380,f17575,f1003,f22570,f22567]) ).
fof(f22567,plain,
( spl0_799
<=> ! [X0,X1] : c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X0,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X1),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X0,v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f22570,plain,
( spl0_800
<=> class_Lattices_Olower__semilattice(tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f17575,plain,
( spl0_709
<=> ! [X0,X14,X6,X16] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f18380,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_Com_Opname)
| c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X0,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X1),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X0,v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)) )
| ~ spl0_1
| ~ spl0_709 ),
inference(resolution,[],[f17576,f1005]) ).
fof(f17576,plain,
( ! [X0,X6,X16,X14] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0)) )
| ~ spl0_709 ),
inference(avatar_component_clause,[],[f17575]) ).
fof(f22565,plain,
( spl0_797
| ~ spl0_798
| ~ spl0_1
| ~ spl0_708 ),
inference(avatar_split_clause,[],[f18361,f17571,f1003,f22562,f22559]) ).
fof(f22559,plain,
( spl0_797
<=> ! [X0,X1] : c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X0,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X1),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X0,v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f22562,plain,
( spl0_798
<=> class_Lattices_Oupper__semilattice(tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f17571,plain,
( spl0_708
<=> ! [X0,X14,X6,X16] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f18361,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_Com_Opname)
| c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X0,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X1),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X0,v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)) )
| ~ spl0_1
| ~ spl0_708 ),
inference(resolution,[],[f17572,f1005]) ).
fof(f17572,plain,
( ! [X0,X6,X16,X14] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0)) )
| ~ spl0_708 ),
inference(avatar_component_clause,[],[f17571]) ).
fof(f22523,plain,
( spl0_796
| ~ spl0_106
| ~ spl0_771 ),
inference(avatar_split_clause,[],[f21635,f21374,f1470,f22521]) ).
fof(f22521,plain,
( spl0_796
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X0,v_U,tc_Com_Opname,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f21635,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X0,v_U,tc_Com_Opname,X1)
| ~ spl0_106
| ~ spl0_771 ),
inference(superposition,[],[f1471,f21375]) ).
fof(f22518,plain,
( spl0_795
| ~ spl0_82
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2255,f2032,f1369,f22516]) ).
fof(f22516,plain,
( spl0_795
<=> ! [X0,X1] : hBOOL(c_in(X0,c_fequal(X0,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f2255,plain,
( ! [X0,X1] : hBOOL(c_in(X0,c_fequal(X0,X1),X1))
| ~ spl0_82
| ~ spl0_186 ),
inference(superposition,[],[f1370,f2033]) ).
fof(f22514,plain,
( spl0_794
| ~ spl0_111
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1866,f1699,f1490,f22512]) ).
fof(f22512,plain,
( spl0_794
<=> ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X0,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f1490,plain,
( spl0_111
<=> ! [X57,X0,X47] :
( X47 = X57
| ~ hBOOL(hAPP(c_fequal(X47,X0),X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1699,plain,
( spl0_142
<=> ! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1866,plain,
( ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X0,X1),X1) = X0
| ~ spl0_111
| ~ spl0_142 ),
inference(resolution,[],[f1700,f1491]) ).
fof(f1491,plain,
( ! [X0,X47,X57] :
( ~ hBOOL(hAPP(c_fequal(X47,X0),X57))
| X47 = X57 )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1490]) ).
fof(f1700,plain,
( ! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0)))
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1699]) ).
fof(f22510,plain,
( spl0_793
| ~ spl0_25
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f1596,f1506,f1123,f22508]) ).
fof(f22508,plain,
( spl0_793
<=> ! [X0] : c_Complete__Lattice_OSup__class_OSup(c_fequal(X0,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f1596,plain,
( ! [X0] : c_Complete__Lattice_OSup__class_OSup(c_fequal(X0,tc_bool),tc_bool) = X0
| ~ spl0_25
| ~ spl0_115 ),
inference(resolution,[],[f1507,f1125]) ).
fof(f22506,plain,
( spl0_792
| ~ spl0_25
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1594,f1502,f1123,f22504]) ).
fof(f22504,plain,
( spl0_792
<=> ! [X0] : c_Complete__Lattice_OInf__class_OInf(c_fequal(X0,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f1594,plain,
( ! [X0] : c_Complete__Lattice_OInf__class_OInf(c_fequal(X0,tc_bool),tc_bool) = X0
| ~ spl0_25
| ~ spl0_114 ),
inference(resolution,[],[f1503,f1125]) ).
fof(f22327,plain,
( spl0_791
| ~ spl0_3
| ~ spl0_390
| ~ spl0_703 ),
inference(avatar_split_clause,[],[f17773,f17551,f6638,f1013,f22325]) ).
fof(f22325,plain,
( spl0_791
<=> ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),tc_fun(t_a,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f6638,plain,
( spl0_390
<=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f17551,plain,
( spl0_703
<=> ! [X20,X0,X6,X25,X8] : c_lessequals(c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X20,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f17773,plain,
( ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),tc_fun(t_a,tc_bool))
| ~ spl0_3
| ~ spl0_390
| ~ spl0_703 ),
inference(forward_demodulation,[],[f17755,f6639]) ).
fof(f6639,plain,
( ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X6)
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f6638]) ).
fof(f17755,plain,
( ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),v_G),tc_fun(t_a,tc_bool))
| ~ spl0_3
| ~ spl0_703 ),
inference(superposition,[],[f17552,f1015]) ).
fof(f17552,plain,
( ! [X0,X8,X6,X25,X20] : c_lessequals(c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X20,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)),tc_fun(X0,tc_bool))
| ~ spl0_703 ),
inference(avatar_component_clause,[],[f17551]) ).
fof(f22323,plain,
( spl0_790
| ~ spl0_3
| ~ spl0_703 ),
inference(avatar_split_clause,[],[f17749,f17551,f1013,f22321]) ).
fof(f22321,plain,
( spl0_790
<=> ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),tc_fun(t_a,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f17749,plain,
( ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),tc_fun(t_a,tc_bool))
| ~ spl0_3
| ~ spl0_703 ),
inference(superposition,[],[f17552,f1015]) ).
fof(f22319,plain,
( spl0_789
| ~ spl0_72
| ~ spl0_771 ),
inference(avatar_split_clause,[],[f21632,f21374,f1327,f22317]) ).
fof(f21632,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),hAPP(X0,v_x)))
| ~ spl0_72
| ~ spl0_771 ),
inference(superposition,[],[f1328,f21375]) ).
fof(f22315,plain,
( spl0_788
| ~ spl0_1
| ~ spl0_688 ),
inference(avatar_split_clause,[],[f16331,f15876,f1003,f22313]) ).
fof(f22313,plain,
( spl0_788
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hBOOL(c_in(X1,v_U,tc_Com_Opname))
| c_Finite__Set_Osetsum(X2,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X2,X1)),c_Finite__Set_Osetsum(X2,v_U,tc_Com_Opname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f15876,plain,
( spl0_688
<=> ! [X20,X0,X14,X33,X25] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X33,X0)
| hBOOL(c_in(X14,X33,X0))
| c_Finite__Set_Osetsum(X25,c_Set_Oinsert(X14,X33,X0),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,X33,X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f16331,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hBOOL(c_in(X1,v_U,tc_Com_Opname))
| c_Finite__Set_Osetsum(X2,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X2,X1)),c_Finite__Set_Osetsum(X2,v_U,tc_Com_Opname,X0)) )
| ~ spl0_1
| ~ spl0_688 ),
inference(resolution,[],[f15877,f1005]) ).
fof(f15877,plain,
( ! [X0,X14,X25,X33,X20] :
( ~ c_Finite__Set_Ofinite(X33,X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| hBOOL(c_in(X14,X33,X0))
| c_Finite__Set_Osetsum(X25,c_Set_Oinsert(X14,X33,X0),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,X33,X0,X20)) )
| ~ spl0_688 ),
inference(avatar_component_clause,[],[f15876]) ).
fof(f22266,plain,
( spl0_787
| ~ spl0_2
| ~ spl0_698 ),
inference(avatar_split_clause,[],[f17440,f15916,f1008,f22264]) ).
fof(f22264,plain,
( spl0_787
<=> ! [X2,X0,X1] : c_Set_Oimage(c_Fun_Ofun__upd(X0,v_x,X1,tc_Com_Opname,X2),v_U,tc_Com_Opname,X2) = c_Set_Oinsert(X1,c_Set_Oimage(X0,c_HOL_Ominus__class_Ominus(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f15916,plain,
( spl0_698
<=> ! [X2,X20,X0,X6,X25,X1] :
( c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) = c_Set_Oinsert(X2,c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X20),tc_fun(X20,tc_bool)),X20,X0),X0)
| ~ hBOOL(c_in(X1,X6,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f17440,plain,
( ! [X2,X0,X1] : c_Set_Oimage(c_Fun_Ofun__upd(X0,v_x,X1,tc_Com_Opname,X2),v_U,tc_Com_Opname,X2) = c_Set_Oinsert(X1,c_Set_Oimage(X0,c_HOL_Ominus__class_Ominus(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,X2),X2)
| ~ spl0_2
| ~ spl0_698 ),
inference(resolution,[],[f15917,f1010]) ).
fof(f15917,plain,
( ! [X2,X0,X1,X6,X25,X20] :
( ~ hBOOL(c_in(X1,X6,X20))
| c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) = c_Set_Oinsert(X2,c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X20),tc_fun(X20,tc_bool)),X20,X0),X0) )
| ~ spl0_698 ),
inference(avatar_component_clause,[],[f15916]) ).
fof(f22073,plain,
( spl0_786
| ~ spl0_3
| ~ spl0_662 ),
inference(avatar_split_clause,[],[f15372,f14552,f1013,f22071]) ).
fof(f22071,plain,
( spl0_786
<=> ! [X0] : c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),v_G) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f14552,plain,
( spl0_662
<=> ! [X20,X0,X6,X25,X8] : c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X20,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f15372,plain,
( ! [X0] : c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),v_G)
| ~ spl0_3
| ~ spl0_662 ),
inference(superposition,[],[f14553,f1015]) ).
fof(f14553,plain,
( ! [X0,X8,X6,X25,X20] : c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X20,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0))
| ~ spl0_662 ),
inference(avatar_component_clause,[],[f14552]) ).
fof(f22069,plain,
( spl0_785
| ~ spl0_3
| ~ spl0_662 ),
inference(avatar_split_clause,[],[f15366,f14552,f1013,f22067]) ).
fof(f22067,plain,
( spl0_785
<=> ! [X0] : c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f15366,plain,
( ! [X0] : c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a))
| ~ spl0_3
| ~ spl0_662 ),
inference(superposition,[],[f14553,f1015]) ).
fof(f21806,plain,
( spl0_784
| ~ spl0_2
| ~ spl0_663 ),
inference(avatar_split_clause,[],[f15468,f14556,f1008,f21804]) ).
fof(f21804,plain,
( spl0_784
<=> ! [X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_U,X0,tc_Com_Opname,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(X0,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_U,X0,tc_Com_Opname,tc_fun(X1,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f14556,plain,
( spl0_663
<=> ! [X54,X20,X0,X6,X28] :
( ~ hBOOL(c_in(X28,X54,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),hAPP(X6,X28)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f15468,plain,
( ! [X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_U,X0,tc_Com_Opname,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(X0,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_U,X0,tc_Com_Opname,tc_fun(X1,tc_bool)))
| ~ spl0_2
| ~ spl0_663 ),
inference(resolution,[],[f14557,f1010]) ).
fof(f14557,plain,
( ! [X28,X0,X54,X6,X20] :
( ~ hBOOL(c_in(X28,X54,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),hAPP(X6,X28)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool))) )
| ~ spl0_663 ),
inference(avatar_component_clause,[],[f14556]) ).
fof(f21802,plain,
( spl0_441
| ~ spl0_782
| spl0_783
| ~ spl0_1
| ~ spl0_2
| ~ spl0_655 ),
inference(avatar_split_clause,[],[f14832,f14524,f1008,f1003,f21800,f21796,f8018]) ).
fof(f8018,plain,
( spl0_441
<=> v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f21796,plain,
( spl0_782
<=> class_Orderings_Olinorder(tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f21800,plain,
( spl0_783
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(v_x,X0,tc_Com_Opname)
| c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_Com_Opname),tc_Com_Opname),v_U),X0,tc_Com_Opname) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f14524,plain,
( spl0_655
<=> ! [X34,X0,X6,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_HOL_Oord__class_Oless(X34,X1,X0)
| ~ hBOOL(c_in(X34,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f14832,plain,
( ! [X0] :
( ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| ~ c_HOL_Oord__class_Oless(v_x,X0,tc_Com_Opname)
| ~ class_Orderings_Olinorder(tc_Com_Opname)
| v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))
| c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_Com_Opname),tc_Com_Opname),v_U),X0,tc_Com_Opname) )
| ~ spl0_2
| ~ spl0_655 ),
inference(resolution,[],[f14525,f1010]) ).
fof(f14525,plain,
( ! [X0,X1,X6,X34] :
( ~ hBOOL(c_in(X34,X6,X0))
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_HOL_Oord__class_Oless(X34,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) )
| ~ spl0_655 ),
inference(avatar_component_clause,[],[f14524]) ).
fof(f21794,plain,
( spl0_781
| ~ spl0_3
| ~ spl0_647 ),
inference(avatar_split_clause,[],[f14373,f14138,f1013,f21792]) ).
fof(f21792,plain,
( spl0_781
<=> ! [X0] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f14138,plain,
( spl0_647
<=> ! [X20,X0,X6,X25,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X20,X0),c_Set_Oimage(X25,X8,X20,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X20,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f14373,plain,
( ! [X0] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ spl0_3
| ~ spl0_647 ),
inference(superposition,[],[f14139,f1015]) ).
fof(f14139,plain,
( ! [X0,X8,X6,X25,X20] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X20,X0),c_Set_Oimage(X25,X8,X20,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X20,X0),tc_fun(X0,tc_bool))
| ~ spl0_647 ),
inference(avatar_component_clause,[],[f14138]) ).
fof(f21790,plain,
( spl0_780
| ~ spl0_3
| ~ spl0_647 ),
inference(avatar_split_clause,[],[f14367,f14138,f1013,f21788]) ).
fof(f21788,plain,
( spl0_780
<=> ! [X0] : c_lessequals(c_HOL_Ominus__class_Ominus(v_G,c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,X0,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f14367,plain,
( ! [X0] : c_lessequals(c_HOL_Ominus__class_Ominus(v_G,c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,X0,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ spl0_3
| ~ spl0_647 ),
inference(superposition,[],[f14139,f1015]) ).
fof(f21777,plain,
( spl0_779
| ~ spl0_3
| ~ spl0_630 ),
inference(avatar_split_clause,[],[f13453,f13228,f1013,f21775]) ).
fof(f21775,plain,
( spl0_779
<=> ! [X0] :
( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
| v_U = X0
| ~ c_Fun_Oinj__on(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f13228,plain,
( spl0_630
<=> ! [X20,X0,X6,X25,X8] :
( X6 = X8
| c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20)
| ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f13453,plain,
( ! [X0] :
( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
| v_U = X0
| ~ c_Fun_Oinj__on(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a) )
| ~ spl0_3
| ~ spl0_630 ),
inference(superposition,[],[f13229,f1015]) ).
fof(f13229,plain,
( ! [X0,X8,X6,X25,X20] :
( c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20)
| X6 = X8
| ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) )
| ~ spl0_630 ),
inference(avatar_component_clause,[],[f13228]) ).
fof(f21773,plain,
( spl0_778
| ~ spl0_3
| ~ spl0_630 ),
inference(avatar_split_clause,[],[f13447,f13228,f1013,f21771]) ).
fof(f21771,plain,
( spl0_778
<=> ! [X0] :
( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
| v_U = X0
| ~ c_Fun_Oinj__on(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f13447,plain,
( ! [X0] :
( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
| v_U = X0
| ~ c_Fun_Oinj__on(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a) )
| ~ spl0_3
| ~ spl0_630 ),
inference(superposition,[],[f13229,f1015]) ).
fof(f21729,plain,
( ~ spl0_777
| ~ spl0_194
| spl0_774 ),
inference(avatar_split_clause,[],[f21685,f21678,f2283,f21726]) ).
fof(f21726,plain,
( spl0_777
<=> c_Fun_Obij(v_mgt__call,tc_Com_Opname,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f2283,plain,
( spl0_194
<=> ! [X20,X0,X25] :
( ~ c_Fun_Obij(X25,X0,X20)
| c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f21678,plain,
( spl0_774
<=> c_Fun_Oinj__on(v_mgt__call,c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f21685,plain,
( ~ c_Fun_Obij(v_mgt__call,tc_Com_Opname,t_a)
| ~ spl0_194
| spl0_774 ),
inference(resolution,[],[f21680,f2284]) ).
fof(f2284,plain,
( ! [X0,X25,X20] :
( c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| ~ c_Fun_Obij(X25,X0,X20) )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2283]) ).
fof(f21680,plain,
( ~ c_Fun_Oinj__on(v_mgt__call,c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a)
| spl0_774 ),
inference(avatar_component_clause,[],[f21678]) ).
fof(f21689,plain,
( spl0_776
| ~ spl0_3
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f11117,f10696,f1013,f21687]) ).
fof(f21687,plain,
( spl0_776
<=> ! [X0,X1] :
( ~ c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
| hBOOL(c_in(hAPP(v_mgt__call,X1),X0,t_a))
| ~ hBOOL(c_in(X1,v_U,tc_Com_Opname)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f10696,plain,
( spl0_550
<=> ! [X8,X20,X0,X6,X25,X1] :
( ~ hBOOL(c_in(X1,X6,X20))
| hBOOL(c_in(hAPP(X25,X1),X8,X0))
| ~ c_lessequals(c_Set_Oimage(X25,X6,X20,X0),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f11117,plain,
( ! [X0,X1] :
( ~ c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
| hBOOL(c_in(hAPP(v_mgt__call,X1),X0,t_a))
| ~ hBOOL(c_in(X1,v_U,tc_Com_Opname)) )
| ~ spl0_3
| ~ spl0_550 ),
inference(superposition,[],[f10697,f1015]) ).
fof(f10697,plain,
( ! [X0,X1,X8,X6,X25,X20] :
( ~ c_lessequals(c_Set_Oimage(X25,X6,X20,X0),X8,tc_fun(X0,tc_bool))
| hBOOL(c_in(hAPP(X25,X1),X8,X0))
| ~ hBOOL(c_in(X1,X6,X20)) )
| ~ spl0_550 ),
inference(avatar_component_clause,[],[f10696]) ).
fof(f21684,plain,
( ~ spl0_774
| spl0_775
| ~ spl0_3
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f11045,f10681,f1013,f21682,f21678]) ).
fof(f21682,plain,
( spl0_775
<=> ! [X0] :
( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
| v_U = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f10681,plain,
( spl0_548
<=> ! [X20,X0,X6,X25,X8] :
( X6 = X8
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f11045,plain,
( ! [X0] :
( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
| ~ c_Fun_Oinj__on(v_mgt__call,c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a)
| v_U = X0 )
| ~ spl0_3
| ~ spl0_548 ),
inference(superposition,[],[f10682,f1015]) ).
fof(f10682,plain,
( ! [X0,X8,X6,X25,X20] :
( c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| X6 = X8 )
| ~ spl0_548 ),
inference(avatar_component_clause,[],[f10681]) ).
fof(f21676,plain,
( spl0_773
| ~ spl0_1
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f10590,f10355,f1003,f21674]) ).
fof(f21674,plain,
( spl0_773
<=> ! [X0] : c_Finite__Set_Ocard(c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(v_U,c_fequal(X0,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f10590,plain,
( ! [X0] : c_Finite__Set_Ocard(c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(v_U,c_fequal(X0,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname))
| ~ spl0_1
| ~ spl0_528 ),
inference(resolution,[],[f10356,f1005]) ).
fof(f21447,plain,
( spl0_772
| ~ spl0_109
| ~ spl0_702 ),
inference(avatar_split_clause,[],[f19018,f17547,f1482,f21445]) ).
fof(f21445,plain,
( spl0_772
<=> ! [X0] :
( v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a)
| ~ hBOOL(hAPP(v_U,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f17547,plain,
( spl0_702
<=> ! [X0] :
( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
| v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f19018,plain,
( ! [X0] :
( v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a)
| ~ hBOOL(hAPP(v_U,X0)) )
| ~ spl0_109
| ~ spl0_702 ),
inference(resolution,[],[f17548,f1483]) ).
fof(f17548,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
| v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) )
| ~ spl0_702 ),
inference(avatar_component_clause,[],[f17547]) ).
fof(f21376,plain,
( spl0_771
| ~ spl0_2
| ~ spl0_527 ),
inference(avatar_split_clause,[],[f10568,f10351,f1008,f21374]) ).
fof(f10351,plain,
( spl0_527
<=> ! [X20,X0,X6,X25,X1] :
( ~ hBOOL(c_in(X1,X6,X0))
| c_Set_Oimage(X25,X6,X0,X20) = c_Set_Oinsert(hAPP(X25,X1),c_Set_Oimage(X25,X6,X0,X20),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f10568,plain,
( ! [X0,X1] : c_Set_Oimage(X0,v_U,tc_Com_Opname,X1) = c_Set_Oinsert(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1)
| ~ spl0_2
| ~ spl0_527 ),
inference(resolution,[],[f10352,f1010]) ).
fof(f10352,plain,
( ! [X0,X1,X6,X25,X20] :
( ~ hBOOL(c_in(X1,X6,X0))
| c_Set_Oimage(X25,X6,X0,X20) = c_Set_Oinsert(hAPP(X25,X1),c_Set_Oimage(X25,X6,X0,X20),X20) )
| ~ spl0_527 ),
inference(avatar_component_clause,[],[f10351]) ).
fof(f21372,plain,
( spl0_770
| ~ spl0_2
| ~ spl0_523 ),
inference(avatar_split_clause,[],[f10437,f10335,f1008,f21370]) ).
fof(f21370,plain,
( spl0_770
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,X0,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f10335,plain,
( spl0_523
<=> ! [X0,X8,X6,X1] :
( ~ hBOOL(c_in(X1,X8,X0))
| c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f10437,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,X0,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool))
| ~ spl0_2
| ~ spl0_523 ),
inference(resolution,[],[f10336,f1010]) ).
fof(f10336,plain,
( ! [X0,X1,X8,X6] :
( ~ hBOOL(c_in(X1,X8,X0))
| c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) )
| ~ spl0_523 ),
inference(avatar_component_clause,[],[f10335]) ).
fof(f21368,plain,
( spl0_769
| ~ spl0_3
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f10265,f9495,f1013,f21366]) ).
fof(f21366,plain,
( spl0_769
<=> ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0),v_U,tc_Com_Opname)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f9495,plain,
( spl0_513
<=> ! [X20,X0,X6,X25,X1] :
( ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X20,X0),X0))
| hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X1),X6,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f10265,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0),v_U,tc_Com_Opname)) )
| ~ spl0_3
| ~ spl0_513 ),
inference(superposition,[],[f9496,f1015]) ).
fof(f9496,plain,
( ! [X0,X1,X6,X25,X20] :
( ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X20,X0),X0))
| hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X1),X6,X20)) )
| ~ spl0_513 ),
inference(avatar_component_clause,[],[f9495]) ).
fof(f21364,plain,
( spl0_768
| ~ spl0_3
| ~ spl0_512 ),
inference(avatar_split_clause,[],[f10250,f9491,f1013,f21362]) ).
fof(f21362,plain,
( spl0_768
<=> ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hAPP(v_mgt__call,hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f9491,plain,
( spl0_512
<=> ! [X2,X20,X0,X6,X25] :
( ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X20,X0),X0))
| hAPP(X25,hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f10250,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hAPP(v_mgt__call,hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0)) = X0 )
| ~ spl0_3
| ~ spl0_512 ),
inference(superposition,[],[f9492,f1015]) ).
fof(f9492,plain,
( ! [X2,X0,X6,X25,X20] :
( ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X20,X0),X0))
| hAPP(X25,hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X2)) = X2 )
| ~ spl0_512 ),
inference(avatar_component_clause,[],[f9491]) ).
fof(f21360,plain,
( spl0_767
| ~ spl0_3
| ~ spl0_509 ),
inference(avatar_split_clause,[],[f10117,f9479,f1013,f21358]) ).
fof(f21358,plain,
( spl0_767
<=> ! [X0] :
( c_lessequals(c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))
| ~ c_lessequals(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f9479,plain,
( spl0_509
<=> ! [X20,X0,X6,X25,X1] :
( ~ c_lessequals(X1,X6,tc_fun(X20,tc_bool))
| c_lessequals(c_Set_Oimage(X25,X1,X20,X0),c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f10117,plain,
( ! [X0] :
( c_lessequals(c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))
| ~ c_lessequals(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)) )
| ~ spl0_3
| ~ spl0_509 ),
inference(superposition,[],[f9480,f1015]) ).
fof(f9480,plain,
( ! [X0,X1,X6,X25,X20] :
( c_lessequals(c_Set_Oimage(X25,X1,X20,X0),c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool))
| ~ c_lessequals(X1,X6,tc_fun(X20,tc_bool)) )
| ~ spl0_509 ),
inference(avatar_component_clause,[],[f9479]) ).
fof(f21356,plain,
( spl0_766
| ~ spl0_3
| ~ spl0_509 ),
inference(avatar_split_clause,[],[f10112,f9479,f1013,f21354]) ).
fof(f21354,plain,
( spl0_766
<=> ! [X0] :
( c_lessequals(v_G,c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f10112,plain,
( ! [X0] :
( c_lessequals(v_G,c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool)) )
| ~ spl0_3
| ~ spl0_509 ),
inference(superposition,[],[f9480,f1015]) ).
fof(f21352,plain,
( spl0_764
| ~ spl0_765
| ~ spl0_1
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f9310,f8169,f1003,f21349,f21345]) ).
fof(f21345,plain,
( spl0_764
<=> c_Complete__Lattice_OSup__class_OSup(v_U,tc_Com_Opname) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_Com_Opname),v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f21349,plain,
( spl0_765
<=> class_Complete__Lattice_Ocomplete__lattice(tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f8169,plain,
( spl0_478
<=> ! [X6,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Complete__Lattice_OSup__class_OSup(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0),X6,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f9310,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(tc_Com_Opname)
| c_Complete__Lattice_OSup__class_OSup(v_U,tc_Com_Opname) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_Com_Opname),v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)
| ~ spl0_1
| ~ spl0_478 ),
inference(resolution,[],[f8170,f1005]) ).
fof(f8170,plain,
( ! [X0,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0),X6,X0,X0),X0) )
| ~ spl0_478 ),
inference(avatar_component_clause,[],[f8169]) ).
fof(f21198,plain,
( spl0_763
| ~ spl0_3
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f9249,f8165,f1013,f21196]) ).
fof(f21196,plain,
( spl0_763
<=> ! [X0] : c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) = c_Set_Oimage(v_mgt__call,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f9249,plain,
( ! [X0] : c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) = c_Set_Oimage(v_mgt__call,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname,t_a)
| ~ spl0_3
| ~ spl0_477 ),
inference(superposition,[],[f8166,f1015]) ).
fof(f21194,plain,
( spl0_762
| ~ spl0_3
| ~ spl0_471 ),
inference(avatar_split_clause,[],[f9150,f8141,f1013,f21192]) ).
fof(f21192,plain,
( spl0_762
<=> ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f8141,plain,
( spl0_471
<=> ! [X16,X20,X0,X6,X25] :
( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0),X6,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f9150,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)) )
| ~ spl0_3
| ~ spl0_471 ),
inference(superposition,[],[f8142,f1015]) ).
fof(f8142,plain,
( ! [X0,X6,X16,X25,X20] :
( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0),X6,X20)) )
| ~ spl0_471 ),
inference(avatar_component_clause,[],[f8141]) ).
fof(f21190,plain,
( spl0_761
| ~ spl0_3
| ~ spl0_470 ),
inference(avatar_split_clause,[],[f9140,f8137,f1013,f21188]) ).
fof(f21188,plain,
( spl0_761
<=> ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hAPP(v_mgt__call,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f8137,plain,
( spl0_470
<=> ! [X19,X20,X0,X6,X25] :
( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
| hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0)) = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f9140,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hAPP(v_mgt__call,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a)) = X0 )
| ~ spl0_3
| ~ spl0_470 ),
inference(superposition,[],[f8138,f1015]) ).
fof(f8138,plain,
( ! [X0,X19,X6,X25,X20] :
( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
| hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0)) = X19 )
| ~ spl0_470 ),
inference(avatar_component_clause,[],[f8137]) ).
fof(f21186,plain,
( spl0_760
| ~ spl0_3
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f9049,f8125,f1013,f21184]) ).
fof(f21184,plain,
( spl0_760
<=> ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0,t_a,tc_Com_Opname) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f9049,plain,
( ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0,t_a,tc_Com_Opname) )
| ~ spl0_3
| ~ spl0_467 ),
inference(superposition,[],[f8126,f1015]) ).
fof(f21182,plain,
( spl0_759
| ~ spl0_82
| ~ spl0_737 ),
inference(avatar_split_clause,[],[f20181,f19332,f1369,f21179]) ).
fof(f21179,plain,
( spl0_759
<=> hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f19332,plain,
( spl0_737
<=> v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f20181,plain,
( hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,t_a))
| ~ spl0_82
| ~ spl0_737 ),
inference(superposition,[],[f1370,f19334]) ).
fof(f19334,plain,
( v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,t_a)
| ~ spl0_737 ),
inference(avatar_component_clause,[],[f19332]) ).
fof(f21177,plain,
( spl0_758
| ~ spl0_3
| ~ spl0_462 ),
inference(avatar_split_clause,[],[f9003,f8103,f1013,f21175]) ).
fof(f21175,plain,
( spl0_758
<=> ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f8103,plain,
( spl0_462
<=> ! [X19,X20,X0,X6,X25] :
( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0),X6,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f9003,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)) )
| ~ spl0_3
| ~ spl0_462 ),
inference(superposition,[],[f8104,f1015]) ).
fof(f8104,plain,
( ! [X0,X19,X6,X25,X20] :
( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0),X6,X20)) )
| ~ spl0_462 ),
inference(avatar_component_clause,[],[f8103]) ).
fof(f21173,plain,
( spl0_757
| ~ spl0_3
| ~ spl0_461 ),
inference(avatar_split_clause,[],[f8989,f8099,f1013,f21171]) ).
fof(f21171,plain,
( spl0_757
<=> ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hAPP(v_mgt__call,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f8099,plain,
( spl0_461
<=> ! [X16,X20,X0,X6,X25] :
( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
| hAPP(X25,c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0)) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f8989,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,v_G,t_a))
| hAPP(v_mgt__call,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a)) = X0 )
| ~ spl0_3
| ~ spl0_461 ),
inference(superposition,[],[f8100,f1015]) ).
fof(f8100,plain,
( ! [X0,X6,X16,X25,X20] :
( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
| hAPP(X25,c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0)) = X16 )
| ~ spl0_461 ),
inference(avatar_component_clause,[],[f8099]) ).
fof(f21169,plain,
( ~ spl0_1
| spl0_755
| ~ spl0_756
| ~ spl0_3
| ~ spl0_460 ),
inference(avatar_split_clause,[],[f8980,f8095,f1013,f21166,f21162,f1003]) ).
fof(f21162,plain,
( spl0_755
<=> c_Fun_Oinj__on(v_mgt__call,v_U,tc_Com_Opname,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f21166,plain,
( spl0_756
<=> c_Finite__Set_Ocard(v_U,tc_Com_Opname) = c_Finite__Set_Ocard(v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f8095,plain,
( spl0_460
<=> ! [X20,X0,X6,X25] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f8980,plain,
( c_Finite__Set_Ocard(v_U,tc_Com_Opname) != c_Finite__Set_Ocard(v_G,t_a)
| c_Fun_Oinj__on(v_mgt__call,v_U,tc_Com_Opname,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| ~ spl0_3
| ~ spl0_460 ),
inference(superposition,[],[f8096,f1015]) ).
fof(f8096,plain,
( ! [X0,X6,X25,X20] :
( c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20)
| c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_Finite__Set_Ofinite(X6,X0) )
| ~ spl0_460 ),
inference(avatar_component_clause,[],[f8095]) ).
fof(f20774,plain,
( spl0_754
| ~ spl0_390
| ~ spl0_399
| ~ spl0_733
| ~ spl0_735
| ~ spl0_753 ),
inference(avatar_split_clause,[],[f20770,f20766,f19324,f19316,f6699,f6638,f20772]) ).
fof(f20772,plain,
( spl0_754
<=> ! [X0,X6,X8,X7] : 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)),X7),X6)),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)),X6),X7)),X8)) = 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)),X7),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f6699,plain,
( spl0_399
<=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f19316,plain,
( spl0_733
<=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = 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)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f19324,plain,
( spl0_735
<=> ! [X0,X6,X8,X7] : 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)),X8),X7)),X6) = 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)),X8),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f20766,plain,
( spl0_753
<=> ! [X0,X6,X8,X7] : 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)),X7),X6)),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)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))) = 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)),X7),X6)),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)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f20770,plain,
( ! [X0,X8,X6,X7] : 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)),X7),X6)),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)),X6),X7)),X8)) = 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)),X7),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)))
| ~ spl0_390
| ~ spl0_399
| ~ spl0_733
| ~ spl0_735
| ~ spl0_753 ),
inference(forward_demodulation,[],[f20769,f19337]) ).
fof(f19337,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))
| ~ spl0_399
| ~ spl0_733 ),
inference(superposition,[],[f19317,f6700]) ).
fof(f6700,plain,
( ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6)
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f6699]) ).
fof(f19317,plain,
( ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = 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)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7))
| ~ spl0_733 ),
inference(avatar_component_clause,[],[f19316]) ).
fof(f20769,plain,
( ! [X0,X8,X6,X7] : 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)),X7),X6)),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)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))) = 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)),X7),X6)),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)),X6),X7)),X8))
| ~ spl0_390
| ~ spl0_735
| ~ spl0_753 ),
inference(forward_demodulation,[],[f20767,f19747]) ).
fof(f19747,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X1)),X2) = 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)),X3),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_390
| ~ spl0_735 ),
inference(superposition,[],[f19325,f6639]) ).
fof(f19325,plain,
( ! [X0,X8,X6,X7] : 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)),X8),X7)),X6) = 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)),X8),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6))
| ~ spl0_735 ),
inference(avatar_component_clause,[],[f19324]) ).
fof(f20767,plain,
( ! [X0,X8,X6,X7] : 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)),X7),X6)),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)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))) = 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)),X7),X6)),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)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)))
| ~ spl0_753 ),
inference(avatar_component_clause,[],[f20766]) ).
fof(f20768,plain,
spl0_753,
inference(avatar_split_clause,[],[f939,f20766]) ).
fof(f939,plain,
! [X0,X8,X6,X7] : 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)),X7),X6)),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)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))) = 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)),X7),X6)),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)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7))),
inference(forward_demodulation,[],[f938,f514]) ).
fof(f514,axiom,
! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f938,plain,
! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)) = 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)),X7),X6)),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)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))),
inference(forward_demodulation,[],[f364,f259]) ).
fof(f259,axiom,
! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f364,axiom,
! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
fof(f20702,plain,
spl0_752,
inference(avatar_split_clause,[],[f333,f20700]) ).
fof(f20700,plain,
( spl0_752
<=> ! [X6,X0,X8] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X6)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f333,axiom,
! [X0,X8,X6] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X6)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__Un_0) ).
fof(f20698,plain,
spl0_751,
inference(avatar_split_clause,[],[f332,f20696]) ).
fof(f20696,plain,
( spl0_751
<=> ! [X6,X0,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X6)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f332,axiom,
! [X0,X8,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X6)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__Un_0) ).
fof(f20579,plain,
spl0_750,
inference(avatar_split_clause,[],[f479,f20577]) ).
fof(f20577,plain,
( spl0_750
<=> ! [X20,X0,X6,X25,X8] :
( ~ c_Fun_Oinj__on(X25,X8,X0,X20)
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)
| c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f479,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X8,X0,X20)
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)
| c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
fof(f20552,plain,
spl0_749,
inference(avatar_split_clause,[],[f178,f20550]) ).
fof(f178,axiom,
! [X21,X0,X8,X6,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).
fof(f20508,plain,
spl0_748,
inference(avatar_split_clause,[],[f38,f20506]) ).
fof(f20506,plain,
( spl0_748
<=> ! [X21,X20,X0,X6,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
| c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f38,axiom,
! [X21,X0,X8,X6,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
| c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).
fof(f20410,plain,
spl0_747,
inference(avatar_split_clause,[],[f452,f20408]) ).
fof(f20408,plain,
( spl0_747
<=> ! [X8,X20,X0,X6,X25,X7] :
( ~ c_Fun_Oinj__on(X25,X7,X0,X20)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,X6,X0,X20)),c_Set_Oimage(X25,X8,X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f452,axiom,
! [X0,X8,X6,X7,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X7,X0,X20)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,X6,X0,X20)),c_Set_Oimage(X25,X8,X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
fof(f20406,plain,
( spl0_746
| ~ spl0_72
| ~ spl0_737 ),
inference(avatar_split_clause,[],[f20180,f19332,f1327,f20403]) ).
fof(f20180,plain,
( hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_x)))
| ~ spl0_72
| ~ spl0_737 ),
inference(superposition,[],[f1328,f19334]) ).
fof(f20363,plain,
spl0_745,
inference(avatar_split_clause,[],[f464,f20361]) ).
fof(f20361,plain,
( spl0_745
<=> ! [X6,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Olinorder__class_OMax(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6)),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f464,axiom,
! [X0,X8,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Olinorder__class_OMax(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6)),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__Un_0) ).
fof(f20359,plain,
spl0_744,
inference(avatar_split_clause,[],[f463,f20357]) ).
fof(f20357,plain,
( spl0_744
<=> ! [X6,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Olinorder__class_OMin(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6)),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f463,axiom,
! [X0,X8,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Olinorder__class_OMin(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6)),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__Un_0) ).
fof(f20240,plain,
spl0_743,
inference(avatar_split_clause,[],[f717,f20238]) ).
fof(f20238,plain,
( spl0_743
<=> ! [X21,X20,X0,X6,X25,X8] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X20)
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_Fun_Oinj__on(X21,X8,X20,X0)
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(X8,X20)
| ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),X8,tc_fun(X20,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X21,X8,X20,X0),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f717,axiom,
! [X21,X0,X8,X6,X25,X20] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X8,X20)
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_Fun_Oinj__on(X21,X8,X20,X0)
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(X8,X20)
| ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),X8,tc_fun(X20,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X21,X8,X20,X0),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).
fof(f20236,plain,
spl0_742,
inference(avatar_split_clause,[],[f478,f20234]) ).
fof(f20234,plain,
( spl0_742
<=> ! [X20,X0,X6,X25,X8] :
( ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)
| c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f478,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)
| c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
fof(f20087,plain,
spl0_741,
inference(avatar_split_clause,[],[f1001,f20085]) ).
fof(f20085,plain,
( spl0_741
<=> ! [X16,X0,X14,X6,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ hBOOL(c_in(X14,X6,X0))
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f1001,plain,
! [X0,X1,X6,X16,X14] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ hBOOL(c_in(X14,X6,X0))
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X1)) ),
inference(forward_demodulation,[],[f319,f926]) ).
fof(f926,plain,
! [X0,X14] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_fequal(X14,X0),
inference(forward_demodulation,[],[f774,f665]) ).
fof(f665,axiom,
! [X0,X26] : c_Collect(X26,X0) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f774,axiom,
! [X0,X14] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Collect(c_fequal(X14,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
fof(f319,axiom,
! [X0,X1,X6,X16,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ hBOOL(c_in(X14,X6,X0))
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X1))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__permute__diff_0) ).
fof(f20083,plain,
spl0_740,
inference(avatar_split_clause,[],[f1000,f20081]) ).
fof(f20081,plain,
( spl0_740
<=> ! [X16,X0,X14,X6,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ hBOOL(c_in(X14,X6,X0))
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1000,plain,
! [X0,X1,X6,X16,X14] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ hBOOL(c_in(X14,X6,X0))
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X1)) ),
inference(forward_demodulation,[],[f320,f926]) ).
fof(f320,axiom,
! [X0,X1,X6,X16,X14] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ hBOOL(c_in(X14,X6,X0))
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X1))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__permute__diff_0) ).
fof(f20079,plain,
spl0_739,
inference(avatar_split_clause,[],[f747,f20077]) ).
fof(f20077,plain,
( spl0_739
<=> ! [X8,X20,X0,X6,X25,X7] :
( ~ c_Fun_Oinj__on(X25,X7,X0,X20)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f747,axiom,
! [X0,X8,X6,X7,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X7,X0,X20)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
fof(f20074,plain,
spl0_738,
inference(avatar_split_clause,[],[f363,f20072]) ).
fof(f20072,plain,
( spl0_738
<=> ! [X15,X0,X14,X16,X22] :
( ~ class_Ring__and__Field_Osemiring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X22)),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X22)),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f363,axiom,
! [X0,X16,X14,X15,X22] :
( ~ class_Ring__and__Field_Osemiring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X22)),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X22)),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f19335,plain,
( spl0_737
| ~ spl0_2
| ~ spl0_702 ),
inference(avatar_split_clause,[],[f19031,f17547,f1008,f19332]) ).
fof(f19031,plain,
( v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,t_a)
| ~ spl0_2
| ~ spl0_702 ),
inference(resolution,[],[f17548,f1010]) ).
fof(f19330,plain,
spl0_736,
inference(avatar_split_clause,[],[f198,f19328]) ).
fof(f19328,plain,
( spl0_736
<=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = 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)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f198,axiom,
! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = 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)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
fof(f19326,plain,
spl0_735,
inference(avatar_split_clause,[],[f197,f19324]) ).
fof(f197,axiom,
! [X0,X8,X6,X7] : 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)),X8),X7)),X6) = 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)),X8),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
fof(f19322,plain,
spl0_734,
inference(avatar_split_clause,[],[f119,f19320]) ).
fof(f19320,plain,
( spl0_734
<=> ! [X0,X6,X8,X7] : 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)),X8),X7)),X6) = 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)),X8),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f119,axiom,
! [X0,X8,X6,X7] : 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)),X8),X7)),X6) = 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)),X8),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
fof(f19318,plain,
spl0_733,
inference(avatar_split_clause,[],[f118,f19316]) ).
fof(f118,axiom,
! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = 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)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
fof(f19036,plain,
spl0_732,
inference(avatar_split_clause,[],[f473,f19034]) ).
fof(f19034,plain,
( spl0_732
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X1,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f473,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X1,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__insert_0) ).
fof(f19017,plain,
spl0_731,
inference(avatar_split_clause,[],[f472,f19015]) ).
fof(f19015,plain,
( spl0_731
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X1,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f472,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X1,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__insert_0) ).
fof(f19013,plain,
spl0_730,
inference(avatar_split_clause,[],[f453,f19011]) ).
fof(f19011,plain,
( spl0_730
<=> ! [X20,X0,X6,X25,X8] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,X6,X0,X20)),c_Set_Oimage(X25,X8,X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f453,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,X6,X0,X20)),c_Set_Oimage(X25,X8,X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
fof(f19009,plain,
spl0_729,
inference(avatar_split_clause,[],[f329,f19007]) ).
fof(f19007,plain,
( spl0_729
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = 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)),X6),X8)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f329,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = 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)),X6),X8)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
fof(f19005,plain,
spl0_728,
inference(avatar_split_clause,[],[f328,f19003]) ).
fof(f19003,plain,
( spl0_728
<=> ! [X0,X6,X8,X7] :
( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) != 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)),X6),X8)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f328,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) != 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)),X6),X8)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
fof(f18999,plain,
spl0_727,
inference(avatar_split_clause,[],[f766,f18997]) ).
fof(f18997,plain,
( spl0_727
<=> ! [X20,X0,X6,X25,X2,X1] :
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X0,X20),X20))
| ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X0,X20),X20))
| hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f766,axiom,
! [X2,X0,X1,X6,X25,X20] :
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X0,X20),X20))
| ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X0,X20),X20))
| hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).
fof(f18843,plain,
spl0_726,
inference(avatar_split_clause,[],[f991,f18841]) ).
fof(f991,plain,
! [X0,X6,X14,X25,X20] :
( c_Finite__Set_Osetsum(X25,X6,X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20))
| ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0)) ),
inference(forward_demodulation,[],[f440,f926]) ).
fof(f440,axiom,
! [X0,X6,X14,X25,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0))
| c_Finite__Set_Osetsum(X25,X6,X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_H_0) ).
fof(f18839,plain,
spl0_725,
inference(avatar_split_clause,[],[f748,f18837]) ).
fof(f18837,plain,
( spl0_725
<=> ! [X48,X20,X0,X6,X8] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X48,X20,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(X6,X48,X20,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X48,X20,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f748,axiom,
! [X48,X0,X8,X6,X20] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X48,X20,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(X6,X48,X20,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X48,X20,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
fof(f18835,plain,
spl0_724,
inference(avatar_split_clause,[],[f426,f18833]) ).
fof(f18833,plain,
( spl0_724
<=> ! [X16,X19,X0,X6,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X2))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X19,c_Set_Oinsert(X16,X6,X0),X0,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f426,axiom,
! [X2,X0,X6,X19,X16] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X2))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X19,c_Set_Oinsert(X16,X6,X0),X0,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__insert__swap_0) ).
fof(f18831,plain,
spl0_723,
inference(avatar_split_clause,[],[f425,f18829]) ).
fof(f18829,plain,
( spl0_723
<=> ! [X16,X19,X0,X6,X2] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X2))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X19,c_Set_Oinsert(X16,X6,X0),X0,X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f425,axiom,
! [X2,X0,X6,X19,X16] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| hBOOL(c_in(X16,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X2))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X19,c_Set_Oinsert(X16,X6,X0),X0,X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__insert__swap_0) ).
fof(f18827,plain,
spl0_722,
inference(avatar_split_clause,[],[f390,f18825]) ).
fof(f18825,plain,
( spl0_722
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f390,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f18823,plain,
spl0_721,
inference(avatar_split_clause,[],[f12,f18821]) ).
fof(f18821,plain,
( spl0_721
<=> ! [X10,X9,X11,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X10)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X10),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f12,axiom,
! [X10,X0,X11,X9,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X10)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X10),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f18695,plain,
( ~ spl0_19
| spl0_720
| ~ spl0_126
| ~ spl0_712 ),
inference(avatar_split_clause,[],[f18442,f17675,f1632,f18693,f1093]) ).
fof(f18693,plain,
( spl0_720
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_U,tc_Com_Opname),c_Finite__Set_Ocard(c_fequal(X0,X1),X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f17675,plain,
( spl0_712
<=> ! [X0,X1] : c_lessequals(c_Finite__Set_Ocard(c_fequal(X0,X1),X1),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f18442,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_U,tc_Com_Opname),c_Finite__Set_Ocard(c_fequal(X0,X1),X1),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_126
| ~ spl0_712 ),
inference(resolution,[],[f17676,f1633]) ).
fof(f17676,plain,
( ! [X0,X1] : c_lessequals(c_Finite__Set_Ocard(c_fequal(X0,X1),X1),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
| ~ spl0_712 ),
inference(avatar_component_clause,[],[f17675]) ).
fof(f18606,plain,
( spl0_719
| ~ spl0_390
| ~ spl0_634
| ~ spl0_716 ),
inference(avatar_split_clause,[],[f18510,f18507,f13536,f6638,f18604]) ).
fof(f18604,plain,
( spl0_719
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f13536,plain,
( spl0_634
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f18507,plain,
( spl0_716
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f18510,plain,
( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),X8,tc_fun(X0,tc_bool))
| ~ spl0_390
| ~ spl0_634
| ~ spl0_716 ),
inference(forward_demodulation,[],[f18508,f13578]) ).
fof(f13578,plain,
( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X0,tc_bool))),X1)
| ~ spl0_390
| ~ spl0_634 ),
inference(superposition,[],[f13537,f6639]) ).
fof(f13537,plain,
( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool)))
| ~ spl0_634 ),
inference(avatar_component_clause,[],[f13536]) ).
fof(f18508,plain,
( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),X7)
| ~ spl0_716 ),
inference(avatar_component_clause,[],[f18507]) ).
fof(f18518,plain,
spl0_718,
inference(avatar_split_clause,[],[f987,f18516]) ).
fof(f18516,plain,
( spl0_718
<=> ! [X19,X20,X0,X6,X25,X2,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0,X20),X2))
| ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),hAPP(hAPP(X25,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f987,plain,
! [X2,X0,X1,X19,X6,X25,X20] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0,X20),X2))
| ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),hAPP(hAPP(X25,X1),X2))) ),
inference(forward_demodulation,[],[f354,f926]) ).
fof(f354,axiom,
! [X2,X0,X1,X6,X19,X25,X20] :
( ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),hAPP(hAPP(X25,X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X20),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
fof(f18514,plain,
spl0_717,
inference(avatar_split_clause,[],[f937,f18512]) ).
fof(f18512,plain,
( spl0_717
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X8),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f937,plain,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X8),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),X8,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f9,f151]) ).
fof(f151,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
fof(f9,axiom,
! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X8),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
fof(f18509,plain,
spl0_716,
inference(avatar_split_clause,[],[f8,f18507]) ).
fof(f8,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
fof(f18505,plain,
spl0_715,
inference(avatar_split_clause,[],[f3,f18503]) ).
fof(f18503,plain,
( spl0_715
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f3,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
fof(f18482,plain,
spl0_714,
inference(avatar_split_clause,[],[f998,f18480]) ).
fof(f18480,plain,
( spl0_714
<=> ! [X0,X8,X6,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X8,X0))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f998,plain,
! [X0,X1,X8,X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X8,X0))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f471,f926]) ).
fof(f471,axiom,
! [X0,X1,X8,X6] :
( hBOOL(c_in(X1,X8,X0))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
fof(f18437,plain,
spl0_713,
inference(avatar_split_clause,[],[f522,f18435]) ).
fof(f18435,plain,
( spl0_713
<=> ! [X20,X0,X6,X25,X8] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f522,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
fof(f17677,plain,
( ~ spl0_1
| spl0_712
| ~ spl0_334
| ~ spl0_483 ),
inference(avatar_split_clause,[],[f9370,f8212,f4268,f17675,f1003]) ).
fof(f4268,plain,
( spl0_334
<=> ! [X6,X20,X0,X25] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20),c_Finite__Set_Ocard(X6,X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f8212,plain,
( spl0_483
<=> ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_Com_Opname),v_U,tc_Com_Opname,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f9370,plain,
( ! [X0,X1] :
( c_lessequals(c_Finite__Set_Ocard(c_fequal(X0,X1),X1),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) )
| ~ spl0_334
| ~ spl0_483 ),
inference(superposition,[],[f4269,f8213]) ).
fof(f8213,plain,
( ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_Com_Opname),v_U,tc_Com_Opname,X1)
| ~ spl0_483 ),
inference(avatar_component_clause,[],[f8212]) ).
fof(f4269,plain,
( ! [X0,X6,X25,X20] :
( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20),c_Finite__Set_Ocard(X6,X0),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0) )
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f4268]) ).
fof(f17585,plain,
spl0_711,
inference(avatar_split_clause,[],[f996,f17583]) ).
fof(f17583,plain,
( spl0_711
<=> ! [X0,X8,X6,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f996,plain,
! [X0,X1,X8,X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f352,f926]) ).
fof(f352,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
fof(f17581,plain,
spl0_710,
inference(avatar_split_clause,[],[f995,f17579]) ).
fof(f17579,plain,
( spl0_710
<=> ! [X0,X8,X6,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f995,plain,
! [X0,X1,X8,X6] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f351,f926]) ).
fof(f351,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
fof(f17577,plain,
spl0_709,
inference(avatar_split_clause,[],[f920,f17575]) ).
fof(f920,plain,
! [X0,X6,X16,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0)) ),
inference(definition_unfolding,[],[f438,f57,f57]) ).
fof(f57,axiom,
! [X0,X19,X6,X25,X20] : c_Finite__Set_Ofold(X25,X19,X6,X20,X0) = c_The(c_Finite__Set_Ofold__graph(X25,X19,X6,X20,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__def_0) ).
fof(f438,axiom,
! [X0,X6,X16,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__insert_0) ).
fof(f17573,plain,
spl0_708,
inference(avatar_split_clause,[],[f919,f17571]) ).
fof(f919,plain,
! [X0,X6,X16,X14] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0)) ),
inference(definition_unfolding,[],[f444,f57,f57]) ).
fof(f444,axiom,
! [X0,X6,X16,X14] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__sup__insert_0) ).
fof(f17569,plain,
spl0_707,
inference(avatar_split_clause,[],[f721,f17567]) ).
fof(f17567,plain,
( spl0_707
<=> ! [X30,X0,X6,X8,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X30,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X30),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f721,axiom,
! [X0,X8,X6,X7,X30] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X30,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X30),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
fof(f17565,plain,
spl0_706,
inference(avatar_split_clause,[],[f515,f17563]) ).
fof(f17563,plain,
( spl0_706
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f515,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
fof(f17561,plain,
spl0_705,
inference(avatar_split_clause,[],[f336,f17559]) ).
fof(f17559,plain,
( spl0_705
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f336,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
fof(f17557,plain,
spl0_704,
inference(avatar_split_clause,[],[f335,f17555]) ).
fof(f17555,plain,
( spl0_704
<=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f335,axiom,
! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
fof(f17553,plain,
spl0_703,
inference(avatar_split_clause,[],[f327,f17551]) ).
fof(f327,axiom,
! [X0,X8,X6,X25,X20] : c_lessequals(c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X20,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
fof(f17549,plain,
( spl0_702
| ~ spl0_185
| ~ spl0_473 ),
inference(avatar_split_clause,[],[f8659,f8149,f2028,f17547]) ).
fof(f8149,plain,
( spl0_473
<=> ! [X0] :
( hBOOL(c_in(hAPP(v_mgt__call,X0),v_G,t_a))
| ~ hBOOL(c_in(X0,v_U,tc_Com_Opname)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f8659,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
| v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) )
| ~ spl0_185
| ~ spl0_473 ),
inference(resolution,[],[f8150,f2029]) ).
fof(f8150,plain,
( ! [X0] :
( hBOOL(c_in(hAPP(v_mgt__call,X0),v_G,t_a))
| ~ hBOOL(c_in(X0,v_U,tc_Com_Opname)) )
| ~ spl0_473 ),
inference(avatar_component_clause,[],[f8149]) ).
fof(f17545,plain,
spl0_701,
inference(avatar_split_clause,[],[f150,f17543]) ).
fof(f17543,plain,
( spl0_701
<=> ! [X30,X0,X6,X8,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X30,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X30),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f150,axiom,
! [X0,X8,X6,X7,X30] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X30,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X30),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
fof(f15926,plain,
spl0_700,
inference(avatar_split_clause,[],[f994,f15924]) ).
fof(f15924,plain,
( spl0_700
<=> ! [X0,X6,X2,X1] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X2,c_fequal(X1,X0),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| ~ hBOOL(c_in(X2,X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f994,plain,
! [X2,X0,X1,X6] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X2,c_fequal(X1,X0),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| ~ hBOOL(c_in(X2,X6,X0)) ),
inference(forward_demodulation,[],[f993,f926]) ).
fof(f993,plain,
! [X2,X0,X1,X6] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| ~ hBOOL(c_in(X2,X6,X0)) ),
inference(forward_demodulation,[],[f992,f934]) ).
fof(f934,plain,
! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_fequal(X14,X0),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f787,f926]) ).
fof(f787,axiom,
! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
fof(f992,plain,
! [X2,X0,X1,X6] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),c_fequal(X2,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| ~ hBOOL(c_in(X2,X6,X0)) ),
inference(forward_demodulation,[],[f485,f926]) ).
fof(f485,axiom,
! [X2,X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| ~ hBOOL(c_in(X2,X6,X0))
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff2__less_0) ).
fof(f15922,plain,
spl0_699,
inference(avatar_split_clause,[],[f988,f15920]) ).
fof(f15920,plain,
( spl0_699
<=> ! [X20,X0,X14,X6,X25] :
( hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20),X20))
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f988,plain,
! [X0,X6,X14,X25,X20] :
( hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20),X20))
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ),
inference(forward_demodulation,[],[f770,f926]) ).
fof(f770,axiom,
! [X0,X6,X14,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20)
| hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X20),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
fof(f15918,plain,
spl0_698,
inference(avatar_split_clause,[],[f959,f15916]) ).
fof(f959,plain,
! [X2,X0,X1,X6,X25,X20] :
( c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) = c_Set_Oinsert(X2,c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X20),tc_fun(X20,tc_bool)),X20,X0),X0)
| ~ hBOOL(c_in(X1,X6,X20)) ),
inference(forward_demodulation,[],[f769,f926]) ).
fof(f769,axiom,
! [X2,X0,X1,X6,X25,X20] :
( ~ hBOOL(c_in(X1,X6,X20))
| c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) = c_Set_Oinsert(X2,c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),tc_fun(X20,tc_bool)),X20,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
fof(f15914,plain,
( ~ spl0_696
| spl0_697
| ~ spl0_140
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6654,f6571,f1691,f15912,f15908]) ).
fof(f15908,plain,
( spl0_696
<=> class_Orderings_Olinorder(tc_fun(t_a,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f15912,plain,
( spl0_697
<=> ! [X0] :
( c_Finite__Set_Ofinite(X0,t_a)
| c_lessequals(v_G,X0,tc_fun(t_a,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f6571,plain,
( spl0_388
<=> ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Finite__Set_Ofinite(X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f6654,plain,
( ! [X0] :
( c_Finite__Set_Ofinite(X0,t_a)
| c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(t_a,tc_bool)) )
| ~ spl0_140
| ~ spl0_388 ),
inference(resolution,[],[f6572,f1692]) ).
fof(f6572,plain,
( ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Finite__Set_Ofinite(X0,t_a) )
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f6571]) ).
fof(f15906,plain,
spl0_695,
inference(avatar_split_clause,[],[f541,f15904]) ).
fof(f15904,plain,
( spl0_695
<=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f541,axiom,
! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
fof(f15902,plain,
spl0_694,
inference(avatar_split_clause,[],[f540,f15900]) ).
fof(f15900,plain,
( spl0_694
<=> ! [X0,X6,X8,X7] : 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)),X6),X8)),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f540,axiom,
! [X0,X8,X6,X7] : 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)),X6),X8)),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
fof(f15898,plain,
spl0_693,
inference(avatar_split_clause,[],[f474,f15896]) ).
fof(f15896,plain,
( spl0_693
<=> ! [X6,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X8),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f474,axiom,
! [X0,X8,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X8),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__antimono_0) ).
fof(f15894,plain,
spl0_692,
inference(avatar_split_clause,[],[f396,f15892]) ).
fof(f15892,plain,
( spl0_692
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f396,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
fof(f15890,plain,
spl0_691,
inference(avatar_split_clause,[],[f371,f15888]) ).
fof(f15888,plain,
( spl0_691
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f371,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastAtMost_0) ).
fof(f15886,plain,
spl0_690,
inference(avatar_split_clause,[],[f307,f15884]) ).
fof(f15884,plain,
( spl0_690
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)),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),X19)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f307,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)),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),X19)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
fof(f15882,plain,
spl0_689,
inference(avatar_split_clause,[],[f306,f15880]) ).
fof(f15880,plain,
( spl0_689
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(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),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f306,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(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),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
fof(f15878,plain,
spl0_688,
inference(avatar_split_clause,[],[f292,f15876]) ).
fof(f292,axiom,
! [X0,X14,X25,X20,X33] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| ~ c_Finite__Set_Ofinite(X33,X0)
| hBOOL(c_in(X14,X33,X0))
| c_Finite__Set_Osetsum(X25,c_Set_Oinsert(X14,X33,X0),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,X33,X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__insert_0) ).
fof(f15874,plain,
spl0_687,
inference(avatar_split_clause,[],[f275,f15872]) ).
fof(f15872,plain,
( spl0_687
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X16,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15,X17,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f275,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X16,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15,X17,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greaterThanAtMost_0) ).
fof(f15870,plain,
spl0_686,
inference(avatar_split_clause,[],[f192,f15868]) ).
fof(f15868,plain,
( spl0_686
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f192,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastLessThan_0) ).
fof(f15862,plain,
spl0_685,
inference(avatar_split_clause,[],[f157,f15860]) ).
fof(f15860,plain,
( spl0_685
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f157,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
fof(f15858,plain,
spl0_684,
inference(avatar_split_clause,[],[f23,f15856]) ).
fof(f15856,plain,
( spl0_684
<=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f23,axiom,
! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
fof(f15854,plain,
spl0_683,
inference(avatar_split_clause,[],[f22,f15852]) ).
fof(f15852,plain,
( spl0_683
<=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f22,axiom,
! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
fof(f15762,plain,
( ~ spl0_31
| spl0_682
| ~ spl0_127
| ~ spl0_639 ),
inference(avatar_split_clause,[],[f14095,f13556,f1636,f15760,f1153]) ).
fof(f1153,plain,
( spl0_31
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f15760,plain,
( spl0_682
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(v_U,X0),hAPP(c_fequal(v_x,tc_Com_Opname),X0),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f13556,plain,
( spl0_639
<=> ! [X0] : c_lessequals(hAPP(c_fequal(v_x,tc_Com_Opname),X0),hAPP(v_U,X0),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f14095,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(hAPP(v_U,X0),hAPP(c_fequal(v_x,tc_Com_Opname),X0),tc_bool)
| ~ class_Orderings_Opreorder(tc_bool) )
| ~ spl0_127
| ~ spl0_639 ),
inference(resolution,[],[f13557,f1637]) ).
fof(f13557,plain,
( ! [X0] : c_lessequals(hAPP(c_fequal(v_x,tc_Com_Opname),X0),hAPP(v_U,X0),tc_bool)
| ~ spl0_639 ),
inference(avatar_component_clause,[],[f13556]) ).
fof(f15687,plain,
spl0_681,
inference(avatar_split_clause,[],[f404,f15685]) ).
fof(f15685,plain,
( spl0_681
<=> ! [X19,X0,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f404,axiom,
! [X2,X0,X1,X19] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
fof(f15680,plain,
spl0_680,
inference(avatar_split_clause,[],[f379,f15678]) ).
fof(f15678,plain,
( spl0_680
<=> ! [X19,X0,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f379,axiom,
! [X2,X0,X1,X19] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
fof(f15676,plain,
spl0_679,
inference(avatar_split_clause,[],[f299,f15674]) ).
fof(f15674,plain,
( spl0_679
<=> ! [X19,X0,X20,X6,X25,X2,X1] :
( hBOOL(c_in(X1,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),X2))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Set_Oinsert(X1,X6,X0),X0,X20),hAPP(hAPP(X25,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f299,axiom,
! [X2,X0,X1,X6,X19,X25,X20] :
( hBOOL(c_in(X1,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),X2))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Set_Oinsert(X1,X6,X0),X0,X20),hAPP(hAPP(X25,X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
fof(f15672,plain,
spl0_678,
inference(avatar_split_clause,[],[f286,f15670]) ).
fof(f15670,plain,
( spl0_678
<=> ! [X19,X0,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X19)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f286,axiom,
! [X2,X0,X1,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X19)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f15668,plain,
spl0_677,
inference(avatar_split_clause,[],[f285,f15666]) ).
fof(f15666,plain,
( spl0_677
<=> ! [X0,X14,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f285,axiom,
! [X0,X16,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f15664,plain,
spl0_676,
inference(avatar_split_clause,[],[f284,f15662]) ).
fof(f15662,plain,
( spl0_676
<=> ! [X0,X14,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f284,axiom,
! [X0,X16,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f15660,plain,
spl0_675,
inference(avatar_split_clause,[],[f261,f15658]) ).
fof(f15658,plain,
( spl0_675
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f261,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
fof(f15656,plain,
spl0_674,
inference(avatar_split_clause,[],[f200,f15654]) ).
fof(f15654,plain,
( spl0_674
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X19),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f200,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X19),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f15652,plain,
spl0_673,
inference(avatar_split_clause,[],[f199,f15650]) ).
fof(f15650,plain,
( spl0_673
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = 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),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f199,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = 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),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f15648,plain,
spl0_672,
inference(avatar_split_clause,[],[f168,f15646]) ).
fof(f15646,plain,
( spl0_672
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X19),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f168,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X19),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
fof(f15644,plain,
spl0_671,
inference(avatar_split_clause,[],[f167,f15642]) ).
fof(f15642,plain,
( spl0_671
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f167,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
fof(f15582,plain,
spl0_670,
inference(avatar_split_clause,[],[f160,f15580]) ).
fof(f15580,plain,
( spl0_670
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X19),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f160,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X19),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
fof(f15578,plain,
spl0_669,
inference(avatar_split_clause,[],[f117,f15576]) ).
fof(f15576,plain,
( spl0_669
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = 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),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f117,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = 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),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f15574,plain,
spl0_668,
inference(avatar_split_clause,[],[f116,f15572]) ).
fof(f15572,plain,
( spl0_668
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X19),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f116,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X19),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f15570,plain,
spl0_667,
inference(avatar_split_clause,[],[f71,f15568]) ).
fof(f15568,plain,
( spl0_667
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X15,X14,X0)
| ~ c_lessequals(X15,X17,X0)
| ~ c_lessequals(X15,X14,X0)
| ~ c_lessequals(X16,X17,X0)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f71,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X15,X14,X0)
| ~ c_lessequals(X15,X17,X0)
| ~ c_lessequals(X15,X14,X0)
| ~ c_lessequals(X16,X17,X0)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).
fof(f15566,plain,
spl0_666,
inference(avatar_split_clause,[],[f70,f15564]) ).
fof(f15564,plain,
( spl0_666
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X16,X17,X0)
| ~ c_lessequals(X15,X17,X0)
| ~ c_lessequals(X15,X14,X0)
| ~ c_lessequals(X16,X17,X0)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f70,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X16,X17,X0)
| ~ c_lessequals(X15,X17,X0)
| ~ c_lessequals(X15,X14,X0)
| ~ c_lessequals(X16,X17,X0)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).
fof(f14569,plain,
spl0_665,
inference(avatar_split_clause,[],[f922,f14567]) ).
fof(f14567,plain,
( spl0_665
<=> ! [X6,X0,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X14,X6,X0))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,X6,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f922,plain,
! [X0,X6,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X14,X6,X0))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,X6,X0,X0),X0) ),
inference(definition_unfolding,[],[f326,f57]) ).
fof(f326,axiom,
! [X0,X6,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X14,X6,X0))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X0),X14,X6,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__eq__fold_0) ).
fof(f14562,plain,
spl0_664,
inference(avatar_split_clause,[],[f921,f14560]) ).
fof(f14560,plain,
( spl0_664
<=> ! [X6,X0,X14] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X14,X6,X0))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,X6,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f921,plain,
! [X0,X6,X14] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X14,X6,X0))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,X6,X0,X0),X0) ),
inference(definition_unfolding,[],[f325,f57]) ).
fof(f325,axiom,
! [X0,X6,X14] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X14,X6,X0))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X0),X14,X6,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__eq__fold_0) ).
fof(f14558,plain,
spl0_663,
inference(avatar_split_clause,[],[f676,f14556]) ).
fof(f676,axiom,
! [X28,X0,X54,X6,X20] :
( ~ hBOOL(c_in(X28,X54,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),hAPP(X6,X28)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
fof(f14554,plain,
spl0_662,
inference(avatar_split_clause,[],[f636,f14552]) ).
fof(f636,axiom,
! [X0,X8,X6,X25,X20] : c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X20,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
fof(f14550,plain,
spl0_661,
inference(avatar_split_clause,[],[f506,f14548]) ).
fof(f14548,plain,
( spl0_661
<=> ! [X20,X0,X6,X25,X8] : c_Set_Ovimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,X6,X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f506,axiom,
! [X0,X8,X6,X25,X20] : c_Set_Ovimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,X6,X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
fof(f14546,plain,
spl0_660,
inference(avatar_split_clause,[],[f468,f14544]) ).
fof(f14544,plain,
( spl0_660
<=> ! [X34,X0,X6,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_lessequals(X1,X34,X0)
| ~ hBOOL(c_in(X34,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X1,hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X0),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f468,axiom,
! [X0,X1,X6,X34] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_lessequals(X1,X34,X0)
| ~ hBOOL(c_in(X34,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X1,hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X0),X6),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).
fof(f14542,plain,
spl0_659,
inference(avatar_split_clause,[],[f467,f14540]) ).
fof(f14540,plain,
( spl0_659
<=> ! [X34,X0,X6,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_lessequals(X34,X1,X0)
| ~ hBOOL(c_in(X34,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f467,axiom,
! [X0,X1,X6,X34] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_lessequals(X34,X1,X0)
| ~ hBOOL(c_in(X34,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__below__iff_2) ).
fof(f14538,plain,
spl0_658,
inference(avatar_split_clause,[],[f446,f14536]) ).
fof(f14536,plain,
( spl0_658
<=> ! [X4,X0,X5,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X5,X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f446,axiom,
! [X3,X0,X4,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X5,X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I22_J_0) ).
fof(f14534,plain,
spl0_657,
inference(avatar_split_clause,[],[f445,f14532]) ).
fof(f14532,plain,
( spl0_657
<=> ! [X4,X0,X5,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X5,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f445,axiom,
! [X3,X0,X4,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X5,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).
fof(f14530,plain,
spl0_656,
inference(avatar_split_clause,[],[f416,f14528]) ).
fof(f14528,plain,
( spl0_656
<=> ! [X20,X0,X6,X25,X8] : c_Set_Ovimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,X6,X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f416,axiom,
! [X0,X8,X6,X25,X20] : c_Set_Ovimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,X6,X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
fof(f14526,plain,
spl0_655,
inference(avatar_split_clause,[],[f324,f14524]) ).
fof(f324,axiom,
! [X0,X1,X6,X34] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_HOL_Oord__class_Oless(X34,X1,X0)
| ~ hBOOL(c_in(X34,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__strict__below__iff_2) ).
fof(f14522,plain,
( spl0_654
| ~ spl0_109
| ~ spl0_622 ),
inference(avatar_split_clause,[],[f14228,f12656,f1482,f14520]) ).
fof(f14520,plain,
( spl0_654
<=> ! [X0] :
( hBOOL(c_in(X0,v_U,tc_Com_Opname))
| ~ hBOOL(hAPP(c_fequal(v_x,tc_Com_Opname),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f12656,plain,
( spl0_622
<=> ! [X0] :
( hBOOL(c_in(X0,v_U,tc_Com_Opname))
| ~ hBOOL(c_in(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f14228,plain,
( ! [X0] :
( hBOOL(c_in(X0,v_U,tc_Com_Opname))
| ~ hBOOL(hAPP(c_fequal(v_x,tc_Com_Opname),X0)) )
| ~ spl0_109
| ~ spl0_622 ),
inference(resolution,[],[f12657,f1483]) ).
fof(f12657,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname))
| hBOOL(c_in(X0,v_U,tc_Com_Opname)) )
| ~ spl0_622 ),
inference(avatar_component_clause,[],[f12656]) ).
fof(f14518,plain,
spl0_653,
inference(avatar_split_clause,[],[f323,f14516]) ).
fof(f14516,plain,
( spl0_653
<=> ! [X34,X0,X6,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_HOL_Oord__class_Oless(X1,X34,X0)
| ~ hBOOL(c_in(X34,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f323,axiom,
! [X0,X1,X6,X34] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_HOL_Oord__class_Oless(X1,X34,X0)
| ~ hBOOL(c_in(X34,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__below__fold1__iff_0) ).
fof(f14514,plain,
spl0_652,
inference(avatar_split_clause,[],[f318,f14512]) ).
fof(f14512,plain,
( spl0_652
<=> ! [X4,X0,X5,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X5,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f318,axiom,
! [X3,X0,X4,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X5,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
fof(f14510,plain,
spl0_651,
inference(avatar_split_clause,[],[f317,f14508]) ).
fof(f14508,plain,
( spl0_651
<=> ! [X4,X0,X5,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X5,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f317,axiom,
! [X3,X0,X4,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X5,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I20_J_0) ).
fof(f14152,plain,
spl0_650,
inference(avatar_split_clause,[],[f694,f14150]) ).
fof(f14150,plain,
( spl0_650
<=> ! [X30,X0,X6,X8,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X30,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X30,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f694,axiom,
! [X0,X8,X6,X7,X30] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X30,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X30,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
fof(f14148,plain,
spl0_649,
inference(avatar_split_clause,[],[f639,f14146]) ).
fof(f14146,plain,
( spl0_649
<=> ! [X21,X20,X0,X25,X1] :
( c_Set_Oimage(X25,X1,X0,X20) = c_Set_Oimage(X21,X1,X0,X20)
| hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20)) != hAPP(X21,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f639,axiom,
! [X21,X0,X1,X25,X20] :
( c_Set_Oimage(X25,X1,X0,X20) = c_Set_Oimage(X21,X1,X0,X20)
| hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20)) != hAPP(X21,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_1) ).
fof(f14144,plain,
spl0_648,
inference(avatar_split_clause,[],[f554,f14142]) ).
fof(f14142,plain,
( spl0_648
<=> ! [X20,X0,X6,X25,X8] :
( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f554,axiom,
! [X0,X8,X6,X25,X20] :
( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
fof(f14140,plain,
spl0_647,
inference(avatar_split_clause,[],[f542,f14138]) ).
fof(f542,axiom,
! [X0,X8,X6,X25,X20] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X20,X0),c_Set_Oimage(X25,X8,X20,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X20,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
fof(f14136,plain,
spl0_646,
inference(avatar_split_clause,[],[f502,f14134]) ).
fof(f14134,plain,
( spl0_646
<=> ! [X8,X20,X0,X6,X25] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
| c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f502,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
| c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
fof(f14132,plain,
spl0_645,
inference(avatar_split_clause,[],[f462,f14130]) ).
fof(f14130,plain,
( spl0_645
<=> ! [X6,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f462,axiom,
! [X0,X1,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__insert_0) ).
fof(f14128,plain,
spl0_644,
inference(avatar_split_clause,[],[f461,f14126]) ).
fof(f14126,plain,
( spl0_644
<=> ! [X6,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f461,axiom,
! [X0,X1,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__insert_0) ).
fof(f14124,plain,
spl0_643,
inference(avatar_split_clause,[],[f305,f14122]) ).
fof(f14122,plain,
( spl0_643
<=> ! [X0,X14,X6,X8] :
( ~ hBOOL(c_in(X14,X6,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f305,axiom,
! [X0,X8,X6,X14] :
( ~ hBOOL(c_in(X14,X6,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
fof(f14093,plain,
spl0_642,
inference(avatar_split_clause,[],[f304,f14091]) ).
fof(f14091,plain,
( spl0_642
<=> ! [X0,X14,X8,X7] :
( ~ hBOOL(c_in(X14,X7,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f304,axiom,
! [X0,X8,X7,X14] :
( ~ hBOOL(c_in(X14,X7,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
fof(f13566,plain,
spl0_641,
inference(avatar_split_clause,[],[f936,f13564]) ).
fof(f13564,plain,
( spl0_641
<=> ! [X20,X0,X14,X25,X8] : c_Set_Ovimage(X25,c_Set_Oinsert(X14,X8,X20),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,c_fequal(X14,X20),X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f936,plain,
! [X0,X8,X14,X25,X20] : c_Set_Ovimage(X25,c_Set_Oinsert(X14,X8,X20),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,c_fequal(X14,X20),X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)),
inference(forward_demodulation,[],[f620,f926]) ).
fof(f620,axiom,
! [X0,X8,X14,X25,X20] : c_Set_Ovimage(X25,c_Set_Oinsert(X14,X8,X20),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
fof(f13562,plain,
spl0_640,
inference(avatar_split_clause,[],[f924,f13560]) ).
fof(f13560,plain,
( spl0_640
<=> ! [X0,X14,X6,X16] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f924,plain,
! [X0,X6,X16,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X0) ),
inference(definition_unfolding,[],[f389,f57]) ).
fof(f389,axiom,
! [X0,X6,X16,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__le__inf_0) ).
fof(f13558,plain,
( spl0_639
| ~ spl0_37
| ~ spl0_369
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f12378,f11986,f5988,f1183,f13556]) ).
fof(f11986,plain,
( spl0_584
<=> c_lessequals(c_fequal(v_x,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f12378,plain,
( ! [X0] :
( ~ class_HOL_Oord(tc_bool)
| c_lessequals(hAPP(c_fequal(v_x,tc_Com_Opname),X0),hAPP(v_U,X0),tc_bool) )
| ~ spl0_369
| ~ spl0_584 ),
inference(resolution,[],[f11988,f5989]) ).
fof(f11988,plain,
( c_lessequals(c_fequal(v_x,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool))
| ~ spl0_584 ),
inference(avatar_component_clause,[],[f11986]) ).
fof(f13554,plain,
spl0_638,
inference(avatar_split_clause,[],[f923,f13552]) ).
fof(f13552,plain,
( spl0_638
<=> ! [X0,X14,X6,X16] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f923,plain,
! [X0,X6,X16,X14] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0),X0) ),
inference(definition_unfolding,[],[f460,f57]) ).
fof(f460,axiom,
! [X0,X6,X16,X14] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__le__fold__sup_0) ).
fof(f13550,plain,
spl0_637,
inference(avatar_split_clause,[],[f710,f13548]) ).
fof(f710,axiom,
! [X0,X8,X6,X14,X20] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X14,X6,X20),X8,X20,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X8,X14)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
fof(f13546,plain,
spl0_636,
inference(avatar_split_clause,[],[f709,f13544]) ).
fof(f13544,plain,
( spl0_636
<=> ! [X48,X0,X49] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X49,X0)
| ~ c_lessequals(X48,X49,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X48
| c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X49),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X48),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f709,axiom,
! [X48,X0,X49] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X49,X0)
| ~ c_lessequals(X48,X49,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X48
| c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X49),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X48),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
fof(f13542,plain,
spl0_635,
inference(avatar_split_clause,[],[f543,f13540]) ).
fof(f13540,plain,
( spl0_635
<=> ! [X48,X0,X49] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X49,X0)
| ~ c_lessequals(X48,X49,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X48
| c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X48),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X49),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f543,axiom,
! [X48,X0,X49] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X49,X0)
| ~ c_lessequals(X48,X49,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X48
| c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X48),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X49),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).
fof(f13538,plain,
spl0_634,
inference(avatar_split_clause,[],[f151,f13536]) ).
fof(f13374,plain,
( spl0_633
| ~ spl0_378
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f12373,f11986,f6030,f13372]) ).
fof(f13372,plain,
( spl0_633
<=> ! [X0,X1] :
( c_Fun_Oinj__on(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname,X1)
| ~ c_Fun_Oinj__on(X0,v_U,tc_Com_Opname,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f12373,plain,
( ! [X0,X1] :
( c_Fun_Oinj__on(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname,X1)
| ~ c_Fun_Oinj__on(X0,v_U,tc_Com_Opname,X1) )
| ~ spl0_378
| ~ spl0_584 ),
inference(resolution,[],[f11988,f6031]) ).
fof(f13238,plain,
spl0_632,
inference(avatar_split_clause,[],[f964,f13236]) ).
fof(f13236,plain,
( spl0_632
<=> ! [X20,X0,X14,X6,X25] :
( ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20),X20))
| ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f964,plain,
! [X0,X6,X14,X25,X20] :
( ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20),X20))
| ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ),
inference(forward_demodulation,[],[f771,f926]) ).
fof(f771,axiom,
! [X0,X6,X14,X25,X20] :
( ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20)
| ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X20),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
fof(f13234,plain,
spl0_631,
inference(avatar_split_clause,[],[f684,f13232]) ).
fof(f13232,plain,
( spl0_631
<=> ! [X17,X4,X20,X0,X14,X16,X15] :
( X14 = X15
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X14,X16,X0,X20),X15,X17,X0,X20) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X15,X17,X0,X20),X14,X16,X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f684,axiom,
! [X0,X16,X14,X4,X17,X15,X20] :
( X14 = X15
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X14,X16,X0,X20),X15,X17,X0,X20) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X15,X17,X0,X20),X14,X16,X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
fof(f13230,plain,
spl0_630,
inference(avatar_split_clause,[],[f672,f13228]) ).
fof(f672,axiom,
! [X0,X8,X6,X25,X20] :
( X6 = X8
| c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20)
| ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
fof(f13226,plain,
spl0_629,
inference(avatar_split_clause,[],[f552,f13224]) ).
fof(f13224,plain,
( spl0_629
<=> ! [X51,X20,X0,X6,X25] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_lessequals(X51,X6,tc_fun(X0,tc_bool))
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),c_Set_Oimage(X25,X51,X0,X20),X20,X0) = X51 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f552,axiom,
! [X51,X0,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_lessequals(X51,X6,tc_fun(X0,tc_bool))
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),c_Set_Oimage(X25,X51,X0,X20),X20,X0) = X51 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).
fof(f13222,plain,
spl0_628,
inference(avatar_split_clause,[],[f508,f13220]) ).
fof(f13220,plain,
( spl0_628
<=> ! [X47,X20,X0,X25] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),c_Set_Oimage(X25,X47,X0,X20),X20,X0) = X47 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f508,axiom,
! [X0,X47,X25,X20] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),c_Set_Oimage(X25,X47,X0,X20),X20,X0) = X47 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).
fof(f13218,plain,
spl0_627,
inference(avatar_split_clause,[],[f477,f13216]) ).
fof(f13216,plain,
( spl0_627
<=> ! [X20,X0,X6,X25,X8] :
( ~ c_Finite__Set_Ofinite(X8,X20)
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X20),tc_nat)
| ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),X8,tc_fun(X20,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f477,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Finite__Set_Ofinite(X8,X20)
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X20),tc_nat)
| ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),X8,tc_fun(X20,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).
fof(f13214,plain,
spl0_626,
inference(avatar_split_clause,[],[f439,f13212]) ).
fof(f13212,plain,
( spl0_626
<=> ! [X0,X14,X6,X8] : c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X6,X0)),c_Set_Oinsert(X14,X8,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f439,axiom,
! [X0,X8,X6,X14] : c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X6,X0)),c_Set_Oinsert(X14,X8,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
fof(f13210,plain,
( spl0_625
| ~ spl0_376
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f12372,f11986,f6022,f13207]) ).
fof(f13207,plain,
( spl0_625
<=> v_U = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),c_fequal(v_x,tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f6022,plain,
( spl0_376
<=> ! [X6,X0,X8] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f12372,plain,
( v_U = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),c_fequal(v_x,tc_Com_Opname))
| ~ spl0_376
| ~ spl0_584 ),
inference(resolution,[],[f11988,f6023]) ).
fof(f6023,plain,
( ! [X0,X8,X6] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X6 )
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f6022]) ).
fof(f13205,plain,
spl0_624,
inference(avatar_split_clause,[],[f395,f13203]) ).
fof(f13203,plain,
( spl0_624
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_HOL_Oord__class_Oless(X15,X14,X0)
| c_HOL_Oord__class_Oless(X16,X17,X0)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f395,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_HOL_Oord__class_Oless(X15,X14,X0)
| c_HOL_Oord__class_Oless(X16,X17,X0)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).
fof(f12965,plain,
( spl0_623
| ~ spl0_375
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f12371,f11986,f6018,f12962]) ).
fof(f12962,plain,
( spl0_623
<=> v_U = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_fequal(v_x,tc_Com_Opname)),v_U) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f6018,plain,
( spl0_375
<=> ! [X6,X0,X8] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f12371,plain,
( v_U = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_fequal(v_x,tc_Com_Opname)),v_U)
| ~ spl0_375
| ~ spl0_584 ),
inference(resolution,[],[f11988,f6019]) ).
fof(f6019,plain,
( ! [X0,X8,X6] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X8 )
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f6018]) ).
fof(f12658,plain,
( spl0_622
| ~ spl0_368
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f12370,f11986,f5984,f12656]) ).
fof(f5984,plain,
( spl0_368
<=> ! [X0,X6,X8,X46] :
( ~ hBOOL(c_in(X46,X6,X0))
| hBOOL(c_in(X46,X8,X0))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f12370,plain,
( ! [X0] :
( hBOOL(c_in(X0,v_U,tc_Com_Opname))
| ~ hBOOL(c_in(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname)) )
| ~ spl0_368
| ~ spl0_584 ),
inference(resolution,[],[f11988,f5985]) ).
fof(f5985,plain,
( ! [X0,X46,X8,X6] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| hBOOL(c_in(X46,X8,X0))
| ~ hBOOL(c_in(X46,X6,X0)) )
| ~ spl0_368 ),
inference(avatar_component_clause,[],[f5984]) ).
fof(f12553,plain,
spl0_621,
inference(avatar_split_clause,[],[f756,f12551]) ).
fof(f12551,plain,
( spl0_621
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f756,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
fof(f12549,plain,
spl0_620,
inference(avatar_split_clause,[],[f675,f12547]) ).
fof(f12547,plain,
( spl0_620
<=> ! [X8,X54,X20,X0,X6,X1] :
( ~ hBOOL(c_in(X1,X54,X20))
| c_lessequals(hAPP(X6,X1),X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X20,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f675,axiom,
! [X0,X1,X54,X6,X8,X20] :
( ~ hBOOL(c_in(X1,X54,X20))
| c_lessequals(hAPP(X6,X1),X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X20,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
fof(f12545,plain,
spl0_619,
inference(avatar_split_clause,[],[f662,f12543]) ).
fof(f12543,plain,
( spl0_619
<=> ! [X20,X0,X6,X25,X8] : c_Set_Ovimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X25,X6,X0,X20),c_Set_Ovimage(X25,X8,X0,X20),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f662,axiom,
! [X0,X8,X6,X25,X20] : c_Set_Ovimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X25,X6,X0,X20),c_Set_Ovimage(X25,X8,X0,X20),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
fof(f12541,plain,
spl0_618,
inference(avatar_split_clause,[],[f646,f12539]) ).
fof(f12539,plain,
( spl0_618
<=> ! [X20,X8,X0,X6,X1] :
( ~ hBOOL(c_in(X1,X6,X20))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X8,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f646,axiom,
! [X0,X1,X8,X6,X20] :
( ~ hBOOL(c_in(X1,X6,X20))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X8,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
fof(f12533,plain,
spl0_617,
inference(avatar_split_clause,[],[f625,f12531]) ).
fof(f12531,plain,
( spl0_617
<=> ! [X6,X25,X0] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Fun_Oinj__on(X25,X6,X0,X0)
| c_Set_Oimage(X25,X6,X0,X0) = X6
| ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X0),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f625,axiom,
! [X0,X6,X25] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Fun_Oinj__on(X25,X6,X0,X0)
| c_Set_Oimage(X25,X6,X0,X0) = X6
| ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X0),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
fof(f12529,plain,
spl0_616,
inference(avatar_split_clause,[],[f563,f12527]) ).
fof(f12527,plain,
( spl0_616
<=> ! [X34,X0,X6,X25,X1,X20] :
( X1 = X34
| ~ hBOOL(c_in(X34,X6,X0))
| ~ hBOOL(c_in(X1,X6,X0))
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| hAPP(X25,X1) != hAPP(X25,X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f563,axiom,
! [X0,X1,X6,X34,X25,X20] :
( X1 = X34
| ~ hBOOL(c_in(X34,X6,X0))
| ~ hBOOL(c_in(X1,X6,X0))
| ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| hAPP(X25,X1) != hAPP(X25,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
fof(f12525,plain,
spl0_615,
inference(avatar_split_clause,[],[f539,f12523]) ).
fof(f12523,plain,
( spl0_615
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f539,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f12521,plain,
spl0_614,
inference(avatar_split_clause,[],[f538,f12519]) ).
fof(f12519,plain,
( spl0_614
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f538,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f12517,plain,
spl0_613,
inference(avatar_split_clause,[],[f537,f12515]) ).
fof(f12515,plain,
( spl0_613
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f537,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f12513,plain,
spl0_612,
inference(avatar_split_clause,[],[f536,f12511]) ).
fof(f12511,plain,
( spl0_612
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f536,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f12509,plain,
spl0_611,
inference(avatar_split_clause,[],[f532,f12507]) ).
fof(f12507,plain,
( spl0_611
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f532,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
fof(f12505,plain,
spl0_610,
inference(avatar_split_clause,[],[f457,f12503]) ).
fof(f12503,plain,
( spl0_610
<=> ! [X20,X0,X6,X25] : c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f457,axiom,
! [X0,X6,X25,X20] : c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
fof(f12501,plain,
spl0_609,
inference(avatar_split_clause,[],[f443,f12499]) ).
fof(f12499,plain,
( spl0_609
<=> ! [X0,X8,X6,X1] :
( hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f443,axiom,
! [X0,X1,X8,X6] :
( hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
fof(f12497,plain,
spl0_608,
inference(avatar_split_clause,[],[f442,f12495]) ).
fof(f12495,plain,
( spl0_608
<=> ! [X0,X8,X6,X1] :
( hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(X1,X6,X0))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f442,axiom,
! [X0,X1,X8,X6] :
( hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(X1,X6,X0))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
fof(f12493,plain,
( ~ spl0_37
| ~ spl0_607
| ~ spl0_254
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f12379,f11986,f2996,f12490,f1183]) ).
fof(f12490,plain,
( spl0_607
<=> c_HOL_Oord__class_Oless(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f12379,plain,
( ~ c_HOL_Oord__class_Oless(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool))
| ~ class_HOL_Oord(tc_bool)
| ~ spl0_254
| ~ spl0_584 ),
inference(resolution,[],[f11988,f2997]) ).
fof(f12488,plain,
spl0_606,
inference(avatar_split_clause,[],[f406,f12486]) ).
fof(f12486,plain,
( spl0_606
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f406,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
fof(f12484,plain,
spl0_605,
inference(avatar_split_clause,[],[f405,f12482]) ).
fof(f12482,plain,
( spl0_605
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f405,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
fof(f12480,plain,
spl0_604,
inference(avatar_split_clause,[],[f301,f12478]) ).
fof(f12478,plain,
( spl0_604
<=> ! [X0,X14,X6,X8] :
( hBOOL(c_in(X14,X6,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f301,axiom,
! [X0,X8,X6,X14] :
( hBOOL(c_in(X14,X6,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
fof(f12476,plain,
spl0_603,
inference(avatar_split_clause,[],[f300,f12474]) ).
fof(f12474,plain,
( spl0_603
<=> ! [X0,X14,X8,X7] :
( hBOOL(c_in(X14,X7,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f300,axiom,
! [X0,X8,X7,X14] :
( hBOOL(c_in(X14,X7,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
fof(f12472,plain,
spl0_602,
inference(avatar_split_clause,[],[f282,f12470]) ).
fof(f12470,plain,
( spl0_602
<=> ! [X11,X0,X12,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f282,axiom,
! [X0,X11,X9,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f12468,plain,
spl0_601,
inference(avatar_split_clause,[],[f281,f12466]) ).
fof(f12466,plain,
( spl0_601
<=> ! [X11,X0,X12,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f281,axiom,
! [X0,X11,X9,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f12464,plain,
spl0_600,
inference(avatar_split_clause,[],[f279,f12462]) ).
fof(f12462,plain,
( spl0_600
<=> ! [X10,X11,X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X10)),X11) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f279,axiom,
! [X10,X0,X11,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X10)),X11) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f12460,plain,
spl0_599,
inference(avatar_split_clause,[],[f278,f12458]) ).
fof(f12458,plain,
( spl0_599
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f278,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f12456,plain,
spl0_598,
inference(avatar_split_clause,[],[f246,f12454]) ).
fof(f12454,plain,
( spl0_598
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f246,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
fof(f12452,plain,
spl0_597,
inference(avatar_split_clause,[],[f245,f12450]) ).
fof(f12450,plain,
( spl0_597
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f245,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
fof(f12448,plain,
( spl0_596
| ~ spl0_272
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f12365,f11986,f3069,f12446]) ).
fof(f12446,plain,
( spl0_596
<=> ! [X0] :
( hBOOL(hAPP(v_U,X0))
| ~ hBOOL(hAPP(c_fequal(v_x,tc_Com_Opname),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f12365,plain,
( ! [X0] :
( hBOOL(hAPP(v_U,X0))
| ~ hBOOL(hAPP(c_fequal(v_x,tc_Com_Opname),X0)) )
| ~ spl0_272
| ~ spl0_584 ),
inference(resolution,[],[f11988,f3070]) ).
fof(f12444,plain,
spl0_595,
inference(avatar_split_clause,[],[f224,f12442]) ).
fof(f12442,plain,
( spl0_595
<=> ! [X17,X0,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f224,axiom,
! [X0,X14,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f12440,plain,
spl0_594,
inference(avatar_split_clause,[],[f223,f12438]) ).
fof(f12438,plain,
( spl0_594
<=> ! [X0,X14,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f223,axiom,
! [X0,X16,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f12436,plain,
spl0_593,
inference(avatar_split_clause,[],[f222,f12434]) ).
fof(f12434,plain,
( spl0_593
<=> ! [X17,X0,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f222,axiom,
! [X0,X14,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(f12432,plain,
spl0_592,
inference(avatar_split_clause,[],[f221,f12430]) ).
fof(f12430,plain,
( spl0_592
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f221,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f12428,plain,
spl0_591,
inference(avatar_split_clause,[],[f220,f12426]) ).
fof(f12426,plain,
( spl0_591
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f220,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f12424,plain,
spl0_590,
inference(avatar_split_clause,[],[f219,f12422]) ).
fof(f12422,plain,
( spl0_590
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f219,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f12420,plain,
spl0_589,
inference(avatar_split_clause,[],[f113,f12418]) ).
fof(f12418,plain,
( spl0_589
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f113,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
fof(f12416,plain,
spl0_588,
inference(avatar_split_clause,[],[f27,f12414]) ).
fof(f12414,plain,
( spl0_588
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f27,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f12412,plain,
spl0_587,
inference(avatar_split_clause,[],[f26,f12410]) ).
fof(f12410,plain,
( spl0_587
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f26,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f12408,plain,
spl0_586,
inference(avatar_split_clause,[],[f25,f12406]) ).
fof(f12406,plain,
( spl0_586
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f25,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f12363,plain,
spl0_585,
inference(avatar_split_clause,[],[f24,f12361]) ).
fof(f12361,plain,
( spl0_585
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f24,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f11989,plain,
( spl0_584
| ~ spl0_78
| ~ spl0_265
| ~ spl0_409
| ~ spl0_569 ),
inference(avatar_split_clause,[],[f11795,f11730,f6739,f3041,f1353,f11986]) ).
fof(f1353,plain,
( spl0_78
<=> ! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f6739,plain,
( spl0_409
<=> ! [X20,X0,X6,X15,X1] :
( c_Set_Oimage(c_COMBK(X15,X20,X0),X6,X0,X20) = c_fequal(X15,X20)
| ~ hBOOL(c_in(X1,X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f11730,plain,
( spl0_569
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,X0),v_U,X0,tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f11795,plain,
( c_lessequals(c_fequal(v_x,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool))
| ~ spl0_78
| ~ spl0_265
| ~ spl0_409
| ~ spl0_569 ),
inference(forward_demodulation,[],[f11788,f7217]) ).
fof(f7217,plain,
( ! [X2,X0,X1] : c_fequal(X0,X1) = c_Set_Oimage(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X1)
| ~ spl0_78
| ~ spl0_409 ),
inference(resolution,[],[f6740,f1354]) ).
fof(f1354,plain,
( ! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0))
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1353]) ).
fof(f6740,plain,
( ! [X0,X1,X6,X15,X20] :
( ~ hBOOL(c_in(X1,X6,X0))
| c_Set_Oimage(c_COMBK(X15,X20,X0),X6,X0,X20) = c_fequal(X15,X20) )
| ~ spl0_409 ),
inference(avatar_component_clause,[],[f6739]) ).
fof(f11788,plain,
( ! [X0] : c_lessequals(c_Set_Oimage(c_COMBK(v_x,tc_Com_Opname,X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool))
| ~ spl0_265
| ~ spl0_569 ),
inference(superposition,[],[f3042,f11731]) ).
fof(f11731,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,X0),v_U,X0,tc_Com_Opname)
| ~ spl0_569 ),
inference(avatar_component_clause,[],[f11730]) ).
fof(f11817,plain,
spl0_583,
inference(avatar_split_clause,[],[f654,f11815]) ).
fof(f11815,plain,
( spl0_583
<=> ! [X0,X8,X6,X1] :
( hBOOL(c_in(X1,X8,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f654,axiom,
! [X0,X1,X8,X6] :
( hBOOL(c_in(X1,X8,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
fof(f11813,plain,
spl0_582,
inference(avatar_split_clause,[],[f600,f11811]) ).
fof(f11811,plain,
( spl0_582
<=> ! [X20,X0,X14,X6,X25] :
( hBOOL(c_in(X14,X6,X0))
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,X6,X0,X20),X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f600,axiom,
! [X0,X6,X14,X25,X20] :
( hBOOL(c_in(X14,X6,X0))
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,X6,X0,X20),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
fof(f11809,plain,
spl0_581,
inference(avatar_split_clause,[],[f598,f11807]) ).
fof(f11807,plain,
( spl0_581
<=> ! [X2,X20,X0,X6,X25,X1] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X0,X20),X20))
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X6,X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f598,axiom,
! [X2,X0,X1,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X0,X20),X20))
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X6,X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
fof(f11805,plain,
spl0_580,
inference(avatar_split_clause,[],[f511,f11803]) ).
fof(f11803,plain,
( spl0_580
<=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f511,axiom,
! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f11801,plain,
spl0_579,
inference(avatar_split_clause,[],[f500,f11799]) ).
fof(f11799,plain,
( spl0_579
<=> ! [X0,X6,X8,X7] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f500,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
fof(f11785,plain,
spl0_578,
inference(avatar_split_clause,[],[f499,f11783]) ).
fof(f11783,plain,
( spl0_578
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f499,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
fof(f11781,plain,
spl0_577,
inference(avatar_split_clause,[],[f458,f11779]) ).
fof(f11779,plain,
( spl0_577
<=> ! [X0,X14,X6,X25,X1] :
( hBOOL(c_in(X14,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X14,X6,X0,X0),X1))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Set_Oinsert(X14,X6,X0),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f458,axiom,
! [X0,X1,X6,X14,X25] :
( hBOOL(c_in(X14,X6,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X14,X6,X0,X0),X1))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Set_Oinsert(X14,X6,X0),X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set_Ointros_0) ).
fof(f11777,plain,
spl0_576,
inference(avatar_split_clause,[],[f456,f11775]) ).
fof(f11775,plain,
( spl0_576
<=> ! [X8,X20,X0,X6,X25] :
( ~ c_Fun_Obij(X25,X0,X20)
| ~ c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool))
| c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f456,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Fun_Obij(X25,X0,X20)
| ~ c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool))
| c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subset__eq_0) ).
fof(f11773,plain,
spl0_575,
inference(avatar_split_clause,[],[f455,f11771]) ).
fof(f11771,plain,
( spl0_575
<=> ! [X8,X20,X0,X6,X25] :
( ~ c_Fun_Obij(X25,X0,X20)
| ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
| c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f455,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Fun_Obij(X25,X0,X20)
| ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
| c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subset__eq_1) ).
fof(f11769,plain,
spl0_574,
inference(avatar_split_clause,[],[f415,f11767]) ).
fof(f11767,plain,
( spl0_574
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ c_lessequals(X15,X17,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f415,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ c_lessequals(X15,X17,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f11765,plain,
spl0_573,
inference(avatar_split_clause,[],[f414,f11763]) ).
fof(f11763,plain,
( spl0_573
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X15,X17,X0)
| ~ c_lessequals(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f414,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X15,X17,X0)
| ~ c_lessequals(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f11761,plain,
spl0_572,
inference(avatar_split_clause,[],[f196,f11759]) ).
fof(f11759,plain,
( spl0_572
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X14,X16,X0)
| ~ c_lessequals(X15,X17,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f196,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X14,X16,X0)
| ~ c_lessequals(X15,X17,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f11757,plain,
spl0_571,
inference(avatar_split_clause,[],[f123,f11755]) ).
fof(f11755,plain,
( spl0_571
<=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f123,axiom,
! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f11753,plain,
spl0_570,
inference(avatar_split_clause,[],[f82,f11751]) ).
fof(f11751,plain,
( spl0_570
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ c_HOL_Oord__class_Oless(X15,X17,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f82,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ c_HOL_Oord__class_Oless(X15,X17,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f11732,plain,
( spl0_569
| ~ spl0_2
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f7752,f7307,f1008,f11730]) ).
fof(f7307,plain,
( spl0_430
<=> ! [X20,X0,X6,X15] :
( ~ hBOOL(c_in(X15,X6,X20))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f7752,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,X0),v_U,X0,tc_Com_Opname)
| ~ spl0_2
| ~ spl0_430 ),
inference(resolution,[],[f7308,f1010]) ).
fof(f7308,plain,
( ! [X0,X6,X15,X20] :
( ~ hBOOL(c_in(X15,X6,X20))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) )
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f7307]) ).
fof(f11236,plain,
spl0_568,
inference(avatar_split_clause,[],[f973,f11234]) ).
fof(f11234,plain,
( spl0_568
<=> ! [X6,X0,X1] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f973,plain,
! [X0,X1,X6] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0)) ),
inference(forward_demodulation,[],[f486,f926]) ).
fof(f486,axiom,
! [X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).
fof(f11232,plain,
spl0_567,
inference(avatar_split_clause,[],[f972,f11230]) ).
fof(f11230,plain,
( spl0_567
<=> ! [X6,X0,X1] :
( c_Finite__Set_Ocard(X6,X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0))
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f972,plain,
! [X0,X1,X6] :
( c_Finite__Set_Ocard(X6,X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0))
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0)) ),
inference(forward_demodulation,[],[f487,f926]) ).
fof(f487,axiom,
! [X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_Finite__Set_Ocard(X6,X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__Diff1_0) ).
fof(f11228,plain,
spl0_566,
inference(avatar_split_clause,[],[f935,f11226]) ).
fof(f11226,plain,
( spl0_566
<=> ! [X0,X14,X6,X8] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f935,plain,
! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f786,f926]) ).
fof(f786,axiom,
! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
fof(f11224,plain,
spl0_565,
inference(avatar_split_clause,[],[f934,f11222]) ).
fof(f11220,plain,
spl0_564,
inference(avatar_split_clause,[],[f918,f11218]) ).
fof(f11218,plain,
( spl0_564
<=> ! [X6,X0,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),c_Complete__Lattice_OInf__class_OInf(X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X8,X6,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f918,plain,
! [X0,X8,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),c_Complete__Lattice_OInf__class_OInf(X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X8,X6,X0,X0),X0) ),
inference(definition_unfolding,[],[f210,f57]) ).
fof(f210,axiom,
! [X0,X8,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),c_Complete__Lattice_OInf__class_OInf(X6,X0)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),X8,X6,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Inf__fold__inf_0) ).
fof(f11216,plain,
spl0_563,
inference(avatar_split_clause,[],[f917,f11214]) ).
fof(f11214,plain,
( spl0_563
<=> ! [X6,X0,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X8),c_Complete__Lattice_OSup__class_OSup(X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X8,X6,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f917,plain,
! [X0,X8,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X8),c_Complete__Lattice_OSup__class_OSup(X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X8,X6,X0,X0),X0) ),
inference(definition_unfolding,[],[f451,f57]) ).
fof(f451,axiom,
! [X0,X8,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X8),c_Complete__Lattice_OSup__class_OSup(X6,X0)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),X8,X6,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Sup__fold__sup_0) ).
fof(f11212,plain,
spl0_562,
inference(avatar_split_clause,[],[f632,f11210]) ).
fof(f11210,plain,
( spl0_562
<=> ! [X0,X14,X8,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f632,axiom,
! [X0,X8,X7,X14] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
fof(f11208,plain,
( ~ spl0_19
| ~ spl0_561
| ~ spl0_126
| ~ spl0_531 ),
inference(avatar_split_clause,[],[f10518,f10370,f1632,f11205,f1093]) ).
fof(f11205,plain,
( spl0_561
<=> c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f10370,plain,
( spl0_531
<=> c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f10518,plain,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ spl0_126
| ~ spl0_531 ),
inference(resolution,[],[f10372,f1633]) ).
fof(f10372,plain,
( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),tc_nat)
| ~ spl0_531 ),
inference(avatar_component_clause,[],[f10370]) ).
fof(f11203,plain,
spl0_560,
inference(avatar_split_clause,[],[f631,f11201]) ).
fof(f11201,plain,
( spl0_560
<=> ! [X0,X14,X6,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f631,axiom,
! [X0,X8,X6,X14] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
fof(f11199,plain,
spl0_559,
inference(avatar_split_clause,[],[f570,f11197]) ).
fof(f11197,plain,
( spl0_559
<=> ! [X16,X20,X0,X14,X6,X8] :
( ~ hBOOL(c_in(X14,X6,X0))
| ~ hBOOL(c_in(X16,hAPP(X8,X14),X20))
| hBOOL(c_in(X16,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f570,axiom,
! [X0,X8,X6,X16,X14,X20] :
( ~ hBOOL(c_in(X14,X6,X0))
| ~ hBOOL(c_in(X16,hAPP(X8,X14),X20))
| hBOOL(c_in(X16,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
fof(f11195,plain,
spl0_558,
inference(avatar_split_clause,[],[f553,f11193]) ).
fof(f11193,plain,
( spl0_558
<=> ! [X20,X21,X25] :
( ~ class_Lattices_Olattice(X20)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X20)),X25),X21),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X20),hAPP(X25,v_x)),hAPP(X21,v_x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f553,axiom,
! [X21,X25,X20] :
( ~ class_Lattices_Olattice(X20)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X20)),X25),X21),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X20),hAPP(X25,v_x)),hAPP(X21,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
fof(f11191,plain,
spl0_557,
inference(avatar_split_clause,[],[f321,f11189]) ).
fof(f11189,plain,
( spl0_557
<=> ! [X4,X13,X0,X27] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X27,X13,X0)
| c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X27,X4,X0),c_SetInterval_Oord__class_OatLeastLessThan(X27,X13,X0),tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X13,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f321,axiom,
! [X0,X27,X4,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X27,X13,X0)
| c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X27,X4,X0),c_SetInterval_Oord__class_OatLeastLessThan(X27,X13,X0),tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X13,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).
fof(f11187,plain,
spl0_556,
inference(avatar_split_clause,[],[f296,f11185]) ).
fof(f296,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(c_in(X1,X8,X0))
| ~ hBOOL(c_in(X1,X6,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f11183,plain,
spl0_555,
inference(avatar_split_clause,[],[f293,f11181]) ).
fof(f11181,plain,
( spl0_555
<=> ! [X6,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f293,axiom,
! [X0,X8,X6] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__psubset_0) ).
fof(f11179,plain,
spl0_554,
inference(avatar_split_clause,[],[f135,f11177]) ).
fof(f11177,plain,
( spl0_554
<=> ! [X20,X21,X25] :
( ~ class_Lattices_Olattice(X20)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X20)),X25),X21),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X20),hAPP(X25,v_x)),hAPP(X21,v_x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f135,axiom,
! [X21,X25,X20] :
( ~ class_Lattices_Olattice(X20)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X20)),X25),X21),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X20),hAPP(X25,v_x)),hAPP(X21,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
fof(f10837,plain,
( spl0_553
| ~ spl0_185
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4130,f4087,f2028,f10835]) ).
fof(f10835,plain,
( spl0_553
<=> ! [X0] : c_Set_Oinsert(X0,v_U,tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f4087,plain,
( spl0_290
<=> ! [X0] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f4130,plain,
( ! [X0] : c_Set_Oinsert(X0,v_U,tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname)
| ~ spl0_185
| ~ spl0_290 ),
inference(resolution,[],[f4088,f2029]) ).
fof(f4088,plain,
( ! [X0] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname))
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f4087]) ).
fof(f10706,plain,
spl0_552,
inference(avatar_split_clause,[],[f974,f10704]) ).
fof(f10704,plain,
( spl0_552
<=> ! [X6,X0,X1] :
( c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X1,X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f974,plain,
! [X0,X1,X6] :
( c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X1,X6,X0)) ),
inference(forward_demodulation,[],[f655,f926]) ).
fof(f655,axiom,
! [X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X1,X6,X0))
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).
fof(f10702,plain,
spl0_551,
inference(avatar_split_clause,[],[f853,f10700]) ).
fof(f10700,plain,
( spl0_551
<=> ! [X0,X8,X6,X1] :
( X6 = X8
| hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| c_Set_Oinsert(X1,X6,X0) != c_Set_Oinsert(X1,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f853,axiom,
! [X0,X1,X8,X6] :
( X6 = X8
| hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,X8,X0))
| c_Set_Oinsert(X1,X6,X0) != c_Set_Oinsert(X1,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f10698,plain,
spl0_550,
inference(avatar_split_clause,[],[f765,f10696]) ).
fof(f765,axiom,
! [X0,X1,X8,X6,X25,X20] :
( ~ hBOOL(c_in(X1,X6,X20))
| hBOOL(c_in(hAPP(X25,X1),X8,X0))
| ~ c_lessequals(c_Set_Oimage(X25,X6,X20,X0),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f10687,plain,
spl0_549,
inference(avatar_split_clause,[],[f744,f10685]) ).
fof(f10685,plain,
( spl0_549
<=> ! [X53,X0,X25,X1] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X53,tc_bool)),X53,X0)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X53,tc_bool)),X25,X53,X0),hAPP(X25,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f744,axiom,
! [X0,X1,X53,X25] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X53,tc_bool)),X53,X0)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X53,tc_bool)),X25,X53,X0),hAPP(X25,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).
fof(f10683,plain,
spl0_548,
inference(avatar_split_clause,[],[f691,f10681]) ).
fof(f691,axiom,
! [X0,X8,X6,X25,X20] :
( X6 = X8
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
fof(f10679,plain,
spl0_547,
inference(avatar_split_clause,[],[f679,f10677]) ).
fof(f10677,plain,
( spl0_547
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(X15,X14,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f679,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(X15,X14,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
fof(f10675,plain,
spl0_546,
inference(avatar_split_clause,[],[f678,f10673]) ).
fof(f10673,plain,
( spl0_546
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(X16,X17,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f678,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(X16,X17,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
fof(f10671,plain,
spl0_545,
inference(avatar_split_clause,[],[f677,f10669]) ).
fof(f10669,plain,
( spl0_545
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X15,X14,X0)
| ~ c_lessequals(X16,X17,X0)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f677,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X15,X14,X0)
| ~ c_lessequals(X16,X17,X0)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
fof(f10667,plain,
spl0_544,
inference(avatar_split_clause,[],[f519,f10665]) ).
fof(f10665,plain,
( spl0_544
<=> ! [X6,X0] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X6
| c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f519,axiom,
! [X0,X6] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X6
| c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
fof(f10663,plain,
spl0_543,
inference(avatar_split_clause,[],[f518,f10661]) ).
fof(f10661,plain,
( spl0_543
<=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f518,axiom,
! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
fof(f10659,plain,
spl0_542,
inference(avatar_split_clause,[],[f517,f10657]) ).
fof(f10657,plain,
( spl0_542
<=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f517,axiom,
! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
fof(f10655,plain,
spl0_541,
inference(avatar_split_clause,[],[f491,f10653]) ).
fof(f10653,plain,
( spl0_541
<=> ! [X15,X0,X6,X8] :
( hBOOL(c_in(X15,X8,X0))
| hBOOL(c_in(X15,X6,X0))
| ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f491,axiom,
! [X0,X8,X6,X15] :
( hBOOL(c_in(X15,X8,X0))
| hBOOL(c_in(X15,X6,X0))
| ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f10651,plain,
spl0_540,
inference(avatar_split_clause,[],[f465,f10649]) ).
fof(f10649,plain,
( spl0_540
<=> ! [X20,X0,X6,X25] :
( ~ c_Fun_Obij(X25,X0,X20)
| c_Set_Ovimage(X25,X6,X0,X20) = c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X6,X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f465,axiom,
! [X0,X6,X25,X20] :
( ~ c_Fun_Obij(X25,X0,X20)
| c_Set_Ovimage(X25,X6,X0,X20) = c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X6,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__vimage__eq__inv__image_0) ).
fof(f10647,plain,
( ~ spl0_19
| ~ spl0_539
| ~ spl0_126
| ~ spl0_515 ),
inference(avatar_split_clause,[],[f10298,f10127,f1632,f10644,f1093]) ).
fof(f10644,plain,
( spl0_539
<=> c_HOL_Oord__class_Oless(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f10127,plain,
( spl0_515
<=> c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f10298,plain,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ spl0_126
| ~ spl0_515 ),
inference(resolution,[],[f10129,f1633]) ).
fof(f10129,plain,
( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),tc_nat)
| ~ spl0_515 ),
inference(avatar_component_clause,[],[f10127]) ).
fof(f10642,plain,
spl0_538,
inference(avatar_split_clause,[],[f421,f10640]) ).
fof(f10640,plain,
( spl0_538
<=> ! [X15,X0,X6,X8] :
( ~ hBOOL(c_in(X15,X6,X0))
| ~ hBOOL(c_in(X15,X8,X0))
| hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f421,axiom,
! [X0,X8,X6,X15] :
( ~ hBOOL(c_in(X15,X6,X0))
| ~ hBOOL(c_in(X15,X8,X0))
| hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
fof(f10638,plain,
spl0_537,
inference(avatar_split_clause,[],[f334,f10636]) ).
fof(f10636,plain,
( spl0_537
<=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f334,axiom,
! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
fof(f10634,plain,
spl0_536,
inference(avatar_split_clause,[],[f316,f10632]) ).
fof(f10632,plain,
( spl0_536
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X15,X17,X0)
| c_lessequals(X14,X16,X0)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f316,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X15,X17,X0)
| c_lessequals(X14,X16,X0)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).
fof(f10630,plain,
spl0_535,
inference(avatar_split_clause,[],[f314,f10628]) ).
fof(f10628,plain,
( spl0_535
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(X15,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f314,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(X15,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).
fof(f10626,plain,
spl0_534,
inference(avatar_split_clause,[],[f313,f10624]) ).
fof(f10624,plain,
( spl0_534
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(X16,X17,X0)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f313,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(X16,X17,X0)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).
fof(f10622,plain,
spl0_533,
inference(avatar_split_clause,[],[f309,f10620]) ).
fof(f10620,plain,
( spl0_533
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X16,X14,X0)
| c_lessequals(X15,X14,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f309,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X16,X14,X0)
| c_lessequals(X15,X14,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).
fof(f10618,plain,
spl0_532,
inference(avatar_split_clause,[],[f308,f10616]) ).
fof(f10616,plain,
( spl0_532
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X16,X14,X0)
| c_lessequals(X16,X17,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f308,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X16,X14,X0)
| c_lessequals(X16,X17,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).
fof(f10373,plain,
( spl0_531
| ~ spl0_148
| ~ spl0_514 ),
inference(avatar_split_clause,[],[f9899,f9657,f1724,f10370]) ).
fof(f1724,plain,
( spl0_148
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f9657,plain,
( spl0_514
<=> ! [X0] :
( c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
| c_lessequals(c_Finite__Set_Ocard(v_G,t_a),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f9899,plain,
( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),tc_nat)
| ~ spl0_148
| ~ spl0_514 ),
inference(resolution,[],[f9658,f1725]) ).
fof(f1725,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1724]) ).
fof(f9658,plain,
( ! [X0] :
( c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
| c_lessequals(c_Finite__Set_Ocard(v_G,t_a),X0,tc_nat) )
| ~ spl0_514 ),
inference(avatar_component_clause,[],[f9657]) ).
fof(f10365,plain,
spl0_530,
inference(avatar_split_clause,[],[f983,f10363]) ).
fof(f10363,plain,
( spl0_530
<=> ! [X0,X6,X1,X26] :
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X26),X0))
| ~ hBOOL(hAPP(X26,X1))
| ~ hBOOL(c_in(X1,X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f983,plain,
! [X0,X1,X6,X26] :
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X26),X0))
| ~ hBOOL(hAPP(X26,X1))
| ~ hBOOL(c_in(X1,X6,X0)) ),
inference(forward_demodulation,[],[f312,f665]) ).
fof(f312,axiom,
! [X0,X1,X6,X26] :
( ~ hBOOL(hAPP(X26,X1))
| ~ hBOOL(c_in(X1,X6,X0))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Collect(X26,X0)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
fof(f10361,plain,
spl0_529,
inference(avatar_split_clause,[],[f965,f10359]) ).
fof(f10359,plain,
( spl0_529
<=> ! [X0,X1] :
( c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = c_Finite__Set_Ocard(c_fequal(X1,X0),X0)
| hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f965,plain,
! [X0,X1] :
( c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = c_Finite__Set_Ocard(c_fequal(X1,X0),X0)
| hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
inference(forward_demodulation,[],[f350,f926]) ).
fof(f350,axiom,
! [X0,X1] :
( hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).
fof(f10357,plain,
spl0_528,
inference(avatar_split_clause,[],[f948,f10355]) ).
fof(f948,plain,
! [X0,X1,X6] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0))
| ~ c_Finite__Set_Ofinite(X6,X0) ),
inference(forward_demodulation,[],[f475,f926]) ).
fof(f475,axiom,
! [X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert_0) ).
fof(f10353,plain,
spl0_527,
inference(avatar_split_clause,[],[f852,f10351]) ).
fof(f852,axiom,
! [X0,X1,X6,X25,X20] :
( ~ hBOOL(c_in(X1,X6,X0))
| c_Set_Oimage(X25,X6,X0,X20) = c_Set_Oinsert(hAPP(X25,X1),c_Set_Oimage(X25,X6,X0,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
fof(f10349,plain,
spl0_526,
inference(avatar_split_clause,[],[f762,f10347]) ).
fof(f10347,plain,
( spl0_526
<=> ! [X21,X20,X0,X25,X1] :
( hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20),X1,X0))
| c_Set_Oimage(X25,X1,X0,X20) = c_Set_Oimage(X21,X1,X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f762,axiom,
! [X21,X0,X1,X25,X20] :
( hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20),X1,X0))
| c_Set_Oimage(X25,X1,X0,X20) = c_Set_Oimage(X21,X1,X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_0) ).
fof(f10345,plain,
spl0_525,
inference(avatar_split_clause,[],[f674,f10343]) ).
fof(f10343,plain,
( spl0_525
<=> ! [X53,X0,X6,X25,X1] :
( ~ hBOOL(c_in(X1,X6,X53))
| ~ c_Fun_Oinj__on(X25,X6,X53,X0)
| hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X53,X0),hAPP(X25,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f674,axiom,
! [X0,X1,X6,X53,X25] :
( ~ hBOOL(c_in(X1,X6,X53))
| ~ c_Fun_Oinj__on(X25,X6,X53,X0)
| hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X53,X0),hAPP(X25,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).
fof(f10341,plain,
spl0_524,
inference(avatar_split_clause,[],[f659,f10339]) ).
fof(f10339,plain,
( spl0_524
<=> ! [X2,X20,X0,X6,X25,X1] :
( hBOOL(c_in(X1,X6,X20))
| c_Set_Oimage(X25,X6,X20,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f659,axiom,
! [X2,X0,X1,X6,X25,X20] :
( hBOOL(c_in(X1,X6,X20))
| c_Set_Oimage(X25,X6,X20,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
fof(f10337,plain,
spl0_523,
inference(avatar_split_clause,[],[f648,f10335]) ).
fof(f648,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(c_in(X1,X8,X0))
| c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
fof(f10333,plain,
spl0_522,
inference(avatar_split_clause,[],[f579,f10331]) ).
fof(f10331,plain,
( spl0_522
<=> ! [X8,X0,X14,X6,X16,X20] :
( ~ hBOOL(c_in(X14,X6,X0))
| ~ hBOOL(hAPP(hAPP(X8,X14),X16))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f579,axiom,
! [X0,X8,X6,X16,X14,X20] :
( ~ hBOOL(c_in(X14,X6,X0))
| ~ hBOOL(hAPP(hAPP(X8,X14),X16))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
fof(f10293,plain,
spl0_521,
inference(avatar_split_clause,[],[f388,f10291]) ).
fof(f10291,plain,
( spl0_521
<=> ! [X4,X0,X5,X3] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f388,axiom,
! [X3,X0,X4,X5] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I14_J_0) ).
fof(f10289,plain,
spl0_520,
inference(avatar_split_clause,[],[f345,f10287]) ).
fof(f10287,plain,
( spl0_520
<=> ! [X20,X0,X25] :
( ~ c_Fun_Obij(X25,X0,X20)
| c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X20,X0) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f345,axiom,
! [X0,X25,X20] :
( ~ c_Fun_Obij(X25,X0,X20)
| c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X20,X0) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__inv__eq_0) ).
fof(f10285,plain,
spl0_519,
inference(avatar_split_clause,[],[f331,f10283]) ).
fof(f331,axiom,
! [X0,X8,X6] :
( c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
fof(f10281,plain,
spl0_518,
inference(avatar_split_clause,[],[f193,f10279]) ).
fof(f10279,plain,
( spl0_518
<=> ! [X4,X0,X5,X3] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f193,axiom,
! [X3,X0,X4,X5] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).
fof(f10277,plain,
spl0_517,
inference(avatar_split_clause,[],[f128,f10275]) ).
fof(f10275,plain,
( spl0_517
<=> ! [X4,X0,X5,X3] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f128,axiom,
! [X3,X0,X4,X5] :
( ~ class_Orderings_Oorder(X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I16_J_0) ).
fof(f10273,plain,
spl0_516,
inference(avatar_split_clause,[],[f2,f10271]) ).
fof(f10271,plain,
( spl0_516
<=> ! [X4,X0,X5,X3] :
( ~ class_Orderings_Oorder(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0)) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2,axiom,
! [X3,X0,X4,X5] :
( ~ class_Orderings_Oorder(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0)) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I15_J_0) ).
fof(f10130,plain,
( spl0_515
| ~ spl0_44
| ~ spl0_514 ),
inference(avatar_split_clause,[],[f9895,f9657,f1215,f10127]) ).
fof(f9895,plain,
( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),tc_nat)
| ~ spl0_44
| ~ spl0_514 ),
inference(resolution,[],[f9658,f1216]) ).
fof(f9659,plain,
( spl0_514
| ~ spl0_77
| ~ spl0_385 ),
inference(avatar_split_clause,[],[f6306,f6058,f1349,f9657]) ).
fof(f6058,plain,
( spl0_385
<=> ! [X0] :
( ~ c_lessequals(X0,c_Finite__Set_Ocard(v_G,t_a),tc_nat)
| c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f6306,plain,
( ! [X0] :
( c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
| c_lessequals(c_Finite__Set_Ocard(v_G,t_a),X0,tc_nat) )
| ~ spl0_77
| ~ spl0_385 ),
inference(resolution,[],[f6059,f1350]) ).
fof(f6059,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Finite__Set_Ocard(v_G,t_a),tc_nat)
| c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) )
| ~ spl0_385 ),
inference(avatar_component_clause,[],[f6058]) ).
fof(f9497,plain,
spl0_513,
inference(avatar_split_clause,[],[f767,f9495]) ).
fof(f767,axiom,
! [X0,X1,X6,X25,X20] :
( ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X20,X0),X0))
| hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X1),X6,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).
fof(f9493,plain,
spl0_512,
inference(avatar_split_clause,[],[f761,f9491]) ).
fof(f761,axiom,
! [X2,X0,X6,X25,X20] :
( ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X20,X0),X0))
| hAPP(X25,hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).
fof(f9489,plain,
spl0_511,
inference(avatar_split_clause,[],[f653,f9487]) ).
fof(f9487,plain,
( spl0_511
<=> ! [X0,X8,X6,X1] :
( hBOOL(c_in(X1,X6,X0))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f653,axiom,
! [X0,X1,X8,X6] :
( hBOOL(c_in(X1,X6,X0))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
fof(f9485,plain,
spl0_510,
inference(avatar_split_clause,[],[f647,f9483]) ).
fof(f9483,plain,
( spl0_510
<=> ! [X0,X8,X6,X1] :
( ~ hBOOL(c_in(X1,X8,X0))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f647,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(c_in(X1,X8,X0))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f9481,plain,
spl0_509,
inference(avatar_split_clause,[],[f637,f9479]) ).
fof(f637,axiom,
! [X0,X1,X6,X25,X20] :
( ~ c_lessequals(X1,X6,tc_fun(X20,tc_bool))
| c_lessequals(c_Set_Oimage(X25,X1,X20,X0),c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
fof(f9477,plain,
spl0_508,
inference(avatar_split_clause,[],[f568,f9475]) ).
fof(f9475,plain,
( spl0_508
<=> ! [X15,X0,X6,X8] :
( ~ hBOOL(c_in(X15,X6,X0))
| hBOOL(c_in(X15,X8,X0))
| hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f568,axiom,
! [X0,X8,X6,X15] :
( ~ hBOOL(c_in(X15,X6,X0))
| hBOOL(c_in(X15,X8,X0))
| hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
fof(f9471,plain,
spl0_507,
inference(avatar_split_clause,[],[f520,f9469]) ).
fof(f9469,plain,
( spl0_507
<=> ! [X20,X0,X6,X25,X8] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Ovimage(X25,X6,X20,X0),c_Set_Ovimage(X25,X8,X20,X0),tc_fun(X20,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f520,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Ovimage(X25,X6,X20,X0),c_Set_Ovimage(X25,X8,X20,X0),tc_fun(X20,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
fof(f9467,plain,
spl0_506,
inference(avatar_split_clause,[],[f510,f9465]) ).
fof(f9465,plain,
( spl0_506
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f510,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f9463,plain,
spl0_505,
inference(avatar_split_clause,[],[f509,f9461]) ).
fof(f9461,plain,
( spl0_505
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f509,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f9459,plain,
spl0_504,
inference(avatar_split_clause,[],[f448,f9457]) ).
fof(f9457,plain,
( spl0_504
<=> ! [X6,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| X6 = X8
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(X8,X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f448,axiom,
! [X0,X8,X6] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| X6 = X8
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(X8,X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).
fof(f9455,plain,
spl0_503,
inference(avatar_split_clause,[],[f410,f9453]) ).
fof(f9453,plain,
( spl0_503
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f410,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
fof(f9451,plain,
spl0_502,
inference(avatar_split_clause,[],[f302,f9449]) ).
fof(f9449,plain,
( spl0_502
<=> ! [X0,X8,X6,X1] :
( ~ hBOOL(c_in(X1,X8,X0))
| c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f302,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(c_in(X1,X8,X0))
| c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
fof(f9447,plain,
spl0_501,
inference(avatar_split_clause,[],[f194,f9445]) ).
fof(f9445,plain,
( spl0_501
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f194,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
fof(f9443,plain,
spl0_500,
inference(avatar_split_clause,[],[f134,f9441]) ).
fof(f9441,plain,
( spl0_500
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f134,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f9439,plain,
spl0_499,
inference(avatar_split_clause,[],[f133,f9437]) ).
fof(f133,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f9435,plain,
spl0_498,
inference(avatar_split_clause,[],[f132,f9433]) ).
fof(f9433,plain,
( spl0_498
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f132,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f9431,plain,
( ~ spl0_1
| spl0_497
| ~ spl0_141
| ~ spl0_483 ),
inference(avatar_split_clause,[],[f9369,f8212,f1695,f9429,f1003]) ).
fof(f9429,plain,
( spl0_497
<=> ! [X0,X1] : c_Finite__Set_Ofinite(c_fequal(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f1695,plain,
( spl0_141
<=> ! [X20,X0,X35,X33] :
( ~ c_Finite__Set_Ofinite(X33,X0)
| c_Finite__Set_Ofinite(c_Set_Oimage(X35,X33,X0,X20),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f9369,plain,
( ! [X0,X1] :
( c_Finite__Set_Ofinite(c_fequal(X0,X1),X1)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) )
| ~ spl0_141
| ~ spl0_483 ),
inference(superposition,[],[f1696,f8213]) ).
fof(f1696,plain,
( ! [X0,X35,X33,X20] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X35,X33,X0,X20),X20)
| ~ c_Finite__Set_Ofinite(X33,X0) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1695]) ).
fof(f9427,plain,
spl0_496,
inference(avatar_split_clause,[],[f131,f9425]) ).
fof(f131,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X14,X16,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f9423,plain,
spl0_495,
inference(avatar_split_clause,[],[f130,f9421]) ).
fof(f9421,plain,
( spl0_495
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f130,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f9419,plain,
spl0_494,
inference(avatar_split_clause,[],[f129,f9417]) ).
fof(f9417,plain,
( spl0_494
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f129,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f9415,plain,
spl0_493,
inference(avatar_split_clause,[],[f122,f9413]) ).
fof(f9413,plain,
( spl0_493
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f122,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f9411,plain,
spl0_492,
inference(avatar_split_clause,[],[f121,f9409]) ).
fof(f9409,plain,
( spl0_492
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f121,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f9407,plain,
spl0_491,
inference(avatar_split_clause,[],[f101,f9405]) ).
fof(f9405,plain,
( spl0_491
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f101,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f9403,plain,
spl0_490,
inference(avatar_split_clause,[],[f100,f9401]) ).
fof(f9401,plain,
( spl0_490
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f100,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f9399,plain,
spl0_489,
inference(avatar_split_clause,[],[f99,f9397]) ).
fof(f9397,plain,
( spl0_489
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X14,X16,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f99,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X14,X16,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f9395,plain,
spl0_488,
inference(avatar_split_clause,[],[f98,f9393]) ).
fof(f98,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f9391,plain,
spl0_487,
inference(avatar_split_clause,[],[f97,f9389]) ).
fof(f97,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X14,X16,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f9368,plain,
spl0_486,
inference(avatar_split_clause,[],[f96,f9366]) ).
fof(f9366,plain,
( spl0_486
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f96,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X14,X16,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f9364,plain,
spl0_485,
inference(avatar_split_clause,[],[f64,f9362]) ).
fof(f9362,plain,
( spl0_485
<=> ! [X20,X0,X25,X21] :
( ~ class_HOL_Oord(X20)
| ~ c_lessequals(X25,X21,tc_fun(X0,X20))
| c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
| c_lessequals(X21,X25,tc_fun(X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f64,axiom,
! [X21,X0,X25,X20] :
( ~ class_HOL_Oord(X20)
| ~ c_lessequals(X25,X21,tc_fun(X0,X20))
| c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
| c_lessequals(X21,X25,tc_fun(X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
fof(f8996,plain,
( spl0_484
| ~ spl0_110
| ~ spl0_473 ),
inference(avatar_split_clause,[],[f8660,f8149,f1486,f8994]) ).
fof(f8994,plain,
( spl0_484
<=> ! [X0] :
( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
| hBOOL(hAPP(v_G,hAPP(v_mgt__call,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f8660,plain,
( ! [X0] :
( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
| hBOOL(hAPP(v_G,hAPP(v_mgt__call,X0))) )
| ~ spl0_110
| ~ spl0_473 ),
inference(resolution,[],[f8150,f1487]) ).
fof(f8214,plain,
( spl0_483
| ~ spl0_2
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f7210,f6739,f1008,f8212]) ).
fof(f7210,plain,
( ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_Com_Opname),v_U,tc_Com_Opname,X1)
| ~ spl0_2
| ~ spl0_409 ),
inference(resolution,[],[f6740,f1010]) ).
fof(f8187,plain,
spl0_482,
inference(avatar_split_clause,[],[f990,f8185]) ).
fof(f8185,plain,
( spl0_482
<=> ! [X6,X0,X1] :
( ~ c_lessequals(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool))
| c_fequal(X1,X0) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f990,plain,
! [X0,X1,X6] :
( ~ c_lessequals(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool))
| c_fequal(X1,X0) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ),
inference(forward_demodulation,[],[f989,f926]) ).
fof(f989,plain,
! [X0,X1,X6] :
( c_fequal(X1,X0) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f775,f926]) ).
fof(f775,axiom,
! [X0,X1,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X6
| ~ c_lessequals(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f8183,plain,
spl0_481,
inference(avatar_split_clause,[],[f978,f8181]) ).
fof(f8181,plain,
( spl0_481
<=> ! [X17,X0,X14,X16,X15] :
( c_Set_Oinsert(X14,c_fequal(X16,X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
| X16 = X17
| X14 = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f978,plain,
! [X0,X16,X14,X17,X15] :
( c_Set_Oinsert(X14,c_fequal(X16,X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
| X16 = X17
| X14 = X17 ),
inference(forward_demodulation,[],[f977,f926]) ).
fof(f977,plain,
! [X0,X16,X14,X17,X15] :
( c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
| X16 = X17
| X14 = X17 ),
inference(forward_demodulation,[],[f825,f926]) ).
fof(f825,axiom,
! [X0,X16,X14,X17,X15] :
( X16 = X17
| X14 = X17
| c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X15,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
fof(f8179,plain,
spl0_480,
inference(avatar_split_clause,[],[f976,f8177]) ).
fof(f8177,plain,
( spl0_480
<=> ! [X17,X0,X14,X16,X15] :
( c_Set_Oinsert(X14,c_fequal(X16,X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
| X14 = X15
| X14 = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f976,plain,
! [X0,X16,X14,X17,X15] :
( c_Set_Oinsert(X14,c_fequal(X16,X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
| X14 = X15
| X14 = X17 ),
inference(forward_demodulation,[],[f975,f926]) ).
fof(f975,plain,
! [X0,X16,X14,X17,X15] :
( c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
| X14 = X15
| X14 = X17 ),
inference(forward_demodulation,[],[f827,f926]) ).
fof(f827,axiom,
! [X0,X16,X14,X17,X15] :
( X14 = X15
| X14 = X17
| c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X15,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
fof(f8175,plain,
spl0_479,
inference(avatar_split_clause,[],[f916,f8173]) ).
fof(f8173,plain,
( spl0_479
<=> ! [X6,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Complete__Lattice_OInf__class_OInf(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),X6,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f916,plain,
! [X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Complete__Lattice_OInf__class_OInf(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),X6,X0,X0),X0) ),
inference(definition_unfolding,[],[f295,f57]) ).
fof(f295,axiom,
! [X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Complete__Lattice_OInf__class_OInf(X6,X0) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),X6,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__fold__inf_0) ).
fof(f8171,plain,
spl0_478,
inference(avatar_split_clause,[],[f915,f8169]) ).
fof(f915,plain,
! [X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Complete__Lattice_OSup__class_OSup(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0),X6,X0,X0),X0) ),
inference(definition_unfolding,[],[f357,f57]) ).
fof(f357,axiom,
! [X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Complete__Lattice_OSup__class_OSup(X6,X0) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0),X6,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__fold__sup_0) ).
fof(f8167,plain,
spl0_477,
inference(avatar_split_clause,[],[f817,f8165]) ).
fof(f817,axiom,
! [X0,X8,X14,X25,X20] : c_Set_Oimage(X25,c_Set_Oinsert(X14,X8,X20),X20,X0) = c_Set_Oinsert(hAPP(X25,X14),c_Set_Oimage(X25,X8,X20,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f8163,plain,
spl0_476,
inference(avatar_split_clause,[],[f803,f8161]) ).
fof(f8161,plain,
( spl0_476
<=> ! [X6,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f803,axiom,
! [X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X6,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).
fof(f8159,plain,
spl0_475,
inference(avatar_split_clause,[],[f802,f8157]) ).
fof(f8157,plain,
( spl0_475
<=> ! [X6,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6),X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f802,axiom,
! [X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6),X6,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).
fof(f8155,plain,
spl0_474,
inference(avatar_split_clause,[],[f773,f8153]) ).
fof(f773,axiom,
! [X0,X8,X6,X14] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
fof(f8151,plain,
( spl0_473
| ~ spl0_3
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f6602,f6050,f1013,f8149]) ).
fof(f6050,plain,
( spl0_383
<=> ! [X53,X0,X6,X25,X1] :
( ~ hBOOL(c_in(X1,X6,X53))
| hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,X6,X53,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f6602,plain,
( ! [X0] :
( hBOOL(c_in(hAPP(v_mgt__call,X0),v_G,t_a))
| ~ hBOOL(c_in(X0,v_U,tc_Com_Opname)) )
| ~ spl0_3
| ~ spl0_383 ),
inference(superposition,[],[f6051,f1015]) ).
fof(f6051,plain,
( ! [X0,X1,X6,X53,X25] :
( hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,X6,X53,X0),X0))
| ~ hBOOL(c_in(X1,X6,X53)) )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f6050]) ).
fof(f8147,plain,
spl0_472,
inference(avatar_split_clause,[],[f772,f8145]) ).
fof(f8145,plain,
( spl0_472
<=> ! [X0,X14,X6,X8] :
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f772,axiom,
! [X0,X8,X6,X14] :
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
fof(f8143,plain,
spl0_471,
inference(avatar_split_clause,[],[f764,f8141]) ).
fof(f764,axiom,
! [X0,X6,X16,X25,X20] :
( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0),X6,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageE_1) ).
fof(f8139,plain,
spl0_470,
inference(avatar_split_clause,[],[f763,f8137]) ).
fof(f763,axiom,
! [X0,X19,X6,X25,X20] :
( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
| hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_1) ).
fof(f8135,plain,
spl0_469,
inference(avatar_split_clause,[],[f732,f8133]) ).
fof(f8133,plain,
( spl0_469
<=> ! [X0,X6,X8,X7] :
( c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f732,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f8131,plain,
spl0_468,
inference(avatar_split_clause,[],[f731,f8129]) ).
fof(f8129,plain,
( spl0_468
<=> ! [X0,X6,X8,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f731,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f8127,plain,
spl0_467,
inference(avatar_split_clause,[],[f692,f8125]) ).
fof(f692,axiom,
! [X0,X8,X6,X25,X20] :
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X8,X0,X20)
| ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).
fof(f8122,plain,
spl0_466,
inference(avatar_split_clause,[],[f690,f8120]) ).
fof(f8120,plain,
( spl0_466
<=> ! [X20,X0,X6,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool))) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f690,axiom,
! [X0,X8,X6,X20] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool))) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
fof(f8117,plain,
spl0_465,
inference(avatar_split_clause,[],[f689,f8115]) ).
fof(f8115,plain,
( spl0_465
<=> ! [X20,X0,X6,X8] : 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(X20,tc_bool)),X6,X20,tc_fun(X0,tc_bool))),X8) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f689,axiom,
! [X0,X8,X6,X20] : 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(X20,tc_bool)),X6,X20,tc_fun(X0,tc_bool))),X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
fof(f8113,plain,
spl0_464,
inference(avatar_split_clause,[],[f686,f8111]) ).
fof(f8111,plain,
( spl0_464
<=> ! [X6,X0,X1,X8] :
( hBOOL(hAPP(X8,X1))
| hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f686,axiom,
! [X0,X1,X8,X6] :
( hBOOL(hAPP(X8,X1))
| hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f8109,plain,
spl0_463,
inference(avatar_split_clause,[],[f664,f8107]) ).
fof(f8107,plain,
( spl0_463
<=> ! [X20,X0,X6,X25] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Ovimage(X25,c_Set_Oimage(X25,X6,X0,X20),X0,X20) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f664,axiom,
! [X0,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
| c_Set_Ovimage(X25,c_Set_Oimage(X25,X6,X0,X20),X0,X20) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
fof(f8105,plain,
spl0_462,
inference(avatar_split_clause,[],[f660,f8103]) ).
fof(f660,axiom,
! [X0,X19,X6,X25,X20] :
( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0),X6,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_0) ).
fof(f8101,plain,
spl0_461,
inference(avatar_split_clause,[],[f658,f8099]) ).
fof(f658,axiom,
! [X0,X6,X16,X25,X20] :
( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
| hAPP(X25,c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0)) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageE_0) ).
fof(f8097,plain,
spl0_460,
inference(avatar_split_clause,[],[f624,f8095]) ).
fof(f624,axiom,
! [X0,X6,X25,X20] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).
fof(f8093,plain,
spl0_459,
inference(avatar_split_clause,[],[f619,f8091]) ).
fof(f8091,plain,
( spl0_459
<=> ! [X6,X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f619,axiom,
! [X0,X8,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f8089,plain,
spl0_458,
inference(avatar_split_clause,[],[f618,f8087]) ).
fof(f8087,plain,
( spl0_458
<=> ! [X6,X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f618,axiom,
! [X0,X8,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f8085,plain,
spl0_457,
inference(avatar_split_clause,[],[f558,f8083]) ).
fof(f8083,plain,
( spl0_457
<=> ! [X20,X0,X14,X6,X8] :
( ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(hAPP(X8,X14),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f558,axiom,
! [X0,X8,X6,X14,X20] :
( ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(hAPP(X8,X14),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
fof(f8081,plain,
spl0_456,
inference(avatar_split_clause,[],[f528,f8079]) ).
fof(f8079,plain,
( spl0_456
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X19,X1,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f528,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X19,X1,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
fof(f8077,plain,
spl0_455,
inference(avatar_split_clause,[],[f516,f8075]) ).
fof(f8075,plain,
( spl0_455
<=> ! [X6,X20,X8] :
( ~ class_HOL_Ominus(X20)
| hAPP(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(t_a,X20)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X6,v_x),hAPP(X8,v_x),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f516,axiom,
! [X8,X6,X20] :
( ~ class_HOL_Ominus(X20)
| hAPP(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(t_a,X20)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X6,v_x),hAPP(X8,v_x),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
fof(f8073,plain,
spl0_454,
inference(avatar_split_clause,[],[f381,f8071]) ).
fof(f8071,plain,
( spl0_454
<=> ! [X0,X6,X8,X7] :
( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f381,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f8069,plain,
spl0_453,
inference(avatar_split_clause,[],[f380,f8067]) ).
fof(f8067,plain,
( spl0_453
<=> ! [X0,X6,X8,X7] :
( c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f380,axiom,
! [X0,X8,X6,X7] :
( c_lessequals(X7,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f8065,plain,
spl0_452,
inference(avatar_split_clause,[],[f355,f8063]) ).
fof(f8063,plain,
( spl0_452
<=> ! [X6,X0,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X0),X6),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f355,axiom,
! [X0,X6,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X14,X6,X0))
| c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X0),X6),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).
fof(f8061,plain,
spl0_451,
inference(avatar_split_clause,[],[f349,f8059]) ).
fof(f8059,plain,
( spl0_451
<=> ! [X6,X0,X1] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X1,X6,X0))
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f349,axiom,
! [X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(c_in(X1,X6,X0))
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(X6,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).
fof(f8057,plain,
spl0_450,
inference(avatar_split_clause,[],[f189,f8055]) ).
fof(f8055,plain,
( spl0_450
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X19,X1,X0)
| ~ c_HOL_Oord__class_Oless(X19,X2,X0)
| c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f189,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X19,X1,X0)
| ~ c_HOL_Oord__class_Oless(X19,X2,X0)
| c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
fof(f8053,plain,
spl0_449,
inference(avatar_split_clause,[],[f186,f8051]) ).
fof(f8051,plain,
( spl0_449
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X19,X0)
| ~ c_HOL_Oord__class_Oless(X2,X19,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f186,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X19,X0)
| ~ c_HOL_Oord__class_Oless(X2,X19,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
fof(f8049,plain,
spl0_448,
inference(avatar_split_clause,[],[f181,f8047]) ).
fof(f8047,plain,
( spl0_448
<=> ! [X0,X14,X16,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X14,X0)
| ~ c_lessequals(X1,X16,X0)
| c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f181,axiom,
! [X0,X1,X16,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X14,X0)
| ~ c_lessequals(X1,X16,X0)
| c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
fof(f8045,plain,
spl0_447,
inference(avatar_split_clause,[],[f174,f8043]) ).
fof(f8043,plain,
( spl0_447
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X19,X0)
| ~ c_lessequals(X2,X19,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f174,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X19,X0)
| ~ c_lessequals(X2,X19,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
fof(f8041,plain,
spl0_446,
inference(avatar_split_clause,[],[f156,f8039]) ).
fof(f8039,plain,
( spl0_446
<=> ! [X6,X0,X1,X8] :
( ~ hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(X8,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f156,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(X8,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f8037,plain,
spl0_445,
inference(avatar_split_clause,[],[f106,f8035]) ).
fof(f8035,plain,
( spl0_445
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,X19,X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f106,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,X19,X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
fof(f8033,plain,
spl0_444,
inference(avatar_split_clause,[],[f53,f8031]) ).
fof(f8031,plain,
( spl0_444
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X19,X1,X0)
| c_lessequals(X19,X2,X0)
| ~ c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f53,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X19,X1,X0)
| c_lessequals(X19,X2,X0)
| ~ c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
fof(f8029,plain,
spl0_443,
inference(avatar_split_clause,[],[f37,f8027]) ).
fof(f8027,plain,
( spl0_443
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X19,X0)
| c_lessequals(X2,X19,X0)
| ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f37,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X19,X0)
| c_lessequals(X2,X19,X0)
| ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
fof(f8025,plain,
( spl0_441
| ~ spl0_442
| ~ spl0_3
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f6583,f6046,f1013,f8022,f8018]) ).
fof(f8022,plain,
( spl0_442
<=> c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) = v_G ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f6046,plain,
( spl0_382
<=> ! [X20,X0,X6,X25] :
( c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X25,X6,X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f6583,plain,
( c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) != v_G
| v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))
| ~ spl0_3
| ~ spl0_382 ),
inference(superposition,[],[f6047,f1015]) ).
fof(f6047,plain,
( ! [X0,X6,X25,X20] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X25,X6,X20,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6 )
| ~ spl0_382 ),
inference(avatar_component_clause,[],[f6046]) ).
fof(f8016,plain,
spl0_440,
inference(avatar_split_clause,[],[f28,f8014]) ).
fof(f8014,plain,
( spl0_440
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X19,X1,X0)
| c_HOL_Oord__class_Oless(X19,X2,X0)
| ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f28,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X19,X1,X0)
| c_HOL_Oord__class_Oless(X19,X2,X0)
| ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
fof(f8012,plain,
spl0_439,
inference(avatar_split_clause,[],[f20,f8010]) ).
fof(f8010,plain,
( spl0_439
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X19,X0)
| c_HOL_Oord__class_Oless(X2,X19,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f20,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X19,X0)
| c_HOL_Oord__class_Oless(X2,X19,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
fof(f7491,plain,
( spl0_438
| ~ spl0_265
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6673,f6571,f3041,f7489]) ).
fof(f7489,plain,
( spl0_438
<=> ! [X0,X1] : c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,v_G,X1,t_a),X1,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f6673,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,v_G,X1,t_a),X1,t_a),t_a)
| ~ spl0_265
| ~ spl0_388 ),
inference(resolution,[],[f6572,f3042]) ).
fof(f7342,plain,
spl0_437,
inference(avatar_split_clause,[],[f971,f7340]) ).
fof(f971,plain,
! [X3,X0,X5] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X3,c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0),X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X5,X0) ),
inference(forward_demodulation,[],[f970,f613]) ).
fof(f613,axiom,
! [X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f970,plain,
! [X3,X0,X5] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X3,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(X3,X5,X0)),X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X5,X0) ),
inference(forward_demodulation,[],[f469,f632]) ).
fof(f469,axiom,
! [X3,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X5,X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I5_J_0) ).
fof(f7338,plain,
spl0_436,
inference(avatar_split_clause,[],[f969,f7336]) ).
fof(f969,plain,
! [X3,X0,X5] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X5,c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0),X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X5,X0) ),
inference(forward_demodulation,[],[f968,f612]) ).
fof(f612,axiom,
! [X0,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f968,plain,
! [X3,X0,X5] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X5,X0) ),
inference(forward_demodulation,[],[f470,f631]) ).
fof(f470,axiom,
! [X3,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X5,X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0)),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).
fof(f7329,plain,
spl0_435,
inference(avatar_split_clause,[],[f963,f7327]) ).
fof(f7327,plain,
( spl0_435
<=> ! [X20,X0,X6,X15] :
( c_Set_Oimage(c_COMBK(X15,X0,X20),X6,X20,X0) = c_fequal(X15,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f963,plain,
! [X0,X6,X15,X20] :
( c_Set_Oimage(c_COMBK(X15,X0,X20),X6,X20,X0) = c_fequal(X15,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6 ),
inference(forward_demodulation,[],[f810,f926]) ).
fof(f810,axiom,
! [X0,X6,X15,X20] :
( c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6
| c_Set_Oimage(c_COMBK(X15,X0,X20),X6,X20,X0) = c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
fof(f7325,plain,
spl0_434,
inference(avatar_split_clause,[],[f961,f7323]) ).
fof(f7323,plain,
( spl0_434
<=> ! [X6,X0,X1] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),c_fequal(X1,X0),tc_fun(X0,tc_bool)) = X6
| hBOOL(c_in(X1,X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f961,plain,
! [X0,X1,X6] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),c_fequal(X1,X0),tc_fun(X0,tc_bool)) = X6
| hBOOL(c_in(X1,X6,X0)) ),
inference(forward_demodulation,[],[f809,f926]) ).
fof(f809,axiom,
! [X0,X1,X6] :
( hBOOL(c_in(X1,X6,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
fof(f7321,plain,
spl0_433,
inference(avatar_split_clause,[],[f947,f7319]) ).
fof(f7319,plain,
( spl0_433
<=> ! [X6,X0,X1] :
( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f947,plain,
! [X0,X1,X6] :
( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0) ),
inference(forward_demodulation,[],[f476,f926]) ).
fof(f476,axiom,
! [X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).
fof(f7317,plain,
spl0_432,
inference(avatar_split_clause,[],[f848,f7315]) ).
fof(f848,axiom,
! [X0,X16,X14] :
( X14 = X16
| c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f7313,plain,
spl0_431,
inference(avatar_split_clause,[],[f804,f7311]) ).
fof(f7311,plain,
( spl0_431
<=> ! [X6,X0,X1] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f804,axiom,
! [X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).
fof(f7309,plain,
spl0_430,
inference(avatar_split_clause,[],[f755,f7307]) ).
fof(f755,axiom,
! [X0,X6,X15,X20] :
( ~ hBOOL(c_in(X15,X6,X20))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).
fof(f7305,plain,
spl0_429,
inference(avatar_split_clause,[],[f737,f7303]) ).
fof(f7303,plain,
( spl0_429
<=> ! [X0,X6,X8,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f737,axiom,
! [X0,X8,X6,X7] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f7301,plain,
spl0_428,
inference(avatar_split_clause,[],[f693,f7299]) ).
fof(f7299,plain,
( spl0_428
<=> ! [X2,X19,X20,X0,X25,X1] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X1,X19,X0,X20) = c_Fun_Ofun__upd(X25,X1,X19,X0,X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f693,axiom,
! [X2,X0,X1,X19,X25,X20] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X1,X19,X0,X20) = c_Fun_Ofun__upd(X25,X1,X19,X0,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
fof(f7297,plain,
spl0_427,
inference(avatar_split_clause,[],[f685,f7295]) ).
fof(f685,axiom,
! [X2,X0,X1,X25,X20] :
( X1 = X2
| hAPP(X25,X1) != hAPP(X25,X2)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
fof(f7293,plain,
spl0_426,
inference(avatar_split_clause,[],[f683,f7291]) ).
fof(f7291,plain,
( spl0_426
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X14,X16,X0)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f683,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X14,X16,X0)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
fof(f7284,plain,
spl0_425,
inference(avatar_split_clause,[],[f627,f7282]) ).
fof(f7282,plain,
( spl0_425
<=> ! [X0,X14,X30,X7] :
( ~ c_lessequals(X7,X30,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X14,X7,X0),c_Set_Oinsert(X14,X30,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f627,axiom,
! [X0,X7,X14,X30] :
( ~ c_lessequals(X7,X30,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X14,X7,X0),c_Set_Oinsert(X14,X30,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f7280,plain,
spl0_424,
inference(avatar_split_clause,[],[f626,f7278]) ).
fof(f7278,plain,
( spl0_424
<=> ! [X6,X25,X0] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Fun_Oinj__on(X25,X6,X0,X0)
| ~ c_lessequals(X6,c_Set_Oimage(X25,X6,X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f626,axiom,
! [X0,X6,X25] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Fun_Oinj__on(X25,X6,X0,X0)
| ~ c_lessequals(X6,c_Set_Oimage(X25,X6,X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
fof(f7276,plain,
spl0_423,
inference(avatar_split_clause,[],[f582,f7274]) ).
fof(f7274,plain,
( spl0_423
<=> ! [X20,X0,X6,X15] :
( hBOOL(c_in(X15,X6,X20))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f582,axiom,
! [X0,X6,X15,X20] :
( hBOOL(c_in(X15,X6,X20))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
fof(f7272,plain,
spl0_422,
inference(avatar_split_clause,[],[f551,f7270]) ).
fof(f7270,plain,
( spl0_422
<=> ! [X35,X20,X0,X33] :
( ~ c_Finite__Set_Ofinite(X33,X0)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X20,X0),X20)
| ~ c_Fun_Oinj__on(X35,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f551,axiom,
! [X0,X35,X33,X20] :
( ~ c_Finite__Set_Ofinite(X33,X0)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X20,X0),X20)
| ~ c_Fun_Oinj__on(X35,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
fof(f7268,plain,
spl0_421,
inference(avatar_split_clause,[],[f546,f7266]) ).
fof(f7266,plain,
( spl0_421
<=> ! [X6,X0,X8] : c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f546,axiom,
! [X0,X8,X6] : c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f7264,plain,
spl0_420,
inference(avatar_split_clause,[],[f521,f7262]) ).
fof(f7262,plain,
( spl0_420
<=> ! [X48,X20,X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X48,X20,X0),X0,X20) = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f521,axiom,
! [X48,X0,X6,X20] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X48,X20,X0),X0,X20) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).
fof(f7260,plain,
spl0_419,
inference(avatar_split_clause,[],[f378,f7258]) ).
fof(f7258,plain,
( spl0_419
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X15 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f378,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X15 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f7256,plain,
spl0_418,
inference(avatar_split_clause,[],[f377,f7254]) ).
fof(f7254,plain,
( spl0_418
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X15 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f377,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X15 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f7252,plain,
spl0_417,
inference(avatar_split_clause,[],[f376,f7250]) ).
fof(f7250,plain,
( spl0_417
<=> ! [X0,X14,X16,X15] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X15 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f376,axiom,
! [X0,X16,X14,X15] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X15 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f7248,plain,
spl0_416,
inference(avatar_split_clause,[],[f330,f7246]) ).
fof(f330,axiom,
! [X0,X8,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
fof(f7244,plain,
( spl0_415
| ~ spl0_212
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6658,f6571,f2486,f7242]) ).
fof(f7242,plain,
( spl0_415
<=> ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),v_G),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f6658,plain,
( ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),v_G),t_a)
| ~ spl0_212
| ~ spl0_388 ),
inference(resolution,[],[f6572,f2487]) ).
fof(f7240,plain,
spl0_414,
inference(avatar_split_clause,[],[f315,f7238]) ).
fof(f7238,plain,
( spl0_414
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X15,X17,X0)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f315,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X15,X17,X0)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).
fof(f7236,plain,
spl0_413,
inference(avatar_split_clause,[],[f212,f7234]) ).
fof(f7234,plain,
( spl0_413
<=> ! [X0,X6,X8,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X8,X7,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f212,axiom,
! [X0,X8,X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X8,X7,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
fof(f7232,plain,
spl0_412,
inference(avatar_split_clause,[],[f142,f7230]) ).
fof(f7230,plain,
( spl0_412
<=> ! [X0,X6,X8,X7] :
( ~ c_HOL_Oord__class_Oless(X8,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f142,axiom,
! [X0,X8,X6,X7] :
( ~ c_HOL_Oord__class_Oless(X8,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
fof(f7228,plain,
spl0_411,
inference(avatar_split_clause,[],[f141,f7226]) ).
fof(f7226,plain,
( spl0_411
<=> ! [X0,X6,X8,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f141,axiom,
! [X0,X8,X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
fof(f7118,plain,
( spl0_410
| ~ spl0_211
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6657,f6571,f2482,f7116]) ).
fof(f7116,plain,
( spl0_410
<=> ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),X0),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f6657,plain,
( ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),X0),t_a)
| ~ spl0_211
| ~ spl0_388 ),
inference(resolution,[],[f6572,f2483]) ).
fof(f6741,plain,
spl0_409,
inference(avatar_split_clause,[],[f956,f6739]) ).
fof(f956,plain,
! [X0,X1,X6,X15,X20] :
( c_Set_Oimage(c_COMBK(X15,X20,X0),X6,X0,X20) = c_fequal(X15,X20)
| ~ hBOOL(c_in(X1,X6,X0)) ),
inference(forward_demodulation,[],[f811,f926]) ).
fof(f811,axiom,
! [X0,X1,X6,X15,X20] :
( ~ hBOOL(c_in(X1,X6,X0))
| c_Set_Oimage(c_COMBK(X15,X20,X0),X6,X0,X20) = c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
fof(f6737,plain,
spl0_408,
inference(avatar_split_clause,[],[f945,f6735]) ).
fof(f6735,plain,
( spl0_408
<=> ! [X0,X16,X14] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,c_fequal(X16,X0),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f945,plain,
! [X0,X16,X14] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,c_fequal(X16,X0),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f454,f926]) ).
fof(f454,axiom,
! [X0,X16,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
fof(f6733,plain,
spl0_407,
inference(avatar_split_clause,[],[f944,f6731]) ).
fof(f6731,plain,
( spl0_407
<=> ! [X0,X16,X14] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,c_fequal(X16,X0),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f944,plain,
! [X0,X16,X14] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,c_fequal(X16,X0),X0),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f621,f926]) ).
fof(f621,axiom,
! [X0,X16,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
fof(f6729,plain,
spl0_406,
inference(avatar_split_clause,[],[f933,f6727]) ).
fof(f6727,plain,
( spl0_406
<=> ! [X20,X0,X14,X8] : c_fequal(X14,X0) = c_Set_Oinsert(X14,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f933,plain,
! [X0,X8,X14,X20] : c_fequal(X14,X0) = c_Set_Oinsert(X14,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),X0),
inference(forward_demodulation,[],[f780,f926]) ).
fof(f780,axiom,
! [X0,X8,X14,X20] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Set_Oinsert(X14,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
fof(f6725,plain,
spl0_405,
inference(avatar_split_clause,[],[f667,f6723]) ).
fof(f6723,plain,
( spl0_405
<=> ! [X6,X0,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,X6,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_Complete__Lattice_OSup__class_OSup(X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f667,axiom,
! [X0,X6,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,X6,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_Complete__Lattice_OSup__class_OSup(X6,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
fof(f6721,plain,
spl0_404,
inference(avatar_split_clause,[],[f581,f6719]) ).
fof(f6719,plain,
( spl0_404
<=> ! [X6,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f581,axiom,
! [X0,X1,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).
fof(f6717,plain,
( spl0_403
| ~ spl0_165
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6671,f6571,f1936,f6715]) ).
fof(f6715,plain,
( spl0_403
<=> ! [X0] : c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v_G,X0,tc_fun(t_a,tc_bool)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f6671,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v_G,X0,tc_fun(t_a,tc_bool)),t_a)
| ~ spl0_165
| ~ spl0_388 ),
inference(resolution,[],[f6572,f1937]) ).
fof(f6713,plain,
spl0_402,
inference(avatar_split_clause,[],[f580,f6711]) ).
fof(f580,axiom,
! [X0,X1,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_lessequals(X1,hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).
fof(f6709,plain,
spl0_401,
inference(avatar_split_clause,[],[f557,f6707]) ).
fof(f6707,plain,
( spl0_401
<=> ! [X48,X20,X0,X6,X27] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| ~ hBOOL(c_in(X27,X6,X0))
| c_lessequals(hAPP(X48,X27),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X48,X0,X20),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f557,axiom,
! [X48,X0,X6,X27,X20] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| ~ hBOOL(c_in(X27,X6,X0))
| c_lessequals(hAPP(X48,X27),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X48,X0,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
fof(f6705,plain,
spl0_400,
inference(avatar_split_clause,[],[f548,f6703]) ).
fof(f548,axiom,
! [X0,X8,X6,X20] : c_HOL_Ominus__class_Ominus(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
fof(f6701,plain,
spl0_399,
inference(avatar_split_clause,[],[f514,f6699]) ).
fof(f6697,plain,
spl0_398,
inference(avatar_split_clause,[],[f504,f6695]) ).
fof(f6695,plain,
( spl0_398
<=> ! [X20,X0,X6,X25,X8] :
( c_Fun_Oinj__on(X25,X8,X0,X20)
| ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f504,axiom,
! [X0,X8,X6,X25,X20] :
( c_Fun_Oinj__on(X25,X8,X0,X20)
| ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
fof(f6693,plain,
spl0_397,
inference(avatar_split_clause,[],[f503,f6691]) ).
fof(f6691,plain,
( spl0_397
<=> ! [X8,X20,X0,X6,X25] :
( c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f503,axiom,
! [X0,X8,X6,X25,X20] :
( c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
fof(f6689,plain,
spl0_396,
inference(avatar_split_clause,[],[f493,f6687]) ).
fof(f6687,plain,
( spl0_396
<=> ! [X15,X0,X6,X8] :
( ~ hBOOL(c_in(X15,X6,X0))
| hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f493,axiom,
! [X0,X8,X6,X15] :
( ~ hBOOL(c_in(X15,X6,X0))
| hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f6685,plain,
spl0_395,
inference(avatar_split_clause,[],[f492,f6683]) ).
fof(f6683,plain,
( spl0_395
<=> ! [X15,X0,X6,X8] :
( ~ hBOOL(c_in(X15,X8,X0))
| hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f492,axiom,
! [X0,X8,X6,X15] :
( ~ hBOOL(c_in(X15,X8,X0))
| hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f6681,plain,
spl0_394,
inference(avatar_split_clause,[],[f449,f6679]) ).
fof(f6679,plain,
( spl0_394
<=> ! [X6,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f449,axiom,
! [X0,X8,X6] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).
fof(f6677,plain,
spl0_393,
inference(avatar_split_clause,[],[f424,f6675]) ).
fof(f6675,plain,
( spl0_393
<=> ! [X15,X0,X6,X8] :
( hBOOL(c_in(X15,X6,X0))
| ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f424,axiom,
! [X0,X8,X6,X15] :
( hBOOL(c_in(X15,X6,X0))
| ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f6648,plain,
spl0_392,
inference(avatar_split_clause,[],[f423,f6646]) ).
fof(f6646,plain,
( spl0_392
<=> ! [X15,X0,X6,X8] :
( hBOOL(c_in(X15,X8,X0))
| ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f423,axiom,
! [X0,X8,X6,X15] :
( hBOOL(c_in(X15,X8,X0))
| ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f6644,plain,
spl0_391,
inference(avatar_split_clause,[],[f344,f6642]) ).
fof(f6642,plain,
( spl0_391
<=> ! [X6,X0,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,X6,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_Complete__Lattice_OInf__class_OInf(X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f344,axiom,
! [X0,X6,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,X6,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_Complete__Lattice_OInf__class_OInf(X6,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
fof(f6640,plain,
spl0_390,
inference(avatar_split_clause,[],[f259,f6638]) ).
fof(f6636,plain,
spl0_389,
inference(avatar_split_clause,[],[f169,f6634]) ).
fof(f6634,plain,
( spl0_389
<=> ! [X6,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f169,axiom,
! [X0,X8,X6] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).
fof(f6573,plain,
( ~ spl0_1
| spl0_388
| ~ spl0_3
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f6568,f6038,f1013,f6571,f1003]) ).
fof(f6038,plain,
( spl0_380
<=> ! [X20,X0,X6,X25,X8] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(X8,X20)
| ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f6568,plain,
( ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Finite__Set_Ofinite(X0,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) )
| ~ spl0_3
| ~ spl0_380 ),
inference(superposition,[],[f6039,f1015]) ).
fof(f6039,plain,
( ! [X0,X8,X6,X25,X20] :
( ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
| c_Finite__Set_Ofinite(X8,X20)
| ~ c_Finite__Set_Ofinite(X6,X0) )
| ~ spl0_380 ),
inference(avatar_component_clause,[],[f6038]) ).
fof(f6068,plain,
spl0_387,
inference(avatar_split_clause,[],[f960,f6066]) ).
fof(f6066,plain,
( spl0_387
<=> ! [X20,X0,X14,X16,X25] :
( ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(X16,X20),X0,X20),X0))
| hAPP(X25,X14) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f960,plain,
! [X0,X16,X14,X25,X20] :
( ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(X16,X20),X0,X20),X0))
| hAPP(X25,X14) = X16 ),
inference(forward_demodulation,[],[f806,f926]) ).
fof(f806,axiom,
! [X0,X16,X14,X25,X20] :
( hAPP(X25,X14) = X16
| ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X0,X20),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
fof(f6064,plain,
spl0_386,
inference(avatar_split_clause,[],[f955,f6062]) ).
fof(f6062,plain,
( spl0_386
<=> ! [X0,X6,X1,X26] :
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X26),X0))
| hBOOL(hAPP(X26,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f955,plain,
! [X0,X1,X6,X26] :
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X26),X0))
| hBOOL(hAPP(X26,X1)) ),
inference(forward_demodulation,[],[f311,f665]) ).
fof(f311,axiom,
! [X0,X1,X6,X26] :
( hBOOL(hAPP(X26,X1))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Collect(X26,X0)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
fof(f6060,plain,
( spl0_385
| ~ spl0_191
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f5687,f5440,f2270,f6058]) ).
fof(f5440,plain,
( spl0_361
<=> c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f5687,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Finite__Set_Ocard(v_G,t_a),tc_nat)
| c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) )
| ~ spl0_191
| ~ spl0_361 ),
inference(resolution,[],[f5442,f2271]) ).
fof(f5442,plain,
( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f5440]) ).
fof(f6056,plain,
spl0_384,
inference(avatar_split_clause,[],[f932,f6054]) ).
fof(f6054,plain,
( spl0_384
<=> ! [X6,X0,X14] : c_Set_Oinsert(X14,X6,X0) = c_Set_Oinsert(X14,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f932,plain,
! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = c_Set_Oinsert(X14,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),
inference(forward_demodulation,[],[f793,f926]) ).
fof(f793,axiom,
! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = c_Set_Oinsert(X14,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
fof(f6052,plain,
spl0_383,
inference(avatar_split_clause,[],[f857,f6050]) ).
fof(f857,axiom,
! [X0,X1,X6,X53,X25] :
( ~ hBOOL(c_in(X1,X6,X53))
| hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,X6,X53,X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
fof(f6048,plain,
spl0_382,
inference(avatar_split_clause,[],[f837,f6046]) ).
fof(f837,axiom,
! [X0,X6,X25,X20] :
( c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X25,X6,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
fof(f6044,plain,
spl0_381,
inference(avatar_split_clause,[],[f829,f6042]) ).
fof(f6042,plain,
( spl0_381
<=> ! [X0,X14,X6,X16] :
( X14 = X16
| hBOOL(c_in(X14,X6,X0))
| ~ hBOOL(c_in(X14,c_Set_Oinsert(X16,X6,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f829,axiom,
! [X0,X6,X16,X14] :
( X14 = X16
| hBOOL(c_in(X14,X6,X0))
| ~ hBOOL(c_in(X14,c_Set_Oinsert(X16,X6,X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f6040,plain,
spl0_380,
inference(avatar_split_clause,[],[f798,f6038]) ).
fof(f798,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(X8,X20)
| ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
fof(f6036,plain,
spl0_379,
inference(avatar_split_clause,[],[f752,f6034]) ).
fof(f752,axiom,
! [X0,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).
fof(f6032,plain,
spl0_378,
inference(avatar_split_clause,[],[f738,f6030]) ).
fof(f738,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X8,X0,X20)
| c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
fof(f6028,plain,
spl0_377,
inference(avatar_split_clause,[],[f708,f6026]) ).
fof(f708,axiom,
! [X0,X8,X6] :
( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) != X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f6024,plain,
spl0_376,
inference(avatar_split_clause,[],[f707,f6022]) ).
fof(f707,axiom,
! [X0,X8,X6] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f6020,plain,
spl0_375,
inference(avatar_split_clause,[],[f706,f6018]) ).
fof(f706,axiom,
! [X0,X8,X6] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f6010,plain,
spl0_374,
inference(avatar_split_clause,[],[f671,f6008]) ).
fof(f6008,plain,
( spl0_374
<=> ! [X6,X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f671,axiom,
! [X0,X6] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
fof(f6006,plain,
spl0_373,
inference(avatar_split_clause,[],[f670,f6004]) ).
fof(f6004,plain,
( spl0_373
<=> ! [X0,X8] : 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))),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f670,axiom,
! [X0,X8] : 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))),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
fof(f6002,plain,
spl0_372,
inference(avatar_split_clause,[],[f588,f6000]) ).
fof(f6000,plain,
( spl0_372
<=> ! [X0,X44,X33] :
( ~ c_Finite__Set_Ofinite(X33,X0)
| ~ c_Finite__Set_Ofinite(X44,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f588,axiom,
! [X0,X44,X33] :
( ~ c_Finite__Set_Ofinite(X33,X0)
| ~ c_Finite__Set_Ofinite(X44,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
fof(f5998,plain,
spl0_371,
inference(avatar_split_clause,[],[f575,f5996]) ).
fof(f5996,plain,
( spl0_371
<=> ! [X20,X14,X0,X6,X25] :
( hBOOL(c_in(hAPP(X25,X14),X6,X20))
| ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,X6,X0,X20),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f575,axiom,
! [X0,X6,X14,X25,X20] :
( hBOOL(c_in(hAPP(X25,X14),X6,X20))
| ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,X6,X0,X20),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
fof(f5994,plain,
spl0_370,
inference(avatar_split_clause,[],[f572,f5992]) ).
fof(f5992,plain,
( spl0_370
<=> ! [X0,X14,X6,X25,X20] :
( ~ hBOOL(c_in(hAPP(X25,X14),X6,X0))
| hBOOL(c_in(X14,c_Set_Ovimage(X25,X6,X20,X0),X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f572,axiom,
! [X0,X6,X14,X25,X20] :
( ~ hBOOL(c_in(hAPP(X25,X14),X6,X0))
| hBOOL(c_in(X14,c_Set_Ovimage(X25,X6,X20,X0),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
fof(f5990,plain,
spl0_369,
inference(avatar_split_clause,[],[f498,f5988]) ).
fof(f498,axiom,
! [X21,X0,X1,X25,X20] :
( ~ class_HOL_Oord(X20)
| ~ c_lessequals(X25,X21,tc_fun(X0,X20))
| c_lessequals(hAPP(X25,X1),hAPP(X21,X1),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f5986,plain,
spl0_368,
inference(avatar_split_clause,[],[f497,f5984]) ).
fof(f497,axiom,
! [X46,X0,X8,X6] :
( ~ hBOOL(c_in(X46,X6,X0))
| hBOOL(c_in(X46,X8,X0))
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
fof(f5982,plain,
spl0_367,
inference(avatar_split_clause,[],[f436,f5980]) ).
fof(f5980,plain,
( spl0_367
<=> ! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f436,axiom,
! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f5978,plain,
spl0_366,
inference(avatar_split_clause,[],[f435,f5976]) ).
fof(f5976,plain,
( spl0_366
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f435,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f5974,plain,
spl0_365,
inference(avatar_split_clause,[],[f422,f5972]) ).
fof(f5972,plain,
( spl0_365
<=> ! [X15,X0,X6,X8] :
( ~ hBOOL(c_in(X15,X6,X0))
| hBOOL(c_in(X15,X8,X0))
| ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f422,axiom,
! [X0,X8,X6,X15] :
( ~ hBOOL(c_in(X15,X6,X0))
| hBOOL(c_in(X15,X8,X0))
| ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
fof(f5970,plain,
( ~ spl0_19
| ~ spl0_364
| ~ spl0_126
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f5690,f5440,f1632,f5967,f1093]) ).
fof(f5967,plain,
( spl0_364
<=> c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_U,tc_Com_Opname),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f5690,plain,
( ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_U,tc_Com_Opname),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ spl0_126
| ~ spl0_361 ),
inference(resolution,[],[f5442,f1633]) ).
fof(f5965,plain,
spl0_363,
inference(avatar_split_clause,[],[f249,f5963]) ).
fof(f249,axiom,
! [X0,X8,X6] :
( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f5961,plain,
spl0_362,
inference(avatar_split_clause,[],[f248,f5959]) ).
fof(f248,axiom,
! [X0,X8,X6] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f5443,plain,
( ~ spl0_1
| spl0_361
| ~ spl0_3
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5407,f4268,f1013,f5440,f1003]) ).
fof(f5407,plain,
( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| ~ spl0_3
| ~ spl0_334 ),
inference(superposition,[],[f4269,f1015]) ).
fof(f5102,plain,
( spl0_360
| ~ spl0_110
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f4890,f4304,f1486,f5100]) ).
fof(f5100,plain,
( spl0_360
<=> ! [X0] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f4304,plain,
( spl0_343
<=> ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f4890,plain,
( ! [X0] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),v_x))
| ~ spl0_110
| ~ spl0_343 ),
inference(resolution,[],[f4305,f1487]) ).
fof(f4305,plain,
( ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname))
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f4304]) ).
fof(f4488,plain,
( spl0_359
| ~ spl0_110
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4348,f4260,f1486,f4486]) ).
fof(f4486,plain,
( spl0_359
<=> ! [X0] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f4260,plain,
( spl0_332
<=> ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f4348,plain,
( ! [X0] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),v_x))
| ~ spl0_110
| ~ spl0_332 ),
inference(resolution,[],[f4261,f1487]) ).
fof(f4261,plain,
( ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname))
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f4260]) ).
fof(f4370,plain,
spl0_358,
inference(avatar_split_clause,[],[f931,f4368]) ).
fof(f931,plain,
! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_fequal(X14,X0)),X6),
inference(forward_demodulation,[],[f795,f926]) ).
fof(f795,axiom,
! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
fof(f4366,plain,
spl0_357,
inference(avatar_split_clause,[],[f843,f4364]) ).
fof(f843,axiom,
! [X2,X0,X1,X6] : c_Set_Oinsert(X1,c_Set_Oinsert(X2,X6,X0),X0) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X6,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f4362,plain,
spl0_356,
inference(avatar_split_clause,[],[f797,f4360]) ).
fof(f797,axiom,
! [X0,X6,X25,X20] :
( c_Finite__Set_Ofinite(X6,X20)
| ~ c_Fun_Oinj__on(X25,X6,X20,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X25,X6,X20,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
fof(f4358,plain,
spl0_355,
inference(avatar_split_clause,[],[f754,f4356]) ).
fof(f4356,plain,
( spl0_355
<=> ! [X2,X19,X20,X0,X25,X1] :
( X1 = X19
| hAPP(X25,X19) = hAPP(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f754,axiom,
! [X2,X0,X1,X19,X25,X20] :
( X1 = X19
| hAPP(X25,X19) = hAPP(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
fof(f4354,plain,
spl0_354,
inference(avatar_split_clause,[],[f746,f4352]) ).
fof(f4352,plain,
( spl0_354
<=> ! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f746,axiom,
! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X16,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
fof(f4346,plain,
spl0_353,
inference(avatar_split_clause,[],[f745,f4344]) ).
fof(f4344,plain,
( spl0_353
<=> ! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X14,X16,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f745,axiom,
! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X14,X16,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
fof(f4342,plain,
spl0_352,
inference(avatar_split_clause,[],[f729,f4340]) ).
fof(f4340,plain,
( spl0_352
<=> ! [X0,X14,X16,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X16,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f729,axiom,
! [X0,X1,X16,X14] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X16,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
fof(f4338,plain,
spl0_351,
inference(avatar_split_clause,[],[f728,f4336]) ).
fof(f4336,plain,
( spl0_351
<=> ! [X0,X14,X16,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X14,X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f728,axiom,
! [X0,X1,X16,X14] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X14,X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f4334,plain,
spl0_350,
inference(avatar_split_clause,[],[f727,f4332]) ).
fof(f4332,plain,
( spl0_350
<=> ! [X0,X14,X16,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X16,X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f727,axiom,
! [X0,X1,X16,X14] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X16,X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f4330,plain,
spl0_349,
inference(avatar_split_clause,[],[f726,f4328]) ).
fof(f4328,plain,
( spl0_349
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X19,X0)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f726,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X19,X0)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
fof(f4326,plain,
spl0_348,
inference(avatar_split_clause,[],[f699,f4324]) ).
fof(f4324,plain,
( spl0_348
<=> ! [X6,X0,X8] :
( X6 = X8
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f699,axiom,
! [X0,X8,X6] :
( X6 = X8
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
fof(f4322,plain,
spl0_347,
inference(avatar_split_clause,[],[f688,f4320]) ).
fof(f688,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(hAPP(X6,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f4318,plain,
spl0_346,
inference(avatar_split_clause,[],[f687,f4316]) ).
fof(f4316,plain,
( spl0_346
<=> ! [X6,X0,X1,X8] :
( ~ hBOOL(hAPP(X8,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f687,axiom,
! [X0,X1,X8,X6] :
( ~ hBOOL(hAPP(X8,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f4314,plain,
spl0_345,
inference(avatar_split_clause,[],[f661,f4312]) ).
fof(f4312,plain,
( spl0_345
<=> ! [X8,X20,X0,X6,X25] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Fun_Oinj__on(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f661,axiom,
! [X0,X8,X6,X25,X20] :
( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
| c_Fun_Oinj__on(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
fof(f4310,plain,
spl0_344,
inference(avatar_split_clause,[],[f634,f4308]) ).
fof(f634,axiom,
! [X0,X1,X8,X6] :
( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
fof(f4306,plain,
( spl0_343
| ~ spl0_221
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f4027,f3748,f2522,f4304]) ).
fof(f3748,plain,
( spl0_281
<=> ! [X0] :
( ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool))
| hBOOL(c_in(v_x,X0,tc_Com_Opname)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f4027,plain,
( ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname))
| ~ spl0_221
| ~ spl0_281 ),
inference(resolution,[],[f3749,f2523]) ).
fof(f3749,plain,
( ! [X0] :
( ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool))
| hBOOL(c_in(v_x,X0,tc_Com_Opname)) )
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f3748]) ).
fof(f4302,plain,
spl0_342,
inference(avatar_split_clause,[],[f633,f4300]) ).
fof(f4300,plain,
( spl0_342
<=> ! [X16,X0,X6,X8] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,c_Set_Oinsert(X16,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f633,axiom,
! [X0,X8,X6,X16] :
( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,c_Set_Oinsert(X16,X8,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
fof(f4298,plain,
spl0_341,
inference(avatar_split_clause,[],[f607,f4296]) ).
fof(f4296,plain,
( spl0_341
<=> ! [X6,X0] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f607,axiom,
! [X0,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f4294,plain,
spl0_340,
inference(avatar_split_clause,[],[f597,f4292]) ).
fof(f4292,plain,
( spl0_340
<=> ! [X6,X0,X8] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X8
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f597,axiom,
! [X0,X8,X6] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X8
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f4290,plain,
spl0_339,
inference(avatar_split_clause,[],[f596,f4288]) ).
fof(f4288,plain,
( spl0_339
<=> ! [X6,X0,X8] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X6
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f596,axiom,
! [X0,X8,X6] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X6
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f4286,plain,
spl0_338,
inference(avatar_split_clause,[],[f513,f4284]) ).
fof(f4284,plain,
( spl0_338
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f513,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f4282,plain,
spl0_337,
inference(avatar_split_clause,[],[f512,f4280]) ).
fof(f512,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f4278,plain,
spl0_336,
inference(avatar_split_clause,[],[f489,f4276]) ).
fof(f489,axiom,
! [X0,X8,X6,X15] :
( ~ hBOOL(c_in(X15,X8,X0))
| ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f4274,plain,
spl0_335,
inference(avatar_split_clause,[],[f488,f4272]) ).
fof(f488,axiom,
! [X0,X8,X6,X15] :
( hBOOL(c_in(X15,X6,X0))
| ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f4270,plain,
spl0_334,
inference(avatar_split_clause,[],[f450,f4268]) ).
fof(f450,axiom,
! [X0,X6,X25,X20] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image__le_0) ).
fof(f4266,plain,
spl0_333,
inference(avatar_split_clause,[],[f434,f4264]) ).
fof(f4264,plain,
( spl0_333
<=> ! [X19,X20,X0,X25,X1] :
( X1 = X19
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f434,axiom,
! [X0,X1,X19,X25,X20] :
( X1 = X19
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
fof(f4262,plain,
( spl0_332
| ~ spl0_220
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f4026,f3748,f2518,f4260]) ).
fof(f4026,plain,
( ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname))
| ~ spl0_220
| ~ spl0_281 ),
inference(resolution,[],[f3749,f2519]) ).
fof(f4258,plain,
spl0_331,
inference(avatar_split_clause,[],[f413,f4256]) ).
fof(f413,axiom,
! [X0,X1,X16,X14] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X16,X0)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
fof(f4254,plain,
spl0_330,
inference(avatar_split_clause,[],[f412,f4252]) ).
fof(f412,axiom,
! [X0,X1,X16,X14] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X14,X0)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
fof(f4250,plain,
spl0_329,
inference(avatar_split_clause,[],[f408,f4248]) ).
fof(f4248,plain,
( spl0_329
<=> ! [X6,X0,X1,X8] :
( hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f408,axiom,
! [X0,X1,X8,X6] :
( hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f4246,plain,
spl0_328,
inference(avatar_split_clause,[],[f407,f4244]) ).
fof(f4244,plain,
( spl0_328
<=> ! [X6,X0,X1,X8] :
( hBOOL(hAPP(X8,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f407,axiom,
! [X0,X1,X8,X6] :
( hBOOL(hAPP(X8,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f4242,plain,
spl0_327,
inference(avatar_split_clause,[],[f397,f4240]) ).
fof(f4240,plain,
( spl0_327
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f397,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
fof(f4238,plain,
spl0_326,
inference(avatar_split_clause,[],[f392,f4236]) ).
fof(f4236,plain,
( spl0_326
<=> ! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f392,axiom,
! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
fof(f4234,plain,
spl0_325,
inference(avatar_split_clause,[],[f391,f4232]) ).
fof(f391,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f4230,plain,
spl0_324,
inference(avatar_split_clause,[],[f387,f4228]) ).
fof(f4228,plain,
( spl0_324
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X19,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f387,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X19,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
fof(f4226,plain,
spl0_323,
inference(avatar_split_clause,[],[f386,f4224]) ).
fof(f4224,plain,
( spl0_323
<=> ! [X19,X0,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f386,axiom,
! [X2,X0,X1,X19] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f4222,plain,
spl0_322,
inference(avatar_split_clause,[],[f385,f4220]) ).
fof(f4220,plain,
( spl0_322
<=> ! [X0,X14,X16,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X16,X1,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f385,axiom,
! [X0,X1,X16,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X16,X1,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f4216,plain,
spl0_321,
inference(avatar_split_clause,[],[f384,f4214]) ).
fof(f4214,plain,
( spl0_321
<=> ! [X0,X14,X16,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X14,X1,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f384,axiom,
! [X0,X1,X16,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X14,X1,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f4212,plain,
spl0_320,
inference(avatar_split_clause,[],[f368,f4210]) ).
fof(f4210,plain,
( spl0_320
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X19,X2,X0)
| ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f368,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X19,X2,X0)
| ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
fof(f4208,plain,
spl0_319,
inference(avatar_split_clause,[],[f367,f4206]) ).
fof(f4206,plain,
( spl0_319
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X19,X1,X0)
| ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f367,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X19,X1,X0)
| ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
fof(f4204,plain,
spl0_318,
inference(avatar_split_clause,[],[f366,f4202]) ).
fof(f4202,plain,
( spl0_318
<=> ! [X0,X14,X16,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X16,X1,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f366,axiom,
! [X0,X1,X16,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X16,X1,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
fof(f4200,plain,
spl0_317,
inference(avatar_split_clause,[],[f365,f4198]) ).
fof(f4198,plain,
( spl0_317
<=> ! [X0,X14,X16,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X1,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f365,axiom,
! [X0,X1,X16,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X1,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
fof(f4196,plain,
spl0_316,
inference(avatar_split_clause,[],[f362,f4194]) ).
fof(f4194,plain,
( spl0_316
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f362,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f4192,plain,
spl0_315,
inference(avatar_split_clause,[],[f361,f4190]) ).
fof(f4190,plain,
( spl0_315
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f361,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f4188,plain,
spl0_314,
inference(avatar_split_clause,[],[f346,f4186]) ).
fof(f4186,plain,
( spl0_314
<=> ! [X20,X0,X25] :
( ~ c_Fun_Obij(X25,X0,X20)
| c_Fun_Obij(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f346,axiom,
! [X0,X25,X20] :
( ~ c_Fun_Obij(X25,X0,X20)
| c_Fun_Obij(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__imp__bij__inv_0) ).
fof(f4184,plain,
spl0_313,
inference(avatar_split_clause,[],[f322,f4182]) ).
fof(f322,axiom,
! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X16,X14,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).
fof(f4180,plain,
spl0_312,
inference(avatar_split_clause,[],[f298,f4178]) ).
fof(f298,axiom,
! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X16,X14,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
fof(f4176,plain,
( spl0_311
| ~ spl0_110
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4131,f4087,f1486,f4174]) ).
fof(f4174,plain,
( spl0_311
<=> ! [X0] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,tc_Com_Opname),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f4131,plain,
( ! [X0] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,tc_Com_Opname),v_x))
| ~ spl0_110
| ~ spl0_290 ),
inference(resolution,[],[f4088,f1487]) ).
fof(f4172,plain,
spl0_310,
inference(avatar_split_clause,[],[f297,f4170]) ).
fof(f297,axiom,
! [X3,X28,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X3,X28,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty_0) ).
fof(f4168,plain,
spl0_309,
inference(avatar_split_clause,[],[f264,f4166]) ).
fof(f4166,plain,
( spl0_309
<=> ! [X6,X0,X8] :
( X6 = X8
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f264,axiom,
! [X0,X8,X6] :
( X6 = X8
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
fof(f4164,plain,
spl0_308,
inference(avatar_split_clause,[],[f260,f4162]) ).
fof(f260,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f4160,plain,
spl0_307,
inference(avatar_split_clause,[],[f258,f4158]) ).
fof(f4158,plain,
( spl0_307
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X19,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f258,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X19,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
fof(f4156,plain,
spl0_306,
inference(avatar_split_clause,[],[f257,f4154]) ).
fof(f4154,plain,
( spl0_306
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X19,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f257,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X19,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
fof(f4152,plain,
spl0_305,
inference(avatar_split_clause,[],[f256,f4150]) ).
fof(f4150,plain,
( spl0_305
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X19,X2,X0)
| c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f256,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X19,X2,X0)
| c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
fof(f4148,plain,
spl0_304,
inference(avatar_split_clause,[],[f255,f4146]) ).
fof(f4146,plain,
( spl0_304
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X19,X1,X0)
| c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f255,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X19,X1,X0)
| c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
fof(f4144,plain,
spl0_303,
inference(avatar_split_clause,[],[f247,f4142]) ).
fof(f4142,plain,
( spl0_303
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f247,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
fof(f4140,plain,
spl0_302,
inference(avatar_split_clause,[],[f205,f4138]) ).
fof(f205,axiom,
! [X0,X16,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f4136,plain,
spl0_301,
inference(avatar_split_clause,[],[f188,f4134]) ).
fof(f188,axiom,
! [X28,X3,X0] :
( ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X28,X3,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_1) ).
fof(f4129,plain,
spl0_300,
inference(avatar_split_clause,[],[f187,f4127]) ).
fof(f4127,plain,
( spl0_300
<=> ! [X0,X28,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X28,X3,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f187,axiom,
! [X28,X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X28,X3,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_0) ).
fof(f4125,plain,
spl0_299,
inference(avatar_split_clause,[],[f146,f4123]) ).
fof(f146,axiom,
! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X14,X16,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
fof(f4121,plain,
spl0_298,
inference(avatar_split_clause,[],[f85,f4119]) ).
fof(f85,axiom,
! [X0,X1,X16,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X14,X1,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
fof(f4117,plain,
spl0_297,
inference(avatar_split_clause,[],[f84,f4115]) ).
fof(f84,axiom,
! [X0,X1,X16,X14] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X16,X1,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
fof(f4113,plain,
spl0_296,
inference(avatar_split_clause,[],[f83,f4111]) ).
fof(f83,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f4109,plain,
spl0_295,
inference(avatar_split_clause,[],[f68,f4107]) ).
fof(f68,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f4105,plain,
spl0_294,
inference(avatar_split_clause,[],[f56,f4103]) ).
fof(f4103,plain,
( spl0_294
<=> ! [X0,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f56,axiom,
! [X0,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f4101,plain,
spl0_293,
inference(avatar_split_clause,[],[f55,f4099]) ).
fof(f55,axiom,
! [X0,X16,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f4097,plain,
spl0_292,
inference(avatar_split_clause,[],[f52,f4095]) ).
fof(f4095,plain,
( spl0_292
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X19,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f52,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X19,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
fof(f4093,plain,
spl0_291,
inference(avatar_split_clause,[],[f51,f4091]) ).
fof(f4091,plain,
( spl0_291
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f51,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
fof(f4089,plain,
( spl0_290
| ~ spl0_104
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f4036,f3748,f1462,f4087]) ).
fof(f4036,plain,
( ! [X0] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname))
| ~ spl0_104
| ~ spl0_281 ),
inference(resolution,[],[f3749,f1463]) ).
fof(f4085,plain,
spl0_289,
inference(avatar_split_clause,[],[f50,f4083]) ).
fof(f4083,plain,
( spl0_289
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X19,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f50,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X19,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
fof(f4081,plain,
spl0_288,
inference(avatar_split_clause,[],[f47,f4079]) ).
fof(f4079,plain,
( spl0_288
<=> ! [X0,X14,X16,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X14,X1,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f47,axiom,
! [X0,X1,X16,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X14,X1,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
fof(f4077,plain,
spl0_287,
inference(avatar_split_clause,[],[f33,f4075]) ).
fof(f33,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X19,X1,X0)
| c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
fof(f4073,plain,
spl0_286,
inference(avatar_split_clause,[],[f32,f4071]) ).
fof(f32,axiom,
! [X0,X1,X16,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X16,X0)
| c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
fof(f4069,plain,
spl0_285,
inference(avatar_split_clause,[],[f30,f4067]) ).
fof(f4067,plain,
( spl0_285
<=> ! [X0,X14,X16,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X16,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f30,axiom,
! [X0,X1,X16,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X16,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
fof(f4065,plain,
spl0_284,
inference(avatar_split_clause,[],[f29,f4063]) ).
fof(f4063,plain,
( spl0_284
<=> ! [X0,X14,X16,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f29,axiom,
! [X0,X1,X16,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
fof(f4061,plain,
spl0_283,
inference(avatar_split_clause,[],[f14,f4059]) ).
fof(f4059,plain,
( spl0_283
<=> ! [X6,X0,X8] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X8
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f14,axiom,
! [X0,X8,X6] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X8
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
fof(f4057,plain,
spl0_282,
inference(avatar_split_clause,[],[f13,f4055]) ).
fof(f4055,plain,
( spl0_282
<=> ! [X6,X0,X8] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X6
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f13,axiom,
! [X0,X8,X6] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X6
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
fof(f3750,plain,
( spl0_281
| ~ spl0_193
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3740,f3037,f2278,f3748]) ).
fof(f2278,plain,
( spl0_193
<=> v_U = c_Set_Oinsert(v_x,v_U,tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f3740,plain,
( ! [X0] :
( ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool))
| hBOOL(c_in(v_x,X0,tc_Com_Opname)) )
| ~ spl0_193
| ~ spl0_264 ),
inference(superposition,[],[f3038,f2280]) ).
fof(f2280,plain,
( v_U = c_Set_Oinsert(v_x,v_U,tc_Com_Opname)
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2278]) ).
fof(f3241,plain,
( ~ spl0_280
| ~ spl0_81
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3100,f3096,f1365,f3238]) ).
fof(f3238,plain,
( spl0_280
<=> hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f1365,plain,
( spl0_81
<=> ! [X0,X15] : ~ hBOOL(c_in(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f3096,plain,
( spl0_278
<=> c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f3100,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
| ~ spl0_81
| ~ spl0_278 ),
inference(superposition,[],[f1366,f3098]) ).
fof(f3098,plain,
( c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f3096]) ).
fof(f1366,plain,
( ! [X0,X15] : ~ hBOOL(c_in(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1365]) ).
fof(f3107,plain,
spl0_279,
inference(avatar_split_clause,[],[f834,f3105]) ).
fof(f3105,plain,
( spl0_279
<=> ! [X0,X6,X2,X1] :
( X1 = X2
| hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,X6,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f834,axiom,
! [X2,X0,X1,X6] :
( X1 = X2
| hBOOL(hAPP(X6,X1))
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,X6,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f3099,plain,
( spl0_278
| ~ spl0_35
| ~ spl0_183
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3094,f3090,f2020,f1173,f3096]) ).
fof(f3090,plain,
( spl0_277
<=> 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) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f3094,plain,
( c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_35
| ~ spl0_183
| ~ spl0_277 ),
inference(forward_demodulation,[],[f3092,f2248]) ).
fof(f3092,plain,
( 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)
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f3090]) ).
fof(f3093,plain,
spl0_277,
inference(avatar_split_clause,[],[f823,f3090]) ).
fof(f823,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(f3088,plain,
spl0_276,
inference(avatar_split_clause,[],[f768,f3086]) ).
fof(f768,axiom,
! [X0,X1,X25,X20] : hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
fof(f3084,plain,
spl0_275,
inference(avatar_split_clause,[],[f750,f3082]) ).
fof(f3082,plain,
( spl0_275
<=> ! [X20,X0,X6,X25,X1] :
( ~ hBOOL(hAPP(X6,hAPP(X25,X1)))
| hBOOL(hAPP(c_Set_Ovimage(X25,X6,X0,X20),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f750,axiom,
! [X0,X1,X6,X25,X20] :
( ~ hBOOL(hAPP(X6,hAPP(X25,X1)))
| hBOOL(hAPP(c_Set_Ovimage(X25,X6,X0,X20),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
fof(f3080,plain,
( spl0_274
| ~ spl0_19
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1557,f1430,f1093,f3077]) ).
fof(f3077,plain,
( spl0_274
<=> c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat) = c_Finite__Set_Olinorder__class_OMin(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f1430,plain,
( spl0_96
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1557,plain,
( c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat) = c_Finite__Set_Olinorder__class_OMin(tc_nat)
| ~ spl0_19
| ~ spl0_96 ),
inference(resolution,[],[f1431,f1095]) ).
fof(f1431,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1430]) ).
fof(f3075,plain,
spl0_273,
inference(avatar_split_clause,[],[f749,f3073]) ).
fof(f3073,plain,
( spl0_273
<=> ! [X20,X0,X6,X25,X1] :
( hBOOL(hAPP(X6,hAPP(X25,X1)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X25,X6,X0,X20),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f749,axiom,
! [X0,X1,X6,X25,X20] :
( hBOOL(hAPP(X6,hAPP(X25,X1)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X25,X6,X0,X20),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
fof(f3071,plain,
spl0_272,
inference(avatar_split_clause,[],[f742,f3069]) ).
fof(f742,axiom,
! [X50,X0,X1,X26] :
( ~ hBOOL(hAPP(X26,X1))
| hBOOL(hAPP(X50,X1))
| ~ c_lessequals(X26,X50,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
fof(f3067,plain,
spl0_271,
inference(avatar_split_clause,[],[f734,f3065]) ).
fof(f734,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X19,X0)
| c_lessequals(X1,X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3063,plain,
spl0_270,
inference(avatar_split_clause,[],[f733,f3061]) ).
fof(f733,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X19,X2,X0)
| c_lessequals(X19,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3059,plain,
spl0_269,
inference(avatar_split_clause,[],[f720,f3057]) ).
fof(f3057,plain,
( spl0_269
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f720,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
fof(f3055,plain,
spl0_268,
inference(avatar_split_clause,[],[f705,f3053]) ).
fof(f705,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f3051,plain,
spl0_267,
inference(avatar_split_clause,[],[f704,f3049]) ).
fof(f3049,plain,
( spl0_267
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f704,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f3047,plain,
spl0_266,
inference(avatar_split_clause,[],[f703,f3045]) ).
fof(f703,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f3043,plain,
spl0_265,
inference(avatar_split_clause,[],[f663,f3041]) ).
fof(f663,axiom,
! [X0,X6,X25,X20] : c_lessequals(c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
fof(f3039,plain,
spl0_264,
inference(avatar_split_clause,[],[f649,f3037]) ).
fof(f649,axiom,
! [X0,X1,X8,X6] :
( hBOOL(c_in(X1,X8,X0))
| ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f3035,plain,
( spl0_263
| ~ spl0_19
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1556,f1426,f1093,f3032]) ).
fof(f3032,plain,
( spl0_263
<=> c_Finite__Set_Olinorder__class_OMax(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f1426,plain,
( spl0_95
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1556,plain,
( c_Finite__Set_Olinorder__class_OMax(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat)
| ~ spl0_19
| ~ spl0_95 ),
inference(resolution,[],[f1427,f1095]) ).
fof(f1427,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1426]) ).
fof(f3030,plain,
spl0_262,
inference(avatar_split_clause,[],[f611,f3028]) ).
fof(f611,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f3026,plain,
spl0_261,
inference(avatar_split_clause,[],[f591,f3024]) ).
fof(f3024,plain,
( spl0_261
<=> ! [X6,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f591,axiom,
! [X0,X8,X6] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
fof(f3022,plain,
spl0_260,
inference(avatar_split_clause,[],[f447,f3020]) ).
fof(f3020,plain,
( spl0_260
<=> ! [X6,X0,X1] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f447,axiom,
! [X0,X1,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).
fof(f3018,plain,
spl0_259,
inference(avatar_split_clause,[],[f339,f3016]) ).
fof(f3016,plain,
( spl0_259
<=> ! [X35,X20,X0,X33] :
( ~ c_Finite__Set_Ofinite(X33,X20)
| ~ c_Fun_Obij(X35,X0,X20)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f339,axiom,
! [X0,X35,X33,X20] :
( ~ c_Finite__Set_Ofinite(X33,X20)
| ~ c_Fun_Obij(X35,X0,X20)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimage__iff_1) ).
fof(f3014,plain,
spl0_258,
inference(avatar_split_clause,[],[f338,f3012]) ).
fof(f338,axiom,
! [X0,X35,X33,X20] :
( c_Finite__Set_Ofinite(X33,X20)
| ~ c_Fun_Obij(X35,X0,X20)
| ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimage__iff_0) ).
fof(f3010,plain,
spl0_257,
inference(avatar_split_clause,[],[f252,f3008]) ).
fof(f252,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f3006,plain,
spl0_256,
inference(avatar_split_clause,[],[f251,f3004]) ).
fof(f3004,plain,
( spl0_256
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f251,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f3002,plain,
spl0_255,
inference(avatar_split_clause,[],[f250,f3000]) ).
fof(f250,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f2998,plain,
spl0_254,
inference(avatar_split_clause,[],[f239,f2996]) ).
fof(f239,axiom,
! [X21,X0,X25,X20] :
( ~ class_HOL_Oord(X20)
| ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
| ~ c_lessequals(X21,X25,tc_fun(X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
fof(f2994,plain,
spl0_253,
inference(avatar_split_clause,[],[f230,f2992]) ).
fof(f230,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f2986,plain,
spl0_252,
inference(avatar_split_clause,[],[f229,f2984]) ).
fof(f2984,plain,
( spl0_252
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f229,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f2982,plain,
spl0_251,
inference(avatar_split_clause,[],[f228,f2980]) ).
fof(f228,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f2978,plain,
spl0_250,
inference(avatar_split_clause,[],[f216,f2976]) ).
fof(f216,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f2974,plain,
spl0_249,
inference(avatar_split_clause,[],[f215,f2972]) ).
fof(f2972,plain,
( spl0_249
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f215,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f2970,plain,
spl0_248,
inference(avatar_split_clause,[],[f214,f2968]) ).
fof(f214,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f2966,plain,
spl0_247,
inference(avatar_split_clause,[],[f213,f2964]) ).
fof(f2964,plain,
( spl0_247
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X19,X2,X0)
| c_HOL_Oord__class_Oless(X19,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f213,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X19,X2,X0)
| c_HOL_Oord__class_Oless(X19,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f2962,plain,
spl0_246,
inference(avatar_split_clause,[],[f211,f2960]) ).
fof(f2960,plain,
( spl0_246
<=> ! [X19,X0,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X19,X0)
| c_HOL_Oord__class_Oless(X1,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f211,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X19,X0)
| c_HOL_Oord__class_Oless(X1,X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f2958,plain,
spl0_245,
inference(avatar_split_clause,[],[f144,f2956]) ).
fof(f144,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X2,X19,X0)
| c_HOL_Oord__class_Oless(X1,X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f2954,plain,
spl0_244,
inference(avatar_split_clause,[],[f143,f2952]) ).
fof(f143,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X19,X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f2950,plain,
spl0_243,
inference(avatar_split_clause,[],[f137,f2948]) ).
fof(f137,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X19,X2,X0)
| ~ c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X19,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f2946,plain,
( spl0_242
| ~ spl0_19
| ~ spl0_15
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1553,f1422,f1073,f1093,f2943]) ).
fof(f1553,plain,
( ~ class_Orderings_Olinorder(tc_nat)
| c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat)
| ~ spl0_15
| ~ spl0_94 ),
inference(resolution,[],[f1423,f1075]) ).
fof(f2941,plain,
spl0_241,
inference(avatar_split_clause,[],[f136,f2939]) ).
fof(f136,axiom,
! [X2,X0,X1,X19] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X19,X2,X0)
| c_HOL_Oord__class_Oless(X19,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f2937,plain,
spl0_240,
inference(avatar_split_clause,[],[f89,f2935]) ).
fof(f2935,plain,
( spl0_240
<=> ! [X20,X0,X25,X21] :
( ~ class_HOL_Oord(X20)
| ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
| c_lessequals(X25,X21,tc_fun(X0,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f89,axiom,
! [X21,X0,X25,X20] :
( ~ class_HOL_Oord(X20)
| ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
| c_lessequals(X25,X21,tc_fun(X0,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
fof(f2933,plain,
spl0_239,
inference(avatar_split_clause,[],[f1,f2931]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f2610,plain,
( spl0_237
| ~ spl0_238
| ~ spl0_26
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f1510,f1382,f1128,f2607,f2603]) ).
fof(f2603,plain,
( spl0_237
<=> c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = c_Orderings_Oord__class_Omax(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2607,plain,
( spl0_238
<=> class_Orderings_Olinorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1510,plain,
( ~ class_Orderings_Olinorder(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = c_Orderings_Oord__class_Omax(tc_bool)
| ~ spl0_26
| ~ spl0_84 ),
inference(resolution,[],[f1383,f1130]) ).
fof(f2590,plain,
spl0_236,
inference(avatar_split_clause,[],[f967,f2588]) ).
fof(f2588,plain,
( spl0_236
<=> ! [X2,X0,X1] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0) = X2
| ~ hBOOL(hAPP(c_fequal(X1,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f967,plain,
! [X2,X0,X1] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0) = X2
| ~ hBOOL(hAPP(c_fequal(X1,X0),X2)) ),
inference(forward_demodulation,[],[f966,f926]) ).
fof(f966,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_fequal(X1,X0),X2))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X2 ),
inference(forward_demodulation,[],[f790,f926]) ).
fof(f790,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X2))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
fof(f2586,plain,
spl0_235,
inference(avatar_split_clause,[],[f929,f2584]) ).
fof(f929,plain,
! [X0,X14,X53,X25] : hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(hAPP(X25,X14),X0),X53,X0),X53)),
inference(forward_demodulation,[],[f807,f926]) ).
fof(f807,axiom,
! [X0,X14,X53,X25] : hBOOL(c_in(X14,c_Set_Ovimage(X25,c_Set_Oinsert(hAPP(X25,X14),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X53,X0),X53)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
fof(f2582,plain,
spl0_234,
inference(avatar_split_clause,[],[f914,f2580]) ).
fof(f2580,plain,
( spl0_234
<=> ! [X20,X0,X19,X25] : c_The(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0),X0) = X19 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f914,plain,
! [X0,X19,X25,X20] : c_The(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0),X0) = X19,
inference(definition_unfolding,[],[f432,f57]) ).
fof(f432,axiom,
! [X0,X19,X25,X20] : c_Finite__Set_Ofold(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__empty_0) ).
fof(f2578,plain,
spl0_233,
inference(avatar_split_clause,[],[f847,f2576]) ).
fof(f847,axiom,
! [X0,X25,X20] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
fof(f2574,plain,
spl0_232,
inference(avatar_split_clause,[],[f815,f2572]) ).
fof(f815,axiom,
! [X0,X8,X16,X14] :
( ~ hBOOL(c_in(X14,X8,X0))
| hBOOL(c_in(X14,c_Set_Oinsert(X16,X8,X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
fof(f2570,plain,
spl0_231,
inference(avatar_split_clause,[],[f759,f2568]) ).
fof(f759,axiom,
! [X0,X1,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
fof(f2566,plain,
spl0_230,
inference(avatar_split_clause,[],[f716,f2564]) ).
fof(f716,axiom,
! [X0,X1,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X6,X0))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
fof(f2562,plain,
spl0_229,
inference(avatar_split_clause,[],[f700,f2560]) ).
fof(f700,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f2552,plain,
spl0_228,
inference(avatar_split_clause,[],[f666,f2550]) ).
fof(f2550,plain,
( spl0_228
<=> ! [X20,X0,X25] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X0,X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f666,axiom,
! [X0,X25,X20] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X0,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
fof(f2548,plain,
spl0_227,
inference(avatar_split_clause,[],[f635,f2546]) ).
fof(f2546,plain,
( spl0_227
<=> ! [X20,X0,X14,X6,X25] :
( c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f635,axiom,
! [X0,X6,X14,X25,X20] :
( c_Fun_Oinj__on(X25,X6,X0,X20)
| ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
fof(f2544,plain,
spl0_226,
inference(avatar_split_clause,[],[f613,f2542]) ).
fof(f2542,plain,
( spl0_226
<=> ! [X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2540,plain,
spl0_225,
inference(avatar_split_clause,[],[f612,f2538]) ).
fof(f2536,plain,
spl0_224,
inference(avatar_split_clause,[],[f601,f2534]) ).
fof(f2534,plain,
( spl0_224
<=> ! [X20,X0,X25] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X0,X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f601,axiom,
! [X0,X25,X20] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X0,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
fof(f2532,plain,
spl0_223,
inference(avatar_split_clause,[],[f587,f2530]) ).
fof(f2530,plain,
( spl0_223
<=> ! [X0,X44,X33] :
( c_Finite__Set_Ofinite(X33,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f587,axiom,
! [X0,X44,X33] :
( c_Finite__Set_Ofinite(X33,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
fof(f2528,plain,
spl0_222,
inference(avatar_split_clause,[],[f586,f2526]) ).
fof(f2526,plain,
( spl0_222
<=> ! [X0,X44,X33] :
( c_Finite__Set_Ofinite(X44,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f586,axiom,
! [X0,X44,X33] :
( c_Finite__Set_Ofinite(X44,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
fof(f2524,plain,
spl0_221,
inference(avatar_split_clause,[],[f534,f2522]) ).
fof(f534,axiom,
! [X0,X8,X6] : c_lessequals(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f2520,plain,
spl0_220,
inference(avatar_split_clause,[],[f533,f2518]) ).
fof(f533,axiom,
! [X0,X8,X6] : c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f2516,plain,
spl0_219,
inference(avatar_split_clause,[],[f505,f2514]) ).
fof(f2514,plain,
( spl0_219
<=> ! [X20,X0,X25,X2,X1] :
( hAPP(X25,X1) = X2
| c_Fun_Ofun__upd(X25,X1,X2,X0,X20) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f505,axiom,
! [X2,X0,X1,X25,X20] :
( hAPP(X25,X1) = X2
| c_Fun_Ofun__upd(X25,X1,X2,X0,X20) != X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
fof(f2512,plain,
spl0_218,
inference(avatar_split_clause,[],[f429,f2510]) ).
fof(f2510,plain,
( spl0_218
<=> ! [X0,X44,X33] :
( ~ c_Finite__Set_Ofinite(X33,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f429,axiom,
! [X0,X44,X33] :
( ~ c_Finite__Set_Ofinite(X33,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X33),X44),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
fof(f2508,plain,
spl0_217,
inference(avatar_split_clause,[],[f428,f2506]) ).
fof(f2506,plain,
( spl0_217
<=> ! [X0,X44,X33] :
( ~ c_Finite__Set_Ofinite(X44,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f428,axiom,
! [X0,X44,X33] :
( ~ c_Finite__Set_Ofinite(X44,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X33),X44),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
fof(f2504,plain,
spl0_216,
inference(avatar_split_clause,[],[f400,f2502]) ).
fof(f400,axiom,
! [X4,X13] :
( c_Suc(X13) = X4
| c_lessequals(X4,X13,tc_nat)
| ~ c_lessequals(X4,c_Suc(X13),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
fof(f2500,plain,
spl0_215,
inference(avatar_split_clause,[],[f372,f2498]) ).
fof(f372,axiom,
! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| c_Suc(X4) = X13
| c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f2496,plain,
spl0_214,
inference(avatar_split_clause,[],[f273,f2494]) ).
fof(f273,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
fof(f2492,plain,
spl0_213,
inference(avatar_split_clause,[],[f271,f2490]) ).
fof(f271,axiom,
! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| X14 = X16
| ~ c_lessequals(X14,X16,X0)
| c_HOL_Oord__class_Oless(X14,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
fof(f2488,plain,
spl0_212,
inference(avatar_split_clause,[],[f111,f2486]) ).
fof(f111,axiom,
! [X0,X8,X6] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f2484,plain,
spl0_211,
inference(avatar_split_clause,[],[f110,f2482]) ).
fof(f110,axiom,
! [X0,X8,X6] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f2480,plain,
spl0_210,
inference(avatar_split_clause,[],[f95,f2478]) ).
fof(f95,axiom,
! [X28,X29,X27] :
( ~ c_HOL_Oord__class_Oless(X27,X29,tc_nat)
| ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X27),X28,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f2476,plain,
spl0_209,
inference(avatar_split_clause,[],[f80,f2474]) ).
fof(f2474,plain,
( spl0_209
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f80,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f2472,plain,
( spl0_208
| ~ spl0_51
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2421,f2311,f1243,f2470]) ).
fof(f2470,plain,
( spl0_208
<=> ! [X0] : hBOOL(hAPP(hAPP(v_P,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f2421,plain,
( ! [X0] : hBOOL(hAPP(hAPP(v_P,X0),X0))
| ~ spl0_51
| ~ spl0_201 ),
inference(resolution,[],[f2312,f1244]) ).
fof(f2468,plain,
spl0_207,
inference(avatar_split_clause,[],[f5,f2466]) ).
fof(f2466,plain,
( spl0_207
<=> ! [X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X8) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f5,axiom,
! [X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
fof(f2464,plain,
spl0_206,
inference(avatar_split_clause,[],[f4,f2462]) ).
fof(f2462,plain,
( spl0_206
<=> ! [X6,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f4,axiom,
! [X0,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
fof(f2335,plain,
spl0_205,
inference(avatar_split_clause,[],[f950,f2333]) ).
fof(f2333,plain,
( spl0_205
<=> ! [X0,X14,X16,X25] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_fequal(X14,X0),X0),X16))
| X14 = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f950,plain,
! [X0,X16,X14,X25] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_fequal(X14,X0),X0),X16))
| X14 = X16 ),
inference(forward_demodulation,[],[f788,f926]) ).
fof(f788,axiom,
! [X0,X16,X14,X25] :
( X14 = X16
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
fof(f2331,plain,
spl0_204,
inference(avatar_split_clause,[],[f835,f2329]) ).
fof(f835,axiom,
! [X0,X1,X6] : c_Set_Oinsert(X1,X6,X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X1,X6,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f2321,plain,
spl0_203,
inference(avatar_split_clause,[],[f669,f2319]) ).
fof(f669,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
fof(f2317,plain,
spl0_202,
inference(avatar_split_clause,[],[f668,f2315]) ).
fof(f668,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
fof(f2313,plain,
spl0_201,
inference(avatar_split_clause,[],[f640,f2311]) ).
fof(f640,axiom,
! [X44,X52] :
( ~ c_lessequals(X52,X44,tc_fun(t_a,tc_bool))
| hBOOL(hAPP(hAPP(v_P,X44),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I1_J_0) ).
fof(f2309,plain,
spl0_200,
inference(avatar_split_clause,[],[f583,f2307]) ).
fof(f583,axiom,
! [X0,X8,X6] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(X6,X0)
| ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
fof(f2305,plain,
spl0_199,
inference(avatar_split_clause,[],[f556,f2303]) ).
fof(f2303,plain,
( spl0_199
<=> ! [X6,X25,X0] : hAPP(c_Finite__Set_Ofold1(X25,X0),X6) = c_The(c_Finite__Set_Ofold1Set(X25,X6,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f556,axiom,
! [X0,X6,X25] : hAPP(c_Finite__Set_Ofold1(X25,X0),X6) = c_The(c_Finite__Set_Ofold1Set(X25,X6,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__def_0) ).
fof(f2301,plain,
spl0_198,
inference(avatar_split_clause,[],[f437,f2299]) ).
fof(f2299,plain,
( spl0_198
<=> ! [X20,X0,X19,X25] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),X19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f437,axiom,
! [X0,X19,X25,X20] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
fof(f2297,plain,
spl0_197,
inference(avatar_split_clause,[],[f431,f2295]) ).
fof(f431,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f2293,plain,
spl0_196,
inference(avatar_split_clause,[],[f430,f2291]) ).
fof(f430,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f2289,plain,
spl0_195,
inference(avatar_split_clause,[],[f427,f2287]) ).
fof(f2287,plain,
( spl0_195
<=> ! [X19,X20,X0,X6,X25,X1] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f427,axiom,
! [X0,X1,X6,X19,X25,X20] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
fof(f2285,plain,
spl0_194,
inference(avatar_split_clause,[],[f337,f2283]) ).
fof(f337,axiom,
! [X0,X25,X20] :
( ~ c_Fun_Obij(X25,X0,X20)
| c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__def_0) ).
fof(f2281,plain,
( spl0_193
| ~ spl0_2
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2250,f2028,f1008,f2278]) ).
fof(f2250,plain,
( v_U = c_Set_Oinsert(v_x,v_U,tc_Com_Opname)
| ~ spl0_2
| ~ spl0_185 ),
inference(resolution,[],[f2029,f1010]) ).
fof(f2276,plain,
spl0_192,
inference(avatar_split_clause,[],[f153,f2274]) ).
fof(f2274,plain,
( spl0_192
<=> ! [X13,X4] :
( X4 = X13
| ~ c_lessequals(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f153,axiom,
! [X4,X13] :
( X4 = X13
| ~ c_lessequals(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
fof(f2272,plain,
spl0_191,
inference(avatar_split_clause,[],[f139,f2270]) ).
fof(f139,axiom,
! [X28,X29,X27] :
( ~ c_lessequals(X27,X29,tc_nat)
| ~ c_lessequals(X29,X28,tc_nat)
| c_lessequals(X27,X28,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f2268,plain,
spl0_190,
inference(avatar_split_clause,[],[f87,f2266]) ).
fof(f2266,plain,
( spl0_190
<=> ! [X6,X0,X8] :
( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f87,axiom,
! [X0,X8,X6] :
( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
| c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
fof(f2264,plain,
spl0_189,
inference(avatar_split_clause,[],[f16,f2262]) ).
fof(f2262,plain,
( spl0_189
<=> ! [X13,X4] :
( X4 = X13
| c_HOL_Oord__class_Oless(X13,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f16,axiom,
! [X4,X13] :
( X4 = X13
| c_HOL_Oord__class_Oless(X13,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
fof(f2242,plain,
( spl0_188
| ~ spl0_89
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1685,f1583,f1402,f2240]) ).
fof(f2240,plain,
( spl0_188
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1583,plain,
( spl0_117
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1685,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_89
| ~ spl0_117 ),
inference(resolution,[],[f1584,f1403]) ).
fof(f1584,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1583]) ).
fof(f2178,plain,
( spl0_187
| ~ spl0_85
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f1523,f1390,f1386,f2176]) ).
fof(f2176,plain,
( spl0_187
<=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1386,plain,
( spl0_85
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1523,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_85
| ~ spl0_86 ),
inference(resolution,[],[f1391,f1387]) ).
fof(f1387,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1386]) ).
fof(f2034,plain,
spl0_186,
inference(avatar_split_clause,[],[f926,f2032]) ).
fof(f2030,plain,
spl0_185,
inference(avatar_split_clause,[],[f854,f2028]) ).
fof(f854,axiom,
! [X0,X6,X14] :
( ~ hBOOL(c_in(X14,X6,X0))
| c_Set_Oinsert(X14,X6,X0) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f2026,plain,
spl0_184,
inference(avatar_split_clause,[],[f851,f2024]) ).
fof(f2024,plain,
( spl0_184
<=> ! [X6,X2,X0,X1] :
( ~ hBOOL(hAPP(X6,X1))
| hBOOL(hAPP(c_Set_Oinsert(X2,X6,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f851,axiom,
! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(X6,X1))
| hBOOL(hAPP(c_Set_Oinsert(X2,X6,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f2022,plain,
spl0_183,
inference(avatar_split_clause,[],[f838,f2020]) ).
fof(f838,axiom,
! [X20] :
( ~ class_Orderings_Obot(X20)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X20)),v_x) = c_Orderings_Obot__class_Obot(X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
fof(f2018,plain,
( spl0_182
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1862,f1691,f2016]) ).
fof(f2016,plain,
( spl0_182
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1862,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_140 ),
inference(factoring,[],[f1692]) ).
fof(f2014,plain,
( spl0_181
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2010,f2007,f2012]) ).
fof(f2012,plain,
( spl0_181
<=> ! [X0,X1] : c_Set_Ocontents(c_fequal(X1,X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f2007,plain,
( spl0_180
<=> ! [X0,X1] : c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f2010,plain,
( ! [X0,X1] : c_Set_Ocontents(c_fequal(X1,X0),X0) = X1
| ~ spl0_180 ),
inference(forward_demodulation,[],[f2008,f926]) ).
fof(f2008,plain,
( ! [X0,X1] : c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f2007]) ).
fof(f2009,plain,
spl0_180,
inference(avatar_split_clause,[],[f789,f2007]) ).
fof(f789,axiom,
! [X0,X1] : c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__eq_0) ).
fof(f2004,plain,
spl0_179,
inference(avatar_split_clause,[],[f783,f2002]) ).
fof(f2002,plain,
( spl0_179
<=> ! [X0,X1] : c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f783,axiom,
! [X0,X1] : c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
fof(f2000,plain,
spl0_178,
inference(avatar_split_clause,[],[f724,f1998]) ).
fof(f724,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
fof(f1996,plain,
spl0_177,
inference(avatar_split_clause,[],[f697,f1994]) ).
fof(f697,axiom,
! [X20] :
( ~ class_Orderings_Otop(X20)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X20)),v_x) = c_Orderings_Otop__class_Otop(X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
fof(f1992,plain,
spl0_176,
inference(avatar_split_clause,[],[f695,f1990]) ).
fof(f695,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
fof(f1988,plain,
spl0_175,
inference(avatar_split_clause,[],[f657,f1986]) ).
fof(f657,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
fof(f1984,plain,
spl0_174,
inference(avatar_split_clause,[],[f615,f1982]) ).
fof(f615,axiom,
! [X0,X6] : c_HOL_Ominus__class_Ominus(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f1980,plain,
spl0_173,
inference(avatar_split_clause,[],[f614,f1978]) ).
fof(f614,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f1966,plain,
spl0_172,
inference(avatar_split_clause,[],[f594,f1964]) ).
fof(f594,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1962,plain,
spl0_171,
inference(avatar_split_clause,[],[f593,f1960]) ).
fof(f593,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1958,plain,
spl0_170,
inference(avatar_split_clause,[],[f592,f1956]) ).
fof(f1956,plain,
( spl0_170
<=> ! [X6,X0,X8] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f592,axiom,
! [X0,X8,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
fof(f1954,plain,
spl0_169,
inference(avatar_split_clause,[],[f530,f1952]) ).
fof(f530,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1950,plain,
spl0_168,
inference(avatar_split_clause,[],[f529,f1948]) ).
fof(f529,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1946,plain,
spl0_167,
inference(avatar_split_clause,[],[f526,f1944]) ).
fof(f526,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f1942,plain,
spl0_166,
inference(avatar_split_clause,[],[f525,f1940]) ).
fof(f525,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f1938,plain,
spl0_165,
inference(avatar_split_clause,[],[f523,f1936]) ).
fof(f523,axiom,
! [X0,X8,X6] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f1934,plain,
spl0_164,
inference(avatar_split_clause,[],[f501,f1932]) ).
fof(f501,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
fof(f1930,plain,
spl0_163,
inference(avatar_split_clause,[],[f266,f1928]) ).
fof(f266,axiom,
! [X4,X13] :
( X4 = X13
| ~ c_lessequals(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(X4,X13,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
fof(f1926,plain,
spl0_162,
inference(avatar_split_clause,[],[f180,f1924]) ).
fof(f180,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1922,plain,
spl0_161,
inference(avatar_split_clause,[],[f179,f1920]) ).
fof(f179,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1918,plain,
spl0_160,
inference(avatar_split_clause,[],[f171,f1916]) ).
fof(f171,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f1914,plain,
spl0_159,
inference(avatar_split_clause,[],[f170,f1912]) ).
fof(f170,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f1910,plain,
spl0_158,
inference(avatar_split_clause,[],[f109,f1908]) ).
fof(f109,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f1906,plain,
spl0_157,
inference(avatar_split_clause,[],[f108,f1904]) ).
fof(f108,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f1902,plain,
spl0_156,
inference(avatar_split_clause,[],[f104,f1900]) ).
fof(f104,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f1898,plain,
spl0_155,
inference(avatar_split_clause,[],[f103,f1896]) ).
fof(f103,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f1894,plain,
spl0_154,
inference(avatar_split_clause,[],[f77,f1892]) ).
fof(f77,axiom,
! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f1890,plain,
spl0_153,
inference(avatar_split_clause,[],[f74,f1888]) ).
fof(f74,axiom,
! [X4,X13] :
( X4 = X13
| ~ c_lessequals(X4,X13,tc_nat)
| ~ c_lessequals(X13,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f1886,plain,
( ~ spl0_1
| spl0_152
| ~ spl0_3
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1865,f1695,f1013,f1883,f1003]) ).
fof(f1883,plain,
( spl0_152
<=> c_Finite__Set_Ofinite(v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1865,plain,
( c_Finite__Set_Ofinite(v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| ~ spl0_3
| ~ spl0_141 ),
inference(superposition,[],[f1696,f1015]) ).
fof(f1881,plain,
spl0_151,
inference(avatar_split_clause,[],[f7,f1879]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
fof(f1877,plain,
spl0_150,
inference(avatar_split_clause,[],[f6,f1875]) ).
fof(f6,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
fof(f1797,plain,
( spl0_149
| ~ spl0_43
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1526,f1398,f1211,f1795]) ).
fof(f1795,plain,
( spl0_149
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1526,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_43
| ~ spl0_88 ),
inference(resolution,[],[f1399,f1212]) ).
fof(f1726,plain,
( spl0_148
| ~ spl0_44
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1524,f1394,f1215,f1724]) ).
fof(f1524,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_44
| ~ spl0_87 ),
inference(resolution,[],[f1395,f1216]) ).
fof(f1721,plain,
spl0_147,
inference(avatar_split_clause,[],[f952,f1719]) ).
fof(f1719,plain,
( spl0_147
<=> ! [X0,X1,X26] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X26
| ~ hBOOL(hAPP(X26,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f952,plain,
! [X0,X1,X26] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X26
| ~ hBOOL(hAPP(X26,X1)) ),
inference(forward_demodulation,[],[f608,f665]) ).
fof(f608,axiom,
! [X0,X1,X26] :
( ~ hBOOL(hAPP(X26,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Collect(X26,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
fof(f1717,plain,
spl0_146,
inference(avatar_split_clause,[],[f949,f1715]) ).
fof(f1715,plain,
( spl0_146
<=> ! [X0,X16,X14] :
( ~ hBOOL(c_in(X16,c_fequal(X14,X0),X0))
| X14 = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f949,plain,
! [X0,X16,X14] :
( ~ hBOOL(c_in(X16,c_fequal(X14,X0),X0))
| X14 = X16 ),
inference(forward_demodulation,[],[f839,f926]) ).
fof(f839,axiom,
! [X0,X16,X14] :
( X14 = X16
| ~ hBOOL(c_in(X16,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f1713,plain,
spl0_145,
inference(avatar_split_clause,[],[f946,f1711]) ).
fof(f946,plain,
! [X0,X14] :
( c_fequal(X14,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X14,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(forward_demodulation,[],[f794,f926]) ).
fof(f794,axiom,
! [X0,X14] :
( ~ class_Orderings_Oorder(X0)
| c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
fof(f1709,plain,
spl0_144,
inference(avatar_split_clause,[],[f941,f1707]) ).
fof(f941,plain,
! [X0,X14] :
( hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_fequal(X14,X0)) = X14
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f792,f926]) ).
fof(f792,axiom,
! [X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
fof(f1705,plain,
spl0_143,
inference(avatar_split_clause,[],[f940,f1703]) ).
fof(f940,plain,
! [X0,X14] :
( hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_fequal(X14,X0)) = X14
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f782,f926]) ).
fof(f782,axiom,
! [X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
fof(f1701,plain,
spl0_142,
inference(avatar_split_clause,[],[f930,f1699]) ).
fof(f930,plain,
! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0))),
inference(forward_demodulation,[],[f779,f926]) ).
fof(f779,axiom,
! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
fof(f1697,plain,
spl0_141,
inference(avatar_split_clause,[],[f828,f1695]) ).
fof(f828,axiom,
! [X0,X35,X33,X20] :
( ~ c_Finite__Set_Ofinite(X33,X0)
| c_Finite__Set_Ofinite(c_Set_Oimage(X35,X33,X0,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
fof(f1693,plain,
spl0_140,
inference(avatar_split_clause,[],[f760,f1691]) ).
fof(f760,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1689,plain,
spl0_139,
inference(avatar_split_clause,[],[f712,f1687]) ).
fof(f1687,plain,
( spl0_139
<=> ! [X20,X0,X25,X2,X1] : hAPP(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f712,axiom,
! [X2,X0,X1,X25,X20] : hAPP(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
fof(f1682,plain,
spl0_138,
inference(avatar_split_clause,[],[f711,f1680]) ).
fof(f711,axiom,
! [X0,X1,X25,X20] : c_Fun_Ofun__upd(X25,X1,hAPP(X25,X1),X20,X0) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
fof(f1678,plain,
spl0_137,
inference(avatar_split_clause,[],[f609,f1676]) ).
fof(f1676,plain,
( spl0_137
<=> ! [X25,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f609,axiom,
! [X0,X1,X25] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
fof(f1674,plain,
spl0_136,
inference(avatar_split_clause,[],[f550,f1672]) ).
fof(f1672,plain,
( spl0_136
<=> ! [X6,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X6) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f550,axiom,
! [X0,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X6) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f1670,plain,
spl0_135,
inference(avatar_split_clause,[],[f549,f1668]) ).
fof(f549,axiom,
! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f1666,plain,
spl0_134,
inference(avatar_split_clause,[],[f419,f1664]) ).
fof(f419,axiom,
! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
fof(f1662,plain,
spl0_133,
inference(avatar_split_clause,[],[f418,f1660]) ).
fof(f418,axiom,
! [X4,X13] :
( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f1658,plain,
spl0_132,
inference(avatar_split_clause,[],[f290,f1656]) ).
fof(f1656,plain,
( spl0_132
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f290,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1654,plain,
spl0_131,
inference(avatar_split_clause,[],[f288,f1652]) ).
fof(f1652,plain,
( spl0_131
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f288,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1650,plain,
spl0_130,
inference(avatar_split_clause,[],[f287,f1648]) ).
fof(f1648,plain,
( spl0_130
<=> ! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X16,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f287,axiom,
! [X0,X16,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X16,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1646,plain,
spl0_129,
inference(avatar_split_clause,[],[f277,f1644]) ).
fof(f277,axiom,
! [X4,X13] :
( ~ c_lessequals(X13,X4,tc_nat)
| c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
fof(f1642,plain,
spl0_128,
inference(avatar_split_clause,[],[f276,f1640]) ).
fof(f276,axiom,
! [X4,X13] :
( c_lessequals(X13,X4,tc_nat)
| ~ c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f1638,plain,
spl0_127,
inference(avatar_split_clause,[],[f240,f1636]) ).
fof(f240,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1634,plain,
spl0_126,
inference(avatar_split_clause,[],[f237,f1632]) ).
fof(f237,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1630,plain,
spl0_125,
inference(avatar_split_clause,[],[f232,f1628]) ).
fof(f232,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f1626,plain,
spl0_124,
inference(avatar_split_clause,[],[f127,f1624]) ).
fof(f127,axiom,
! [X0,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X6) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f1622,plain,
spl0_123,
inference(avatar_split_clause,[],[f126,f1620]) ).
fof(f126,axiom,
! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f1618,plain,
spl0_122,
inference(avatar_split_clause,[],[f91,f1616]) ).
fof(f1616,plain,
( spl0_122
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f91,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1614,plain,
spl0_121,
inference(avatar_split_clause,[],[f90,f1612]) ).
fof(f1612,plain,
( spl0_121
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f90,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1610,plain,
spl0_120,
inference(avatar_split_clause,[],[f81,f1608]) ).
fof(f81,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1606,plain,
spl0_119,
inference(avatar_split_clause,[],[f69,f1604]) ).
fof(f69,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1602,plain,
( spl0_118
| ~ spl0_2
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1589,f1486,f1008,f1599]) ).
fof(f1589,plain,
( hBOOL(hAPP(v_U,v_x))
| ~ spl0_2
| ~ spl0_110 ),
inference(resolution,[],[f1487,f1010]) ).
fof(f1585,plain,
( spl0_117
| ~ spl0_40
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f1527,f1402,f1199,f1583]) ).
fof(f1527,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_40
| ~ spl0_89 ),
inference(resolution,[],[f1403,f1200]) ).
fof(f1516,plain,
( spl0_116
| ~ spl0_19
| ~ spl0_14
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f1509,f1382,f1068,f1093,f1513]) ).
fof(f1509,plain,
( ~ class_Orderings_Olinorder(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat)
| ~ spl0_14
| ~ spl0_84 ),
inference(resolution,[],[f1383,f1070]) ).
fof(f1070,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f1508,plain,
spl0_115,
inference(avatar_split_clause,[],[f943,f1506]) ).
fof(f943,plain,
! [X0,X14] :
( c_Complete__Lattice_OSup__class_OSup(c_fequal(X14,X0),X0) = X14
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f778,f926]) ).
fof(f778,axiom,
! [X0,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
fof(f1504,plain,
spl0_114,
inference(avatar_split_clause,[],[f942,f1502]) ).
fof(f942,plain,
! [X0,X14] :
( c_Complete__Lattice_OInf__class_OInf(c_fequal(X14,X0),X0) = X14
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f796,f926]) ).
fof(f796,axiom,
! [X0,X14] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
fof(f1500,plain,
spl0_113,
inference(avatar_split_clause,[],[f928,f1498]) ).
fof(f1498,plain,
( spl0_113
<=> ! [X25,X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_fequal(X1,X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f928,plain,
! [X0,X1,X25] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_fequal(X1,X0),X0),X1)),
inference(forward_demodulation,[],[f781,f926]) ).
fof(f781,axiom,
! [X0,X1,X25] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
fof(f1496,plain,
spl0_112,
inference(avatar_split_clause,[],[f927,f1494]) ).
fof(f927,plain,
! [X0,X14,X25] : hAPP(c_Finite__Set_Ofold1(X25,X0),c_fequal(X14,X0)) = X14,
inference(forward_demodulation,[],[f791,f926]) ).
fof(f791,axiom,
! [X0,X14,X25] : hAPP(c_Finite__Set_Ofold1(X25,X0),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
fof(f1492,plain,
spl0_111,
inference(avatar_split_clause,[],[f913,f1490]) ).
fof(f913,axiom,
! [X0,X47,X57] :
( X47 = X57
| ~ hBOOL(hAPP(c_fequal(X47,X0),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1488,plain,
spl0_110,
inference(avatar_split_clause,[],[f845,f1486]) ).
fof(f845,axiom,
! [X51,X0,X1] :
( hBOOL(hAPP(X51,X1))
| ~ hBOOL(c_in(X1,X51,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1484,plain,
spl0_109,
inference(avatar_split_clause,[],[f844,f1482]) ).
fof(f844,axiom,
! [X51,X0,X1] :
( ~ hBOOL(hAPP(X51,X1))
| hBOOL(c_in(X1,X51,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1480,plain,
spl0_108,
inference(avatar_split_clause,[],[f833,f1478]) ).
fof(f1478,plain,
( spl0_108
<=> ! [X6,X0,X14] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X14,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f833,axiom,
! [X0,X6,X14] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X14,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
fof(f1476,plain,
spl0_107,
inference(avatar_split_clause,[],[f832,f1474]) ).
fof(f1474,plain,
( spl0_107
<=> ! [X6,X0,X14] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X14,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f832,axiom,
! [X0,X6,X14] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X14,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
fof(f1472,plain,
spl0_106,
inference(avatar_split_clause,[],[f822,f1470]) ).
fof(f822,axiom,
! [X0,X6,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X14,X6,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
fof(f1468,plain,
spl0_105,
inference(avatar_split_clause,[],[f722,f1466]) ).
fof(f722,axiom,
! [X0,X6] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
fof(f1464,plain,
spl0_104,
inference(avatar_split_clause,[],[f630,f1462]) ).
fof(f630,axiom,
! [X0,X8,X14] : c_lessequals(X8,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f1460,plain,
spl0_103,
inference(avatar_split_clause,[],[f616,f1458]) ).
fof(f616,axiom,
! [X0,X6] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f1456,plain,
spl0_102,
inference(avatar_split_clause,[],[f610,f1454]) ).
fof(f1454,plain,
( spl0_102
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f610,axiom,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
fof(f1452,plain,
spl0_101,
inference(avatar_split_clause,[],[f433,f1450]) ).
fof(f1450,plain,
( spl0_101
<=> ! [X6,X0] : ~ c_HOL_Oord__class_Oless(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f433,axiom,
! [X0,X6] : ~ c_HOL_Oord__class_Oless(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
fof(f1448,plain,
spl0_100,
inference(avatar_split_clause,[],[f403,f1446]) ).
fof(f403,axiom,
! [X4,X13] :
( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1444,plain,
spl0_99,
inference(avatar_split_clause,[],[f402,f1442]) ).
fof(f402,axiom,
! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1440,plain,
spl0_98,
inference(avatar_split_clause,[],[f374,f1438]) ).
fof(f374,axiom,
! [X4,X13] :
( c_lessequals(X4,X13,tc_nat)
| c_lessequals(c_Suc(X13),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f1436,plain,
spl0_97,
inference(avatar_split_clause,[],[f373,f1434]) ).
fof(f373,axiom,
! [X4,X13] :
( ~ c_lessequals(X4,X13,tc_nat)
| ~ c_lessequals(c_Suc(X13),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f1432,plain,
spl0_96,
inference(avatar_split_clause,[],[f348,f1430]) ).
fof(f348,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).
fof(f1428,plain,
spl0_95,
inference(avatar_split_clause,[],[f347,f1426]) ).
fof(f347,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__def__raw_0) ).
fof(f1424,plain,
spl0_94,
inference(avatar_split_clause,[],[f227,f1422]) ).
fof(f227,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X0) = c_Orderings_Oord__class_Omin(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__min_0) ).
fof(f1420,plain,
spl0_93,
inference(avatar_split_clause,[],[f202,f1418]) ).
fof(f202,axiom,
! [X4,X13] :
( c_lessequals(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f1416,plain,
spl0_92,
inference(avatar_split_clause,[],[f201,f1414]) ).
fof(f201,axiom,
! [X4,X13] :
( ~ c_lessequals(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f1412,plain,
spl0_91,
inference(avatar_split_clause,[],[f164,f1410]) ).
fof(f164,axiom,
! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X4,tc_nat)
| c_lessequals(c_Suc(X13),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
fof(f1408,plain,
spl0_90,
inference(avatar_split_clause,[],[f163,f1406]) ).
fof(f163,axiom,
! [X4,X13] :
( c_HOL_Oord__class_Oless(X13,X4,tc_nat)
| ~ c_lessequals(c_Suc(X13),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
fof(f1404,plain,
spl0_89,
inference(avatar_split_clause,[],[f155,f1402]) ).
fof(f155,axiom,
! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f1400,plain,
spl0_88,
inference(avatar_split_clause,[],[f154,f1398]) ).
fof(f154,axiom,
! [X4,X13] :
( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f1396,plain,
spl0_87,
inference(avatar_split_clause,[],[f115,f1394]) ).
fof(f115,axiom,
! [X4,X13] :
( ~ c_lessequals(X4,X13,tc_nat)
| c_lessequals(X4,c_Suc(X13),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
fof(f1392,plain,
spl0_86,
inference(avatar_split_clause,[],[f114,f1390]) ).
fof(f114,axiom,
! [X4,X13] :
( c_lessequals(X4,X13,tc_nat)
| ~ c_lessequals(c_Suc(X4),X13,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
fof(f1388,plain,
( spl0_85
| ~ spl0_43
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1377,f1345,f1211,f1386]) ).
fof(f1377,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_43
| ~ spl0_76 ),
inference(resolution,[],[f1346,f1212]) ).
fof(f1384,plain,
spl0_84,
inference(avatar_split_clause,[],[f21,f1382]) ).
fof(f21,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X0) = c_Orderings_Oord__class_Omax(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__max_0) ).
fof(f1375,plain,
spl0_83,
inference(avatar_split_clause,[],[f870,f1373]) ).
fof(f1373,plain,
( spl0_83
<=> ! [X55,X56] :
( ~ class_Finite__Set_Ofinite_Ofinite(X55)
| ~ class_Finite__Set_Ofinite_Ofinite(X56)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f870,axiom,
! [X56,X55] :
( ~ class_Finite__Set_Ofinite_Ofinite(X55)
| ~ class_Finite__Set_Ofinite_Ofinite(X56)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f1371,plain,
spl0_82,
inference(avatar_split_clause,[],[f842,f1369]) ).
fof(f842,axiom,
! [X0,X1,X8] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X8,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f1367,plain,
spl0_81,
inference(avatar_split_clause,[],[f820,f1365]) ).
fof(f820,axiom,
! [X0,X15] : ~ hBOOL(c_in(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f1363,plain,
spl0_80,
inference(avatar_split_clause,[],[f617,f1361]) ).
fof(f617,axiom,
! [X0,X25,X20] : c_Fun_Oinj__on(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
fof(f1359,plain,
spl0_79,
inference(avatar_split_clause,[],[f547,f1357]) ).
fof(f547,axiom,
! [X50,X0,X26,X20] : hAPP(c_COMBK(X26,X0,X20),X50) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f1355,plain,
spl0_78,
inference(avatar_split_clause,[],[f490,f1353]) ).
fof(f490,axiom,
! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f1351,plain,
spl0_77,
inference(avatar_split_clause,[],[f289,f1349]) ).
fof(f289,axiom,
! [X4,X13] :
( c_lessequals(X4,X13,tc_nat)
| c_lessequals(X13,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1347,plain,
spl0_76,
inference(avatar_split_clause,[],[f86,f1345]) ).
fof(f86,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
fof(f1343,plain,
spl0_75,
inference(avatar_split_clause,[],[f43,f1341]) ).
fof(f1341,plain,
( spl0_75
<=> ! [X24,X23] :
( X23 = X24
| c_Suc(X23) != c_Suc(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f43,axiom,
! [X24,X23] :
( X23 = X24
| c_Suc(X23) != c_Suc(X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
fof(f1339,plain,
( ~ spl0_74
| ~ spl0_44
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1334,f1319,f1215,f1336]) ).
fof(f1336,plain,
( spl0_74
<=> class_Orderings_Otop(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1334,plain,
( ~ class_Orderings_Otop(tc_nat)
| ~ spl0_44
| ~ spl0_70 ),
inference(resolution,[],[f1320,f1216]) ).
fof(f1333,plain,
spl0_73,
inference(avatar_split_clause,[],[f830,f1331]) ).
fof(f1331,plain,
( spl0_73
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f830,axiom,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f1329,plain,
spl0_72,
inference(avatar_split_clause,[],[f816,f1327]) ).
fof(f816,axiom,
! [X0,X1,X6] : hBOOL(hAPP(c_Set_Oinsert(X1,X6,X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f1325,plain,
spl0_71,
inference(avatar_split_clause,[],[f751,f1323]) ).
fof(f1323,plain,
( spl0_71
<=> ! [X0,X1] : c_The(c_fequal(X1,X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f751,axiom,
! [X0,X1] : c_The(c_fequal(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
fof(f1321,plain,
spl0_70,
inference(avatar_split_clause,[],[f723,f1319]) ).
fof(f723,axiom,
! [X0,X1] :
( ~ class_Orderings_Otop(X0)
| c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
fof(f1317,plain,
spl0_69,
inference(avatar_split_clause,[],[f696,f1315]) ).
fof(f1315,plain,
( spl0_69
<=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f696,axiom,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
fof(f1313,plain,
spl0_68,
inference(avatar_split_clause,[],[f595,f1311]) ).
fof(f595,axiom,
! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1309,plain,
spl0_67,
inference(avatar_split_clause,[],[f912,f1307]) ).
fof(f1307,plain,
( spl0_67
<=> ! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f912,axiom,
! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1305,plain,
spl0_66,
inference(avatar_split_clause,[],[f877,f1303]) ).
fof(f1303,plain,
( spl0_66
<=> ! [X55,X56] :
( ~ class_HOL_Oord(X56)
| class_HOL_Oord(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f877,axiom,
! [X56,X55] :
( ~ class_HOL_Oord(X56)
| class_HOL_Oord(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f1301,plain,
spl0_65,
inference(avatar_split_clause,[],[f876,f1299]) ).
fof(f1299,plain,
( spl0_65
<=> ! [X55,X56] :
( ~ class_HOL_Ominus(X56)
| class_HOL_Ominus(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f876,axiom,
! [X56,X55] :
( ~ class_HOL_Ominus(X56)
| class_HOL_Ominus(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
fof(f1297,plain,
spl0_64,
inference(avatar_split_clause,[],[f875,f1295]) ).
fof(f875,axiom,
! [X56,X55] :
( ~ class_Orderings_Obot(X56)
| class_Orderings_Obot(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1293,plain,
spl0_63,
inference(avatar_split_clause,[],[f874,f1291]) ).
fof(f874,axiom,
! [X56,X55] :
( ~ class_Orderings_Otop(X56)
| class_Orderings_Otop(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
fof(f1289,plain,
spl0_62,
inference(avatar_split_clause,[],[f873,f1287]) ).
fof(f873,axiom,
! [X56,X55] :
( ~ class_Orderings_Oorder(X56)
| class_Orderings_Oorder(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1285,plain,
spl0_61,
inference(avatar_split_clause,[],[f872,f1283]) ).
fof(f1283,plain,
( spl0_61
<=> ! [X55,X56] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Olattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f872,axiom,
! [X56,X55] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Olattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f1281,plain,
spl0_60,
inference(avatar_split_clause,[],[f871,f1279]) ).
fof(f1279,plain,
( spl0_60
<=> ! [X55,X56] :
( ~ class_Orderings_Opreorder(X56)
| class_Orderings_Opreorder(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f871,axiom,
! [X56,X55] :
( ~ class_Orderings_Opreorder(X56)
| class_Orderings_Opreorder(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1277,plain,
spl0_59,
inference(avatar_split_clause,[],[f869,f1275]) ).
fof(f869,axiom,
! [X56,X55] :
( ~ class_Lattices_Obounded__lattice(X56)
| class_Lattices_Obounded__lattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f1273,plain,
spl0_58,
inference(avatar_split_clause,[],[f868,f1271]) ).
fof(f1271,plain,
( spl0_58
<=> ! [X55,X56] :
( ~ class_Lattices_Odistrib__lattice(X56)
| class_Lattices_Odistrib__lattice(tc_fun(X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f868,axiom,
! [X56,X55] :
( ~ class_Lattices_Odistrib__lattice(X56)
| class_Lattices_Odistrib__lattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f1269,plain,
spl0_57,
inference(avatar_split_clause,[],[f867,f1267]) ).
fof(f867,axiom,
! [X56,X55] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Olower__semilattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f1265,plain,
spl0_56,
inference(avatar_split_clause,[],[f866,f1263]) ).
fof(f866,axiom,
! [X56,X55] :
( ~ class_Lattices_Olattice(X56)
| class_Lattices_Oupper__semilattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f1261,plain,
spl0_55,
inference(avatar_split_clause,[],[f865,f1259]) ).
fof(f865,axiom,
! [X56,X55] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X56)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X55,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f1257,plain,
spl0_54,
inference(avatar_split_clause,[],[f831,f1255]) ).
fof(f831,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(f1253,plain,
spl0_53,
inference(avatar_split_clause,[],[f741,f1251]) ).
fof(f741,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1249,plain,
spl0_52,
inference(avatar_split_clause,[],[f740,f1247]) ).
fof(f740,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1245,plain,
spl0_51,
inference(avatar_split_clause,[],[f735,f1243]) ).
fof(f735,axiom,
! [X0,X1] : c_lessequals(X1,X1,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
fof(f1241,plain,
spl0_50,
inference(avatar_split_clause,[],[f67,f1239]) ).
fof(f1239,plain,
( spl0_50
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f67,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1237,plain,
spl0_49,
inference(avatar_split_clause,[],[f66,f1235]) ).
fof(f1235,plain,
( spl0_49
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f66,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1233,plain,
spl0_48,
inference(avatar_split_clause,[],[f65,f1231]) ).
fof(f65,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1229,plain,
spl0_47,
inference(avatar_split_clause,[],[f61,f1227]) ).
fof(f1227,plain,
( spl0_47
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f61,axiom,
! [X0,X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
fof(f1225,plain,
spl0_46,
inference(avatar_split_clause,[],[f856,f1223]) ).
fof(f856,axiom,
! [X0,X6] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
fof(f1221,plain,
spl0_45,
inference(avatar_split_clause,[],[f665,f1219]) ).
fof(f1219,plain,
( spl0_45
<=> ! [X0,X26] : c_Collect(X26,X0) = X26 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1217,plain,
spl0_44,
inference(avatar_split_clause,[],[f120,f1215]) ).
fof(f120,axiom,
! [X13] : ~ c_lessequals(c_Suc(X13),X13,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f1213,plain,
spl0_43,
inference(avatar_split_clause,[],[f94,f1211]) ).
fof(f94,axiom,
! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f1209,plain,
spl0_42,
inference(avatar_split_clause,[],[f138,f1207]) ).
fof(f138,axiom,
! [X13] : c_lessequals(X13,X13,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f1205,plain,
spl0_41,
inference(avatar_split_clause,[],[f124,f1203]) ).
fof(f1203,plain,
( spl0_41
<=> ! [X13] : c_Suc(X13) != X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f124,axiom,
! [X13] : c_Suc(X13) != X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f1201,plain,
spl0_40,
inference(avatar_split_clause,[],[f62,f1199]) ).
fof(f62,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f1197,plain,
( ~ spl0_39
| spl0_38 ),
inference(avatar_split_clause,[],[f1192,f1188,f1194]) ).
fof(f1188,plain,
( spl0_38
<=> hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1192,plain,
( ~ hBOOL(hAPP(hAPP(v_P,v_G),c_fequal(hAPP(v_mgt__call,v_x),t_a)))
| spl0_38 ),
inference(forward_demodulation,[],[f1190,f926]) ).
fof(f1190,plain,
( ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| spl0_38 ),
inference(avatar_component_clause,[],[f1188]) ).
fof(f1191,plain,
~ spl0_38,
inference(avatar_split_clause,[],[f925,f1188]) ).
fof(f925,plain,
~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
inference(forward_demodulation,[],[f864,f862]) ).
fof(f862,axiom,
v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f864,axiom,
~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1186,plain,
spl0_37,
inference(avatar_split_clause,[],[f911,f1183]) ).
fof(f911,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f1181,plain,
spl0_36,
inference(avatar_split_clause,[],[f910,f1178]) ).
fof(f1178,plain,
( spl0_36
<=> class_HOL_Ominus(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f910,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
fof(f1176,plain,
spl0_35,
inference(avatar_split_clause,[],[f909,f1173]) ).
fof(f909,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f1171,plain,
spl0_34,
inference(avatar_split_clause,[],[f908,f1168]) ).
fof(f908,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
fof(f1166,plain,
spl0_33,
inference(avatar_split_clause,[],[f907,f1163]) ).
fof(f907,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f1161,plain,
spl0_32,
inference(avatar_split_clause,[],[f906,f1158]) ).
fof(f906,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f1156,plain,
spl0_31,
inference(avatar_split_clause,[],[f905,f1153]) ).
fof(f905,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f1151,plain,
spl0_30,
inference(avatar_split_clause,[],[f904,f1148]) ).
fof(f1148,plain,
( spl0_30
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f904,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f1146,plain,
spl0_29,
inference(avatar_split_clause,[],[f903,f1143]) ).
fof(f903,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f1141,plain,
spl0_28,
inference(avatar_split_clause,[],[f902,f1138]) ).
fof(f1138,plain,
( spl0_28
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f902,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f1136,plain,
spl0_27,
inference(avatar_split_clause,[],[f901,f1133]) ).
fof(f901,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f1131,plain,
spl0_26,
inference(avatar_split_clause,[],[f900,f1128]) ).
fof(f900,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f1126,plain,
spl0_25,
inference(avatar_split_clause,[],[f899,f1123]) ).
fof(f899,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(f1121,plain,
spl0_24,
inference(avatar_split_clause,[],[f898,f1118]) ).
fof(f1118,plain,
( spl0_24
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f898,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
fof(f1116,plain,
spl0_23,
inference(avatar_split_clause,[],[f897,f1113]) ).
fof(f1113,plain,
( spl0_23
<=> class_HOL_Ominus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f897,axiom,
class_HOL_Ominus(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
fof(f1111,plain,
spl0_22,
inference(avatar_split_clause,[],[f896,f1108]) ).
fof(f896,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f1106,plain,
spl0_21,
inference(avatar_split_clause,[],[f895,f1103]) ).
fof(f895,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1101,plain,
spl0_20,
inference(avatar_split_clause,[],[f894,f1098]) ).
fof(f894,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f1096,plain,
spl0_19,
inference(avatar_split_clause,[],[f893,f1093]) ).
fof(f893,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1091,plain,
spl0_18,
inference(avatar_split_clause,[],[f892,f1088]) ).
fof(f1088,plain,
( spl0_18
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f892,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1086,plain,
spl0_17,
inference(avatar_split_clause,[],[f891,f1083]) ).
fof(f1083,plain,
( spl0_17
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f891,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1081,plain,
spl0_16,
inference(avatar_split_clause,[],[f890,f1078]) ).
fof(f1078,plain,
( spl0_16
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f890,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f1076,plain,
spl0_15,
inference(avatar_split_clause,[],[f889,f1073]) ).
fof(f889,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f1071,plain,
spl0_14,
inference(avatar_split_clause,[],[f888,f1068]) ).
fof(f888,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f1066,plain,
spl0_13,
inference(avatar_split_clause,[],[f887,f1063]) ).
fof(f887,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1061,plain,
spl0_12,
inference(avatar_split_clause,[],[f886,f1058]) ).
fof(f1058,plain,
( spl0_12
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f886,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1056,plain,
spl0_11,
inference(avatar_split_clause,[],[f885,f1053]) ).
fof(f1053,plain,
( spl0_11
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f885,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1051,plain,
spl0_10,
inference(avatar_split_clause,[],[f884,f1048]) ).
fof(f1048,plain,
( spl0_10
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f884,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1046,plain,
spl0_9,
inference(avatar_split_clause,[],[f883,f1043]) ).
fof(f883,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1041,plain,
spl0_8,
inference(avatar_split_clause,[],[f882,f1038]) ).
fof(f1038,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f882,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1036,plain,
spl0_7,
inference(avatar_split_clause,[],[f881,f1033]) ).
fof(f1033,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f881,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1031,plain,
spl0_6,
inference(avatar_split_clause,[],[f880,f1028]) ).
fof(f1028,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f880,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1026,plain,
spl0_5,
inference(avatar_split_clause,[],[f879,f1023]) ).
fof(f1023,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f879,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1021,plain,
spl0_4,
inference(avatar_split_clause,[],[f878,f1018]) ).
fof(f1018,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f878,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1016,plain,
spl0_3,
inference(avatar_split_clause,[],[f862,f1013]) ).
fof(f1011,plain,
spl0_2,
inference(avatar_split_clause,[],[f863,f1008]) ).
fof(f863,axiom,
hBOOL(c_in(v_x,v_U,tc_Com_Opname)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1006,plain,
spl0_1,
inference(avatar_split_clause,[],[f861,f1003]) ).
fof(f861,axiom,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV879-1 : TPTP v8.2.0. Released v4.1.0.
% 0.11/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 07:09:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (11502)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43 % (11506)WARNING: value z3 for option sas not known
% 0.20/0.43 % (11505)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.43 % (11508)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)
% 0.20/0.43 % (11507)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.43 % (11509)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)
% 0.20/0.43 % (11504)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.43 % (11506)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)
% 0.20/0.43 % (11510)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)
% 1.71/0.68 TRYING [1]
% 1.71/0.72 TRYING [2]
% 6.90/1.40 TRYING [3]
% 8.01/1.54 TRYING [1]
% 8.57/1.69 TRYING [2]
% 9.12/1.77 TRYING [1]
% 9.87/1.81 TRYING [2]
% 14.04/2.42 TRYING [3]
% 20.88/3.42 % (11508)First to succeed.
% 21.63/3.49 % (11508)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11502"
% 21.63/3.50 % (11508)Refutation found. Thanks to Tanya!
% 21.63/3.50 % SZS status Unsatisfiable for theBenchmark
% 21.63/3.50 % SZS output start Proof for theBenchmark
% See solution above
% 21.84/3.54 % (11508)------------------------------
% 21.84/3.54 % (11508)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 21.84/3.54 % (11508)Termination reason: Refutation
% 21.84/3.54
% 21.84/3.54 % (11508)Memory used [KB]: 21635
% 21.84/3.54 % (11508)Time elapsed: 3.051 s
% 21.84/3.54 % (11508)Instructions burned: 4311 (million)
% 21.84/3.54 % (11502)Success in time 3.172 s
%------------------------------------------------------------------------------