TSTP Solution File: SCT058-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT058-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:55:34 EDT 2024
% Result : Unsatisfiable 10.36s 1.81s
% Output : Refutation 10.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1232
% Syntax : Number of formulae : 2371 ( 711 unt; 0 def)
% Number of atoms : 5554 ( 729 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 5589 (2406 ~;2487 |; 0 &)
% ( 696 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 724 ( 722 usr; 697 prp; 0-5 aty)
% Number of functors : 84 ( 84 usr; 11 con; 0-7 aty)
% Number of variables : 4987 (4987 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18630,plain,
$false,
inference(avatar_sat_refutation,[],[f735,f740,f745,f750,f755,f760,f765,f770,f775,f780,f785,f790,f795,f799,f803,f807,f811,f815,f819,f823,f827,f831,f835,f839,f843,f847,f851,f855,f859,f863,f867,f871,f875,f879,f883,f887,f891,f895,f899,f903,f907,f911,f915,f919,f923,f927,f931,f936,f940,f944,f948,f952,f956,f960,f964,f968,f972,f976,f980,f984,f992,f996,f1000,f1004,f1008,f1012,f1016,f1020,f1024,f1028,f1032,f1036,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1072,f1096,f1107,f1111,f1115,f1119,f1123,f1127,f1131,f1135,f1139,f1143,f1147,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1189,f1222,f1229,f1231,f1235,f1239,f1243,f1247,f1252,f1256,f1260,f1264,f1268,f1272,f1276,f1280,f1284,f1288,f1292,f1296,f1300,f1304,f1308,f1312,f1316,f1320,f1324,f1328,f1333,f1338,f1343,f1393,f1396,f1426,f1427,f1435,f1439,f1443,f1447,f1451,f1455,f1459,f1463,f1472,f1476,f1480,f1484,f1488,f1492,f1576,f1642,f1646,f1650,f1654,f1658,f1662,f1666,f1670,f1674,f1678,f1683,f1687,f1691,f1695,f1699,f1703,f1707,f1711,f1715,f1719,f1723,f1728,f1732,f1736,f1740,f1744,f1748,f1752,f1756,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2063,f2067,f2071,f2075,f2079,f2083,f2087,f2091,f2102,f2106,f2110,f2114,f2118,f2122,f2126,f2130,f2134,f2138,f2142,f2146,f2150,f2154,f2158,f2162,f2166,f2170,f2174,f2178,f2183,f2188,f2193,f2201,f2205,f2209,f2213,f2274,f2558,f2642,f2646,f2650,f2654,f2655,f2659,f2663,f2667,f2671,f2675,f2679,f2683,f2687,f2691,f2695,f2699,f2703,f2938,f2942,f2946,f2950,f2954,f2958,f2962,f2966,f2970,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3002,f3006,f3010,f3014,f3019,f3023,f3027,f3249,f3253,f3257,f3261,f3265,f3269,f3273,f3277,f3281,f3285,f3289,f3293,f3297,f3301,f3305,f3309,f3313,f3317,f3321,f3325,f3329,f3333,f3337,f3341,f3345,f3349,f3353,f3357,f3361,f3365,f3369,f3373,f3377,f3381,f3385,f3713,f3717,f3721,f3725,f3729,f3733,f3737,f3741,f3745,f3749,f3753,f3757,f3761,f3765,f3769,f3773,f3777,f3907,f4111,f4131,f4135,f4139,f4143,f4147,f4151,f4155,f4159,f4163,f4167,f4171,f4175,f4179,f4183,f4420,f4448,f4452,f4456,f4460,f4464,f4468,f4472,f4476,f4477,f4481,f4485,f4489,f4493,f4497,f4501,f4505,f4509,f4513,f4517,f4521,f4525,f4529,f4533,f4635,f4995,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5027,f5031,f5035,f5039,f5044,f5048,f5052,f5056,f5060,f5531,f5782,f5786,f5790,f5794,f5798,f5802,f5807,f5862,f5866,f5870,f5874,f6100,f6104,f6108,f6112,f6116,f6120,f6124,f6129,f6133,f6137,f6141,f6145,f6149,f6153,f6157,f7014,f7057,f7061,f7065,f7069,f7073,f7077,f7081,f7085,f7089,f7403,f7407,f7411,f7415,f7419,f7423,f7427,f7431,f7435,f7439,f7440,f7444,f7448,f7452,f7456,f7460,f7464,f7468,f7472,f7476,f7480,f7909,f8242,f8246,f8250,f8254,f8258,f8262,f8266,f8337,f8411,f8415,f8419,f8423,f8427,f8431,f8435,f8439,f8443,f8447,f8451,f8455,f8459,f8463,f8467,f8471,f8476,f8480,f9063,f9067,f9072,f9076,f9080,f9084,f9088,f9092,f9097,f9200,f9204,f9208,f9212,f9216,f9220,f9224,f9228,f9232,f9236,f9240,f9244,f9248,f9253,f9257,f9261,f9265,f9269,f9274,f9309,f10436,f10969,f11061,f11065,f11069,f11073,f11077,f11081,f11085,f11089,f11093,f11097,f11101,f11105,f11109,f11113,f11118,f11387,f11615,f11735,f11739,f11743,f11747,f11751,f11755,f11759,f11763,f11767,f11771,f11775,f11779,f12349,f12353,f12357,f12361,f12365,f12369,f12638,f12642,f12646,f12650,f12654,f12658,f12988,f12992,f12996,f13000,f13001,f13040,f13044,f13297,f13301,f13305,f13309,f13480,f13484,f13576,f13580,f13584,f13779,f13783,f13788,f13792,f13899,f13903,f13907,f13911,f14117,f14121,f14125,f14285,f14289,f14294,f14298,f14456,f14513,f14517,f14635,f14639,f14696,f14700,f14704,f14982,f15026,f15030,f15034,f15110,f15114,f15249,f15253,f15352,f15427,f15431,f15432,f15588,f15594,f15947,f16009,f16055,f16063,f16226,f16276,f16280,f16284,f16288,f16289,f16295,f16299,f16309,f16335,f16345,f16376,f16380,f16384,f16388,f16401,f16410,f16422,f16432,f16437,f16472,f16513,f16517,f16521,f16555,f16559,f16567,f16716,f16806,f16810,f16855,f16859,f16863,f16867,f16876,f16880,f16961,f17001,f17005,f17009,f17013,f17017,f17021,f17026,f17030,f17034,f17038,f17042,f17046,f17050,f17054,f17301,f17350,f17354,f17494,f17498,f17502,f17506,f17510,f17514,f17518,f17522,f17526,f17530,f17534,f17538,f17542,f17546,f17550,f17554,f17558,f17603,f17677,f17690,f17695,f17753,f17757,f17761,f17765,f17769,f17774,f17778,f17782,f17786,f17790,f17794,f17798,f17802,f17806,f17810,f17814,f17818,f17822,f17826,f17830,f17834,f17838,f17842,f17846,f17850,f17854,f17859,f17863,f17867,f17871,f17875,f18322,f18330,f18414,f18418,f18597,f18603,f18608,f18613,f18617,f18621,f18622,f18629]) ).
fof(f18629,plain,
( spl0_450
| ~ spl0_104
| ~ spl0_431 ),
inference(avatar_split_clause,[],[f13018,f8256,f1226,f8473]) ).
fof(f8473,plain,
( spl0_450
<=> hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f1226,plain,
( spl0_104
<=> hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f8256,plain,
( spl0_431
<=> ! [X19,X0,X22,X23,X8] :
( hBOOL(c_in(c_Pair(X22,X23,X8,X0),X19,tc_prod(X8,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),hAPP(c_Relation_Oconverse(X8,X0),X19),tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f13018,plain,
( hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_104
| ~ spl0_431 ),
inference(resolution,[],[f1227,f8257]) ).
fof(f8257,plain,
( ! [X0,X8,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),hAPP(c_Relation_Oconverse(X8,X0),X19),tc_prod(X0,X8)))
| hBOOL(c_in(c_Pair(X22,X23,X8,X0),X19,tc_prod(X8,X0))) )
| ~ spl0_431 ),
inference(avatar_component_clause,[],[f8256]) ).
fof(f1227,plain,
( hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1226]) ).
fof(f18622,plain,
( spl0_103
| ~ spl0_433
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f15115,f8473,f8264,f1219]) ).
fof(f1219,plain,
( spl0_103
<=> hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f8264,plain,
( spl0_433
<=> ! [X58] :
( ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f15115,plain,
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_433
| ~ spl0_450 ),
inference(resolution,[],[f8474,f8265]) ).
fof(f8265,plain,
( ! [X58] :
( ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_433 ),
inference(avatar_component_clause,[],[f8264]) ).
fof(f8474,plain,
( hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_450 ),
inference(avatar_component_clause,[],[f8473]) ).
fof(f18621,plain,
( spl0_696
| ~ spl0_73
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1825,f1668,f1038,f18619]) ).
fof(f18619,plain,
( spl0_696
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f1038,plain,
( spl0_73
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1668,plain,
( spl0_156
<=> ! [X0,X23,X22,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X22,X0)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1825,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_73
| ~ spl0_156 ),
inference(duplicate_literal_removal,[],[f1814]) ).
fof(f1814,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ class_Lattices_Olower__semilattice(X3) )
| ~ spl0_73
| ~ spl0_156 ),
inference(resolution,[],[f1669,f1039]) ).
fof(f1039,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1669,plain,
( ! [X0,X1,X22,X23] :
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X0),X0)
| c_lessequals(X1,X22,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1668]) ).
fof(f18617,plain,
( spl0_695
| ~ spl0_39
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1540,f1437,f897,f18615]) ).
fof(f18615,plain,
( spl0_695
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f897,plain,
( spl0_39
<=> ! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1437,plain,
( spl0_135
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1540,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_39
| ~ spl0_135 ),
inference(resolution,[],[f1438,f898]) ).
fof(f898,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f1438,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X2 )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1437]) ).
fof(f18613,plain,
( spl0_694
| ~ spl0_39
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1512,f1424,f897,f18611]) ).
fof(f18611,plain,
( spl0_694
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1424,plain,
( spl0_133
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1512,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_39
| ~ spl0_133 ),
inference(resolution,[],[f1425,f898]) ).
fof(f1425,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X1 )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f18608,plain,
( ~ spl0_24
| spl0_693 ),
inference(avatar_contradiction_clause,[],[f18605]) ).
fof(f18605,plain,
( $false
| ~ spl0_24
| spl0_693 ),
inference(resolution,[],[f18602,f838]) ).
fof(f838,plain,
( ! [X0,X4] : c_lessequals(X4,X4,tc_fun(X0,tc_bool))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f837,plain,
( spl0_24
<=> ! [X4,X0] : c_lessequals(X4,X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f18602,plain,
( ~ c_lessequals(c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
| spl0_693 ),
inference(avatar_component_clause,[],[f18600]) ).
fof(f18600,plain,
( spl0_693
<=> c_lessequals(c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f18603,plain,
( ~ spl0_693
| ~ spl0_110
| ~ spl0_318
| ~ spl0_407
| ~ spl0_688
| spl0_692 ),
inference(avatar_split_clause,[],[f18598,f18594,f18324,f7401,f4137,f1254,f18600]) ).
fof(f1254,plain,
( spl0_110
<=> ! [X5,X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f4137,plain,
( spl0_318
<=> ! [X5,X23,X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X23,X5,X0),X6,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f7401,plain,
( spl0_407
<=> ! [X4,X0,X14,X5,X8] : c_Relation_OImage(X14,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X8,tc_bool)),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X14,X4,X8,X0),c_Relation_OImage(X14,X5,X8,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f18324,plain,
( spl0_688
<=> c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f18594,plain,
( spl0_692
<=> c_lessequals(c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f18598,plain,
( ~ c_lessequals(c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
| ~ spl0_110
| ~ spl0_318
| ~ spl0_407
| ~ spl0_688
| spl0_692 ),
inference(forward_demodulation,[],[f18595,f18369]) ).
fof(f18369,plain,
( ! [X0] : c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_110
| ~ spl0_318
| ~ spl0_407
| ~ spl0_688 ),
inference(forward_demodulation,[],[f18368,f1255]) ).
fof(f1255,plain,
( ! [X0,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) = X5
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1254]) ).
fof(f18368,plain,
( ! [X0] : c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_b____,c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_110
| ~ spl0_318
| ~ spl0_407
| ~ spl0_688 ),
inference(forward_demodulation,[],[f18367,f4138]) ).
fof(f4138,plain,
( ! [X0,X6,X5,X23] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X23,X5,X0),X6,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),X0)
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f4137]) ).
fof(f18367,plain,
( ! [X0] : c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_110
| ~ spl0_318
| ~ spl0_407
| ~ spl0_688 ),
inference(forward_demodulation,[],[f18366,f1255]) ).
fof(f18366,plain,
( ! [X0] : c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_318
| ~ spl0_407
| ~ spl0_688 ),
inference(forward_demodulation,[],[f18365,f4138]) ).
fof(f18365,plain,
( ! [X0] : c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_407
| ~ spl0_688 ),
inference(forward_demodulation,[],[f18344,f7402]) ).
fof(f7402,plain,
( ! [X0,X8,X14,X4,X5] : c_Relation_OImage(X14,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X8,tc_bool)),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X14,X4,X8,X0),c_Relation_OImage(X14,X5,X8,X0),tc_fun(X0,tc_bool))
| ~ spl0_407 ),
inference(avatar_component_clause,[],[f7401]) ).
fof(f18344,plain,
( ! [X0] : c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
| ~ spl0_407
| ~ spl0_688 ),
inference(superposition,[],[f7402,f18326]) ).
fof(f18326,plain,
( c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_688 ),
inference(avatar_component_clause,[],[f18324]) ).
fof(f18595,plain,
( ~ c_lessequals(c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
| spl0_692 ),
inference(avatar_component_clause,[],[f18594]) ).
fof(f18597,plain,
( spl0_692
| spl0_689
| ~ spl0_104
| ~ spl0_553 ),
inference(avatar_split_clause,[],[f14474,f14454,f1226,f18328,f18594]) ).
fof(f18328,plain,
( spl0_689
<=> ! [X0] : ~ c_Equiv__Relations_Oequiv(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f14454,plain,
( spl0_553
<=> ! [X4,X19,X0,X23,X22] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| c_lessequals(c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f14474,plain,
( ! [X0] :
( ~ c_Equiv__Relations_Oequiv(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt)
| c_lessequals(c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) )
| ~ spl0_104
| ~ spl0_553 ),
inference(resolution,[],[f14455,f1227]) ).
fof(f14455,plain,
( ! [X0,X19,X4,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| c_lessequals(c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)) )
| ~ spl0_553 ),
inference(avatar_component_clause,[],[f14454]) ).
fof(f18418,plain,
( spl0_691
| ~ spl0_104
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f13034,f7063,f1226,f18416]) ).
fof(f18416,plain,
( spl0_691
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f7063,plain,
( spl0_400
<=> ! [X4,X0,X5,X23] :
( ~ hBOOL(c_in(X23,X4,X0))
| c_Set_Oinsert(X23,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f13034,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_104
| ~ spl0_400 ),
inference(resolution,[],[f1227,f7064]) ).
fof(f7064,plain,
( ! [X0,X4,X5,X23] :
( ~ hBOOL(c_in(X23,X4,X0))
| c_Set_Oinsert(X23,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) )
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f7063]) ).
fof(f18414,plain,
( spl0_690
| ~ spl0_104
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f13033,f7059,f1226,f18412]) ).
fof(f18412,plain,
( spl0_690
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f7059,plain,
( spl0_399
<=> ! [X5,X23,X0,X6] :
( ~ hBOOL(c_in(X23,X6,X0))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X23,X5,X0),X6,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f13033,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_104
| ~ spl0_399 ),
inference(resolution,[],[f1227,f7060]) ).
fof(f7060,plain,
( ! [X0,X6,X5,X23] :
( ~ hBOOL(c_in(X23,X6,X0))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X23,X5,X0),X6,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f7059]) ).
fof(f18330,plain,
( spl0_688
| spl0_689
| ~ spl0_104
| ~ spl0_544 ),
inference(avatar_split_clause,[],[f14024,f13905,f1226,f18328,f18324]) ).
fof(f13905,plain,
( spl0_544
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| c_Relation_OImage(X19,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) = c_Relation_OImage(X19,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f14024,plain,
( ! [X0] :
( ~ c_Equiv__Relations_Oequiv(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Set_Oinsert(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_104
| ~ spl0_544 ),
inference(resolution,[],[f13906,f1227]) ).
fof(f13906,plain,
( ! [X2,X0,X1,X19,X4] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| c_Relation_OImage(X19,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) = c_Relation_OImage(X19,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) )
| ~ spl0_544 ),
inference(avatar_component_clause,[],[f13905]) ).
fof(f18322,plain,
( spl0_687
| ~ spl0_104
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f13035,f7075,f1226,f18320]) ).
fof(f18320,plain,
( spl0_687
<=> ! [X0] :
( ~ c_Equiv__Relations_Oequiv(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(X0,c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f7075,plain,
( spl0_403
<=> ! [X4,X0,X23,X19] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X23,X4,X0))
| hBOOL(c_in(X23,c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f13035,plain,
( ! [X0] :
( ~ c_Equiv__Relations_Oequiv(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(X0,c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_104
| ~ spl0_403 ),
inference(resolution,[],[f1227,f7076]) ).
fof(f7076,plain,
( ! [X0,X19,X4,X23] :
( ~ hBOOL(c_in(X23,X4,X0))
| ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| hBOOL(c_in(X23,c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),X0)) )
| ~ spl0_403 ),
inference(avatar_component_clause,[],[f7075]) ).
fof(f17875,plain,
( spl0_686
| ~ spl0_174
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f7977,f7450,f1742,f17873]) ).
fof(f17873,plain,
( spl0_686
<=> ! [X2,X0,X1] : ~ hBOOL(c_in(X0,c_Relation_OImage(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f1742,plain,
( spl0_174
<=> ! [X11,X50,X1] : ~ hBOOL(c_in(c_Pair(X11,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f7450,plain,
( spl0_419
<=> ! [X4,X19,X0,X22,X8] :
( ~ hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X8,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X22,X19,X8,X0),X22,X8,X0),X19,tc_prod(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f7977,plain,
( ! [X2,X0,X1] : ~ hBOOL(c_in(X0,c_Relation_OImage(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_174
| ~ spl0_419 ),
inference(resolution,[],[f7451,f1743]) ).
fof(f1743,plain,
( ! [X50,X11,X1] : ~ hBOOL(c_in(c_Pair(X11,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1742]) ).
fof(f7451,plain,
( ! [X0,X8,X19,X4,X22] :
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X22,X19,X8,X0),X22,X8,X0),X19,tc_prod(X8,X0)))
| ~ hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X8,X0),X0)) )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f7450]) ).
fof(f17871,plain,
( spl0_685
| ~ spl0_52
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f5598,f5017,f950,f17869]) ).
fof(f17869,plain,
( spl0_685
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| ~ hBOOL(c_in(X2,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f950,plain,
( spl0_52
<=> ! [X4,X0] : c_Lattices_Olower__semilattice__class_Oinf(X4,X4,tc_fun(X0,tc_bool)) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f5017,plain,
( spl0_359
<=> ! [X4,X0,X5,X1] :
( ~ hBOOL(c_in(X1,X5,X0))
| ~ hBOOL(c_in(X1,X4,X0))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f5598,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| ~ hBOOL(c_in(X2,X0,X1)) )
| ~ spl0_52
| ~ spl0_359 ),
inference(duplicate_literal_removal,[],[f5588]) ).
fof(f5588,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X0
| ~ hBOOL(c_in(X2,X0,X1))
| ~ hBOOL(c_in(X2,X0,X1)) )
| ~ spl0_52
| ~ spl0_359 ),
inference(superposition,[],[f5018,f951]) ).
fof(f951,plain,
( ! [X0,X4] : c_Lattices_Olower__semilattice__class_Oinf(X4,X4,tc_fun(X0,tc_bool)) = X4
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f5018,plain,
( ! [X0,X1,X4,X5] :
( c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(X1,X5,X0)) )
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f5017]) ).
fof(f17867,plain,
( spl0_684
| ~ spl0_171
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4870,f4519,f1730,f17865]) ).
fof(f17865,plain,
( spl0_684
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Relation_Orefl__on(X1,c_Transitive__Closure_Ortrancl(X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f1730,plain,
( spl0_171
<=> ! [X0,X1,X14] : hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f4519,plain,
( spl0_348
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| hBOOL(c_in(X2,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f4870,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Relation_Orefl__on(X1,c_Transitive__Closure_Ortrancl(X3,X2),X2) )
| ~ spl0_171
| ~ spl0_348 ),
inference(resolution,[],[f4520,f1731]) ).
fof(f1731,plain,
( ! [X0,X1,X14] : hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0)))
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1730]) ).
fof(f4520,plain,
( ! [X2,X0,X1,X19,X4] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(X2,X4,X0))
| ~ c_Relation_Orefl__on(X4,X19,X0) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f4519]) ).
fof(f17863,plain,
( spl0_683
| ~ spl0_171
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4805,f4503,f1730,f17861]) ).
fof(f17861,plain,
( spl0_683
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Equiv__Relations_Oequiv(X1,c_Transitive__Closure_Ortrancl(X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f4503,plain,
( spl0_344
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| hBOOL(c_in(X2,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f4805,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Equiv__Relations_Oequiv(X1,c_Transitive__Closure_Ortrancl(X3,X2),X2) )
| ~ spl0_171
| ~ spl0_344 ),
inference(resolution,[],[f4504,f1731]) ).
fof(f4504,plain,
( ! [X2,X0,X1,X19,X4] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(X2,X4,X0))
| ~ c_Equiv__Relations_Oequiv(X4,X19,X0) )
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f4503]) ).
fof(f17859,plain,
( ~ spl0_682
| ~ spl0_80
| spl0_597 ),
inference(avatar_split_clause,[],[f16449,f16429,f1066,f17856]) ).
fof(f17856,plain,
( spl0_682
<=> hBOOL(hAPP(c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),v_b____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1066,plain,
( spl0_80
<=> ! [X0,X1,X15] :
( ~ hBOOL(hAPP(X15,X1))
| hBOOL(c_in(X1,X15,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f16429,plain,
( spl0_597
<=> hBOOL(c_in(v_b____,c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f16449,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),v_b____))
| ~ spl0_80
| spl0_597 ),
inference(resolution,[],[f16430,f1067]) ).
fof(f1067,plain,
( ! [X0,X1,X15] :
( hBOOL(c_in(X1,X15,X0))
| ~ hBOOL(hAPP(X15,X1)) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f16430,plain,
( ~ hBOOL(c_in(v_b____,c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| spl0_597 ),
inference(avatar_component_clause,[],[f16429]) ).
fof(f17854,plain,
( spl0_681
| ~ spl0_213
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f4427,f4181,f2172,f17852]) ).
fof(f17852,plain,
( spl0_681
<=> ! [X2,X0,X1] :
( hBOOL(c_in(X0,c_Relation_ODomain(X1,X2,X2),X2))
| ~ c_Nitpick_Orefl_H(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f2172,plain,
( spl0_213
<=> ! [X0,X1,X19] :
( ~ c_Nitpick_Orefl_H(X19,X0)
| hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f4181,plain,
( spl0_329
<=> ! [X19,X0,X22,X23,X8] :
( hBOOL(c_in(X23,c_Relation_ODomain(X19,X0,X8),X0))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f4427,plain,
( ! [X2,X0,X1] :
( hBOOL(c_in(X0,c_Relation_ODomain(X1,X2,X2),X2))
| ~ c_Nitpick_Orefl_H(X1,X2) )
| ~ spl0_213
| ~ spl0_329 ),
inference(resolution,[],[f4182,f2173]) ).
fof(f2173,plain,
( ! [X0,X1,X19] :
( hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_Nitpick_Orefl_H(X19,X0) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2172]) ).
fof(f4182,plain,
( ! [X0,X8,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8)))
| hBOOL(c_in(X23,c_Relation_ODomain(X19,X0,X8),X0)) )
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f4181]) ).
fof(f17850,plain,
( spl0_680
| ~ spl0_55
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3697,f3371,f962,f17848]) ).
fof(f17848,plain,
( spl0_680
<=> ! [X0,X3,X2,X1] : ~ c_FunDef_Oin__rel(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X2,X3,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f962,plain,
( spl0_55
<=> ! [X0,X31] : ~ hBOOL(c_in(X31,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f3371,plain,
( spl0_294
<=> ! [X0,X8,X14,X2,X1] :
( ~ c_FunDef_Oin__rel(X14,X1,X2,X0,X8)
| hBOOL(c_in(c_Pair(X1,X2,X0,X8),X14,tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3697,plain,
( ! [X2,X3,X0,X1] : ~ c_FunDef_Oin__rel(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_bool)),X2,X3,X0,X1)
| ~ spl0_55
| ~ spl0_294 ),
inference(resolution,[],[f3372,f963]) ).
fof(f963,plain,
( ! [X31,X0] : ~ hBOOL(c_in(X31,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f962]) ).
fof(f3372,plain,
( ! [X2,X0,X1,X8,X14] :
( hBOOL(c_in(c_Pair(X1,X2,X0,X8),X14,tc_prod(X0,X8)))
| ~ c_FunDef_Oin__rel(X14,X1,X2,X0,X8) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3371]) ).
fof(f17846,plain,
( spl0_679
| ~ spl0_257
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3687,f3371,f3004,f17844]) ).
fof(f17844,plain,
( spl0_679
<=> ! [X0,X3,X2,X1] :
( ~ c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),X2,X3,X1,X1)
| X2 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f3004,plain,
( spl0_257
<=> ! [X4,X0,X2,X1] :
( X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f3687,plain,
( ! [X2,X3,X0,X1] :
( ~ c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),X2,X3,X1,X1)
| X2 = X3 )
| ~ spl0_257
| ~ spl0_294 ),
inference(resolution,[],[f3372,f3005]) ).
fof(f3005,plain,
( ! [X2,X0,X1,X4] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0)))
| X1 = X2 )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f3004]) ).
fof(f17842,plain,
( spl0_678
| ~ spl0_258
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3673,f3367,f3008,f17840]) ).
fof(f17840,plain,
( spl0_678
<=> ! [X0,X1] :
( c_FunDef_Oin__rel(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f3008,plain,
( spl0_258
<=> ! [X22,X23] :
( X22 = X23
| hBOOL(c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X23,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f3367,plain,
( spl0_293
<=> ! [X0,X8,X14,X2,X1] :
( c_FunDef_Oin__rel(X14,X1,X2,X0,X8)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X8),X14,tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f3673,plain,
( ! [X0,X1] :
( c_FunDef_Oin__rel(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1 )
| ~ spl0_258
| ~ spl0_293 ),
inference(resolution,[],[f3368,f3009]) ).
fof(f3009,plain,
( ! [X22,X23] :
( hBOOL(c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X23,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X22 = X23 )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f3008]) ).
fof(f3368,plain,
( ! [X2,X0,X1,X8,X14] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X8),X14,tc_prod(X0,X8)))
| c_FunDef_Oin__rel(X14,X1,X2,X0,X8) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3367]) ).
fof(f17838,plain,
( spl0_677
| ~ spl0_262
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3672,f3367,f3025,f17836]) ).
fof(f17836,plain,
( spl0_677
<=> ! [X2,X0,X1] :
( c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f3025,plain,
( spl0_262
<=> ! [X2,X50,X1] :
( X1 = X2
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f3672,plain,
( ! [X2,X0,X1] :
( c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X2 )
| ~ spl0_262
| ~ spl0_293 ),
inference(resolution,[],[f3368,f3026]) ).
fof(f3026,plain,
( ! [X50,X2,X1] :
( hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2 )
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f3025]) ).
fof(f17834,plain,
( spl0_676
| ~ spl0_261
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3671,f3367,f3021,f17832]) ).
fof(f17832,plain,
( spl0_676
<=> ! [X2,X0,X1] :
( c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f3021,plain,
( spl0_261
<=> ! [X50,X11,X1] :
( X1 = X11
| hBOOL(c_in(c_Pair(X11,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f3671,plain,
( ! [X2,X0,X1] :
( c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X2 )
| ~ spl0_261
| ~ spl0_293 ),
inference(resolution,[],[f3368,f3022]) ).
fof(f3022,plain,
( ! [X50,X11,X1] :
( hBOOL(c_in(c_Pair(X11,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X11 )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f3021]) ).
fof(f17830,plain,
( spl0_675
| ~ spl0_150
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2835,f2681,f1644,f17828]) ).
fof(f17828,plain,
( spl0_675
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X1),X2))
| ~ hBOOL(hAPP(c_Relation_OId(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1644,plain,
( spl0_150
<=> ! [X4,X5,X1,X0] :
( ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f2681,plain,
( spl0_234
<=> ! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X14,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2835,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X1),X2))
| ~ hBOOL(hAPP(c_Relation_OId(X1),X2)) )
| ~ spl0_150
| ~ spl0_234 ),
inference(superposition,[],[f1645,f2682]) ).
fof(f2682,plain,
( ! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X14,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2681]) ).
fof(f1645,plain,
( ! [X0,X1,X4,X5] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X1))
| ~ hBOOL(hAPP(X5,X1)) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1644]) ).
fof(f17826,plain,
( spl0_674
| ~ spl0_105
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2833,f2681,f1233,f17824]) ).
fof(f17824,plain,
( spl0_674
<=> ! [X0,X1] : c_lessequals(c_Relation_OId(X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f1233,plain,
( spl0_105
<=> ! [X5,X4,X0] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f2833,plain,
( ! [X0,X1] : c_lessequals(c_Relation_OId(X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool))
| ~ spl0_105
| ~ spl0_234 ),
inference(superposition,[],[f1234,f2682]) ).
fof(f1234,plain,
( ! [X0,X4,X5] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1233]) ).
fof(f17822,plain,
( spl0_673
| ~ spl0_80
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2603,f2176,f1066,f17820]) ).
fof(f17820,plain,
( spl0_673
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| ~ hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f2176,plain,
( spl0_214
<=> ! [X0,X23,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(c_Pair(X23,X23,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2603,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| ~ hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))) )
| ~ spl0_80
| ~ spl0_214 ),
inference(resolution,[],[f2177,f1067]) ).
fof(f2177,plain,
( ! [X0,X19,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X23,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_Wellfounded_Owf(X19,X0) )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2176]) ).
fof(f17818,plain,
( spl0_672
| ~ spl0_81
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2597,f2172,f1070,f17816]) ).
fof(f17816,plain,
( spl0_672
<=> ! [X2,X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1070,plain,
( spl0_81
<=> ! [X0,X1,X15] :
( hBOOL(hAPP(X15,X1))
| ~ hBOOL(c_in(X1,X15,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f2597,plain,
( ! [X2,X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))) )
| ~ spl0_81
| ~ spl0_213 ),
inference(resolution,[],[f2173,f1071]) ).
fof(f1071,plain,
( ! [X0,X1,X15] :
( ~ hBOOL(c_in(X1,X15,X0))
| hBOOL(hAPP(X15,X1)) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1070]) ).
fof(f17814,plain,
( spl0_671
| ~ spl0_80
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2589,f2168,f1066,f17812]) ).
fof(f17812,plain,
( spl0_671
<=> ! [X2,X0,X1] :
( ~ c_Relation_Oirrefl(X0,X1)
| ~ hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f2168,plain,
( spl0_212
<=> ! [X0,X1,X19] :
( ~ c_Relation_Oirrefl(X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2589,plain,
( ! [X2,X0,X1] :
( ~ c_Relation_Oirrefl(X0,X1)
| ~ hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))) )
| ~ spl0_80
| ~ spl0_212 ),
inference(resolution,[],[f2169,f1067]) ).
fof(f2169,plain,
( ! [X0,X1,X19] :
( ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_Relation_Oirrefl(X19,X0) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2168]) ).
fof(f17810,plain,
( spl0_670
| ~ spl0_62
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2545,f2124,f994,f17808]) ).
fof(f17808,plain,
( spl0_670
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f994,plain,
( spl0_62
<=> ! [X4,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f2124,plain,
( spl0_201
<=> ! [X20,X0,X19] :
( ~ c_Wellfounded_Oacyclic(X20,X0)
| c_Wellfounded_Oacyclic(X19,X0)
| ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2545,plain,
( ! [X0,X1] :
( c_Wellfounded_Oacyclic(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl0_62
| ~ spl0_201 ),
inference(resolution,[],[f2125,f995]) ).
fof(f995,plain,
( ! [X0,X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool))
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f994]) ).
fof(f2125,plain,
( ! [X0,X19,X20] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))
| c_Wellfounded_Oacyclic(X19,X0)
| ~ c_Wellfounded_Oacyclic(X20,X0) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2124]) ).
fof(f17806,plain,
( spl0_669
| ~ spl0_64
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2527,f2124,f1002,f17804]) ).
fof(f17804,plain,
( spl0_669
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1002,plain,
( spl0_64
<=> ! [X5,X0,X23] : c_lessequals(X5,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f2527,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) )
| ~ spl0_64
| ~ spl0_201 ),
inference(resolution,[],[f2125,f1003]) ).
fof(f1003,plain,
( ! [X0,X5,X23] : c_lessequals(X5,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool))
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1002]) ).
fof(f17802,plain,
( spl0_668
| ~ spl0_62
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2499,f2116,f994,f17800]) ).
fof(f17800,plain,
( spl0_668
<=> ! [X0,X1] :
( c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Relation_Oantisym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f2116,plain,
( spl0_199
<=> ! [X20,X0,X19] :
( ~ c_Relation_Oantisym(X20,X0)
| c_Relation_Oantisym(X19,X0)
| ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f2499,plain,
( ! [X0,X1] :
( c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Relation_Oantisym(X1,X0) )
| ~ spl0_62
| ~ spl0_199 ),
inference(resolution,[],[f2117,f995]) ).
fof(f2117,plain,
( ! [X0,X19,X20] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))
| c_Relation_Oantisym(X19,X0)
| ~ c_Relation_Oantisym(X20,X0) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f2116]) ).
fof(f17798,plain,
( spl0_667
| ~ spl0_64
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2481,f2116,f1002,f17796]) ).
fof(f17796,plain,
( spl0_667
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f2481,plain,
( ! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) )
| ~ spl0_64
| ~ spl0_199 ),
inference(resolution,[],[f2117,f1003]) ).
fof(f17794,plain,
( spl0_666
| ~ spl0_62
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2476,f2112,f994,f17792]) ).
fof(f17792,plain,
( spl0_666
<=> ! [X0,X1] :
( c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f2112,plain,
( spl0_198
<=> ! [X0,X19,X35] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(X35,X0)
| ~ c_lessequals(X35,X19,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2476,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(X1,X0) )
| ~ spl0_62
| ~ spl0_198 ),
inference(resolution,[],[f2113,f995]) ).
fof(f2113,plain,
( ! [X0,X19,X35] :
( ~ c_lessequals(X35,X19,tc_fun(tc_prod(X0,X0),tc_bool))
| c_Wellfounded_Owf(X35,X0)
| ~ c_Wellfounded_Owf(X19,X0) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2112]) ).
fof(f17790,plain,
( spl0_665
| ~ spl0_64
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2458,f2112,f1002,f17788]) ).
fof(f17788,plain,
( spl0_665
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f2458,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(X2,X0,tc_prod(X1,X1)),X1) )
| ~ spl0_64
| ~ spl0_198 ),
inference(resolution,[],[f2113,f1003]) ).
fof(f17786,plain,
( spl0_664
| ~ spl0_64
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2373,f2073,f1002,f17784]) ).
fof(f17784,plain,
( spl0_664
<=> ! [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_664])]) ).
fof(f2073,plain,
( spl0_190
<=> ! [X4,X0,X5,X1] :
( hBOOL(c_in(X1,X5,X0))
| ~ c_lessequals(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f2373,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3))
| ~ spl0_64
| ~ spl0_190 ),
inference(resolution,[],[f2074,f1003]) ).
fof(f2074,plain,
( ! [X0,X1,X4,X5] :
( ~ c_lessequals(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X5,X0)) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f2073]) ).
fof(f17782,plain,
( spl0_663
| ~ spl0_64
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2240,f2029,f1002,f17780]) ).
fof(f17780,plain,
( spl0_663
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f2029,plain,
( spl0_179
<=> ! [X5,X4,X0] :
( ~ c_lessequals(X5,X4,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f2240,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool)) = X1
| ~ spl0_64
| ~ spl0_179 ),
inference(resolution,[],[f2030,f1003]) ).
fof(f2030,plain,
( ! [X0,X4,X5] :
( ~ c_lessequals(X5,X4,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = X5 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f2029]) ).
fof(f17778,plain,
( spl0_662
| ~ spl0_64
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2217,f2025,f1002,f17776]) ).
fof(f17776,plain,
( spl0_662
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f2025,plain,
( spl0_178
<=> ! [X5,X4,X0] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f2217,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)) = X0
| ~ spl0_64
| ~ spl0_178 ),
inference(resolution,[],[f2026,f1003]) ).
fof(f2026,plain,
( ! [X0,X4,X5] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = X4 )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f2025]) ).
fof(f17774,plain,
( ~ spl0_661
| ~ spl0_92
| spl0_654 ),
inference(avatar_split_clause,[],[f17691,f17687,f1141,f17771]) ).
fof(f17771,plain,
( spl0_661
<=> c_Relation_Otrans(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f1141,plain,
( spl0_92
<=> ! [X0,X19] :
( ~ c_Relation_Otrans(X19,X0)
| c_Relation_Otrans(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f17687,plain,
( spl0_654
<=> c_Relation_Otrans(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f17691,plain,
( ~ c_Relation_Otrans(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_92
| spl0_654 ),
inference(resolution,[],[f17689,f1142]) ).
fof(f1142,plain,
( ! [X0,X19] :
( c_Relation_Otrans(hAPP(c_Relation_Oconverse(X0,X0),X19),X0)
| ~ c_Relation_Otrans(X19,X0) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1141]) ).
fof(f17689,plain,
( ~ c_Relation_Otrans(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_654 ),
inference(avatar_component_clause,[],[f17687]) ).
fof(f17769,plain,
( spl0_660
| ~ spl0_80
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1614,f1457,f1066,f17767]) ).
fof(f17767,plain,
( spl0_660
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f1457,plain,
( spl0_140
<=> ! [X0,X19] :
( c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X19,X0),c_Wellfounded_Oacc(X19,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1614,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X0,X1))) )
| ~ spl0_80
| ~ spl0_140 ),
inference(resolution,[],[f1458,f1067]) ).
fof(f1458,plain,
( ! [X0,X19] :
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X19,X0),c_Wellfounded_Oacc(X19,X0),X0))
| c_Wellfounded_Owf(X19,X0) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1457]) ).
fof(f17765,plain,
( spl0_659
| ~ spl0_80
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1612,f1453,f1066,f17763]) ).
fof(f17763,plain,
( spl0_659
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f1453,plain,
( spl0_139
<=> ! [X0,X19] :
( c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X19,X0),c_Wellfounded_Oacc(X19,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1612,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X0,X1))) )
| ~ spl0_80
| ~ spl0_139 ),
inference(resolution,[],[f1454,f1067]) ).
fof(f1454,plain,
( ! [X0,X19] :
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X19,X0),c_Wellfounded_Oacc(X19,X0),X0))
| c_Wellfounded_Owf(X19,X0) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1453]) ).
fof(f17761,plain,
( spl0_658
| ~ spl0_39
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1603,f1449,f897,f17759]) ).
fof(f17759,plain,
( spl0_658
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f1449,plain,
( spl0_138
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1603,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_39
| ~ spl0_138 ),
inference(resolution,[],[f1450,f898]) ).
fof(f1450,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2 )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f17757,plain,
( spl0_657
| ~ spl0_39
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1566,f1441,f897,f17755]) ).
fof(f17755,plain,
( spl0_657
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f1441,plain,
( spl0_136
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1566,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_39
| ~ spl0_136 ),
inference(resolution,[],[f1442,f898]) ).
fof(f1442,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1 )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1441]) ).
fof(f17753,plain,
( spl0_656
| ~ spl0_23
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1399,f1314,f833,f17751]) ).
fof(f17751,plain,
( spl0_656
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f833,plain,
( spl0_23
<=> ! [X0,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Oacyclic(X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1314,plain,
( spl0_125
<=> ! [X0,X14] :
( ~ c_Wellfounded_Owf(X14,X0)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X14,X14,X0,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1399,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1) )
| ~ spl0_23
| ~ spl0_125 ),
inference(resolution,[],[f1315,f834]) ).
fof(f834,plain,
( ! [X0,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Oacyclic(X19,X0) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f1315,plain,
( ! [X0,X14] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(X14,X14,X0,X0,X0),X0)
| ~ c_Wellfounded_Owf(X14,X0) )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f17695,plain,
( spl0_655
| ~ spl0_104
| ~ spl0_238
| ~ spl0_296
| ~ spl0_421
| ~ spl0_552 ),
inference(avatar_split_clause,[],[f14439,f14296,f7458,f3379,f2697,f1226,f17693]) ).
fof(f17693,plain,
( spl0_655
<=> ! [X0] :
( hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(hAPP(v_P____,v_x),c_Transitive__Closure_Ortrancl(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2697,plain,
( spl0_238
<=> ! [X0,X19] : c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Transitive__Closure_Ortrancl(X19,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f3379,plain,
( spl0_296
<=> ! [X0,X19] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X19,X0),X19,X0,X0,X0) = c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f7458,plain,
( spl0_421
<=> ! [X18,X19,X0,X8,X20] : hAPP(c_Relation_Oconverse(X8,X0),c_Relation_Orel__comp(X19,X20,X8,X18,X0)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X18,X0),X20),hAPP(c_Relation_Oconverse(X8,X18),X19),X0,X18,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f14296,plain,
( spl0_552
<=> ! [X31,X0,X14,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X14,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X14,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f14439,plain,
( ! [X0] :
( hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(hAPP(v_P____,v_x),c_Transitive__Closure_Ortrancl(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_104
| ~ spl0_238
| ~ spl0_296
| ~ spl0_421
| ~ spl0_552 ),
inference(forward_demodulation,[],[f14438,f3380]) ).
fof(f3380,plain,
( ! [X0,X19] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X19,X0),X19,X0,X0,X0) = c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0)
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f3379]) ).
fof(f14438,plain,
( ! [X0] :
( hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_104
| ~ spl0_238
| ~ spl0_421
| ~ spl0_552 ),
inference(forward_demodulation,[],[f14400,f8040]) ).
fof(f8040,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Relation_Oconverse(X0,X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X0),X3,X0,X0,X2)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X2),X3),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X1),X0),X2,X0,X0)
| ~ spl0_238
| ~ spl0_421 ),
inference(superposition,[],[f7459,f2698]) ).
fof(f2698,plain,
( ! [X0,X19] : c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Transitive__Closure_Ortrancl(X19,X0))
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2697]) ).
fof(f7459,plain,
( ! [X0,X18,X8,X19,X20] : hAPP(c_Relation_Oconverse(X8,X0),c_Relation_Orel__comp(X19,X20,X8,X18,X0)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X18,X0),X20),hAPP(c_Relation_Oconverse(X8,X18),X19),X0,X18,X8)
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f7458]) ).
fof(f14400,plain,
( ! [X0] :
( ~ hBOOL(c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_104
| ~ spl0_552 ),
inference(resolution,[],[f14297,f1227]) ).
fof(f14297,plain,
( ! [X31,X0,X14,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X14,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X14,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0))) )
| ~ spl0_552 ),
inference(avatar_component_clause,[],[f14296]) ).
fof(f17690,plain,
( spl0_653
| ~ spl0_654
| ~ spl0_104
| ~ spl0_535 ),
inference(avatar_split_clause,[],[f13602,f13574,f1226,f17687,f17684]) ).
fof(f17684,plain,
( spl0_653
<=> ! [X0] :
( ~ hBOOL(c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f13574,plain,
( spl0_535
<=> ! [X31,X19,X0,X23,X22] :
( ~ c_Relation_Otrans(X19,X0)
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f13602,plain,
( ! [X0] :
( ~ c_Relation_Otrans(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_104
| ~ spl0_535 ),
inference(resolution,[],[f13575,f1227]) ).
fof(f13575,plain,
( ! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_Relation_Otrans(X19,X0)
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),X19,tc_prod(X0,X0))) )
| ~ spl0_535 ),
inference(avatar_component_clause,[],[f13574]) ).
fof(f17677,plain,
( ~ spl0_652
| ~ spl0_80
| spl0_596 ),
inference(avatar_split_clause,[],[f16443,f16425,f1066,f17674]) ).
fof(f17674,plain,
( spl0_652
<=> hBOOL(hAPP(c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f16425,plain,
( spl0_596
<=> hBOOL(c_in(v_a____,c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f16443,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),v_a____))
| ~ spl0_80
| spl0_596 ),
inference(resolution,[],[f16427,f1067]) ).
fof(f16427,plain,
( ~ hBOOL(c_in(v_a____,c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| spl0_596 ),
inference(avatar_component_clause,[],[f16425]) ).
fof(f17603,plain,
( ~ spl0_651
| ~ spl0_294
| spl0_593 ),
inference(avatar_split_clause,[],[f16412,f16403,f3371,f17600]) ).
fof(f17600,plain,
( spl0_651
<=> c_FunDef_Oin__rel(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f16403,plain,
( spl0_593
<=> hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f16412,plain,
( ~ c_FunDef_Oin__rel(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_294
| spl0_593 ),
inference(resolution,[],[f16405,f3372]) ).
fof(f16405,plain,
( ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| spl0_593 ),
inference(avatar_component_clause,[],[f16403]) ).
fof(f17558,plain,
( spl0_650
| ~ spl0_173
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6807,f6131,f1738,f17556]) ).
fof(f17556,plain,
( spl0_650
<=> ! [X0,X1] : ~ hBOOL(c_in(X0,c_Relation_ODomain(c_Arrow__Order__Mirabelle_Omktop(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f1738,plain,
( spl0_173
<=> ! [X50,X1,X2] : ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f6131,plain,
( spl0_390
<=> ! [X19,X0,X23,X8] :
( ~ hBOOL(c_in(X23,c_Relation_ODomain(X19,X0,X8),X0))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X23,X19,X0,X8),X0,X8),X19,tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f6807,plain,
( ! [X0,X1] : ~ hBOOL(c_in(X0,c_Relation_ODomain(c_Arrow__Order__Mirabelle_Omktop(X1,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_173
| ~ spl0_390 ),
inference(resolution,[],[f6132,f1739]) ).
fof(f1739,plain,
( ! [X50,X2,X1] : ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1738]) ).
fof(f6132,plain,
( ! [X0,X8,X19,X23] :
( hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X23,X19,X0,X8),X0,X8),X19,tc_prod(X0,X8)))
| ~ hBOOL(c_in(X23,c_Relation_ODomain(X19,X0,X8),X0)) )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f6131]) ).
fof(f17554,plain,
( spl0_649
| ~ spl0_146
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4871,f4519,f1486,f17552]) ).
fof(f17552,plain,
( spl0_649
<=> ! [X2,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Relation_Orefl__on(X1,c_Relation_OId(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f1486,plain,
( spl0_146
<=> ! [X0,X1] : hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f4871,plain,
( ! [X2,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Relation_Orefl__on(X1,c_Relation_OId(X2),X2) )
| ~ spl0_146
| ~ spl0_348 ),
inference(resolution,[],[f4520,f1487]) ).
fof(f1487,plain,
( ! [X0,X1] : hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0)))
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1486]) ).
fof(f17550,plain,
( spl0_648
| ~ spl0_146
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4806,f4503,f1486,f17548]) ).
fof(f17548,plain,
( spl0_648
<=> ! [X2,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_OId(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f4806,plain,
( ! [X2,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_OId(X2),X2) )
| ~ spl0_146
| ~ spl0_344 ),
inference(resolution,[],[f4504,f1487]) ).
fof(f17546,plain,
( spl0_647
| ~ spl0_171
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f4430,f4181,f1730,f17544]) ).
fof(f17544,plain,
( spl0_647
<=> ! [X2,X0,X1] : hBOOL(c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f4430,plain,
( ! [X2,X0,X1] : hBOOL(c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2))
| ~ spl0_171
| ~ spl0_329 ),
inference(resolution,[],[f4182,f1731]) ).
fof(f17542,plain,
( spl0_646
| ~ spl0_212
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4118,f3775,f2168,f17540]) ).
fof(f17540,plain,
( spl0_646
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ c_Relation_Oirrefl(c_Relation_OId__on(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f3775,plain,
( spl0_314
<=> ! [X4,X0,X1] :
( ~ hBOOL(c_in(X1,X4,X0))
| hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f4118,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ c_Relation_Oirrefl(c_Relation_OId__on(X1,X2),X2) )
| ~ spl0_212
| ~ spl0_314 ),
inference(resolution,[],[f3776,f2169]) ).
fof(f3776,plain,
( ! [X0,X1,X4] :
( hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(X1,X4,X0)) )
| ~ spl0_314 ),
inference(avatar_component_clause,[],[f3775]) ).
fof(f17538,plain,
( spl0_645
| ~ spl0_214
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4117,f3775,f2176,f17536]) ).
fof(f17536,plain,
( spl0_645
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ c_Wellfounded_Owf(c_Relation_OId__on(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f4117,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ c_Wellfounded_Owf(c_Relation_OId__on(X1,X2),X2) )
| ~ spl0_214
| ~ spl0_314 ),
inference(resolution,[],[f3776,f2177]) ).
fof(f17534,plain,
( spl0_644
| ~ spl0_213
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4114,f3771,f2172,f17532]) ).
fof(f17532,plain,
( spl0_644
<=> ! [X2,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Nitpick_Orefl_H(c_Relation_OId__on(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f3771,plain,
( spl0_313
<=> ! [X2,X4,X0,X1] :
( hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f4114,plain,
( ! [X2,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ c_Nitpick_Orefl_H(c_Relation_OId__on(X1,X2),X2) )
| ~ spl0_213
| ~ spl0_313 ),
inference(resolution,[],[f3772,f2173]) ).
fof(f3772,plain,
( ! [X2,X0,X1,X4] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0)))
| hBOOL(c_in(X1,X4,X0)) )
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f3771]) ).
fof(f17530,plain,
( spl0_643
| ~ spl0_239
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3686,f3371,f2701,f17528]) ).
fof(f17528,plain,
( spl0_643
<=> ! [X2,X0,X1] :
( ~ c_FunDef_Oin__rel(c_Relation_OId(X0),X1,X2,X0,X0)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f2701,plain,
( spl0_239
<=> ! [X22,X0,X23] :
( X22 = X23
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f3686,plain,
( ! [X2,X0,X1] :
( ~ c_FunDef_Oin__rel(c_Relation_OId(X0),X1,X2,X0,X0)
| X1 = X2 )
| ~ spl0_239
| ~ spl0_294 ),
inference(resolution,[],[f3372,f2702]) ).
fof(f2702,plain,
( ! [X0,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0)))
| X22 = X23 )
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2701]) ).
fof(f17526,plain,
( spl0_642
| ~ spl0_42
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2887,f2693,f909,f17524]) ).
fof(f17524,plain,
( spl0_642
<=> ! [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_642])]) ).
fof(f909,plain,
( spl0_42
<=> ! [X4,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,X4,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f2693,plain,
( spl0_237
<=> ! [X2,X4,X0,X1] : c_Set_Oinsert(X1,c_Set_Oinsert(X2,X4,X0),X0) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X4,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2887,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0))
| ~ spl0_42
| ~ spl0_237 ),
inference(superposition,[],[f910,f2694]) ).
fof(f2694,plain,
( ! [X2,X0,X1,X4] : c_Set_Oinsert(X1,c_Set_Oinsert(X2,X4,X0),X0) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X4,X0),X0)
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2693]) ).
fof(f910,plain,
( ! [X0,X1,X4] : hBOOL(hAPP(c_Set_Oinsert(X1,X4,X0),X1))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f909]) ).
fof(f17522,plain,
( spl0_641
| ~ spl0_80
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f2008,f1742,f1066,f17520]) ).
fof(f17520,plain,
( spl0_641
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f2008,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_80
| ~ spl0_174 ),
inference(resolution,[],[f1743,f1067]) ).
fof(f17518,plain,
( spl0_640
| ~ spl0_80
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1995,f1738,f1066,f17516]) ).
fof(f17516,plain,
( spl0_640
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omktop(X0,X1),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f1995,plain,
( ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omktop(X0,X1),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_80
| ~ spl0_173 ),
inference(resolution,[],[f1739,f1067]) ).
fof(f17514,plain,
( spl0_639
| ~ spl0_81
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1993,f1730,f1070,f17512]) ).
fof(f17512,plain,
( spl0_639
<=> ! [X2,X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X1),c_Pair(X2,X2,X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f1993,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X1),c_Pair(X2,X2,X1,X1)))
| ~ spl0_81
| ~ spl0_171 ),
inference(resolution,[],[f1731,f1071]) ).
fof(f17510,plain,
( spl0_638
| ~ spl0_80
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1376,f1306,f1066,f17508]) ).
fof(f17508,plain,
( spl0_638
<=> ! [X2,X0,X1] :
( c_Set_Oinsert(X0,X1,X2) = X1
| ~ hBOOL(hAPP(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f1306,plain,
( spl0_123
<=> ! [X4,X0,X23] :
( ~ hBOOL(c_in(X23,X4,X0))
| c_Set_Oinsert(X23,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1376,plain,
( ! [X2,X0,X1] :
( c_Set_Oinsert(X0,X1,X2) = X1
| ~ hBOOL(hAPP(X1,X0)) )
| ~ spl0_80
| ~ spl0_123 ),
inference(resolution,[],[f1307,f1067]) ).
fof(f1307,plain,
( ! [X0,X4,X23] :
( ~ hBOOL(c_in(X23,X4,X0))
| c_Set_Oinsert(X23,X4,X0) = X4 )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1306]) ).
fof(f17506,plain,
( spl0_637
| ~ spl0_23
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1205,f1161,f833,f17504]) ).
fof(f17504,plain,
( spl0_637
<=> ! [X0,X3,X2,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X2,X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f1161,plain,
( spl0_97
<=> ! [X19,X0,X8,X7] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X19,X7,X0,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1205,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X2,X1,X3),X3) )
| ~ spl0_23
| ~ spl0_97 ),
inference(resolution,[],[f1162,f834]) ).
fof(f1162,plain,
( ! [X0,X8,X19,X7] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X19,X7,X0,X8),X8)
| ~ c_Wellfounded_Owf(X19,X0) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1161]) ).
fof(f17502,plain,
( spl0_636
| ~ spl0_53
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f1099,f1062,f954,f17500]) ).
fof(f17500,plain,
( spl0_636
<=> ! [X0,X1] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Ortrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f954,plain,
( spl0_53
<=> ! [X0,X19] :
( ~ c_Wellfounded_Oacyclic(X19,X0)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1062,plain,
( spl0_79
<=> ! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X19,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1099,plain,
( ! [X0,X1] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Ortrancl(X0,X1),X1) )
| ~ spl0_53
| ~ spl0_79 ),
inference(superposition,[],[f955,f1063]) ).
fof(f1063,plain,
( ! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X19,X0),X0)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f955,plain,
( ! [X0,X19] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X19,X0),X0)
| ~ c_Wellfounded_Oacyclic(X19,X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f954]) ).
fof(f17498,plain,
( spl0_635
| ~ spl0_30
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f988,f946,f861,f17496]) ).
fof(f17496,plain,
( spl0_635
<=> ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f861,plain,
( spl0_30
<=> ! [X60,X59] :
( ~ class_Lattices_Olattice(X60)
| class_Lattices_Olower__semilattice(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f946,plain,
( spl0_51
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f988,plain,
( ! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_30
| ~ spl0_51 ),
inference(resolution,[],[f947,f862]) ).
fof(f862,plain,
( ! [X59,X60] :
( class_Lattices_Olower__semilattice(tc_fun(X59,X60))
| ~ class_Lattices_Olattice(X60) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f947,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f946]) ).
fof(f17494,plain,
( spl0_634
| ~ spl0_29
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f986,f934,f857,f17492]) ).
fof(f17492,plain,
( spl0_634
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f857,plain,
( spl0_29
<=> ! [X60,X59] :
( ~ class_Lattices_Olattice(X60)
| class_Lattices_Oupper__semilattice(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f934,plain,
( spl0_48
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f986,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_29
| ~ spl0_48 ),
inference(resolution,[],[f935,f858]) ).
fof(f858,plain,
( ! [X59,X60] :
( class_Lattices_Oupper__semilattice(tc_fun(X59,X60))
| ~ class_Lattices_Olattice(X60) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f857]) ).
fof(f935,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f17354,plain,
( spl0_633
| spl0_103
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f13004,f7071,f1219,f17352]) ).
fof(f17352,plain,
( spl0_633
<=> ! [X0] : c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P_H____,v_x),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(X0,hAPP(v_P_H____,v_x),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f7071,plain,
( spl0_402
<=> ! [X4,X0,X5,X1] :
( hBOOL(c_in(X1,X5,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f13004,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P_H____,v_x),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(X0,hAPP(v_P_H____,v_x),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| spl0_103
| ~ spl0_402 ),
inference(resolution,[],[f1220,f7072]) ).
fof(f7072,plain,
( ! [X0,X1,X4,X5] :
( hBOOL(c_in(X1,X5,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f7071]) ).
fof(f1220,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| spl0_103 ),
inference(avatar_component_clause,[],[f1219]) ).
fof(f17350,plain,
( spl0_632
| ~ spl0_104
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4856,f4515,f1226,f17348]) ).
fof(f17348,plain,
( spl0_632
<=> ! [X0] :
( ~ c_Relation_Orefl__on(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_Pair(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f4515,plain,
( spl0_347
<=> ! [X4,X19,X0,X1] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| ~ hBOOL(c_in(X1,X4,X0))
| hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f4856,plain,
( ! [X0] :
( ~ c_Relation_Orefl__on(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_Pair(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) )
| ~ spl0_104
| ~ spl0_347 ),
inference(resolution,[],[f4516,f1227]) ).
fof(f4516,plain,
( ! [X0,X1,X19,X4] :
( ~ hBOOL(c_in(X1,X4,X0))
| ~ c_Relation_Orefl__on(X4,X19,X0)
| hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0))) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f4515]) ).
fof(f17301,plain,
( spl0_631
| ~ spl0_104
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f5074,f4993,f1226,f17299]) ).
fof(f17299,plain,
( spl0_631
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f4993,plain,
( spl0_353
<=> ! [X4,X0,X5,X1] :
( ~ hBOOL(c_in(X1,X5,X0))
| c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f5074,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_104
| ~ spl0_353 ),
inference(resolution,[],[f4994,f1227]) ).
fof(f4994,plain,
( ! [X0,X1,X4,X5] :
( ~ hBOOL(c_in(X1,X5,X0))
| c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f4993]) ).
fof(f17054,plain,
( spl0_630
| ~ spl0_174
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f5650,f5042,f1742,f17052]) ).
fof(f17052,plain,
( spl0_630
<=> ! [X0,X1] : hBOOL(c_in(X0,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f5042,plain,
( spl0_365
<=> ! [X0,X1,X14] :
( hBOOL(c_in(X1,c_Wellfounded_Oacc(X14,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X14,X1,X0),X1,X0,X0),X14,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f5650,plain,
( ! [X0,X1] : hBOOL(c_in(X0,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_174
| ~ spl0_365 ),
inference(resolution,[],[f5043,f1743]) ).
fof(f5043,plain,
( ! [X0,X1,X14] :
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X14,X1,X0),X1,X0,X0),X14,tc_prod(X0,X0)))
| hBOOL(c_in(X1,c_Wellfounded_Oacc(X14,X0),X0)) )
| ~ spl0_365 ),
inference(avatar_component_clause,[],[f5042]) ).
fof(f17050,plain,
( spl0_629
| ~ spl0_146
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f4431,f4181,f1486,f17048]) ).
fof(f17048,plain,
( spl0_629
<=> ! [X0,X1] : hBOOL(c_in(X0,c_Relation_ODomain(c_Relation_OId(X1),X1,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f4431,plain,
( ! [X0,X1] : hBOOL(c_in(X0,c_Relation_ODomain(c_Relation_OId(X1),X1,X1),X1))
| ~ spl0_146
| ~ spl0_329 ),
inference(resolution,[],[f4182,f1487]) ).
fof(f17046,plain,
( spl0_628
| ~ spl0_76
| ~ spl0_78
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4418,f4177,f1058,f1050,f17044]) ).
fof(f17044,plain,
( spl0_628
<=> ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f1050,plain,
( spl0_76
<=> ! [X0] : c_Relation_OId(X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1058,plain,
( spl0_78
<=> ! [X0,X8,X14] : c_Relation_Orel__comp(X14,c_Relation_OId(X8),X0,X8,X8) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f4177,plain,
( spl0_328
<=> ! [X0,X19] :
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X19,X0,X0),X19,X0)
| c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),X19,X0,X0,X0) != X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f4418,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0)
| ~ spl0_76
| ~ spl0_78
| ~ spl0_328 ),
inference(trivial_inequality_removal,[],[f4417]) ).
fof(f4417,plain,
( ! [X0] :
( c_Relation_OId(X0) != c_Relation_OId(X0)
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
| ~ spl0_76
| ~ spl0_78
| ~ spl0_328 ),
inference(forward_demodulation,[],[f4412,f1059]) ).
fof(f1059,plain,
( ! [X0,X8,X14] : c_Relation_Orel__comp(X14,c_Relation_OId(X8),X0,X8,X8) = X14
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f4412,plain,
( ! [X0] :
( c_Relation_OId(X0) != c_Relation_Orel__comp(c_Relation_OId(X0),c_Relation_OId(X0),X0,X0,X0)
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
| ~ spl0_76
| ~ spl0_328 ),
inference(superposition,[],[f4178,f1051]) ).
fof(f1051,plain,
( ! [X0] : c_Relation_OId(X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId(X0))
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1050]) ).
fof(f4178,plain,
( ! [X0,X19] :
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),X19,X0,X0,X0) != X19
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X19,X0,X0),X19,X0) )
| ~ spl0_328 ),
inference(avatar_component_clause,[],[f4177]) ).
fof(f17042,plain,
( spl0_627
| ~ spl0_212
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3685,f3371,f2168,f17040]) ).
fof(f17040,plain,
( spl0_627
<=> ! [X2,X0,X1] :
( ~ c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
| ~ c_Relation_Oirrefl(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f3685,plain,
( ! [X2,X0,X1] :
( ~ c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
| ~ c_Relation_Oirrefl(X0,X2) )
| ~ spl0_212
| ~ spl0_294 ),
inference(resolution,[],[f3372,f2169]) ).
fof(f17038,plain,
( spl0_626
| ~ spl0_214
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3684,f3371,f2176,f17036]) ).
fof(f17036,plain,
( spl0_626
<=> ! [X2,X0,X1] :
( ~ c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
| ~ c_Wellfounded_Owf(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f3684,plain,
( ! [X2,X0,X1] :
( ~ c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
| ~ c_Wellfounded_Owf(X0,X2) )
| ~ spl0_214
| ~ spl0_294 ),
inference(resolution,[],[f3372,f2177]) ).
fof(f17034,plain,
( spl0_625
| ~ spl0_213
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3667,f3367,f2172,f17032]) ).
fof(f17032,plain,
( spl0_625
<=> ! [X2,X0,X1] :
( c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
| ~ c_Nitpick_Orefl_H(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f3667,plain,
( ! [X2,X0,X1] :
( c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
| ~ c_Nitpick_Orefl_H(X0,X2) )
| ~ spl0_213
| ~ spl0_293 ),
inference(resolution,[],[f3368,f2173]) ).
fof(f17030,plain,
( spl0_624
| ~ spl0_81
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1638,f1486,f1070,f17028]) ).
fof(f17028,plain,
( spl0_624
<=> ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Pair(X1,X1,X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f1638,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Pair(X1,X1,X0,X0)))
| ~ spl0_81
| ~ spl0_146 ),
inference(resolution,[],[f1487,f1071]) ).
fof(f17026,plain,
( spl0_623
| ~ spl0_8
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1405,f1322,f767,f17023]) ).
fof(f17023,plain,
( spl0_623
<=> 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_623])]) ).
fof(f767,plain,
( spl0_8
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1322,plain,
( spl0_127
<=> ! [X8] :
( ~ class_Orderings_Obot(X8)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X8)),v_x) = c_Orderings_Obot__class_Obot(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1405,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_8
| ~ spl0_127 ),
inference(resolution,[],[f1323,f769]) ).
fof(f769,plain,
( class_Orderings_Obot(tc_bool)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f1323,plain,
( ! [X8] :
( ~ class_Orderings_Obot(X8)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X8)),v_x) = c_Orderings_Obot__class_Obot(X8) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f17021,plain,
( spl0_622
| ~ spl0_349
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f15119,f8473,f4523,f17019]) ).
fof(f17019,plain,
( spl0_622
<=> ! [X0] :
( hBOOL(c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f4523,plain,
( spl0_349
<=> ! [X2,X4,X19,X0,X1] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f15119,plain,
( ! [X0] :
( hBOOL(c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_349
| ~ spl0_450 ),
inference(resolution,[],[f8474,f4524]) ).
fof(f4524,plain,
( ! [X2,X0,X1,X19,X4] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(X1,X4,X0))
| ~ c_Relation_Orefl__on(X4,X19,X0) )
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f4523]) ).
fof(f17017,plain,
( spl0_621
| ~ spl0_1
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1368,f1282,f732,f17015]) ).
fof(f17015,plain,
( spl0_621
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f732,plain,
( spl0_1
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1282,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1368,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool)
| ~ spl0_1
| ~ spl0_117 ),
inference(resolution,[],[f1283,f734]) ).
fof(f734,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f1283,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1282]) ).
fof(f17013,plain,
( spl0_620
| ~ spl0_2
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1362,f1270,f737,f17011]) ).
fof(f17011,plain,
( spl0_620
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f737,plain,
( spl0_2
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1270,plain,
( spl0_114
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1362,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool)
| ~ spl0_2
| ~ spl0_114 ),
inference(resolution,[],[f1271,f739]) ).
fof(f739,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f1271,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1270]) ).
fof(f17009,plain,
( spl0_619
| ~ spl0_6
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1360,f1266,f757,f17007]) ).
fof(f17007,plain,
( spl0_619
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f757,plain,
( spl0_6
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1266,plain,
( spl0_113
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1360,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0
| ~ spl0_6
| ~ spl0_113 ),
inference(resolution,[],[f1267,f759]) ).
fof(f759,plain,
( class_Lattices_Olattice(tc_bool)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f1267,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f17005,plain,
( spl0_618
| ~ spl0_6
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1358,f1262,f757,f17003]) ).
fof(f17003,plain,
( spl0_618
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f1262,plain,
( spl0_112
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1358,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = X0
| ~ spl0_6
| ~ spl0_112 ),
inference(resolution,[],[f1263,f759]) ).
fof(f1263,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f17001,plain,
( spl0_617
| ~ spl0_81
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1204,f1153,f1070,f16999]) ).
fof(f16999,plain,
( spl0_617
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1153,plain,
( spl0_95
<=> ! [X0,X1,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1204,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) )
| ~ spl0_81
| ~ spl0_95 ),
inference(resolution,[],[f1154,f1071]) ).
fof(f1154,plain,
( ! [X0,X1,X19] :
( hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,X0),X0))
| ~ c_Wellfounded_Owf(X19,X0) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1153]) ).
fof(f16961,plain,
( spl0_616
| ~ spl0_104
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f5466,f5005,f1226,f16959]) ).
fof(f16959,plain,
( spl0_616
<=> ! [X0,X1] : c_Set_Oimage(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) = c_Set_Oinsert(hAPP(X0,c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Set_Oimage(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f5005,plain,
( spl0_356
<=> ! [X4,X0,X8,X1,X7] :
( ~ hBOOL(c_in(X1,X4,X0))
| c_Set_Oimage(X7,X4,X0,X8) = c_Set_Oinsert(hAPP(X7,X1),c_Set_Oimage(X7,X4,X0,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f5466,plain,
( ! [X0,X1] : c_Set_Oimage(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) = c_Set_Oinsert(hAPP(X0,c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Set_Oimage(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1)
| ~ spl0_104
| ~ spl0_356 ),
inference(resolution,[],[f5006,f1227]) ).
fof(f5006,plain,
( ! [X0,X1,X8,X7,X4] :
( ~ hBOOL(c_in(X1,X4,X0))
| c_Set_Oimage(X7,X4,X0,X8) = c_Set_Oinsert(hAPP(X7,X1),c_Set_Oimage(X7,X4,X0,X8),X8) )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f5005]) ).
fof(f16880,plain,
( spl0_615
| ~ spl0_104
| ~ spl0_545 ),
inference(avatar_split_clause,[],[f14077,f13909,f1226,f16878]) ).
fof(f16878,plain,
( spl0_615
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,X1),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,X1)))
| hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,X1),c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f13909,plain,
( spl0_545
<=> ! [X18,X31,X19,X0,X8,X23,X22,X20] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X8,X18),X20,tc_prod(X8,X18)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X18),c_Relation_Orel__comp(X19,X20,X0,X8,X18),tc_prod(X0,X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f14077,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,X1),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,X1)))
| hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,X1),c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,X1))) )
| ~ spl0_104
| ~ spl0_545 ),
inference(resolution,[],[f13910,f1227]) ).
fof(f13910,plain,
( ! [X31,X0,X18,X8,X19,X22,X23,X20] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X8,X18),X20,tc_prod(X8,X18)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X18),c_Relation_Orel__comp(X19,X20,X0,X8,X18),tc_prod(X0,X18))) )
| ~ spl0_545 ),
inference(avatar_component_clause,[],[f13909]) ).
fof(f16876,plain,
( spl0_614
| ~ spl0_348
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f15118,f8473,f4519,f16874]) ).
fof(f16874,plain,
( spl0_614
<=> ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f15118,plain,
( ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_348
| ~ spl0_450 ),
inference(resolution,[],[f8474,f4520]) ).
fof(f16867,plain,
( spl0_613
| ~ spl0_173
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3682,f3371,f1738,f16865]) ).
fof(f16865,plain,
( spl0_613
<=> ! [X2,X0,X1] : ~ c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f3682,plain,
( ! [X2,X0,X1] : ~ c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_173
| ~ spl0_294 ),
inference(resolution,[],[f3372,f1739]) ).
fof(f16863,plain,
( spl0_612
| ~ spl0_174
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3681,f3371,f1742,f16861]) ).
fof(f16861,plain,
( spl0_612
<=> ! [X2,X0,X1] : ~ c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f3681,plain,
( ! [X2,X0,X1] : ~ c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_174
| ~ spl0_294 ),
inference(resolution,[],[f3372,f1743]) ).
fof(f16859,plain,
( spl0_611
| ~ spl0_171
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3669,f3367,f1730,f16857]) ).
fof(f16857,plain,
( spl0_611
<=> ! [X2,X0,X1] : c_FunDef_Oin__rel(c_Transitive__Closure_Ortrancl(X0,X1),X2,X2,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f3669,plain,
( ! [X2,X0,X1] : c_FunDef_Oin__rel(c_Transitive__Closure_Ortrancl(X0,X1),X2,X2,X1,X1)
| ~ spl0_171
| ~ spl0_293 ),
inference(resolution,[],[f3368,f1731]) ).
fof(f16855,plain,
( spl0_610
| ~ spl0_55
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2595,f2172,f962,f16853]) ).
fof(f16853,plain,
( spl0_610
<=> ! [X0] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f2595,plain,
( ! [X0] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_55
| ~ spl0_213 ),
inference(resolution,[],[f2173,f963]) ).
fof(f16810,plain,
( spl0_609
| ~ spl0_345
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f15117,f8473,f4507,f16808]) ).
fof(f16808,plain,
( spl0_609
<=> ! [X0] :
( hBOOL(c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f4507,plain,
( spl0_345
<=> ! [X2,X4,X19,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f15117,plain,
( ! [X0] :
( hBOOL(c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_345
| ~ spl0_450 ),
inference(resolution,[],[f8474,f4508]) ).
fof(f4508,plain,
( ! [X2,X0,X1,X19,X4] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(X1,X4,X0))
| ~ c_Equiv__Relations_Oequiv(X4,X19,X0) )
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f4507]) ).
fof(f16806,plain,
( spl0_608
| ~ spl0_108
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1372,f1290,f1245,f16804]) ).
fof(f16804,plain,
( spl0_608
<=> ! [X0] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1245,plain,
( spl0_108
<=> ! [X4,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1290,plain,
( spl0_119
<=> ! [X0,X19] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1372,plain,
( ! [X0] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_108
| ~ spl0_119 ),
inference(superposition,[],[f1291,f1246]) ).
fof(f1246,plain,
( ! [X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X4,tc_fun(X0,tc_bool))
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1245]) ).
fof(f1291,plain,
( ! [X0,X19] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1290]) ).
fof(f16716,plain,
( spl0_607
| ~ spl0_104
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f13024,f8248,f1226,f16713]) ).
fof(f16713,plain,
( spl0_607
<=> c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Pair(c_ATP__Linkup_Osko__Relation__XconverseE__1__2(hAPP(v_P____,v_x),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_ATP__Linkup_Osko__Relation__XconverseE__1__1(hAPP(v_P____,v_x),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f8248,plain,
( spl0_429
<=> ! [X19,X0,X8,X45] :
( ~ hBOOL(c_in(X45,hAPP(c_Relation_Oconverse(X8,X0),X19),tc_prod(X0,X8)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XconverseE__1__2(X19,X45,X8,X0),c_ATP__Linkup_Osko__Relation__XconverseE__1__1(X19,X45,X8,X0),X0,X8) = X45 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f13024,plain,
( c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Pair(c_ATP__Linkup_Osko__Relation__XconverseE__1__2(hAPP(v_P____,v_x),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_ATP__Linkup_Osko__Relation__XconverseE__1__1(hAPP(v_P____,v_x),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_104
| ~ spl0_429 ),
inference(resolution,[],[f1227,f8249]) ).
fof(f8249,plain,
( ! [X0,X8,X19,X45] :
( ~ hBOOL(c_in(X45,hAPP(c_Relation_Oconverse(X8,X0),X19),tc_prod(X0,X8)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XconverseE__1__2(X19,X45,X8,X0),c_ATP__Linkup_Osko__Relation__XconverseE__1__1(X19,X45,X8,X0),X0,X8) = X45 )
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f8248]) ).
fof(f16567,plain,
( spl0_605
| ~ spl0_606
| ~ spl0_104
| ~ spl0_493 ),
inference(avatar_split_clause,[],[f13019,f11103,f1226,f16564,f16561]) ).
fof(f16561,plain,
( spl0_605
<=> ! [X0] :
( ~ hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| v_a____ = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f16564,plain,
( spl0_606
<=> c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f11103,plain,
( spl0_493
<=> ! [X19,X0,X8,X3,X2,X1] :
( X2 = X3
| ~ c_Relation_Osingle__valued(X19,X0,X8)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X8),X19,tc_prod(X0,X8)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X8),X19,tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f13019,plain,
( ! [X0] :
( ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| v_a____ = X0 )
| ~ spl0_104
| ~ spl0_493 ),
inference(resolution,[],[f1227,f11104]) ).
fof(f11104,plain,
( ! [X2,X3,X0,X1,X8,X19] :
( ~ hBOOL(c_in(c_Pair(X1,X3,X0,X8),X19,tc_prod(X0,X8)))
| ~ c_Relation_Osingle__valued(X19,X0,X8)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X8),X19,tc_prod(X0,X8)))
| X2 = X3 )
| ~ spl0_493 ),
inference(avatar_component_clause,[],[f11103]) ).
fof(f16559,plain,
( spl0_604
| spl0_103
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f5557,f5013,f1219,f16557]) ).
fof(f16557,plain,
( spl0_604
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P_H____,v_x),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,hAPP(v_P_H____,v_x),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f5013,plain,
( spl0_358
<=> ! [X5,X23,X0,X6] :
( hBOOL(c_in(X23,X6,X0))
| c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X23,X5,X0),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f5557,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P_H____,v_x),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,hAPP(v_P_H____,v_x),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| spl0_103
| ~ spl0_358 ),
inference(resolution,[],[f5014,f1220]) ).
fof(f5014,plain,
( ! [X0,X6,X5,X23] :
( hBOOL(c_in(X23,X6,X0))
| c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X23,X5,X0),X6,tc_fun(X0,tc_bool)) )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f5013]) ).
fof(f16555,plain,
( spl0_603
| spl0_103
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f5501,f5009,f1219,f16553]) ).
fof(f16553,plain,
( spl0_603
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(hAPP(v_P_H____,v_x),X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(v_P_H____,v_x),c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f5009,plain,
( spl0_357
<=> ! [X4,X0,X5,X23] :
( hBOOL(c_in(X23,X4,X0))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f5501,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(hAPP(v_P_H____,v_x),X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(v_P_H____,v_x),c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| spl0_103
| ~ spl0_357 ),
inference(resolution,[],[f5010,f1220]) ).
fof(f5010,plain,
( ! [X0,X4,X5,X23] :
( hBOOL(c_in(X23,X4,X0))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) )
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f5009]) ).
fof(f16521,plain,
( spl0_602
| ~ spl0_104
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3159,f2972,f1226,f16519]) ).
fof(f16519,plain,
( spl0_602
<=> ! [X0] :
( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f2972,plain,
( spl0_249
<=> ! [X34,X0,X14,X1] :
( ~ c_Wellfounded_Owf(X14,X0)
| ~ hBOOL(c_in(X1,X34,X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X34,X14,X0),X34,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f3159,plain,
( ! [X0] :
( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_104
| ~ spl0_249 ),
inference(resolution,[],[f2973,f1227]) ).
fof(f2973,plain,
( ! [X0,X1,X14,X34] :
( ~ hBOOL(c_in(X1,X34,X0))
| ~ c_Wellfounded_Owf(X14,X0)
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X34,X14,X0),X34,X0)) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2972]) ).
fof(f16517,plain,
( spl0_601
| ~ spl0_104
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3145,f2968,f1226,f16515]) ).
fof(f16515,plain,
( spl0_601
<=> ! [X0] :
( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f2968,plain,
( spl0_248
<=> ! [X11,X34,X0,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(X11,X34,X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X34,X19,X0),X34,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3145,plain,
( ! [X0] :
( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_104
| ~ spl0_248 ),
inference(resolution,[],[f2969,f1227]) ).
fof(f2969,plain,
( ! [X0,X11,X19,X34] :
( ~ hBOOL(c_in(X11,X34,X0))
| ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X34,X19,X0),X34,X0)) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2968]) ).
fof(f16513,plain,
( spl0_600
| ~ spl0_146
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3670,f3367,f1486,f16511]) ).
fof(f16511,plain,
( spl0_600
<=> ! [X0,X1] : c_FunDef_Oin__rel(c_Relation_OId(X0),X1,X1,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f3670,plain,
( ! [X0,X1] : c_FunDef_Oin__rel(c_Relation_OId(X0),X1,X1,X0,X0)
| ~ spl0_146
| ~ spl0_293 ),
inference(resolution,[],[f3368,f1487]) ).
fof(f16472,plain,
( spl0_599
| spl0_103
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5836,f5805,f1219,f16469]) ).
fof(f16469,plain,
( spl0_599
<=> hAPP(v_P_H____,v_x) = c_HOL_Ominus__class_Ominus(hAPP(v_P_H____,v_x),c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f5805,plain,
( spl0_377
<=> ! [X4,X0,X1] :
( c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X4
| hBOOL(c_in(X1,X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f5836,plain,
( hAPP(v_P_H____,v_x) = c_HOL_Ominus__class_Ominus(hAPP(v_P_H____,v_x),c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| spl0_103
| ~ spl0_377 ),
inference(resolution,[],[f5806,f1220]) ).
fof(f5806,plain,
( ! [X0,X1,X4] :
( hBOOL(c_in(X1,X4,X0))
| c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X4 )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f5805]) ).
fof(f16437,plain,
( ~ spl0_598
| ~ spl0_88
| spl0_595 ),
inference(avatar_split_clause,[],[f16423,f16419,f1125,f16434]) ).
fof(f16434,plain,
( spl0_598
<=> c_Relation_Osym(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1125,plain,
( spl0_88
<=> ! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| c_Relation_Osym(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f16419,plain,
( spl0_595
<=> c_Relation_Osym(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f16423,plain,
( ~ c_Relation_Osym(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_88
| spl0_595 ),
inference(resolution,[],[f16421,f1126]) ).
fof(f1126,plain,
( ! [X0,X19] :
( c_Relation_Osym(hAPP(c_Relation_Oconverse(X0,X0),X19),X0)
| ~ c_Relation_Osym(X19,X0) )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1125]) ).
fof(f16421,plain,
( ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_595 ),
inference(avatar_component_clause,[],[f16419]) ).
fof(f16432,plain,
( ~ spl0_596
| spl0_597
| ~ spl0_104
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f13016,f7474,f1226,f16429,f16425]) ).
fof(f7474,plain,
( spl0_425
<=> ! [X19,X0,X23,X22] :
( ~ hBOOL(c_in(X22,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f13016,plain,
( hBOOL(c_in(v_b____,c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_a____,c_Wellfounded_Oacc(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_104
| ~ spl0_425 ),
inference(resolution,[],[f1227,f7475]) ).
fof(f7475,plain,
( ! [X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(X22,c_Wellfounded_Oacc(X19,X0),X0)) )
| ~ spl0_425 ),
inference(avatar_component_clause,[],[f7474]) ).
fof(f16422,plain,
( spl0_593
| ~ spl0_595
| ~ spl0_104
| ~ spl0_424 ),
inference(avatar_split_clause,[],[f13015,f7470,f1226,f16419,f16403]) ).
fof(f7470,plain,
( spl0_424
<=> ! [X19,X0,X2,X1] :
( ~ c_Relation_Osym(X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f13015,plain,
( ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_104
| ~ spl0_424 ),
inference(resolution,[],[f1227,f7471]) ).
fof(f7471,plain,
( ! [X2,X0,X1,X19] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_Relation_Osym(X19,X0)
| hBOOL(c_in(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0))) )
| ~ spl0_424 ),
inference(avatar_component_clause,[],[f7470]) ).
fof(f16410,plain,
( ~ spl0_593
| ~ spl0_594
| ~ spl0_104
| ~ spl0_423 ),
inference(avatar_split_clause,[],[f13014,f7466,f1226,f16407,f16403]) ).
fof(f16407,plain,
( spl0_594
<=> c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f7466,plain,
( spl0_423
<=> ! [X19,X0,X23,X1] :
( ~ c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(c_Pair(X23,X1,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X23,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f13014,plain,
( ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_104
| ~ spl0_423 ),
inference(resolution,[],[f1227,f7467]) ).
fof(f7467,plain,
( ! [X0,X1,X19,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X1,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X23,X0,X0),X19,tc_prod(X0,X0))) )
| ~ spl0_423 ),
inference(avatar_component_clause,[],[f7466]) ).
fof(f16401,plain,
( spl0_592
| ~ spl0_104
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f5640,f5037,f1226,f16399]) ).
fof(f16399,plain,
( spl0_592
<=> ! [X0,X1] : c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f5037,plain,
( spl0_364
<=> ! [X31,X4,X0,X8,X1] :
( ~ hBOOL(c_in(X1,X4,X0))
| c_Set_Oimage(c_COMBK(X31,X8,X0),X4,X0,X8) = c_Set_Oinsert(X31,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f5640,plain,
( ! [X0,X1] : c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1)
| ~ spl0_104
| ~ spl0_364 ),
inference(resolution,[],[f5038,f1227]) ).
fof(f5038,plain,
( ! [X31,X0,X1,X8,X4] :
( ~ hBOOL(c_in(X1,X4,X0))
| c_Set_Oimage(c_COMBK(X31,X8,X0),X4,X0,X8) = c_Set_Oinsert(X31,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8) )
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f5037]) ).
fof(f16388,plain,
( spl0_591
| ~ spl0_344
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f15116,f8473,f4503,f16386]) ).
fof(f16386,plain,
( spl0_591
<=> ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f15116,plain,
( ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_344
| ~ spl0_450 ),
inference(resolution,[],[f8474,f4504]) ).
fof(f16384,plain,
( spl0_590
| ~ spl0_214
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f4082,f3759,f2176,f16382]) ).
fof(f16382,plain,
( spl0_590
<=> ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| ~ c_Wellfounded_Owf(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f3759,plain,
( spl0_310
<=> ! [X0,X19] :
( c_Relation_Oirrefl(X19,X0)
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X19,X0),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f4082,plain,
( ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_214
| ~ spl0_310 ),
inference(resolution,[],[f3760,f2177]) ).
fof(f3760,plain,
( ! [X0,X19] :
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X19,X0),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X19,X0),X0,X0),X19,tc_prod(X0,X0)))
| c_Relation_Oirrefl(X19,X0) )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f3759]) ).
fof(f16380,plain,
( spl0_589
| ~ spl0_213
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2599,f2176,f2172,f16378]) ).
fof(f16378,plain,
( spl0_589
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| ~ c_Nitpick_Orefl_H(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f2599,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| ~ c_Nitpick_Orefl_H(X0,X1) )
| ~ spl0_213
| ~ spl0_214 ),
inference(resolution,[],[f2177,f2173]) ).
fof(f16376,plain,
( spl0_588
| ~ spl0_212
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2594,f2172,f2168,f16374]) ).
fof(f16374,plain,
( spl0_588
<=> ! [X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f2594,plain,
( ! [X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1) )
| ~ spl0_212
| ~ spl0_213 ),
inference(resolution,[],[f2173,f2169]) ).
fof(f16345,plain,
( spl0_587
| ~ spl0_104
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1397,f1306,f1226,f16342]) ).
fof(f16342,plain,
( spl0_587
<=> hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)) = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1397,plain,
( hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)) = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_104
| ~ spl0_123 ),
inference(resolution,[],[f1227,f1307]) ).
fof(f16335,plain,
( spl0_586
| ~ spl0_171
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4103,f3763,f1730,f16333]) ).
fof(f16333,plain,
( spl0_586
<=> ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f3763,plain,
( spl0_311
<=> ! [X0,X19] :
( c_Nitpick_Orefl_H(X19,X0)
| ~ hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X19,X0),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f4103,plain,
( ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_171
| ~ spl0_311 ),
inference(resolution,[],[f3764,f1731]) ).
fof(f3764,plain,
( ! [X0,X19] :
( ~ hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X19,X0),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X19,X0),X0,X0),X19,tc_prod(X0,X0)))
| c_Nitpick_Orefl_H(X19,X0) )
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f3763]) ).
fof(f16309,plain,
( spl0_585
| ~ spl0_104
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f13020,f7478,f1226,f16307]) ).
fof(f16307,plain,
( spl0_585
<=> ! [X0] :
( hBOOL(c_in(v_a____,c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f7478,plain,
( spl0_426
<=> ! [X4,X19,X0,X22,X23,X8] :
( ~ hBOOL(c_in(X23,X4,X0))
| hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X0,X8),X8))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f13020,plain,
( ! [X0] :
( hBOOL(c_in(v_a____,c_Relation_OImage(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)) )
| ~ spl0_104
| ~ spl0_426 ),
inference(resolution,[],[f1227,f7479]) ).
fof(f7479,plain,
( ! [X0,X8,X19,X4,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8)))
| hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X0,X8),X8))
| ~ hBOOL(c_in(X23,X4,X0)) )
| ~ spl0_426 ),
inference(avatar_component_clause,[],[f7478]) ).
fof(f16299,plain,
( spl0_584
| ~ spl0_104
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f6977,f6147,f1226,f16297]) ).
fof(f16297,plain,
( spl0_584
<=> ! [X0,X1] : hAPP(X0,v_b____) = hAPP(c_Recdef_Ocut(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),v_a____,tc_Arrow__Order__Mirabelle_Oalt,X1),v_b____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f6147,plain,
( spl0_394
<=> ! [X19,X0,X8,X23,X1,X7] :
( ~ hBOOL(c_in(c_Pair(X1,X23,X0,X0),X19,tc_prod(X0,X0)))
| hAPP(X7,X1) = hAPP(c_Recdef_Ocut(X7,X19,X23,X0,X8),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f6977,plain,
( ! [X0,X1] : hAPP(X0,v_b____) = hAPP(c_Recdef_Ocut(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),v_a____,tc_Arrow__Order__Mirabelle_Oalt,X1),v_b____)
| ~ spl0_104
| ~ spl0_394 ),
inference(resolution,[],[f6148,f1227]) ).
fof(f6148,plain,
( ! [X0,X1,X8,X19,X7,X23] :
( ~ hBOOL(c_in(c_Pair(X1,X23,X0,X0),X19,tc_prod(X0,X0)))
| hAPP(X7,X1) = hAPP(c_Recdef_Ocut(X7,X19,X23,X0,X8),X1) )
| ~ spl0_394 ),
inference(avatar_component_clause,[],[f6147]) ).
fof(f16295,plain,
( spl0_583
| ~ spl0_146
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4104,f3763,f1486,f16293]) ).
fof(f16293,plain,
( spl0_583
<=> ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f4104,plain,
( ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0)
| ~ spl0_146
| ~ spl0_311 ),
inference(resolution,[],[f3764,f1487]) ).
fof(f16289,plain,
( spl0_474
| ~ spl0_81
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f15136,f8473,f1070,f9250]) ).
fof(f9250,plain,
( spl0_474
<=> hBOOL(hAPP(hAPP(v_P____,v_x),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f15136,plain,
( hBOOL(hAPP(hAPP(v_P____,v_x),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_81
| ~ spl0_450 ),
inference(resolution,[],[f8474,f1071]) ).
fof(f16288,plain,
( spl0_582
| ~ spl0_104
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4888,f4523,f1226,f16286]) ).
fof(f16286,plain,
( spl0_582
<=> ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f4888,plain,
( ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_104
| ~ spl0_349 ),
inference(resolution,[],[f4524,f1227]) ).
fof(f16284,plain,
( spl0_581
| ~ spl0_104
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4869,f4519,f1226,f16282]) ).
fof(f16282,plain,
( spl0_581
<=> ! [X0] :
( hBOOL(c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f4869,plain,
( ! [X0] :
( hBOOL(c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_104
| ~ spl0_348 ),
inference(resolution,[],[f4520,f1227]) ).
fof(f16280,plain,
( spl0_580
| ~ spl0_104
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f4823,f4507,f1226,f16278]) ).
fof(f16278,plain,
( spl0_580
<=> ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f4823,plain,
( ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_104
| ~ spl0_345 ),
inference(resolution,[],[f4508,f1227]) ).
fof(f16276,plain,
( spl0_579
| ~ spl0_104
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4804,f4503,f1226,f16274]) ).
fof(f16274,plain,
( spl0_579
<=> ! [X0] :
( hBOOL(c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f4804,plain,
( ! [X0] :
( hBOOL(c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_104
| ~ spl0_344 ),
inference(resolution,[],[f4504,f1227]) ).
fof(f16226,plain,
spl0_578,
inference(avatar_split_clause,[],[f730,f16224]) ).
fof(f16224,plain,
( spl0_578
<=> ! [X19,X0,X23,X22] :
( ~ hBOOL(c_in(X22,c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0))
| ~ hBOOL(c_in(X23,c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0))
| ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X19,X0)
| ~ c_Relation_Oantisym(X19,X0)
| X22 = X23
| c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f730,plain,
! [X0,X19,X22,X23] :
( ~ hBOOL(c_in(X22,c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0))
| ~ hBOOL(c_in(X23,c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0))
| ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X19,X0)
| ~ c_Relation_Oantisym(X19,X0)
| X22 = X23
| c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ),
inference(forward_demodulation,[],[f729,f163]) ).
fof(f163,axiom,
! [X0,X8,X4,X5] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X0,X8),tc_bool)),X0,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X4,X0,X8),c_Relation_ODomain(X5,X0,X8),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
fof(f729,plain,
! [X0,X19,X22,X23] :
( ~ hBOOL(c_in(X23,c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0))
| ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X19,X0)
| ~ c_Relation_Oantisym(X19,X0)
| X22 = X23
| ~ hBOOL(c_in(X22,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),X0))
| c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ),
inference(forward_demodulation,[],[f728,f163]) ).
fof(f728,plain,
! [X0,X19,X22,X23] :
( ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X19,X0)
| ~ c_Relation_Oantisym(X19,X0)
| X22 = X23
| ~ hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X22,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),X0))
| c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ),
inference(forward_demodulation,[],[f704,f163]) ).
fof(f704,plain,
! [X0,X19,X22,X23] :
( ~ c_Relation_Oantisym(X19,X0)
| X22 = X23
| ~ c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),X19,X0)
| ~ hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X22,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),X0))
| c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ),
inference(definition_unfolding,[],[f382,f642,f642,f642]) ).
fof(f642,plain,
! [X0,X19] : c_Relation_OField(X19,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f232,f507]) ).
fof(f507,axiom,
! [X0,X8,X19] : c_Relation_ORange(X19,X8,X0) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__def_0) ).
fof(f232,axiom,
! [X0,X19] : c_Relation_OField(X19,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ORange(X19,X0,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Field__def_0) ).
fof(f382,axiom,
! [X0,X19,X22,X23] :
( ~ c_Relation_Oantisym(X19,X0)
| X22 = X23
| ~ c_Relation_Orefl__on(c_Relation_OField(X19,X0),X19,X0)
| ~ hBOOL(c_in(X23,c_Relation_OField(X19,X0),X0))
| ~ hBOOL(c_in(X22,c_Relation_OField(X19,X0),X0))
| c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Refl__antisym__eq__Image1__Image1__iff_0) ).
fof(f16063,plain,
( spl0_577
| ~ spl0_383
| ~ spl0_401
| ~ spl0_576 ),
inference(avatar_split_clause,[],[f16059,f16053,f7067,f6102,f16061]) ).
fof(f16061,plain,
( spl0_577
<=> ! [X20,X0,X19] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),X20),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),tc_fun(X0,tc_bool)) = c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))),tc_fun(tc_prod(X0,X0),tc_bool)),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f6102,plain,
( spl0_383
<=> ! [X5,X4,X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f7067,plain,
( spl0_401
<=> ! [X4,X0,X5,X8] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X0,X8),tc_bool)),X0,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X4,X0,X8),c_Relation_ODomain(X5,X0,X8),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f16053,plain,
( spl0_576
<=> ! [X20,X0,X19] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))),X0,X0),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X20,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X20),X0,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f16059,plain,
( ! [X0,X19,X20] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),X20),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),tc_fun(X0,tc_bool)) = c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))),tc_fun(tc_prod(X0,X0),tc_bool)),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0)
| ~ spl0_383
| ~ spl0_401
| ~ spl0_576 ),
inference(forward_demodulation,[],[f16058,f6103]) ).
fof(f6103,plain,
( ! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f6102]) ).
fof(f16058,plain,
( ! [X0,X19,X20] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),X20),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),tc_fun(X0,tc_bool)) = c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),hAPP(c_Relation_Oconverse(X0,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0)
| ~ spl0_401
| ~ spl0_576 ),
inference(forward_demodulation,[],[f16057,f7068]) ).
fof(f7068,plain,
( ! [X0,X8,X4,X5] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X0,X8),tc_bool)),X0,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X4,X0,X8),c_Relation_ODomain(X5,X0,X8),tc_fun(X0,tc_bool))
| ~ spl0_401 ),
inference(avatar_component_clause,[],[f7067]) ).
fof(f16057,plain,
( ! [X0,X19,X20] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))),X0,X0),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),X20),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),tc_fun(X0,tc_bool))
| ~ spl0_401
| ~ spl0_576 ),
inference(forward_demodulation,[],[f16056,f7068]) ).
fof(f16056,plain,
( ! [X0,X19,X20] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))),X0,X0),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),X20),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),tc_fun(X0,tc_bool))
| ~ spl0_401
| ~ spl0_576 ),
inference(forward_demodulation,[],[f16054,f7068]) ).
fof(f16054,plain,
( ! [X0,X19,X20] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))),X0,X0),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X20,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X20),X0,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_576 ),
inference(avatar_component_clause,[],[f16053]) ).
fof(f16055,plain,
spl0_576,
inference(avatar_split_clause,[],[f660,f16053]) ).
fof(f660,plain,
! [X0,X19,X20] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))),X0,X0),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X20,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X20),X0,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f148,f642,f642,f642]) ).
fof(f148,axiom,
! [X0,X19,X20] : c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(X19,X0),c_Relation_OField(X20,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Field__Un_0) ).
fof(f16009,plain,
spl0_575,
inference(avatar_split_clause,[],[f446,f16007]) ).
fof(f16007,plain,
( spl0_575
<=> ! [X19,X0,X3,X2,X1] :
( ~ c_Relation_Osingle__valued(X19,X0,X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X2,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X3,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f446,axiom,
! [X2,X3,X0,X1,X19] :
( ~ c_Relation_Osingle__valued(X19,X0,X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X2,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X3,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
fof(f15947,plain,
spl0_574,
inference(avatar_split_clause,[],[f700,f15945]) ).
fof(f15945,plain,
( spl0_574
<=> ! [X31,X19,X0,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f700,plain,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f549,f506,f506,f506]) ).
fof(f506,axiom,
! [X0,X19] : c_Transitive__Closure_Otrancl(X19,X0) = c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
fof(f549,axiom,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
fof(f15594,plain,
( spl0_573
| ~ spl0_153
| ~ spl0_161
| ~ spl0_453
| ~ spl0_465
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f15590,f15586,f9214,f9065,f1689,f1656,f15592]) ).
fof(f15592,plain,
( spl0_573
<=> ! [X5,X4,X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X4,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f1656,plain,
( spl0_153
<=> ! [X5,X4,X0] : c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1689,plain,
( spl0_161
<=> ! [X5,X4,X0] : c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f9065,plain,
( spl0_453
<=> ! [X5,X4,X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f9214,plain,
( spl0_465
<=> ! [X5,X4,X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f15586,plain,
( spl0_572
<=> ! [X5,X4,X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X4,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f15590,plain,
( ! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X4,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_153
| ~ spl0_161
| ~ spl0_453
| ~ spl0_465
| ~ spl0_572 ),
inference(forward_demodulation,[],[f15589,f9360]) ).
fof(f9360,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_153
| ~ spl0_453 ),
inference(superposition,[],[f9066,f1657]) ).
fof(f1657,plain,
( ! [X0,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,X4,tc_fun(X0,tc_bool))
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1656]) ).
fof(f9066,plain,
( ! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f9065]) ).
fof(f15589,plain,
( ! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X4,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_161
| ~ spl0_465
| ~ spl0_572 ),
inference(forward_demodulation,[],[f15587,f10075]) ).
fof(f10075,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_161
| ~ spl0_465 ),
inference(superposition,[],[f9215,f1690]) ).
fof(f1690,plain,
( ! [X0,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,tc_fun(X0,tc_bool))
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1689]) ).
fof(f9215,plain,
( ! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_465 ),
inference(avatar_component_clause,[],[f9214]) ).
fof(f15587,plain,
( ! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X4,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_572 ),
inference(avatar_component_clause,[],[f15586]) ).
fof(f15588,plain,
spl0_572,
inference(avatar_split_clause,[],[f715,f15586]) ).
fof(f715,plain,
! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X4,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f128,f119]) ).
fof(f119,axiom,
! [X0,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f128,axiom,
! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
fof(f15432,plain,
( spl0_454
| ~ spl0_293
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f15135,f8473,f3367,f9069]) ).
fof(f9069,plain,
( spl0_454
<=> c_FunDef_Oin__rel(hAPP(v_P____,v_x),v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f15135,plain,
( c_FunDef_Oin__rel(hAPP(v_P____,v_x),v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_293
| ~ spl0_450 ),
inference(resolution,[],[f8474,f3368]) ).
fof(f15431,plain,
spl0_571,
inference(avatar_split_clause,[],[f699,f15429]) ).
fof(f15429,plain,
( spl0_571
<=> ! [X19,X0,X3,X1] :
( hBOOL(c_in(c_Pair(X1,X3,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X19,X1,X3,X0),X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f699,plain,
! [X3,X0,X1,X19] :
( hBOOL(c_in(c_Pair(X1,X3,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X19,X1,X3,X0),X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f326,f506,f506]) ).
fof(f326,axiom,
! [X3,X0,X1,X19] :
( hBOOL(c_in(c_Pair(X1,X3,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X19,X1,X3,X0),X3,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
fof(f15427,plain,
spl0_570,
inference(avatar_split_clause,[],[f698,f15425]) ).
fof(f15425,plain,
( spl0_570
<=> ! [X19,X0,X23,X22] :
( hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X23,X22,X19,X0),X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f698,plain,
! [X0,X19,X22,X23] :
( hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X23,X22,X19,X0),X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f331,f506,f506]) ).
fof(f331,axiom,
! [X0,X19,X22,X23] :
( hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X23,X22,X19,X0),X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclE_0) ).
fof(f15352,plain,
spl0_569,
inference(avatar_split_clause,[],[f695,f15350]) ).
fof(f15350,plain,
( spl0_569
<=> ! [X38,X37,X19] :
( hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),X19,tc_prod(t_a,t_a)))
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(X37,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X37,X38,X19),t_a,t_a),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f695,plain,
! [X38,X37,X19] :
( hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),X19,tc_prod(t_a,t_a)))
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(X37,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X37,X38,X19),t_a,t_a),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a))) ),
inference(definition_unfolding,[],[f328,f506,f506]) ).
fof(f328,axiom,
! [X38,X37,X19] :
( hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),X19,tc_prod(t_a,t_a)))
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Transitive__Closure_Otrancl(X19,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(X37,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X37,X38,X19),t_a,t_a),c_Transitive__Closure_Otrancl(X19,t_a),tc_prod(t_a,t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
fof(f15253,plain,
spl0_568,
inference(avatar_split_clause,[],[f702,f15251]) ).
fof(f15251,plain,
( spl0_568
<=> ! [X19,X0,X3,X2,X1] :
( ~ hBOOL(c_in(c_Pair(X2,X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f702,plain,
! [X2,X3,X0,X1,X19] :
( ~ hBOOL(c_in(c_Pair(X2,X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f449,f506,f506]) ).
fof(f449,axiom,
! [X2,X3,X0,X1,X19] :
( ~ hBOOL(c_in(c_Pair(X2,X3,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
fof(f15249,plain,
spl0_567,
inference(avatar_split_clause,[],[f701,f15247]) ).
fof(f15247,plain,
( spl0_567
<=> ! [X31,X19,X0,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f701,plain,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f448,f506,f506]) ).
fof(f448,axiom,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
fof(f15114,plain,
spl0_566,
inference(avatar_split_clause,[],[f691,f15112]) ).
fof(f15112,plain,
( spl0_566
<=> ! [X31,X19,X0,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f691,plain,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f527,f506,f506]) ).
fof(f527,axiom,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
fof(f15110,plain,
spl0_565,
inference(avatar_split_clause,[],[f690,f15108]) ).
fof(f15108,plain,
( spl0_565
<=> ! [X31,X19,X0,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f690,plain,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f526,f506,f506]) ).
fof(f526,axiom,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
fof(f15034,plain,
spl0_564,
inference(avatar_split_clause,[],[f383,f15032]) ).
fof(f15032,plain,
( spl0_564
<=> ! [X4,X19,X0,X23,X22] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X22,X4,X0))
| hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_lessequals(c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f383,axiom,
! [X0,X19,X4,X22,X23] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X22,X4,X0))
| hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ c_lessequals(c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
fof(f15030,plain,
spl0_563,
inference(avatar_split_clause,[],[f380,f15028]) ).
fof(f15028,plain,
( spl0_563
<=> ! [X4,X19,X0,X2,X1] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X2,X4,X0))
| ~ hBOOL(c_in(X1,X4,X0))
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X19,X0) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f380,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X2,X4,X0))
| ~ hBOOL(c_in(X1,X4,X0))
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X19,X0) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).
fof(f15026,plain,
spl0_562,
inference(avatar_split_clause,[],[f379,f15024]) ).
fof(f15024,plain,
( spl0_562
<=> ! [X2,X4,X19,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(X2,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X19,X0) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f379,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(X2,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X19,X0) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).
fof(f14982,plain,
spl0_561,
inference(avatar_split_clause,[],[f384,f14980]) ).
fof(f14980,plain,
( spl0_561
<=> ! [X4,X19,X0,X23,X22,X1] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f384,axiom,
! [X0,X1,X19,X4,X22,X23] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
fof(f14704,plain,
spl0_560,
inference(avatar_split_clause,[],[f714,f14702]) ).
fof(f14702,plain,
( spl0_560
<=> ! [X19,X0,X23,X22] : c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X23,c_Relation_ODomain(X19,X0,X0),X0),c_Set_Oinsert(X22,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f714,plain,
! [X0,X19,X22,X23] : c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X23,c_Relation_ODomain(X19,X0,X0),X0),c_Set_Oinsert(X22,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),X0),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f713,f339]) ).
fof(f339,axiom,
! [X0,X8,X19,X22,X23] : c_Relation_ODomain(c_Set_Oinsert(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8)),X0,X8) = c_Set_Oinsert(X23,c_Relation_ODomain(X19,X0,X8),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
fof(f713,plain,
! [X0,X19,X22,X23] : c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)),X0,X0),c_Set_Oinsert(X22,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),X0),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f712,f661]) ).
fof(f661,plain,
! [X0,X8,X19,X22,X23] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),c_Set_Oinsert(c_Pair(X23,X22,X8,X0),X19,tc_prod(X8,X0))),X0,X8) = c_Set_Oinsert(X22,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),X0),
inference(definition_unfolding,[],[f341,f507,f507]) ).
fof(f341,axiom,
! [X0,X8,X19,X22,X23] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X23,X22,X8,X0),X19,tc_prod(X8,X0)),X8,X0) = c_Set_Oinsert(X22,c_Relation_ORange(X19,X8,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__insert_0) ).
fof(f712,plain,
! [X0,X19,X22,X23] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)),X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0))),X0,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),X0),X0),
inference(forward_demodulation,[],[f711,f163]) ).
fof(f711,plain,
! [X0,X19,X22,X23] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)),X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0))),X0,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),X0),X0),
inference(forward_demodulation,[],[f710,f164]) ).
fof(f164,axiom,
! [X0,X4,X23] : c_Set_Oinsert(X23,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
fof(f710,plain,
! [X0,X19,X22,X23] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)),X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0))),X0,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0),
inference(forward_demodulation,[],[f664,f44]) ).
fof(f44,axiom,
! [X0,X6,X5,X23] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X23,X5,X0),X6,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
fof(f664,plain,
! [X0,X19,X22,X23] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)),X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0))),X0,X0),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f129,f642,f642]) ).
fof(f129,axiom,
! [X0,X19,X22,X23] : c_Relation_OField(c_Set_Oinsert(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),c_Relation_OField(X19,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Field__insert_0) ).
fof(f14700,plain,
spl0_559,
inference(avatar_split_clause,[],[f697,f14698]) ).
fof(f14698,plain,
( spl0_559
<=> ! [X19,X0,X23,X22] :
( hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X23,X22,X19,X0),X22,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f697,plain,
! [X0,X19,X22,X23] :
( hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X23,X22,X19,X0),X22,X0,X0),X19,tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f330,f506]) ).
fof(f330,axiom,
! [X0,X19,X22,X23] :
( hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X23,X22,X19,X0),X22,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclE_1) ).
fof(f14696,plain,
spl0_558,
inference(avatar_split_clause,[],[f696,f14694]) ).
fof(f14694,plain,
( spl0_558
<=> ! [X19,X0,X3,X1] :
( hBOOL(c_in(c_Pair(X1,X3,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X19,X1,X3,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f696,plain,
! [X3,X0,X1,X19] :
( hBOOL(c_in(c_Pair(X1,X3,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X19,X1,X3,X0),X0,X0),X19,tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f333,f506]) ).
fof(f333,axiom,
! [X3,X0,X1,X19] :
( hBOOL(c_in(c_Pair(X1,X3,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X19,X1,X3,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
fof(f14639,plain,
spl0_557,
inference(avatar_split_clause,[],[f694,f14637]) ).
fof(f14637,plain,
( spl0_557
<=> ! [X38,X37,X19] :
( hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),X19,tc_prod(t_a,t_a)))
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X37,X38,X19),X38,t_a,t_a),X19,tc_prod(t_a,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f694,plain,
! [X38,X37,X19] :
( hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),X19,tc_prod(t_a,t_a)))
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X37,X38,X19),X38,t_a,t_a),X19,tc_prod(t_a,t_a))) ),
inference(definition_unfolding,[],[f334,f506]) ).
fof(f334,axiom,
! [X38,X37,X19] :
( hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),X19,tc_prod(t_a,t_a)))
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Transitive__Closure_Otrancl(X19,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X37,X38,X19),X38,t_a,t_a),X19,tc_prod(t_a,t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
fof(f14635,plain,
spl0_556,
inference(avatar_split_clause,[],[f417,f14633]) ).
fof(f14633,plain,
( spl0_556
<=> ! [X4,X19,X0,X23,X22] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X22,X4,X0))
| hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f417,axiom,
! [X0,X19,X4,X22,X23] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X22,X4,X0))
| hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
fof(f14517,plain,
spl0_555,
inference(avatar_split_clause,[],[f719,f14515]) ).
fof(f14515,plain,
( spl0_555
<=> ! [X20,X0,X19] :
( c_lessequals(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),X20),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),tc_fun(X0,tc_bool))
| ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f719,plain,
! [X0,X19,X20] :
( c_lessequals(c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),X20),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),tc_fun(X0,tc_bool))
| ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)) ),
inference(forward_demodulation,[],[f718,f163]) ).
fof(f718,plain,
! [X0,X19,X20] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X20,hAPP(c_Relation_Oconverse(X0,X0),X20),tc_fun(tc_prod(X0,X0),tc_bool)),X0,X0),tc_fun(X0,tc_bool))
| ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)) ),
inference(forward_demodulation,[],[f673,f163]) ).
fof(f673,plain,
! [X0,X19,X20] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0),tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X20,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X20),X0,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f228,f642,f642]) ).
fof(f228,axiom,
! [X0,X19,X20] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Relation_OField(X19,X0),c_Relation_OField(X20,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mono__Field_0) ).
fof(f14513,plain,
spl0_554,
inference(avatar_split_clause,[],[f692,f14511]) ).
fof(f14511,plain,
( spl0_554
<=> ! [X31,X19,X0,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f692,plain,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f442,f506]) ).
fof(f442,axiom,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
fof(f14456,plain,
spl0_553,
inference(avatar_split_clause,[],[f381,f14454]) ).
fof(f381,axiom,
! [X0,X19,X4,X22,X23] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| c_lessequals(c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X19,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
fof(f14298,plain,
spl0_552,
inference(avatar_split_clause,[],[f689,f14296]) ).
fof(f689,plain,
! [X31,X0,X14,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X14,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X14,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f548,f506]) ).
fof(f548,axiom,
! [X31,X0,X14,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X14,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X14,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Otrancl(X14,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
fof(f14294,plain,
( spl0_551
| ~ spl0_81
| ~ spl0_540 ),
inference(avatar_split_clause,[],[f13996,f13785,f1070,f14291]) ).
fof(f14291,plain,
( spl0_551
<=> hBOOL(hAPP(c_Relation_ODomain(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f13785,plain,
( spl0_540
<=> hBOOL(c_in(v_a____,c_Relation_ODomain(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f13996,plain,
( hBOOL(hAPP(c_Relation_ODomain(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____))
| ~ spl0_81
| ~ spl0_540 ),
inference(resolution,[],[f13787,f1071]) ).
fof(f13787,plain,
( hBOOL(c_in(v_a____,c_Relation_ODomain(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_540 ),
inference(avatar_component_clause,[],[f13785]) ).
fof(f14289,plain,
spl0_550,
inference(avatar_split_clause,[],[f277,f14287]) ).
fof(f14287,plain,
( spl0_550
<=> ! [X23,X19,X0,X12,X22] :
( ~ hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X22))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X12,X23,X19,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X12,X23,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f277,axiom,
! [X0,X19,X22,X12,X23] :
( ~ hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X22))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X12,X23,X19,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X12,X23,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
fof(f14285,plain,
spl0_549,
inference(avatar_split_clause,[],[f276,f14283]) ).
fof(f14283,plain,
( spl0_549
<=> ! [X23,X19,X0,X12,X22] :
( ~ hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X12,X22,X19,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X12,X22,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f276,axiom,
! [X0,X19,X22,X12,X23] :
( ~ hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X12,X22,X19,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X12,X22,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).
fof(f14125,plain,
spl0_548,
inference(avatar_split_clause,[],[f663,f14123]) ).
fof(f14123,plain,
( spl0_548
<=> ! [X4,X0,X5,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X4),X0,X8),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X5),X0,X8),tc_fun(X0,tc_bool)),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(tc_prod(X8,X0),tc_bool))),X0,X8),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f663,plain,
! [X0,X8,X4,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X4),X0,X8),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X5),X0,X8),tc_fun(X0,tc_bool)),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(tc_prod(X8,X0),tc_bool))),X0,X8),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f40,f507,f507,f507]) ).
fof(f40,axiom,
! [X0,X8,X4,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X4,X8,X0),c_Relation_ORange(X5,X8,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(tc_prod(X8,X0),tc_bool)),X8,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).
fof(f14121,plain,
spl0_547,
inference(avatar_split_clause,[],[f583,f14119]) ).
fof(f14119,plain,
( spl0_547
<=> ! [X4,X11,X19,X0,X1] :
( X1 = X11
| ~ c_Relation_Ototal__on(X4,X19,X0)
| ~ hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(X11,X4,X0))
| hBOOL(c_in(c_Pair(X1,X11,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X11,X1,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f583,axiom,
! [X0,X11,X1,X19,X4] :
( X1 = X11
| ~ c_Relation_Ototal__on(X4,X19,X0)
| ~ hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(X11,X4,X0))
| hBOOL(c_in(c_Pair(X1,X11,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X11,X1,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__def_0) ).
fof(f14117,plain,
spl0_546,
inference(avatar_split_clause,[],[f531,f14115]) ).
fof(f14115,plain,
( spl0_546
<=> ! [X31,X19,X0,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f531,axiom,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
fof(f13911,plain,
spl0_545,
inference(avatar_split_clause,[],[f547,f13909]) ).
fof(f547,axiom,
! [X31,X0,X18,X8,X19,X22,X23,X20] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X8,X18),X20,tc_prod(X8,X18)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X18),c_Relation_Orel__comp(X19,X20,X0,X8,X18),tc_prod(X0,X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compI_0) ).
fof(f13907,plain,
spl0_544,
inference(avatar_split_clause,[],[f413,f13905]) ).
fof(f413,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| c_Relation_OImage(X19,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) = c_Relation_OImage(X19,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
fof(f13903,plain,
spl0_543,
inference(avatar_split_clause,[],[f314,f13901]) ).
fof(f13901,plain,
( spl0_543
<=> ! [X23,X19,X0,X12,X22] :
( ~ hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X22))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X12,X23,X19,X0),X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f314,axiom,
! [X0,X19,X22,X12,X23] :
( ~ hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X22))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X12,X23,X19,X0),X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
fof(f13899,plain,
spl0_542,
inference(avatar_split_clause,[],[f313,f13897]) ).
fof(f13897,plain,
( spl0_542
<=> ! [X23,X19,X0,X12,X22] :
( ~ hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X12,X22,X19,X0),X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f313,axiom,
! [X0,X19,X22,X12,X23] :
( ~ hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X12,X22,X19,X0),X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).
fof(f13792,plain,
spl0_541,
inference(avatar_split_clause,[],[f703,f13790]) ).
fof(f13790,plain,
( spl0_541
<=> ! [X20,X0,X19] :
( ~ c_Wellfounded_Owf(X20,X0)
| ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X20),X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f703,plain,
! [X0,X19,X20] :
( ~ c_Wellfounded_Owf(X20,X0)
| ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X19,X0,X0),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X20),X0,X0),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f297,f507]) ).
fof(f297,axiom,
! [X0,X19,X20] :
( ~ c_Wellfounded_Owf(X20,X0)
| ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X19,X0,X0),c_Relation_ORange(X20,X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Un_0) ).
fof(f13788,plain,
( spl0_540
| ~ spl0_104
| ~ spl0_128
| ~ spl0_396 ),
inference(avatar_split_clause,[],[f13036,f6155,f1326,f1226,f13785]) ).
fof(f1326,plain,
( spl0_128
<=> ! [X0,X8,X19] : hAPP(c_Relation_Oconverse(X8,X0),hAPP(c_Relation_Oconverse(X0,X8),X19)) = X19 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f6155,plain,
( spl0_396
<=> ! [X19,X0,X23,X8,X1] :
( hBOOL(c_in(X23,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),X0))
| ~ hBOOL(c_in(c_Pair(X1,X23,X8,X0),X19,tc_prod(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f13036,plain,
( hBOOL(c_in(v_a____,c_Relation_ODomain(hAPP(v_P____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_104
| ~ spl0_128
| ~ spl0_396 ),
inference(forward_demodulation,[],[f13021,f1327]) ).
fof(f1327,plain,
( ! [X0,X8,X19] : hAPP(c_Relation_Oconverse(X8,X0),hAPP(c_Relation_Oconverse(X0,X8),X19)) = X19
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1326]) ).
fof(f13021,plain,
( hBOOL(c_in(v_a____,c_Relation_ODomain(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x))),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_104
| ~ spl0_396 ),
inference(resolution,[],[f1227,f6156]) ).
fof(f6156,plain,
( ! [X0,X1,X8,X19,X23] :
( ~ hBOOL(c_in(c_Pair(X1,X23,X8,X0),X19,tc_prod(X8,X0)))
| hBOOL(c_in(X23,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),X0)) )
| ~ spl0_396 ),
inference(avatar_component_clause,[],[f6155]) ).
fof(f13783,plain,
spl0_539,
inference(avatar_split_clause,[],[f529,f13781]) ).
fof(f13781,plain,
( spl0_539
<=> ! [X31,X19,X0,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f529,axiom,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
fof(f13779,plain,
spl0_538,
inference(avatar_split_clause,[],[f528,f13777]) ).
fof(f13777,plain,
( spl0_538
<=> ! [X31,X19,X0,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f528,axiom,
! [X31,X0,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
fof(f13584,plain,
spl0_537,
inference(avatar_split_clause,[],[f688,f13582]) ).
fof(f13582,plain,
( spl0_537
<=> ! [X35,X20,X0,X19] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ hBOOL(c_in(X35,c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(X35,c_Relation_Orel__comp(X20,c_Transitive__Closure_Ortrancl(X20,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f688,plain,
! [X0,X19,X35,X20] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ hBOOL(c_in(X35,c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(X35,c_Relation_Orel__comp(X20,c_Transitive__Closure_Ortrancl(X20,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f286,f506,f506]) ).
fof(f286,axiom,
! [X0,X19,X35,X20] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ hBOOL(c_in(X35,c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(X35,c_Transitive__Closure_Otrancl(X20,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
fof(f13580,plain,
spl0_536,
inference(avatar_split_clause,[],[f662,f13578]) ).
fof(f13578,plain,
( spl0_536
<=> ! [X4,X0,X5,X8] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X8,X0),tc_bool))),X0,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X4),X0,X8),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X5),X0,X8),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f662,plain,
! [X0,X8,X4,X5] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X8,X0),tc_bool))),X0,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X4),X0,X8),c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X5),X0,X8),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f229,f507,f507,f507]) ).
fof(f229,axiom,
! [X0,X8,X4,X5] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X8,X0),tc_bool)),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X4,X8,X0),c_Relation_ORange(X5,X8,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
fof(f13576,plain,
spl0_535,
inference(avatar_split_clause,[],[f524,f13574]) ).
fof(f524,axiom,
! [X31,X0,X19,X22,X23] :
( ~ c_Relation_Otrans(X19,X0)
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X22,X31,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X31,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transD_0) ).
fof(f13484,plain,
spl0_534,
inference(avatar_split_clause,[],[f682,f13482]) ).
fof(f13482,plain,
( spl0_534
<=> ! [X0,X14,X2,X1] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X14,X1,X2,X0),X2,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f682,plain,
! [X2,X0,X1,X14] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X14,X1,X2,X0),X2,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f377,f506]) ).
fof(f377,axiom,
! [X2,X0,X1,X14] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Otrancl(X14,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X14,X1,X2,X0),X2,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_1) ).
fof(f13480,plain,
spl0_533,
inference(avatar_split_clause,[],[f681,f13478]) ).
fof(f13478,plain,
( spl0_533
<=> ! [X0,X14,X2,X1] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X14,X1,X2,X0),X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f681,plain,
! [X2,X0,X1,X14] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X14,X1,X2,X0),X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f376,f506]) ).
fof(f376,axiom,
! [X2,X0,X1,X14] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Otrancl(X14,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X14,X1,X2,X0),X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_0) ).
fof(f13309,plain,
spl0_532,
inference(avatar_split_clause,[],[f686,f13307]) ).
fof(f13307,plain,
( spl0_532
<=> ! [X0,X14,X23,X22] :
( X22 = X23
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f686,plain,
! [X0,X14,X22,X23] :
( X22 = X23
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f445,f506]) ).
fof(f445,axiom,
! [X0,X14,X22,X23] :
( X22 = X23
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Otrancl(X14,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclD_0) ).
fof(f13305,plain,
spl0_531,
inference(avatar_split_clause,[],[f337,f13303]) ).
fof(f13303,plain,
( spl0_531
<=> ! [X18,X31,X19,X20,X0,X23,X8] :
( ~ hBOOL(c_in(c_Pair(X23,X31,X0,X8),c_Relation_Orel__comp(X19,X20,X0,X18,X8),tc_prod(X0,X8)))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X23,X31,X19,X20,X0,X8,X18),X0,X18),X19,tc_prod(X0,X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f337,axiom,
! [X31,X0,X18,X8,X19,X23,X20] :
( ~ hBOOL(c_in(c_Pair(X23,X31,X0,X8),c_Relation_Orel__comp(X19,X20,X0,X18,X8),tc_prod(X0,X8)))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X23,X31,X19,X20,X0,X8,X18),X0,X18),X19,tc_prod(X0,X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
fof(f13301,plain,
spl0_530,
inference(avatar_split_clause,[],[f336,f13299]) ).
fof(f13299,plain,
( spl0_530
<=> ! [X18,X31,X19,X20,X0,X23,X8] :
( ~ hBOOL(c_in(c_Pair(X23,X31,X0,X8),c_Relation_Orel__comp(X19,X20,X0,X18,X8),tc_prod(X0,X8)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X23,X31,X19,X20,X0,X8,X18),X31,X18,X8),X20,tc_prod(X18,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f336,axiom,
! [X31,X0,X18,X8,X19,X23,X20] :
( ~ hBOOL(c_in(c_Pair(X23,X31,X0,X8),c_Relation_Orel__comp(X19,X20,X0,X18,X8),tc_prod(X0,X8)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X23,X31,X19,X20,X0,X8,X18),X31,X18,X8),X20,tc_prod(X18,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
fof(f13297,plain,
spl0_529,
inference(avatar_split_clause,[],[f23,f13295]) ).
fof(f13295,plain,
( spl0_529
<=> ! [X18,X19,X0,X16,X17,X8,X20] :
( ~ c_lessequals(X16,X19,tc_fun(tc_prod(X0,X8),tc_bool))
| ~ c_lessequals(X17,X20,tc_fun(tc_prod(X8,X18),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X16,X17,X0,X8,X18),c_Relation_Orel__comp(X19,X20,X0,X8,X18),tc_fun(tc_prod(X0,X18),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f23,axiom,
! [X0,X18,X8,X19,X16,X17,X20] :
( ~ c_lessequals(X16,X19,tc_fun(tc_prod(X0,X8),tc_bool))
| ~ c_lessequals(X17,X20,tc_fun(tc_prod(X8,X18),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X16,X17,X0,X8,X18),c_Relation_Orel__comp(X19,X20,X0,X8,X18),tc_fun(tc_prod(X0,X18),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
fof(f13044,plain,
spl0_528,
inference(avatar_split_clause,[],[f680,f13042]) ).
fof(f13042,plain,
( spl0_528
<=> ! [X0,X14,X2,X1] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X14,X1,X2,X0),X2,X0,X0),X14,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f680,plain,
! [X2,X0,X1,X14] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X14,X1,X2,X0),X2,X0,X0),X14,tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f332,f506]) ).
fof(f332,axiom,
! [X2,X0,X1,X14] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Otrancl(X14,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X14,X1,X2,X0),X2,X0,X0),X14,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_1) ).
fof(f13040,plain,
spl0_527,
inference(avatar_split_clause,[],[f679,f13038]) ).
fof(f13038,plain,
( spl0_527
<=> ! [X0,X14,X2,X1] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X14,X1,X2,X0),X0,X0),X14,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f679,plain,
! [X2,X0,X1,X14] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X14,X1,X2,X0),X0,X0),X14,tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f327,f506]) ).
fof(f327,axiom,
! [X2,X0,X1,X14] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Otrancl(X14,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X14,X1,X2,X0),X0,X0),X14,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_0) ).
fof(f13001,plain,
( spl0_450
| ~ spl0_103
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f10437,f8260,f1219,f8473]) ).
fof(f8260,plain,
( spl0_432
<=> ! [X58] :
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f10437,plain,
( hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_103
| ~ spl0_432 ),
inference(resolution,[],[f1221,f8261]) ).
fof(f8261,plain,
( ! [X58] :
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_432 ),
inference(avatar_component_clause,[],[f8260]) ).
fof(f1221,plain,
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1219]) ).
fof(f13000,plain,
spl0_526,
inference(avatar_split_clause,[],[f677,f12998]) ).
fof(f12998,plain,
( spl0_526
<=> ! [X0,X1,X19] :
( ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X19,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X19,X0),X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f677,plain,
! [X0,X1,X19] :
( ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X19,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X19,X0),X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f325,f506]) ).
fof(f325,axiom,
! [X0,X1,X19] :
( ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X19,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X19,X0),X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
fof(f12996,plain,
spl0_525,
inference(avatar_split_clause,[],[f354,f12994]) ).
fof(f12994,plain,
( spl0_525
<=> ! [X4,X0,X14,X5,X8] :
( ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(X8,X0),X14),X0,X8)
| c_Relation_OImage(X14,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X8,tc_bool)),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X14,X4,X8,X0),c_Relation_OImage(X14,X5,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f354,axiom,
! [X0,X8,X14,X4,X5] :
( ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(X8,X0),X14),X0,X8)
| c_Relation_OImage(X14,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X8,tc_bool)),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X14,X4,X8,X0),c_Relation_OImage(X14,X5,X8,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
fof(f12992,plain,
spl0_524,
inference(avatar_split_clause,[],[f320,f12990]) ).
fof(f12990,plain,
( spl0_524
<=> ! [X19,X0,X23,X22] :
( X22 = X23
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X23,X22,X19,X0),X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f320,axiom,
! [X0,X19,X22,X23] :
( X22 = X23
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X23,X22,X19,X0),X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclE_0) ).
fof(f12988,plain,
spl0_523,
inference(avatar_split_clause,[],[f210,f12986]) ).
fof(f12986,plain,
( spl0_523
<=> ! [X0,X3,X19,X1] :
( X1 = X3
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X19,X1,X3,X0),X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f210,axiom,
! [X3,X0,X1,X19] :
( X1 = X3
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X19,X1,X3,X0),X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).
fof(f12658,plain,
spl0_522,
inference(avatar_split_clause,[],[f725,f12656]) ).
fof(f12656,plain,
( spl0_522
<=> ! [X0,X14,X15] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X14,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f725,plain,
! [X0,X14,X15] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X14,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f724,f146]) ).
fof(f146,axiom,
! [X28,X0,X18,X8,X14,X15] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X15,X28,tc_fun(tc_prod(X0,X18),tc_bool)),X14,X0,X18,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X14,X0,X18,X8),c_Relation_Orel__comp(X28,X14,X0,X18,X8),tc_fun(tc_prod(X0,X8),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
fof(f724,plain,
! [X0,X14,X15] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X14,X14,X0,X0,X0),c_Relation_Orel__comp(X15,X14,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f296,f160]) ).
fof(f160,axiom,
! [X0,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f296,axiom,
! [X0,X14,X15] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X14,X14,X0,X0,X0),c_Relation_Orel__comp(X15,X14,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
fof(f12654,plain,
spl0_521,
inference(avatar_split_clause,[],[f723,f12652]) ).
fof(f12652,plain,
( spl0_521
<=> ! [X0,X14,X15] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X14,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f723,plain,
! [X0,X14,X15] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X14,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f722,f146]) ).
fof(f722,plain,
! [X0,X14,X15] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X14,X14,X0,X0,X0),c_Relation_Orel__comp(X15,X14,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f295,f160]) ).
fof(f295,axiom,
! [X0,X14,X15] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X14,X14,X0,X0,X0),c_Relation_Orel__comp(X15,X14,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
fof(f12650,plain,
spl0_520,
inference(avatar_split_clause,[],[f316,f12648]) ).
fof(f12648,plain,
( spl0_520
<=> ! [X38,X37,X19] :
( X37 = X38
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Transitive__Closure_Ortrancl(X19,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(X37,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X37,X38,X19),t_a,t_a),c_Transitive__Closure_Ortrancl(X19,t_a),tc_prod(t_a,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f316,axiom,
! [X38,X37,X19] :
( X37 = X38
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Transitive__Closure_Ortrancl(X19,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(X37,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X37,X38,X19),t_a,t_a),c_Transitive__Closure_Ortrancl(X19,t_a),tc_prod(t_a,t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).
fof(f12646,plain,
spl0_519,
inference(avatar_split_clause,[],[f179,f12644]) ).
fof(f12644,plain,
( spl0_519
<=> ! [X21,X19,X0,X8,X1,X7] :
( c_Recdef_Ocut(X7,X19,X1,X0,X8) = c_Recdef_Ocut(X21,X19,X1,X0,X8)
| hAPP(X7,c_List_Osko__Recdef__Xcuts__eq__1__1(X7,X21,X19,X1,X0,X8)) != hAPP(X21,c_List_Osko__Recdef__Xcuts__eq__1__1(X7,X21,X19,X1,X0,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f179,axiom,
! [X21,X0,X1,X8,X19,X7] :
( c_Recdef_Ocut(X7,X19,X1,X0,X8) = c_Recdef_Ocut(X21,X19,X1,X0,X8)
| hAPP(X7,c_List_Osko__Recdef__Xcuts__eq__1__1(X7,X21,X19,X1,X0,X8)) != hAPP(X21,c_List_Osko__Recdef__Xcuts__eq__1__1(X7,X21,X19,X1,X0,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
fof(f12642,plain,
spl0_518,
inference(avatar_split_clause,[],[f147,f12640]) ).
fof(f12640,plain,
( spl0_518
<=> ! [X15,X18,X0,X8,X14,X28] : c_Relation_Orel__comp(X14,c_Lattices_Oupper__semilattice__class_Osup(X15,X28,tc_fun(tc_prod(X18,X8),tc_bool)),X0,X18,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X14,X15,X0,X18,X8),c_Relation_Orel__comp(X14,X28,X0,X18,X8),tc_fun(tc_prod(X0,X8),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f147,axiom,
! [X28,X0,X18,X8,X14,X15] : c_Relation_Orel__comp(X14,c_Lattices_Oupper__semilattice__class_Osup(X15,X28,tc_fun(tc_prod(X18,X8),tc_bool)),X0,X18,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X14,X15,X0,X18,X8),c_Relation_Orel__comp(X14,X28,X0,X18,X8),tc_fun(tc_prod(X0,X8),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
fof(f12638,plain,
spl0_517,
inference(avatar_split_clause,[],[f146,f12636]) ).
fof(f12636,plain,
( spl0_517
<=> ! [X28,X18,X15,X0,X14,X8] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X15,X28,tc_fun(tc_prod(X0,X18),tc_bool)),X14,X0,X18,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X14,X0,X18,X8),c_Relation_Orel__comp(X28,X14,X0,X18,X8),tc_fun(tc_prod(X0,X8),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f12369,plain,
spl0_516,
inference(avatar_split_clause,[],[f539,f12367]) ).
fof(f12367,plain,
( spl0_516
<=> ! [X1,X8,X19,X0,X21,X2,X7] :
( hAPP(X7,X2) = hAPP(X21,X2)
| ~ hBOOL(c_in(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)))
| c_Recdef_Ocut(X7,X19,X1,X0,X8) != c_Recdef_Ocut(X21,X19,X1,X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f539,axiom,
! [X2,X21,X0,X1,X8,X19,X7] :
( hAPP(X7,X2) = hAPP(X21,X2)
| ~ hBOOL(c_in(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)))
| c_Recdef_Ocut(X7,X19,X1,X0,X8) != c_Recdef_Ocut(X21,X19,X1,X0,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
fof(f12365,plain,
spl0_515,
inference(avatar_split_clause,[],[f371,f12363]) ).
fof(f12363,plain,
( spl0_515
<=> ! [X40,X12,X19,X1] :
( hBOOL(hAPP(X12,X1))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a))
| hBOOL(c_in(X40,c_Wellfounded_Oacc(X19,t_a),t_a))
| ~ hBOOL(c_in(c_Pair(X40,v_sko__Wellfounded__Xacc__Xinduct__1(X12,X19),t_a,t_a),X19,tc_prod(t_a,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f371,axiom,
! [X40,X1,X19,X12] :
( hBOOL(hAPP(X12,X1))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a))
| hBOOL(c_in(X40,c_Wellfounded_Oacc(X19,t_a),t_a))
| ~ hBOOL(c_in(c_Pair(X40,v_sko__Wellfounded__Xacc__Xinduct__1(X12,X19),t_a,t_a),X19,tc_prod(t_a,t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
fof(f12361,plain,
spl0_514,
inference(avatar_split_clause,[],[f369,f12359]) ).
fof(f12359,plain,
( spl0_514
<=> ! [X40,X12,X19,X1] :
( hBOOL(hAPP(X12,X1))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a))
| hBOOL(c_in(X40,c_Wellfounded_Oacc(X19,t_a),t_a))
| ~ hBOOL(c_in(c_Pair(X40,v_sko__Wellfounded__Xacc__Xinducts__1(X12,X19),t_a,t_a),X19,tc_prod(t_a,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f369,axiom,
! [X40,X1,X19,X12] :
( hBOOL(hAPP(X12,X1))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a))
| hBOOL(c_in(X40,c_Wellfounded_Oacc(X19,t_a),t_a))
| ~ hBOOL(c_in(c_Pair(X40,v_sko__Wellfounded__Xacc__Xinducts__1(X12,X19),t_a,t_a),X19,tc_prod(t_a,t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
fof(f12357,plain,
spl0_513,
inference(avatar_split_clause,[],[f311,f12355]) ).
fof(f12355,plain,
( spl0_513
<=> ! [X0,X3,X19,X1] :
( X1 = X3
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X19,X1,X3,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f311,axiom,
! [X3,X0,X1,X19] :
( X1 = X3
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X19,X1,X3,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).
fof(f12353,plain,
spl0_512,
inference(avatar_split_clause,[],[f209,f12351]) ).
fof(f12351,plain,
( spl0_512
<=> ! [X19,X0,X23,X22] :
( X22 = X23
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X23,X22,X19,X0),X22,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f209,axiom,
! [X0,X19,X22,X23] :
( X22 = X23
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X23,X22,X19,X0),X22,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclE_1) ).
fof(f12349,plain,
spl0_511,
inference(avatar_split_clause,[],[f35,f12347]) ).
fof(f12347,plain,
( spl0_511
<=> ! [X4,X0,X5,X1] :
( ~ hBOOL(c_in(X1,X4,X0))
| c_lessequals(X4,c_Set_Oinsert(X1,X5,X0),tc_fun(X0,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f35,axiom,
! [X0,X1,X4,X5] :
( ~ hBOOL(c_in(X1,X4,X0))
| c_lessequals(X4,c_Set_Oinsert(X1,X5,X0),tc_fun(X0,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
fof(f11779,plain,
spl0_510,
inference(avatar_split_clause,[],[f591,f11777]) ).
fof(f11777,plain,
( spl0_510
<=> ! [X19,X0,X2,X1] :
( ~ hBOOL(c_in(c_Pair(X2,X1,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f591,axiom,
! [X2,X0,X1,X19] :
( ~ hBOOL(c_in(c_Pair(X2,X1,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
fof(f11775,plain,
spl0_509,
inference(avatar_split_clause,[],[f590,f11773]) ).
fof(f11773,plain,
( spl0_509
<=> ! [X19,X0,X2,X1] :
( hBOOL(c_in(c_Pair(X2,X1,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f590,axiom,
! [X2,X0,X1,X19] :
( hBOOL(c_in(c_Pair(X2,X1,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
fof(f11771,plain,
spl0_508,
inference(avatar_split_clause,[],[f563,f11769]) ).
fof(f11769,plain,
( spl0_508
<=> ! [X50,X3,X2,X1] :
( X2 = X3
| X1 = X3
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f563,axiom,
! [X50,X2,X3,X1] :
( X2 = X3
| X1 = X3
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
fof(f11767,plain,
spl0_507,
inference(avatar_split_clause,[],[f562,f11765]) ).
fof(f11765,plain,
( spl0_507
<=> ! [X50,X3,X2,X1] :
( X2 = X3
| X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f562,axiom,
! [X50,X2,X3,X1] :
( X2 = X3
| X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
fof(f11763,plain,
spl0_506,
inference(avatar_split_clause,[],[f555,f11761]) ).
fof(f11761,plain,
( spl0_506
<=> ! [X50,X3,X2,X1] :
( X1 = X3
| X2 = X3
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f555,axiom,
! [X50,X2,X3,X1] :
( X1 = X3
| X2 = X3
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_3) ).
fof(f11759,plain,
spl0_505,
inference(avatar_split_clause,[],[f554,f11757]) ).
fof(f11757,plain,
( spl0_505
<=> ! [X50,X3,X2,X1] :
( X1 = X3
| X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f554,axiom,
! [X50,X2,X3,X1] :
( X1 = X3
| X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_5) ).
fof(f11755,plain,
spl0_504,
inference(avatar_split_clause,[],[f544,f11753]) ).
fof(f11753,plain,
( spl0_504
<=> ! [X2,X1,X0,X8,X19,X7] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Oinv__image(X19,X7,X8,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(hAPP(X7,X1),hAPP(X7,X2),X8,X8),X19,tc_prod(X8,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f544,axiom,
! [X2,X0,X1,X8,X19,X7] :
( ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Oinv__image(X19,X7,X8,X0),tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(hAPP(X7,X1),hAPP(X7,X2),X8,X8),X19,tc_prod(X8,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
fof(f11751,plain,
spl0_503,
inference(avatar_split_clause,[],[f543,f11749]) ).
fof(f11749,plain,
( spl0_503
<=> ! [X19,X7,X8,X0,X2,X1] :
( ~ hBOOL(c_in(c_Pair(hAPP(X7,X1),hAPP(X7,X2),X8,X8),X19,tc_prod(X8,X8)))
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Oinv__image(X19,X7,X8,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f543,axiom,
! [X2,X0,X1,X8,X19,X7] :
( ~ hBOOL(c_in(c_Pair(hAPP(X7,X1),hAPP(X7,X2),X8,X8),X19,tc_prod(X8,X8)))
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_Oinv__image(X19,X7,X8,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
fof(f11747,plain,
spl0_502,
inference(avatar_split_clause,[],[f514,f11745]) ).
fof(f11745,plain,
( spl0_502
<=> ! [X19,X0,X8,X45] :
( ~ hBOOL(c_in(X45,hAPP(c_Relation_Oconverse(X8,X0),X19),tc_prod(X0,X8)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XconverseE__1__1(X19,X45,X8,X0),c_ATP__Linkup_Osko__Relation__XconverseE__1__2(X19,X45,X8,X0),X8,X0),X19,tc_prod(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f514,axiom,
! [X0,X8,X19,X45] :
( ~ hBOOL(c_in(X45,hAPP(c_Relation_Oconverse(X8,X0),X19),tc_prod(X0,X8)))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XconverseE__1__1(X19,X45,X8,X0),c_ATP__Linkup_Osko__Relation__XconverseE__1__2(X19,X45,X8,X0),X8,X0),X19,tc_prod(X8,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseE_1) ).
fof(f11743,plain,
spl0_501,
inference(avatar_split_clause,[],[f346,f11741]) ).
fof(f11741,plain,
( spl0_501
<=> ! [X21,X19,X0,X8,X1,X7] :
( c_Recdef_Ocut(X7,X19,X1,X0,X8) = c_Recdef_Ocut(X21,X19,X1,X0,X8)
| hBOOL(c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X7,X21,X19,X1,X0,X8),X1,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f346,axiom,
! [X21,X0,X1,X8,X19,X7] :
( c_Recdef_Ocut(X7,X19,X1,X0,X8) = c_Recdef_Ocut(X21,X19,X1,X0,X8)
| hBOOL(c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X7,X21,X19,X1,X0,X8),X1,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
fof(f11739,plain,
spl0_500,
inference(avatar_split_clause,[],[f318,f11737]) ).
fof(f11737,plain,
( spl0_500
<=> ! [X38,X37,X19] :
( X37 = X38
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Transitive__Closure_Ortrancl(X19,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X37,X38,X19),X38,t_a,t_a),X19,tc_prod(t_a,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f318,axiom,
! [X38,X37,X19] :
( X37 = X38
| ~ hBOOL(c_in(c_Pair(X37,X38,t_a,t_a),c_Transitive__Closure_Ortrancl(X19,t_a),tc_prod(t_a,t_a)))
| hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X37,X38,X19),X38,t_a,t_a),X19,tc_prod(t_a,t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
fof(f11735,plain,
( spl0_499
| ~ spl0_103
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f10441,f4523,f1219,f11733]) ).
fof(f11733,plain,
( spl0_499
<=> ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f10441,plain,
( ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_103
| ~ spl0_349 ),
inference(resolution,[],[f1221,f4524]) ).
fof(f11615,plain,
( spl0_498
| ~ spl0_296
| ~ spl0_393
| ~ spl0_495 ),
inference(avatar_split_clause,[],[f11114,f11111,f6143,f3379,f11613]) ).
fof(f11613,plain,
( spl0_498
<=> ! [X0,X19] : c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X19,X0),c_Relation_Orel__comp(X19,X19,X0,X0,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f6143,plain,
( spl0_393
<=> ! [X28,X18,X15,X42,X0,X14,X8] : c_Relation_Orel__comp(c_Relation_Orel__comp(X14,X15,X0,X42,X18),X28,X0,X18,X8) = c_Relation_Orel__comp(X14,c_Relation_Orel__comp(X15,X28,X42,X18,X8),X0,X42,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f11111,plain,
( spl0_495
<=> ! [X0,X19] : c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_Orel__comp(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X19,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f11114,plain,
( ! [X0,X19] : c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X19,X0),c_Relation_Orel__comp(X19,X19,X0,X0,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_296
| ~ spl0_393
| ~ spl0_495 ),
inference(forward_demodulation,[],[f11112,f6931]) ).
fof(f6931,plain,
( ! [X2,X3,X0,X1] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,X1),c_Relation_Orel__comp(X0,X2,X1,X1,X3),X1,X1,X3) = c_Relation_Orel__comp(c_Relation_Orel__comp(X0,c_Transitive__Closure_Ortrancl(X0,X1),X1,X1,X1),X2,X1,X1,X3)
| ~ spl0_296
| ~ spl0_393 ),
inference(superposition,[],[f6144,f3380]) ).
fof(f6144,plain,
( ! [X28,X0,X18,X8,X14,X15,X42] : c_Relation_Orel__comp(c_Relation_Orel__comp(X14,X15,X0,X42,X18),X28,X0,X18,X8) = c_Relation_Orel__comp(X14,c_Relation_Orel__comp(X15,X28,X42,X18,X8),X0,X42,X8)
| ~ spl0_393 ),
inference(avatar_component_clause,[],[f6143]) ).
fof(f11112,plain,
( ! [X0,X19] : c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_Orel__comp(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X19,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f11111]) ).
fof(f11387,plain,
( spl0_497
| ~ spl0_103
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f10440,f4519,f1219,f11385]) ).
fof(f11385,plain,
( spl0_497
<=> ! [X0] :
( hBOOL(c_in(v_c____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f10440,plain,
( ! [X0] :
( hBOOL(c_in(v_c____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_103
| ~ spl0_348 ),
inference(resolution,[],[f1221,f4520]) ).
fof(f11118,plain,
spl0_496,
inference(avatar_split_clause,[],[f661,f11116]) ).
fof(f11116,plain,
( spl0_496
<=> ! [X19,X0,X8,X23,X22] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),c_Set_Oinsert(c_Pair(X23,X22,X8,X0),X19,tc_prod(X8,X0))),X0,X8) = c_Set_Oinsert(X22,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f11113,plain,
spl0_495,
inference(avatar_split_clause,[],[f659,f11111]) ).
fof(f659,plain,
! [X0,X19] : c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_Orel__comp(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X19,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
inference(definition_unfolding,[],[f298,f506,f506]) ).
fof(f298,axiom,
! [X0,X19] : c_Transitive__Closure_Otrancl(X19,X0) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X19,X0),X19,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
fof(f11109,plain,
spl0_494,
inference(avatar_split_clause,[],[f657,f11107]) ).
fof(f11107,plain,
( spl0_494
<=> ! [X0,X19] : hAPP(c_Relation_Oconverse(X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f657,plain,
! [X0,X19] : hAPP(c_Relation_Oconverse(X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0),X0,X0,X0),
inference(definition_unfolding,[],[f432,f506,f506]) ).
fof(f432,axiom,
! [X0,X19] : c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Transitive__Closure_Otrancl(X19,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
fof(f11105,plain,
spl0_493,
inference(avatar_split_clause,[],[f518,f11103]) ).
fof(f518,axiom,
! [X2,X3,X0,X1,X8,X19] :
( X2 = X3
| ~ c_Relation_Osingle__valued(X19,X0,X8)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X8),X19,tc_prod(X0,X8)))
| ~ hBOOL(c_in(c_Pair(X1,X3,X0,X8),X19,tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
fof(f11101,plain,
spl0_492,
inference(avatar_split_clause,[],[f372,f11099]) ).
fof(f11099,plain,
( spl0_492
<=> ! [X23,X19,X0,X12,X2] :
( hBOOL(hAPP(X12,X2))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f372,axiom,
! [X2,X0,X19,X12,X23] :
( hBOOL(hAPP(X12,X2))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_1) ).
fof(f11097,plain,
( spl0_491
| ~ spl0_103
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f10439,f4507,f1219,f11095]) ).
fof(f11095,plain,
( spl0_491
<=> ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f10439,plain,
( ! [X0] :
( hBOOL(c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_103
| ~ spl0_345 ),
inference(resolution,[],[f1221,f4508]) ).
fof(f11093,plain,
spl0_490,
inference(avatar_split_clause,[],[f366,f11091]) ).
fof(f11091,plain,
( spl0_490
<=> ! [X23,X19,X0,X12,X2] :
( hBOOL(hAPP(X12,X2))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f366,axiom,
! [X2,X0,X19,X12,X23] :
( hBOOL(hAPP(X12,X2))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
fof(f11089,plain,
spl0_489,
inference(avatar_split_clause,[],[f319,f11087]) ).
fof(f11087,plain,
( spl0_489
<=> ! [X23,X19,X0,X12,X22] :
( ~ hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X12,X22,X19,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f319,axiom,
! [X0,X19,X22,X12,X23] :
( ~ hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X12,X22,X19,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
fof(f11085,plain,
spl0_488,
inference(avatar_split_clause,[],[f317,f11083]) ).
fof(f11083,plain,
( spl0_488
<=> ! [X23,X19,X0,X12,X22] :
( ~ hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X12,X23,X19,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f317,axiom,
! [X0,X19,X22,X12,X23] :
( ~ hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X12,X23,X19,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).
fof(f11081,plain,
spl0_487,
inference(avatar_split_clause,[],[f315,f11079]) ).
fof(f11079,plain,
( spl0_487
<=> ! [X23,X19,X0,X12,X22] :
( ~ hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X22))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X12,X23,X19,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f315,axiom,
! [X0,X19,X22,X12,X23] :
( ~ hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X22))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X12,X23,X19,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).
fof(f11077,plain,
spl0_486,
inference(avatar_split_clause,[],[f312,f11075]) ).
fof(f11075,plain,
( spl0_486
<=> ! [X23,X19,X0,X12,X22] :
( ~ hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X12,X22,X19,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f312,axiom,
! [X0,X19,X22,X12,X23] :
( ~ hBOOL(hAPP(X12,X22))
| hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X12,X22,X19,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).
fof(f11073,plain,
spl0_485,
inference(avatar_split_clause,[],[f202,f11071]) ).
fof(f11071,plain,
( spl0_485
<=> ! [X19,X20,X0,X8] : hAPP(c_Relation_Oconverse(X8,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X8,X0),tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_Oconverse(X8,X0),X19),hAPP(c_Relation_Oconverse(X8,X0),X20),tc_fun(tc_prod(X0,X8),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f202,axiom,
! [X0,X8,X19,X20] : hAPP(c_Relation_Oconverse(X8,X0),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X8,X0),tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_Oconverse(X8,X0),X19),hAPP(c_Relation_Oconverse(X8,X0),X20),tc_fun(tc_prod(X0,X8),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Un_0) ).
fof(f11069,plain,
spl0_484,
inference(avatar_split_clause,[],[f65,f11067]) ).
fof(f11067,plain,
( spl0_484
<=> ! [X0,X14,X15] :
( ~ c_Wellfounded_Owf(X14,X0)
| ~ c_Wellfounded_Owf(X15,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_lessequals(c_Relation_Orel__comp(X14,X15,X0,X0,X0),X14,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f65,axiom,
! [X0,X14,X15] :
( ~ c_Wellfounded_Owf(X14,X0)
| ~ c_Wellfounded_Owf(X15,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_lessequals(c_Relation_Orel__comp(X14,X15,X0,X0,X0),X14,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
fof(f11065,plain,
spl0_483,
inference(avatar_split_clause,[],[f61,f11063]) ).
fof(f11063,plain,
( spl0_483
<=> ! [X5,X4,X0,X6] :
( ~ c_lessequals(X6,X4,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f61,axiom,
! [X0,X6,X4,X5] :
( ~ c_lessequals(X6,X4,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
fof(f11061,plain,
spl0_482,
inference(avatar_split_clause,[],[f60,f11059]) ).
fof(f11059,plain,
( spl0_482
<=> ! [X5,X4,X0,X6] :
( c_lessequals(X6,X4,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f60,axiom,
! [X0,X6,X4,X5] :
( c_lessequals(X6,X4,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
fof(f10969,plain,
( spl0_481
| ~ spl0_103
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f10438,f4503,f1219,f10967]) ).
fof(f10967,plain,
( spl0_481
<=> ! [X0] :
( hBOOL(c_in(v_c____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f10438,plain,
( ! [X0] :
( hBOOL(c_in(v_c____,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_103
| ~ spl0_344 ),
inference(resolution,[],[f1221,f4504]) ).
fof(f10436,plain,
( spl0_103
| ~ spl0_54
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1467,f1390,f958,f1219]) ).
fof(f958,plain,
( spl0_54
<=> ! [X5,X0,X1] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X5,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1390,plain,
( spl0_132
<=> hAPP(v_P_H____,v_x) = c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1467,plain,
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_54
| ~ spl0_132 ),
inference(superposition,[],[f959,f1392]) ).
fof(f1392,plain,
( hAPP(v_P_H____,v_x) = c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1390]) ).
fof(f959,plain,
( ! [X0,X1,X5] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X5,X0),X0))
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f958]) ).
fof(f9309,plain,
spl0_480,
inference(avatar_split_clause,[],[f709,f9307]) ).
fof(f9307,plain,
( spl0_480
<=> ! [X6,X4,X0,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f709,plain,
! [X0,X6,X4,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f81,f258]) ).
fof(f258,axiom,
! [X0,X6,X4,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
fof(f81,axiom,
! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
fof(f9274,plain,
( spl0_479
| ~ spl0_235
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f9270,f9267,f2685,f9272]) ).
fof(f9272,plain,
( spl0_479
<=> ! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2685,plain,
( spl0_235
<=> ! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f9267,plain,
( spl0_478
<=> ! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f9270,plain,
( ! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0)
| ~ spl0_235
| ~ spl0_478 ),
inference(forward_demodulation,[],[f9268,f2686]) ).
fof(f2686,plain,
( ! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2685]) ).
fof(f9268,plain,
( ! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),X0,X0,X0)
| ~ spl0_478 ),
inference(avatar_component_clause,[],[f9267]) ).
fof(f9269,plain,
spl0_478,
inference(avatar_split_clause,[],[f643,f9267]) ).
fof(f643,plain,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),X0,X0,X0),
inference(definition_unfolding,[],[f348,f506]) ).
fof(f348,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
fof(f9265,plain,
spl0_477,
inference(avatar_split_clause,[],[f593,f9263]) ).
fof(f9263,plain,
( spl0_477
<=> ! [X18,X51,X0,X1,X8,X9,X7,X52,X53,X21,X42] :
( hAPP(X7,hAPP(X21,X1)) != hAPP(X51,hAPP(X52,X9))
| hAPP(c_Fun_Ocomp(X7,X21,X8,X0,X18),X1) = hAPP(c_Fun_Ocomp(X51,X52,X42,X0,X53),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f593,axiom,
! [X21,X51,X0,X1,X8,X18,X9,X7,X52,X53,X42] :
( hAPP(X7,hAPP(X21,X1)) != hAPP(X51,hAPP(X52,X9))
| hAPP(c_Fun_Ocomp(X7,X21,X8,X0,X18),X1) = hAPP(c_Fun_Ocomp(X51,X52,X42,X0,X53),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__cong_0) ).
fof(f9261,plain,
spl0_476,
inference(avatar_split_clause,[],[f535,f9259]) ).
fof(f9259,plain,
( spl0_476
<=> ! [X19,X0,X2,X1] :
( ~ c_Relation_Oantisym(X19,X0)
| X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f535,axiom,
! [X2,X0,X1,X19] :
( ~ c_Relation_Oantisym(X19,X0)
| X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__def_0) ).
fof(f9257,plain,
spl0_475,
inference(avatar_split_clause,[],[f374,f9255]) ).
fof(f9255,plain,
( spl0_475
<=> ! [X19,X0,X2,X1] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)),X0)
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f374,axiom,
! [X2,X0,X1,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)),X0)
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_2) ).
fof(f9253,plain,
( ~ spl0_474
| ~ spl0_80
| spl0_450 ),
inference(avatar_split_clause,[],[f8800,f8473,f1066,f9250]) ).
fof(f8800,plain,
( ~ hBOOL(hAPP(hAPP(v_P____,v_x),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_80
| spl0_450 ),
inference(resolution,[],[f8475,f1067]) ).
fof(f8475,plain,
( ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| spl0_450 ),
inference(avatar_component_clause,[],[f8473]) ).
fof(f9248,plain,
spl0_473,
inference(avatar_split_clause,[],[f370,f9246]) ).
fof(f9246,plain,
( spl0_473
<=> ! [X19,X12,X2,X1] :
( hBOOL(hAPP(X12,X2))
| hBOOL(hAPP(X12,X1))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a))
| ~ hBOOL(c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X12,X19),t_a,t_a),X19,tc_prod(t_a,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f370,axiom,
! [X2,X1,X19,X12] :
( hBOOL(hAPP(X12,X2))
| hBOOL(hAPP(X12,X1))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a))
| ~ hBOOL(c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X12,X19),t_a,t_a),X19,tc_prod(t_a,t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
fof(f9244,plain,
spl0_472,
inference(avatar_split_clause,[],[f367,f9242]) ).
fof(f9242,plain,
( spl0_472
<=> ! [X19,X12,X2,X1] :
( hBOOL(hAPP(X12,X2))
| hBOOL(hAPP(X12,X1))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a))
| ~ hBOOL(c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X12,X19),t_a,t_a),X19,tc_prod(t_a,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f367,axiom,
! [X2,X1,X19,X12] :
( hBOOL(hAPP(X12,X2))
| hBOOL(hAPP(X12,X1))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a))
| ~ hBOOL(c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X12,X19),t_a,t_a),X19,tc_prod(t_a,t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
fof(f9240,plain,
spl0_471,
inference(avatar_split_clause,[],[f274,f9238]) ).
fof(f9238,plain,
( spl0_471
<=> ! [X19,X0,X2,X1] :
( ~ c_Wellfounded_Oacyclic(X19,X0)
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)),X0)
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f274,axiom,
! [X2,X0,X1,X19] :
( ~ c_Wellfounded_Oacyclic(X19,X0)
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)),X0)
| hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
fof(f9236,plain,
spl0_470,
inference(avatar_split_clause,[],[f271,f9234]) ).
fof(f9234,plain,
( spl0_470
<=> ! [X16,X4,X19,X0,X36,X8] :
( ~ c_lessequals(X36,X4,tc_fun(X0,tc_bool))
| ~ c_lessequals(X16,X19,tc_fun(tc_prod(X0,X8),tc_bool))
| c_lessequals(c_Relation_OImage(X16,X36,X0,X8),c_Relation_OImage(X19,X4,X0,X8),tc_fun(X8,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f271,axiom,
! [X0,X36,X8,X19,X16,X4] :
( ~ c_lessequals(X36,X4,tc_fun(X0,tc_bool))
| ~ c_lessequals(X16,X19,tc_fun(tc_prod(X0,X8),tc_bool))
| c_lessequals(c_Relation_OImage(X16,X36,X0,X8),c_Relation_OImage(X19,X4,X0,X8),tc_fun(X8,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__mono_0) ).
fof(f9232,plain,
spl0_469,
inference(avatar_split_clause,[],[f261,f9230]) ).
fof(f9230,plain,
( spl0_469
<=> ! [X5,X4,X0,X6] : c_HOL_Ominus__class_Ominus(X4,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f261,axiom,
! [X0,X6,X4,X5] : c_HOL_Ominus__class_Ominus(X4,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
fof(f9228,plain,
spl0_468,
inference(avatar_split_clause,[],[f257,f9226]) ).
fof(f9226,plain,
( spl0_468
<=> ! [X5,X4,X0,X6] : c_HOL_Ominus__class_Ominus(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f257,axiom,
! [X0,X6,X4,X5] : c_HOL_Ominus__class_Ominus(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
fof(f9224,plain,
spl0_467,
inference(avatar_split_clause,[],[f256,f9222]) ).
fof(f9222,plain,
( spl0_467
<=> ! [X5,X4,X0,X6,X26] :
( ~ c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X26,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X26,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f256,axiom,
! [X0,X6,X26,X4,X5] :
( ~ c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X26,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X26,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
fof(f9220,plain,
spl0_466,
inference(avatar_split_clause,[],[f222,f9218]) ).
fof(f9218,plain,
( spl0_466
<=> ! [X5,X4,X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X4,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f222,axiom,
! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X4,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
fof(f9216,plain,
spl0_465,
inference(avatar_split_clause,[],[f221,f9214]) ).
fof(f221,axiom,
! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
fof(f9212,plain,
spl0_464,
inference(avatar_split_clause,[],[f158,f9210]) ).
fof(f9210,plain,
( spl0_464
<=> ! [X5,X4,X0,X6] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X4,X6,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f158,axiom,
! [X0,X6,X4,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X4,X6,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
fof(f9208,plain,
spl0_463,
inference(avatar_split_clause,[],[f107,f9206]) ).
fof(f9206,plain,
( spl0_463
<=> ! [X5,X4,X0,X6,X26] :
( ~ c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X26,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X26,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f107,axiom,
! [X0,X6,X26,X4,X5] :
( ~ c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X26,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X26,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
fof(f9204,plain,
spl0_462,
inference(avatar_split_clause,[],[f85,f9202]) ).
fof(f9202,plain,
( spl0_462
<=> ! [X6,X4,X0,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f85,axiom,
! [X0,X6,X4,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
fof(f9200,plain,
spl0_461,
inference(avatar_split_clause,[],[f83,f9198]) ).
fof(f9198,plain,
( spl0_461
<=> ! [X5,X4,X0,X6,X26] :
( ~ c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X26,X5,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X26,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f83,axiom,
! [X0,X6,X26,X4,X5] :
( ~ c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X26,X5,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X26,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
fof(f9097,plain,
( spl0_460
| ~ spl0_459 ),
inference(avatar_split_clause,[],[f9093,f9090,f9095]) ).
fof(f9095,plain,
( spl0_460
<=> ! [X6,X4,X0,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f9090,plain,
( spl0_459
<=> ! [X5,X4,X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f9093,plain,
( ! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool))
| ~ spl0_459 ),
inference(forward_demodulation,[],[f9091,f85]) ).
fof(f9091,plain,
( ! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_459 ),
inference(avatar_component_clause,[],[f9090]) ).
fof(f9092,plain,
spl0_459,
inference(avatar_split_clause,[],[f82,f9090]) ).
fof(f82,axiom,
! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
fof(f9088,plain,
spl0_458,
inference(avatar_split_clause,[],[f59,f9086]) ).
fof(f9086,plain,
( spl0_458
<=> ! [X4,X0,X14,X5,X8] : c_lessequals(c_Relation_OImage(X14,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X8,tc_bool)),X8,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X14,X4,X8,X0),c_Relation_OImage(X14,X5,X8,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f59,axiom,
! [X0,X8,X14,X4,X5] : c_lessequals(c_Relation_OImage(X14,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X8,tc_bool)),X8,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X14,X4,X8,X0),c_Relation_OImage(X14,X5,X8,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
fof(f9084,plain,
spl0_457,
inference(avatar_split_clause,[],[f58,f9082]) ).
fof(f9082,plain,
( spl0_457
<=> ! [X4,X0,X5,X8,X7] : c_lessequals(c_Set_Oimage(X7,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X8,tc_bool)),X8,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X7,X4,X8,X0),c_Set_Oimage(X7,X5,X8,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f58,axiom,
! [X0,X8,X7,X4,X5] : c_lessequals(c_Set_Oimage(X7,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X8,tc_bool)),X8,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X7,X4,X8,X0),c_Set_Oimage(X7,X5,X8,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
fof(f9080,plain,
spl0_456,
inference(avatar_split_clause,[],[f42,f9078]) ).
fof(f9078,plain,
( spl0_456
<=> ! [X0,X14,X15] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X14,X0),c_Transitive__Closure_Ortrancl(X15,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f42,axiom,
! [X0,X14,X15] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X14,X0),c_Transitive__Closure_Ortrancl(X15,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
fof(f9076,plain,
spl0_455,
inference(avatar_split_clause,[],[f29,f9074]) ).
fof(f9074,plain,
( spl0_455
<=> ! [X5,X4,X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X4,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f29,axiom,
! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X4,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
fof(f9072,plain,
( ~ spl0_454
| ~ spl0_294
| spl0_450 ),
inference(avatar_split_clause,[],[f8795,f8473,f3371,f9069]) ).
fof(f8795,plain,
( ~ c_FunDef_Oin__rel(hAPP(v_P____,v_x),v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_294
| spl0_450 ),
inference(resolution,[],[f8475,f3372]) ).
fof(f9067,plain,
spl0_453,
inference(avatar_split_clause,[],[f28,f9065]) ).
fof(f28,axiom,
! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
fof(f9063,plain,
spl0_452,
inference(avatar_split_clause,[],[f15,f9061]) ).
fof(f9061,plain,
( spl0_452
<=> ! [X4,X0,X5,X8,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X7,X4,X8,X0),c_Set_Oimage(X7,X5,X8,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X7,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X8,tc_bool)),X8,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f15,axiom,
! [X0,X8,X7,X4,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X7,X4,X8,X0),c_Set_Oimage(X7,X5,X8,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X7,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X8,tc_bool)),X8,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
fof(f8480,plain,
spl0_451,
inference(avatar_split_clause,[],[f672,f8478]) ).
fof(f8478,plain,
( spl0_451
<=> ! [X19,X0,X8,X22] :
( ~ hBOOL(c_in(X22,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X22,X19,X0,X8),X22,X8,X0),X19,tc_prod(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f672,plain,
! [X0,X8,X19,X22] :
( ~ hBOOL(c_in(X22,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X22,X19,X0,X8),X22,X8,X0),X19,tc_prod(X8,X0))) ),
inference(definition_unfolding,[],[f375,f507]) ).
fof(f375,axiom,
! [X0,X8,X19,X22] :
( ~ hBOOL(c_in(X22,c_Relation_ORange(X19,X8,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X22,X19,X0,X8),X22,X8,X0),X19,tc_prod(X8,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeE_0) ).
fof(f8476,plain,
( ~ spl0_450
| spl0_104
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f8357,f8252,f1226,f8473]) ).
fof(f8252,plain,
( spl0_430
<=> ! [X19,X0,X8,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8)))
| hBOOL(c_in(c_Pair(X22,X23,X8,X0),hAPP(c_Relation_Oconverse(X0,X8),X19),tc_prod(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f8357,plain,
( ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| spl0_104
| ~ spl0_430 ),
inference(resolution,[],[f8253,f1228]) ).
fof(f1228,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| spl0_104 ),
inference(avatar_component_clause,[],[f1226]) ).
fof(f8253,plain,
( ! [X0,X8,X19,X22,X23] :
( hBOOL(c_in(c_Pair(X22,X23,X8,X0),hAPP(c_Relation_Oconverse(X0,X8),X19),tc_prod(X8,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8))) )
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f8252]) ).
fof(f8471,plain,
spl0_449,
inference(avatar_split_clause,[],[f671,f8469]) ).
fof(f8469,plain,
( spl0_449
<=> ! [X19,X0,X23,X8] :
( ~ hBOOL(c_in(X23,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X23,X19,X0,X8),X23,X8,X0),X19,tc_prod(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f671,plain,
! [X0,X8,X19,X23] :
( ~ hBOOL(c_in(X23,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X23,X19,X0,X8),X23,X8,X0),X19,tc_prod(X8,X0))) ),
inference(definition_unfolding,[],[f513,f507]) ).
fof(f513,axiom,
! [X0,X8,X19,X23] :
( ~ hBOOL(c_in(X23,c_Relation_ORange(X19,X8,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X23,X19,X0,X8),X23,X8,X0),X19,tc_prod(X8,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_0) ).
fof(f8467,plain,
spl0_448,
inference(avatar_split_clause,[],[f567,f8465]) ).
fof(f8465,plain,
( spl0_448
<=> ! [X5,X4,X0,X22,X23,X8] :
( ~ hBOOL(c_in(X23,X4,X0))
| ~ hBOOL(c_in(X22,hAPP(X5,X23),X8))
| hBOOL(c_in(c_Pair(X23,X22,X0,X8),c_Product__Type_OSigma(X4,X5,X0,X8),tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f567,axiom,
! [X0,X8,X4,X22,X5,X23] :
( ~ hBOOL(c_in(X23,X4,X0))
| ~ hBOOL(c_in(X22,hAPP(X5,X23),X8))
| hBOOL(c_in(c_Pair(X23,X22,X0,X8),c_Product__Type_OSigma(X4,X5,X0,X8),tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
fof(f8463,plain,
spl0_447,
inference(avatar_split_clause,[],[f565,f8461]) ).
fof(f8461,plain,
( spl0_447
<=> ! [X50,X3,X2,X1] :
( X1 = X3
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f565,axiom,
! [X50,X2,X3,X1] :
( X1 = X3
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
fof(f8459,plain,
spl0_446,
inference(avatar_split_clause,[],[f558,f8457]) ).
fof(f8457,plain,
( spl0_446
<=> ! [X50,X3,X2,X1] :
( X2 = X3
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f558,axiom,
! [X50,X2,X3,X1] :
( X2 = X3
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_2) ).
fof(f8455,plain,
spl0_445,
inference(avatar_split_clause,[],[f420,f8453]) ).
fof(f8453,plain,
( spl0_445
<=> ! [X19,X0,X23,X22] :
( ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(X22,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_Pair(X22,X23,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f420,axiom,
! [X0,X19,X22,X23] :
( ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(X22,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_Pair(X22,X23,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
fof(f8451,plain,
spl0_444,
inference(avatar_split_clause,[],[f395,f8449]) ).
fof(f8449,plain,
( spl0_444
<=> ! [X41,X0,X31,X23,X22] :
( X23 = X31
| X23 = X41
| c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X31,c_Set_Oinsert(X41,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f395,axiom,
! [X31,X41,X0,X22,X23] :
( X23 = X31
| X23 = X41
| c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X31,c_Set_Oinsert(X41,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
fof(f8447,plain,
spl0_443,
inference(avatar_split_clause,[],[f392,f8445]) ).
fof(f8445,plain,
( spl0_443
<=> ! [X41,X0,X31,X23,X22] :
( X22 = X41
| X22 = X31
| c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X31,c_Set_Oinsert(X41,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f392,axiom,
! [X31,X41,X0,X22,X23] :
( X22 = X41
| X22 = X31
| c_Set_Oinsert(X23,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X31,c_Set_Oinsert(X41,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
fof(f8443,plain,
spl0_442,
inference(avatar_split_clause,[],[f359,f8441]) ).
fof(f8441,plain,
( spl0_442
<=> ! [X2,X11,X34,X0,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(X11,X34,X0))
| ~ hBOOL(c_in(X2,X34,X0))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X34,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f359,axiom,
! [X2,X0,X11,X19,X34] :
( ~ c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(X11,X34,X0))
| ~ hBOOL(c_in(X2,X34,X0))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X34,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
fof(f8439,plain,
spl0_441,
inference(avatar_split_clause,[],[f358,f8437]) ).
fof(f8437,plain,
( spl0_441
<=> ! [X2,X34,X0,X14,X1] :
( ~ c_Wellfounded_Owf(X14,X0)
| ~ hBOOL(c_in(X1,X34,X0))
| ~ hBOOL(c_in(X2,X34,X0))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X34,X14,X0),X0,X0),X14,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f358,axiom,
! [X2,X0,X1,X14,X34] :
( ~ c_Wellfounded_Owf(X14,X0)
| ~ hBOOL(c_in(X1,X34,X0))
| ~ hBOOL(c_in(X2,X34,X0))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X34,X14,X0),X0,X0),X14,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_1) ).
fof(f8435,plain,
spl0_440,
inference(avatar_split_clause,[],[f260,f8433]) ).
fof(f8433,plain,
( spl0_440
<=> ! [X4,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X4
| ~ c_lessequals(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f260,axiom,
! [X0,X1,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X4
| ~ c_lessequals(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f8431,plain,
spl0_439,
inference(avatar_split_clause,[],[f131,f8429]) ).
fof(f8429,plain,
( spl0_439
<=> ! [X24,X0,X8,X6,X25] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X24,X25,tc_fun(X0,tc_bool)),X6,X0,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X24,X6,X0,X8),c_Product__Type_OSigma(X25,X6,X0,X8),tc_fun(tc_prod(X0,X8),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f131,axiom,
! [X0,X8,X6,X24,X25] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X24,X25,tc_fun(X0,tc_bool)),X6,X0,X8) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X24,X6,X0,X8),c_Product__Type_OSigma(X25,X6,X0,X8),tc_fun(tc_prod(X0,X8),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
fof(f8427,plain,
spl0_438,
inference(avatar_split_clause,[],[f62,f8425]) ).
fof(f8425,plain,
( spl0_438
<=> ! [X24,X0,X8,X6,X25] : c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X24,X25,tc_fun(X0,tc_bool)),X6,X0,X8) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X24,X6,X0,X8),c_Product__Type_OSigma(X25,X6,X0,X8),tc_fun(tc_prod(X0,X8),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f62,axiom,
! [X0,X8,X6,X24,X25] : c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X24,X25,tc_fun(X0,tc_bool)),X6,X0,X8) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X24,X6,X0,X8),c_Product__Type_OSigma(X25,X6,X0,X8),tc_fun(tc_prod(X0,X8),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).
fof(f8423,plain,
spl0_437,
inference(avatar_split_clause,[],[f49,f8421]) ).
fof(f8421,plain,
( spl0_437
<=> ! [X4,X0,X5,X23] : c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f49,axiom,
! [X0,X4,X5,X23] : c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
fof(f8419,plain,
spl0_436,
inference(avatar_split_clause,[],[f48,f8417]) ).
fof(f8417,plain,
( spl0_436
<=> ! [X4,X0,X5,X23] : c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f48,axiom,
! [X0,X4,X5,X23] : c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
fof(f8415,plain,
spl0_435,
inference(avatar_split_clause,[],[f30,f8413]) ).
fof(f8413,plain,
( spl0_435
<=> ! [X4,X0,X5,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X4,X0,X8),c_Relation_ODomain(X5,X0,X8),tc_fun(X0,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(tc_prod(X0,X8),tc_bool)),X0,X8),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f30,axiom,
! [X0,X8,X4,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X4,X0,X8),c_Relation_ODomain(X5,X0,X8),tc_fun(X0,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(tc_prod(X0,X8),tc_bool)),X0,X8),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).
fof(f8411,plain,
spl0_434,
inference(avatar_split_clause,[],[f22,f8409]) ).
fof(f8409,plain,
( spl0_434
<=> ! [X15,X4,X0,X14,X8] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X8,X0),tc_bool)),X4,X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X14,X4,X8,X0),c_Relation_OImage(X15,X4,X8,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f22,axiom,
! [X0,X8,X14,X4,X15] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X8,X0),tc_bool)),X4,X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X14,X4,X8,X0),c_Relation_OImage(X15,X4,X8,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Image_0) ).
fof(f8337,plain,
( ~ spl0_315
| spl0_104
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3909,f3371,f1226,f3904]) ).
fof(f3904,plain,
( spl0_315
<=> c_FunDef_Oin__rel(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f3909,plain,
( ~ c_FunDef_Oin__rel(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| spl0_104
| ~ spl0_294 ),
inference(resolution,[],[f1228,f3372]) ).
fof(f8266,plain,
spl0_433,
inference(avatar_split_clause,[],[f612,f8264]) ).
fof(f612,axiom,
! [X58] :
( ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f8262,plain,
spl0_432,
inference(avatar_split_clause,[],[f602,f8260]) ).
fof(f602,axiom,
! [X58] :
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iff_1) ).
fof(f8258,plain,
spl0_431,
inference(avatar_split_clause,[],[f599,f8256]) ).
fof(f599,axiom,
! [X0,X8,X19,X22,X23] :
( hBOOL(c_in(c_Pair(X22,X23,X8,X0),X19,tc_prod(X8,X0)))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),hAPP(c_Relation_Oconverse(X8,X0),X19),tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseD_0) ).
fof(f8254,plain,
spl0_430,
inference(avatar_split_clause,[],[f598,f8252]) ).
fof(f598,axiom,
! [X0,X8,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8)))
| hBOOL(c_in(c_Pair(X22,X23,X8,X0),hAPP(c_Relation_Oconverse(X0,X8),X19),tc_prod(X8,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseI_0) ).
fof(f8250,plain,
spl0_429,
inference(avatar_split_clause,[],[f515,f8248]) ).
fof(f515,axiom,
! [X0,X8,X19,X45] :
( ~ hBOOL(c_in(X45,hAPP(c_Relation_Oconverse(X8,X0),X19),tc_prod(X0,X8)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XconverseE__1__2(X19,X45,X8,X0),c_ATP__Linkup_Osko__Relation__XconverseE__1__1(X19,X45,X8,X0),X0,X8) = X45 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseE_0) ).
fof(f8246,plain,
spl0_428,
inference(avatar_split_clause,[],[f411,f8244]) ).
fof(f8244,plain,
( spl0_428
<=> ! [X19,X0,X8,X23,X22] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X8,X0),X19,tc_prod(X8,X0)))
| hBOOL(c_in(X22,c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),X8,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f411,axiom,
! [X0,X8,X19,X22,X23] :
( ~ hBOOL(c_in(c_Pair(X23,X22,X8,X0),X19,tc_prod(X8,X0)))
| hBOOL(c_in(X22,c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),X8,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
fof(f8242,plain,
spl0_427,
inference(avatar_split_clause,[],[f385,f8240]) ).
fof(f8240,plain,
( spl0_427
<=> ! [X19,X0,X8,X23,X22] :
( hBOOL(c_in(c_Pair(X23,X22,X8,X0),X19,tc_prod(X8,X0)))
| ~ hBOOL(c_in(X22,c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),X8,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f385,axiom,
! [X0,X8,X19,X22,X23] :
( hBOOL(c_in(c_Pair(X23,X22,X8,X0),X19,tc_prod(X8,X0)))
| ~ hBOOL(c_in(X22,c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),X8,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
fof(f7909,plain,
( spl0_109
| ~ spl0_42
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1468,f1390,f909,f1249]) ).
fof(f1249,plain,
( spl0_109
<=> hBOOL(hAPP(hAPP(v_P_H____,v_x),c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1468,plain,
( hBOOL(hAPP(hAPP(v_P_H____,v_x),c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_42
| ~ spl0_132 ),
inference(superposition,[],[f910,f1392]) ).
fof(f7480,plain,
spl0_426,
inference(avatar_split_clause,[],[f571,f7478]) ).
fof(f571,axiom,
! [X0,X8,X19,X4,X22,X23] :
( ~ hBOOL(c_in(X23,X4,X0))
| hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X0,X8),X8))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
fof(f7476,plain,
spl0_425,
inference(avatar_split_clause,[],[f569,f7474]) ).
fof(f569,axiom,
! [X0,X19,X22,X23] :
( ~ hBOOL(c_in(X22,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downward_0) ).
fof(f7472,plain,
spl0_424,
inference(avatar_split_clause,[],[f545,f7470]) ).
fof(f545,axiom,
! [X2,X0,X1,X19] :
( ~ c_Relation_Osym(X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__def_0) ).
fof(f7468,plain,
spl0_423,
inference(avatar_split_clause,[],[f534,f7466]) ).
fof(f534,axiom,
! [X0,X1,X19,X23] :
( ~ c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(c_Pair(X23,X1,X0,X0),X19,tc_prod(X0,X0)))
| ~ hBOOL(c_in(c_Pair(X1,X23,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__asym_0) ).
fof(f7464,plain,
spl0_422,
inference(avatar_split_clause,[],[f511,f7462]) ).
fof(f7462,plain,
( spl0_422
<=> ! [X4,X19,X0,X22,X8] :
( ~ hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X8,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X4,X22,X19,X8,X0),X22,X8,X0),X19,tc_prod(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f511,axiom,
! [X0,X8,X19,X4,X22] :
( ~ hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X8,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X4,X22,X19,X8,X0),X22,X8,X0),X19,tc_prod(X8,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_1) ).
fof(f7460,plain,
spl0_421,
inference(avatar_split_clause,[],[f427,f7458]) ).
fof(f427,axiom,
! [X0,X18,X8,X19,X20] : hAPP(c_Relation_Oconverse(X8,X0),c_Relation_Orel__comp(X19,X20,X8,X18,X0)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X18,X0),X20),hAPP(c_Relation_Oconverse(X8,X18),X19),X0,X18,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
fof(f7456,plain,
spl0_420,
inference(avatar_split_clause,[],[f373,f7454]) ).
fof(f7454,plain,
( spl0_420
<=> ! [X19,X0,X2,X1] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f373,axiom,
! [X2,X0,X1,X19] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_1) ).
fof(f7452,plain,
spl0_419,
inference(avatar_split_clause,[],[f361,f7450]) ).
fof(f361,axiom,
! [X0,X8,X19,X4,X22] :
( ~ hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X8,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X22,X19,X8,X0),X22,X8,X0),X19,tc_prod(X8,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_0) ).
fof(f7448,plain,
spl0_418,
inference(avatar_split_clause,[],[f324,f7446]) ).
fof(f7446,plain,
( spl0_418
<=> ! [X2,X23,X0,X12,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X2))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f324,axiom,
! [X2,X0,X19,X12,X23] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X2))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct_0) ).
fof(f7444,plain,
spl0_417,
inference(avatar_split_clause,[],[f323,f7442]) ).
fof(f7442,plain,
( spl0_417
<=> ! [X2,X0,X14,X12,X39] :
( ~ c_Wellfounded_Owf(X14,X0)
| hBOOL(hAPP(X12,X39))
| hBOOL(hAPP(X12,X2))
| ~ hBOOL(c_in(c_Pair(X2,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X12,X14,X0),X0,X0),X14,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f323,axiom,
! [X2,X39,X0,X14,X12] :
( ~ c_Wellfounded_Owf(X14,X0)
| hBOOL(hAPP(X12,X39))
| hBOOL(hAPP(X12,X2))
| ~ hBOOL(c_in(c_Pair(X2,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X12,X14,X0),X0,X0),X14,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
fof(f7440,plain,
( spl0_370
| ~ spl0_81
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f7389,f4632,f1070,f5528]) ).
fof(f5528,plain,
( spl0_370
<=> hBOOL(hAPP(c_Relation_ODomain(hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f4632,plain,
( spl0_352
<=> hBOOL(c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f7389,plain,
( hBOOL(hAPP(c_Relation_ODomain(hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____))
| ~ spl0_81
| ~ spl0_352 ),
inference(resolution,[],[f4634,f1071]) ).
fof(f4634,plain,
( hBOOL(c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f4632]) ).
fof(f7439,plain,
spl0_416,
inference(avatar_split_clause,[],[f322,f7437]) ).
fof(f7437,plain,
( spl0_416
<=> ! [X2,X11,X0,X12,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X11))
| hBOOL(hAPP(X12,X2))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f322,axiom,
! [X2,X0,X11,X19,X12] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X11))
| hBOOL(hAPP(X12,X2))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__def_0) ).
fof(f7435,plain,
spl0_415,
inference(avatar_split_clause,[],[f321,f7433]) ).
fof(f7433,plain,
( spl0_415
<=> ! [X2,X23,X0,X12,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X2))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f321,axiom,
! [X2,X0,X19,X12,X23] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X23))
| hBOOL(hAPP(X12,X2))
| ~ hBOOL(c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X12,X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
fof(f7431,plain,
spl0_414,
inference(avatar_split_clause,[],[f285,f7429]) ).
fof(f7429,plain,
( spl0_414
<=> ! [X15,X0,X14,X1] :
( ~ hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(X15,X0),tc_prod(X0,X0)))
| hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f285,axiom,
! [X0,X1,X14,X15] :
( ~ hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(X15,X0),tc_prod(X0,X0)))
| hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
fof(f7427,plain,
spl0_413,
inference(avatar_split_clause,[],[f284,f7425]) ).
fof(f7425,plain,
( spl0_413
<=> ! [X15,X0,X14,X1] :
( ~ hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0)))
| hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f284,axiom,
! [X0,X1,X14,X15] :
( ~ hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0)))
| hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
fof(f7423,plain,
spl0_412,
inference(avatar_split_clause,[],[f275,f7421]) ).
fof(f7421,plain,
( spl0_412
<=> ! [X19,X0,X2,X1] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f275,axiom,
! [X2,X0,X1,X19] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X2,X1,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
fof(f7419,plain,
spl0_411,
inference(avatar_split_clause,[],[f270,f7417]) ).
fof(f7417,plain,
( spl0_411
<=> ! [X4,X0,X5,X8,X7] : c_Set_Oimage(X7,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X8,tc_bool)),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X7,X4,X8,X0),c_Set_Oimage(X7,X5,X8,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f270,axiom,
! [X0,X8,X7,X4,X5] : c_Set_Oimage(X7,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X8,tc_bool)),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X7,X4,X8,X0),c_Set_Oimage(X7,X5,X8,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
fof(f7415,plain,
spl0_410,
inference(avatar_split_clause,[],[f263,f7413]) ).
fof(f7413,plain,
( spl0_410
<=> ! [X6,X4,X0,X5] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ominus__class_Ominus(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f263,axiom,
! [X0,X6,X4,X5] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ominus__class_Ominus(X6,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
fof(f7411,plain,
spl0_409,
inference(avatar_split_clause,[],[f172,f7409]) ).
fof(f7409,plain,
( spl0_409
<=> ! [X0,X14,X15] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X14,X0),c_Transitive__Closure_Ortrancl(X15,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f172,axiom,
! [X0,X14,X15] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool)),X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X14,X0),c_Transitive__Closure_Ortrancl(X15,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
fof(f7407,plain,
spl0_408,
inference(avatar_split_clause,[],[f125,f7405]) ).
fof(f7405,plain,
( spl0_408
<=> ! [X0,X14,X15] :
( c_Transitive__Closure_Ortrancl(X14,X0) = c_Transitive__Closure_Ortrancl(X15,X0)
| ~ c_lessequals(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ c_lessequals(X15,c_Transitive__Closure_Ortrancl(X14,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f125,axiom,
! [X0,X14,X15] :
( c_Transitive__Closure_Ortrancl(X14,X0) = c_Transitive__Closure_Ortrancl(X15,X0)
| ~ c_lessequals(X14,X15,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ c_lessequals(X15,c_Transitive__Closure_Ortrancl(X14,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
fof(f7403,plain,
spl0_407,
inference(avatar_split_clause,[],[f21,f7401]) ).
fof(f21,axiom,
! [X0,X8,X14,X4,X5] : c_Relation_OImage(X14,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X8,tc_bool)),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X14,X4,X8,X0),c_Relation_OImage(X14,X5,X8,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Un_0) ).
fof(f7089,plain,
spl0_406,
inference(avatar_split_clause,[],[f650,f7087]) ).
fof(f7087,plain,
( spl0_406
<=> ! [X0,X19] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0)),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f650,plain,
! [X0,X19] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),X19),X0,X0) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0)),X0,X0),
inference(definition_unfolding,[],[f477,f507,f507,f506]) ).
fof(f477,axiom,
! [X0,X19] : c_Relation_ORange(X19,X0,X0) = c_Relation_ORange(c_Transitive__Closure_Otrancl(X19,X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__range_0) ).
fof(f7085,plain,
spl0_405,
inference(avatar_split_clause,[],[f594,f7083]) ).
fof(f7083,plain,
( spl0_405
<=> ! [X31,X41,X0,X18,X54,X8,X22,X42,X23] :
( hAPP(X23,hAPP(X22,X54)) = hAPP(X31,hAPP(X41,X54))
| c_Fun_Ocomp(X23,X22,X18,X8,X0) != c_Fun_Ocomp(X31,X41,X42,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f594,axiom,
! [X31,X41,X0,X18,X54,X8,X22,X42,X23] :
( hAPP(X23,hAPP(X22,X54)) = hAPP(X31,hAPP(X41,X54))
| c_Fun_Ocomp(X23,X22,X18,X8,X0) != c_Fun_Ocomp(X31,X41,X42,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
fof(f7081,plain,
spl0_404,
inference(avatar_split_clause,[],[f512,f7079]) ).
fof(f7079,plain,
( spl0_404
<=> ! [X0,X14,X2,X1] :
( X1 = X2
| hBOOL(c_in(X1,c_Relation_ODomain(X14,X0,X0),X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f512,axiom,
! [X2,X0,X1,X14] :
( X1 = X2
| hBOOL(c_in(X1,c_Relation_ODomain(X14,X0,X0),X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
fof(f7077,plain,
spl0_403,
inference(avatar_split_clause,[],[f386,f7075]) ).
fof(f386,axiom,
! [X0,X19,X4,X23] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| ~ hBOOL(c_in(X23,X4,X0))
| hBOOL(c_in(X23,c_Relation_OImage(X19,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
fof(f7073,plain,
spl0_402,
inference(avatar_split_clause,[],[f173,f7071]) ).
fof(f173,axiom,
! [X0,X1,X4,X5] :
( hBOOL(c_in(X1,X5,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
fof(f7069,plain,
spl0_401,
inference(avatar_split_clause,[],[f163,f7067]) ).
fof(f7065,plain,
spl0_400,
inference(avatar_split_clause,[],[f105,f7063]) ).
fof(f105,axiom,
! [X0,X4,X5,X23] :
( ~ hBOOL(c_in(X23,X4,X0))
| c_Set_Oinsert(X23,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
fof(f7061,plain,
spl0_399,
inference(avatar_split_clause,[],[f104,f7059]) ).
fof(f104,axiom,
! [X0,X6,X5,X23] :
( ~ hBOOL(c_in(X23,X6,X0))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X23,X5,X0),X6,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
fof(f7057,plain,
spl0_398,
inference(avatar_split_clause,[],[f69,f7055]) ).
fof(f7055,plain,
( spl0_398
<=> ! [X4,X20,X0,X5,X19] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| ~ c_Relation_Orefl__on(X5,X20,X0)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f69,axiom,
! [X0,X19,X4,X5,X20] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| ~ c_Relation_Orefl__on(X5,X20,X0)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
fof(f7014,plain,
( spl0_397
| ~ spl0_81
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f6483,f6126,f1070,f7011]) ).
fof(f7011,plain,
( spl0_397
<=> hBOOL(hAPP(c_Relation_ODomain(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f6126,plain,
( spl0_389
<=> hBOOL(c_in(v_b____,c_Relation_ODomain(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f6483,plain,
( hBOOL(hAPP(c_Relation_ODomain(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____))
| ~ spl0_81
| ~ spl0_389 ),
inference(resolution,[],[f6128,f1071]) ).
fof(f6128,plain,
( hBOOL(c_in(v_b____,c_Relation_ODomain(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f6126]) ).
fof(f6157,plain,
spl0_396,
inference(avatar_split_clause,[],[f674,f6155]) ).
fof(f674,plain,
! [X0,X1,X8,X19,X23] :
( hBOOL(c_in(X23,c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),X19),X0,X8),X0))
| ~ hBOOL(c_in(c_Pair(X1,X23,X8,X0),X19,tc_prod(X8,X0))) ),
inference(definition_unfolding,[],[f577,f507]) ).
fof(f577,axiom,
! [X0,X1,X8,X19,X23] :
( hBOOL(c_in(X23,c_Relation_ORange(X19,X8,X0),X0))
| ~ hBOOL(c_in(c_Pair(X1,X23,X8,X0),X19,tc_prod(X8,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_1) ).
fof(f6153,plain,
spl0_395,
inference(avatar_split_clause,[],[f601,f6151]) ).
fof(f6151,plain,
( spl0_395
<=> ! [X42,X57,X0,X18,X21,X8,X7] : c_Fun_Ocomp(X7,c_Fun_Ocomp(X21,X57,X42,X18,X0),X18,X8,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X7,X21,X18,X8,X42),X57,X42,X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f601,axiom,
! [X21,X0,X18,X8,X57,X7,X42] : c_Fun_Ocomp(X7,c_Fun_Ocomp(X21,X57,X42,X18,X0),X18,X8,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X7,X21,X18,X8,X42),X57,X42,X8,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
fof(f6149,plain,
spl0_394,
inference(avatar_split_clause,[],[f520,f6147]) ).
fof(f520,axiom,
! [X0,X1,X8,X19,X7,X23] :
( ~ hBOOL(c_in(c_Pair(X1,X23,X0,X0),X19,tc_prod(X0,X0)))
| hAPP(X7,X1) = hAPP(c_Recdef_Ocut(X7,X19,X23,X0,X8),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut__apply_0) ).
fof(f6145,plain,
spl0_393,
inference(avatar_split_clause,[],[f489,f6143]) ).
fof(f489,axiom,
! [X28,X0,X18,X8,X14,X15,X42] : c_Relation_Orel__comp(c_Relation_Orel__comp(X14,X15,X0,X42,X18),X28,X0,X18,X8) = c_Relation_Orel__comp(X14,c_Relation_Orel__comp(X15,X28,X42,X18,X8),X0,X42,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_O__assoc_0) ).
fof(f6141,plain,
spl0_392,
inference(avatar_split_clause,[],[f378,f6139]) ).
fof(f6139,plain,
( spl0_392
<=> ! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| ~ c_Relation_Otrans(X19,X0)
| c_lessequals(c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),X19,X0,X0,X0),X19,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f378,axiom,
! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| ~ c_Relation_Otrans(X19,X0)
| c_lessequals(c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),X19,X0,X0,X0),X19,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
fof(f6137,plain,
spl0_391,
inference(avatar_split_clause,[],[f364,f6135]) ).
fof(f6135,plain,
( spl0_391
<=> ! [X19,X0,X23,X8] :
( ~ hBOOL(c_in(X23,c_Relation_ODomain(X19,X0,X8),X0))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X23,X19,X0,X8),X0,X8),X19,tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f364,axiom,
! [X0,X8,X19,X23] :
( ~ hBOOL(c_in(X23,c_Relation_ODomain(X19,X0,X8),X0))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X23,X19,X0,X8),X0,X8),X19,tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
fof(f6133,plain,
spl0_390,
inference(avatar_split_clause,[],[f363,f6131]) ).
fof(f363,axiom,
! [X0,X8,X19,X23] :
( ~ hBOOL(c_in(X23,c_Relation_ODomain(X19,X0,X8),X0))
| hBOOL(c_in(c_Pair(X23,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X23,X19,X0,X8),X0,X8),X19,tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainE_0) ).
fof(f6129,plain,
( spl0_389
| ~ spl0_104
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f4639,f4181,f1226,f6126]) ).
fof(f4639,plain,
( hBOOL(c_in(v_b____,c_Relation_ODomain(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_104
| ~ spl0_329 ),
inference(resolution,[],[f1227,f4182]) ).
fof(f6124,plain,
spl0_388,
inference(avatar_split_clause,[],[f258,f6122]) ).
fof(f6122,plain,
( spl0_388
<=> ! [X5,X4,X0,X6] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f6120,plain,
spl0_387,
inference(avatar_split_clause,[],[f218,f6118]) ).
fof(f6118,plain,
( spl0_387
<=> ! [X5,X4,X0,X6] :
( ~ c_lessequals(X6,X4,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X5,tc_fun(X0,tc_bool))
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f218,axiom,
! [X0,X6,X4,X5] :
( ~ c_lessequals(X6,X4,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,X5,tc_fun(X0,tc_bool))
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
fof(f6116,plain,
spl0_386,
inference(avatar_split_clause,[],[f75,f6114]) ).
fof(f6114,plain,
( spl0_386
<=> ! [X5,X4,X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f75,axiom,
! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
fof(f6112,plain,
spl0_385,
inference(avatar_split_clause,[],[f74,f6110]) ).
fof(f6110,plain,
( spl0_385
<=> ! [X5,X4,X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f74,axiom,
! [X0,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
fof(f6108,plain,
spl0_384,
inference(avatar_split_clause,[],[f14,f6106]) ).
fof(f6106,plain,
( spl0_384
<=> ! [X5,X4,X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f14,axiom,
! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
fof(f6104,plain,
spl0_383,
inference(avatar_split_clause,[],[f13,f6102]) ).
fof(f13,axiom,
! [X0,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
fof(f6100,plain,
spl0_382,
inference(avatar_split_clause,[],[f8,f6098]) ).
fof(f6098,plain,
( spl0_382
<=> ! [X5,X4,X0,X6] :
( ~ c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f8,axiom,
! [X0,X6,X4,X5] :
( ~ c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
fof(f5874,plain,
spl0_381,
inference(avatar_split_clause,[],[f581,f5872]) ).
fof(f5872,plain,
( spl0_381
<=> ! [X4,X23,X8,X0,X5,X22] :
( hBOOL(c_in(X22,hAPP(X5,X23),X8))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),c_Product__Type_OSigma(X4,X5,X0,X8),tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f581,axiom,
! [X0,X8,X4,X22,X5,X23] :
( hBOOL(c_in(X22,hAPP(X5,X23),X8))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),c_Product__Type_OSigma(X4,X5,X0,X8),tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
fof(f5870,plain,
spl0_380,
inference(avatar_split_clause,[],[f409,f5868]) ).
fof(f5868,plain,
( spl0_380
<=> ! [X4,X0,X5,X1] :
( X4 = X5
| hBOOL(c_in(X1,X4,X0))
| hBOOL(c_in(X1,X5,X0))
| c_Set_Oinsert(X1,X5,X0) != c_Set_Oinsert(X1,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f409,axiom,
! [X0,X1,X4,X5] :
( X4 = X5
| hBOOL(c_in(X1,X4,X0))
| hBOOL(c_in(X1,X5,X0))
| c_Set_Oinsert(X1,X5,X0) != c_Set_Oinsert(X1,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f5866,plain,
spl0_379,
inference(avatar_split_clause,[],[f345,f5864]) ).
fof(f5864,plain,
( spl0_379
<=> ! [X4,X0,X31] :
( ~ hBOOL(c_in(X31,c_Relation_OId__on(X4,X0),tc_prod(X0,X0)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X31,X0),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X31,X0),X0,X0) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f345,axiom,
! [X31,X0,X4] :
( ~ hBOOL(c_in(X31,c_Relation_OId__on(X4,X0),tc_prod(X0,X0)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X31,X0),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X31,X0),X0,X0) = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__onE_1) ).
fof(f5862,plain,
spl0_378,
inference(avatar_split_clause,[],[f335,f5860]) ).
fof(f5860,plain,
( spl0_378
<=> ! [X31,X4,X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X4
| c_Set_Oimage(c_COMBK(X31,X0,X8),X4,X8,X0) = c_Set_Oinsert(X31,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f335,axiom,
! [X31,X0,X8,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X4
| c_Set_Oimage(c_COMBK(X31,X0,X8),X4,X8,X0) = c_Set_Oinsert(X31,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
fof(f5807,plain,
( spl0_377
| ~ spl0_54
| ~ spl0_353
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5803,f5800,f4993,f958,f5805]) ).
fof(f5800,plain,
( spl0_376
<=> ! [X4,X0,X1] :
( hBOOL(c_in(X1,X4,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X0),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f5803,plain,
( ! [X0,X1,X4] :
( c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X4
| hBOOL(c_in(X1,X4,X0)) )
| ~ spl0_54
| ~ spl0_353
| ~ spl0_376 ),
inference(forward_demodulation,[],[f5801,f5061]) ).
fof(f5061,plain,
( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X0,X3),c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ spl0_54
| ~ spl0_353 ),
inference(resolution,[],[f4994,f959]) ).
fof(f5801,plain,
( ! [X0,X1,X4] :
( hBOOL(c_in(X1,X4,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X0),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X4 )
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f5800]) ).
fof(f5802,plain,
spl0_376,
inference(avatar_split_clause,[],[f208,f5800]) ).
fof(f208,axiom,
! [X0,X1,X4] :
( hBOOL(c_in(X1,X4,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X0),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
fof(f5798,plain,
spl0_375,
inference(avatar_split_clause,[],[f178,f5796]) ).
fof(f5796,plain,
( spl0_375
<=> ! [X5,X4,X0,X6] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f178,axiom,
! [X0,X6,X4,X5] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
fof(f5794,plain,
spl0_374,
inference(avatar_split_clause,[],[f177,f5792]) ).
fof(f5792,plain,
( spl0_374
<=> ! [X5,X4,X0,X6] :
( ~ c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f177,axiom,
! [X0,X6,X4,X5] :
( ~ c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
fof(f5790,plain,
spl0_373,
inference(avatar_split_clause,[],[f101,f5788]) ).
fof(f5788,plain,
( spl0_373
<=> ! [X20,X0,X19] :
( ~ c_lessequals(X19,c_Transitive__Closure_Ortrancl(X20,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X19,X0),c_Transitive__Closure_Ortrancl(X20,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f101,axiom,
! [X0,X19,X20] :
( ~ c_lessequals(X19,c_Transitive__Closure_Ortrancl(X20,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X19,X0),c_Transitive__Closure_Ortrancl(X20,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
fof(f5786,plain,
spl0_372,
inference(avatar_split_clause,[],[f50,f5784]) ).
fof(f5784,plain,
( spl0_372
<=> ! [X4,X0,X5,X23] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X23,X4,X0),c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f50,axiom,
! [X0,X4,X5,X23] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X23,X4,X0),c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
fof(f5782,plain,
spl0_371,
inference(avatar_split_clause,[],[f33,f5780]) ).
fof(f5780,plain,
( spl0_371
<=> ! [X4,X0,X8,X5,X1,X7] :
( ~ hBOOL(c_in(X1,X4,X8))
| hBOOL(c_in(hAPP(X7,X1),X5,X0))
| ~ c_lessequals(c_Set_Oimage(X7,X4,X8,X0),X5,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f33,axiom,
! [X0,X1,X8,X7,X4,X5] :
( ~ hBOOL(c_in(X1,X4,X8))
| hBOOL(c_in(hAPP(X7,X1),X5,X0))
| ~ c_lessequals(c_Set_Oimage(X7,X4,X8,X0),X5,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f5531,plain,
( ~ spl0_370
| ~ spl0_80
| spl0_352 ),
inference(avatar_split_clause,[],[f5040,f4632,f1066,f5528]) ).
fof(f5040,plain,
( ~ hBOOL(hAPP(c_Relation_ODomain(hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____))
| ~ spl0_80
| spl0_352 ),
inference(resolution,[],[f4633,f1067]) ).
fof(f4633,plain,
( ~ hBOOL(c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| spl0_352 ),
inference(avatar_component_clause,[],[f4632]) ).
fof(f5060,plain,
spl0_369,
inference(avatar_split_clause,[],[f670,f5058]) ).
fof(f5058,plain,
( spl0_369
<=> ! [X0,X19] :
( ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X0,X0),X19),X0)
| c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f670,plain,
! [X0,X19] :
( ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X0,X0),X19),X0)
| c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0)),X0) ),
inference(definition_unfolding,[],[f469,f506]) ).
fof(f469,axiom,
! [X0,X19] :
( ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X0,X0),X19),X0)
| c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X0,X0),c_Transitive__Closure_Otrancl(X19,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
fof(f5056,plain,
spl0_368,
inference(avatar_split_clause,[],[f669,f5054]) ).
fof(f5054,plain,
( spl0_368
<=> ! [X0,X19,X35] :
( ~ hBOOL(c_in(X35,X19,tc_prod(X0,X0)))
| hBOOL(c_in(X35,c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f669,plain,
! [X0,X19,X35] :
( ~ hBOOL(c_in(X35,X19,tc_prod(X0,X0)))
| hBOOL(c_in(X35,c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f440,f506]) ).
fof(f440,axiom,
! [X0,X19,X35] :
( ~ hBOOL(c_in(X35,X19,tc_prod(X0,X0)))
| hBOOL(c_in(X35,c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
fof(f5052,plain,
spl0_367,
inference(avatar_split_clause,[],[f665,f5050]) ).
fof(f5050,plain,
( spl0_367
<=> ! [X0,X1,X19] :
( ~ c_Wellfounded_Oacyclic(X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f665,plain,
! [X0,X1,X19] :
( ~ c_Wellfounded_Oacyclic(X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_prod(X0,X0))) ),
inference(definition_unfolding,[],[f329,f506]) ).
fof(f329,axiom,
! [X0,X1,X19] :
( ~ c_Wellfounded_Oacyclic(X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
fof(f5048,plain,
spl0_366,
inference(avatar_split_clause,[],[f368,f5046]) ).
fof(f5046,plain,
( spl0_366
<=> ! [X0,X1,X19] :
( hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X19,X1,X0),X1,X0,X0),X19,tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f368,axiom,
! [X0,X1,X19] :
( hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X19,X1,X0),X1,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
fof(f5044,plain,
spl0_365,
inference(avatar_split_clause,[],[f365,f5042]) ).
fof(f365,axiom,
! [X0,X1,X14] :
( hBOOL(c_in(X1,c_Wellfounded_Oacc(X14,X0),X0))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X14,X1,X0),X1,X0,X0),X14,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
fof(f5039,plain,
spl0_364,
inference(avatar_split_clause,[],[f362,f5037]) ).
fof(f362,axiom,
! [X31,X0,X1,X8,X4] :
( ~ hBOOL(c_in(X1,X4,X0))
| c_Set_Oimage(c_COMBK(X31,X8,X0),X4,X0,X8) = c_Set_Oinsert(X31,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
fof(f5035,plain,
spl0_363,
inference(avatar_split_clause,[],[f351,f5033]) ).
fof(f5033,plain,
( spl0_363
<=> ! [X4,X0,X19] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| c_lessequals(X19,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),X19,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f351,axiom,
! [X0,X19,X4] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| c_lessequals(X19,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),X19,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
fof(f5031,plain,
spl0_362,
inference(avatar_split_clause,[],[f339,f5029]) ).
fof(f5029,plain,
( spl0_362
<=> ! [X19,X0,X22,X23,X8] : c_Relation_ODomain(c_Set_Oinsert(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8)),X0,X8) = c_Set_Oinsert(X23,c_Relation_ODomain(X19,X0,X8),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f5027,plain,
spl0_361,
inference(avatar_split_clause,[],[f294,f5025]) ).
fof(f5025,plain,
( spl0_361
<=> ! [X23,X0,X12,X19] :
( hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X12,X19,X0),c_Wellfounded_Oacc(X19,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f294,axiom,
! [X0,X19,X12,X23] :
( hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X12,X19,X0),c_Wellfounded_Oacc(X19,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_0) ).
fof(f5023,plain,
spl0_360,
inference(avatar_split_clause,[],[f289,f5021]) ).
fof(f5021,plain,
( spl0_360
<=> ! [X23,X0,X12,X19] :
( hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X12,X19,X0),c_Wellfounded_Oacc(X19,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f289,axiom,
! [X0,X19,X12,X23] :
( hBOOL(hAPP(X12,X23))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X12,X19,X0),c_Wellfounded_Oacc(X19,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
fof(f5019,plain,
spl0_359,
inference(avatar_split_clause,[],[f278,f5017]) ).
fof(f278,axiom,
! [X0,X1,X4,X5] :
( ~ hBOOL(c_in(X1,X5,X0))
| ~ hBOOL(c_in(X1,X4,X0))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f5015,plain,
spl0_358,
inference(avatar_split_clause,[],[f138,f5013]) ).
fof(f138,axiom,
! [X0,X6,X5,X23] :
( hBOOL(c_in(X23,X6,X0))
| c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X23,X5,X0),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
fof(f5011,plain,
spl0_357,
inference(avatar_split_clause,[],[f137,f5009]) ).
fof(f137,axiom,
! [X0,X4,X5,X23] :
( hBOOL(c_in(X23,X4,X0))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
fof(f5007,plain,
spl0_356,
inference(avatar_split_clause,[],[f132,f5005]) ).
fof(f132,axiom,
! [X0,X1,X8,X7,X4] :
( ~ hBOOL(c_in(X1,X4,X0))
| c_Set_Oimage(X7,X4,X0,X8) = c_Set_Oinsert(hAPP(X7,X1),c_Set_Oimage(X7,X4,X0,X8),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
fof(f5003,plain,
spl0_355,
inference(avatar_split_clause,[],[f124,f5001]) ).
fof(f5001,plain,
( spl0_355
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f124,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
fof(f4999,plain,
spl0_354,
inference(avatar_split_clause,[],[f84,f4997]) ).
fof(f4997,plain,
( spl0_354
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f84,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
fof(f4995,plain,
spl0_353,
inference(avatar_split_clause,[],[f37,f4993]) ).
fof(f37,axiom,
! [X0,X1,X4,X5] :
( ~ hBOOL(c_in(X1,X5,X0))
| c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
fof(f4635,plain,
( spl0_352
| ~ spl0_103
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f4429,f4181,f1219,f4632]) ).
fof(f4429,plain,
( hBOOL(c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_x),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_103
| ~ spl0_329 ),
inference(resolution,[],[f4182,f1221]) ).
fof(f4533,plain,
spl0_351,
inference(avatar_split_clause,[],[f708,f4531]) ).
fof(f4531,plain,
( spl0_351
<=> ! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f708,plain,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
inference(forward_demodulation,[],[f350,f652]) ).
fof(f652,plain,
! [X0,X19] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X19,X0),X19,X0,X0,X0) = c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),
inference(definition_unfolding,[],[f505,f506]) ).
fof(f505,axiom,
! [X0,X19] : c_Transitive__Closure_Otrancl(X19,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X19,X0),X19,X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
fof(f350,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X19,X0),X19,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
fof(f4529,plain,
spl0_350,
inference(avatar_split_clause,[],[f655,f4527]) ).
fof(f4527,plain,
( spl0_350
<=> ! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f655,plain,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),
inference(definition_unfolding,[],[f349,f506]) ).
fof(f349,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X19,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
fof(f4525,plain,
spl0_349,
inference(avatar_split_clause,[],[f586,f4523]) ).
fof(f586,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
fof(f4521,plain,
spl0_348,
inference(avatar_split_clause,[],[f585,f4519]) ).
fof(f585,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| hBOOL(c_in(X2,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
fof(f4517,plain,
spl0_347,
inference(avatar_split_clause,[],[f584,f4515]) ).
fof(f584,axiom,
! [X0,X1,X19,X4] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| ~ hBOOL(c_in(X1,X4,X0))
| hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
fof(f4513,plain,
spl0_346,
inference(avatar_split_clause,[],[f582,f4511]) ).
fof(f4511,plain,
( spl0_346
<=> ! [X5,X4,X0,X22,X23,X8] :
( hBOOL(c_in(X23,X4,X0))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),c_Product__Type_OSigma(X4,X5,X0,X8),tc_prod(X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f582,axiom,
! [X0,X8,X4,X22,X5,X23] :
( hBOOL(c_in(X23,X4,X0))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),c_Product__Type_OSigma(X4,X5,X0,X8),tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
fof(f4509,plain,
spl0_345,
inference(avatar_split_clause,[],[f576,f4507]) ).
fof(f576,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
fof(f4505,plain,
spl0_344,
inference(avatar_split_clause,[],[f575,f4503]) ).
fof(f575,axiom,
! [X2,X0,X1,X19,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| hBOOL(c_in(X2,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
fof(f4501,plain,
spl0_343,
inference(avatar_split_clause,[],[f267,f4499]) ).
fof(f4499,plain,
( spl0_343
<=> ! [X4,X0,X8,X1,X7] :
( ~ c_lessequals(X1,X4,tc_fun(X8,tc_bool))
| c_lessequals(c_Set_Oimage(X7,X1,X8,X0),c_Set_Oimage(X7,X4,X8,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f267,axiom,
! [X0,X1,X8,X7,X4] :
( ~ c_lessequals(X1,X4,tc_fun(X8,tc_bool))
| c_lessequals(c_Set_Oimage(X7,X1,X8,X0),c_Set_Oimage(X7,X4,X8,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
fof(f4497,plain,
spl0_342,
inference(avatar_split_clause,[],[f259,f4495]) ).
fof(f4495,plain,
( spl0_342
<=> ! [X19,X20,X0,X8] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X8),tc_bool))
| c_lessequals(c_Relation_ODomain(X19,X0,X8),c_Relation_ODomain(X20,X0,X8),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f259,axiom,
! [X0,X8,X19,X20] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X8),tc_bool))
| c_lessequals(c_Relation_ODomain(X19,X0,X8),c_Relation_ODomain(X20,X0,X8),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
fof(f4493,plain,
spl0_341,
inference(avatar_split_clause,[],[f224,f4491]) ).
fof(f4491,plain,
( spl0_341
<=> ! [X4,X0,X5,X1] :
( ~ hBOOL(c_in(X1,X5,X0))
| ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f224,axiom,
! [X0,X1,X4,X5] :
( ~ hBOOL(c_in(X1,X5,X0))
| ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f4489,plain,
spl0_340,
inference(avatar_split_clause,[],[f220,f4487]) ).
fof(f4487,plain,
( spl0_340
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f220,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f4485,plain,
spl0_339,
inference(avatar_split_clause,[],[f219,f4483]) ).
fof(f4483,plain,
( spl0_339
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f219,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f4481,plain,
spl0_338,
inference(avatar_split_clause,[],[f201,f4479]) ).
fof(f4479,plain,
( spl0_338
<=> ! [X18,X19,X0,X21,X8,X7] : c_Set_Oimage(c_Fun_Ocomp(X7,X21,X18,X0,X8),X19,X8,X0) = c_Set_Oimage(X7,c_Set_Oimage(X21,X19,X8,X18),X18,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f201,axiom,
! [X21,X0,X18,X8,X19,X7] : c_Set_Oimage(c_Fun_Ocomp(X7,X21,X18,X0,X8),X19,X8,X0) = c_Set_Oimage(X7,c_Set_Oimage(X21,X19,X8,X18),X18,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__compose_0) ).
fof(f4477,plain,
( spl0_298
| ~ spl0_103
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4421,f3367,f1219,f3710]) ).
fof(f3710,plain,
( spl0_298
<=> c_FunDef_Oin__rel(hAPP(v_P_H____,v_x),v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f4421,plain,
( c_FunDef_Oin__rel(hAPP(v_P_H____,v_x),v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_103
| ~ spl0_293 ),
inference(resolution,[],[f1221,f3368]) ).
fof(f4476,plain,
spl0_337,
inference(avatar_split_clause,[],[f196,f4474]) ).
fof(f4474,plain,
( spl0_337
<=> ! [X31,X4,X0,X5] :
( ~ hBOOL(c_in(X31,X4,X0))
| hBOOL(c_in(X31,X5,X0))
| hBOOL(c_in(X31,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f196,axiom,
! [X31,X0,X4,X5] :
( ~ hBOOL(c_in(X31,X4,X0))
| hBOOL(c_in(X31,X5,X0))
| hBOOL(c_in(X31,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
fof(f4472,plain,
spl0_336,
inference(avatar_split_clause,[],[f190,f4470]) ).
fof(f4470,plain,
( spl0_336
<=> ! [X31,X4,X0,X5] :
( hBOOL(c_in(X31,X5,X0))
| hBOOL(c_in(X31,X4,X0))
| ~ hBOOL(c_in(X31,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f190,axiom,
! [X31,X0,X4,X5] :
( hBOOL(c_in(X31,X5,X0))
| hBOOL(c_in(X31,X4,X0))
| ~ hBOOL(c_in(X31,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f4468,plain,
spl0_335,
inference(avatar_split_clause,[],[f183,f4466]) ).
fof(f4466,plain,
( spl0_335
<=> ! [X31,X4,X0,X5] :
( ~ hBOOL(c_in(X31,X4,X0))
| ~ hBOOL(c_in(X31,X5,X0))
| hBOOL(c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f183,axiom,
! [X31,X0,X4,X5] :
( ~ hBOOL(c_in(X31,X4,X0))
| ~ hBOOL(c_in(X31,X5,X0))
| hBOOL(c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
fof(f4464,plain,
spl0_334,
inference(avatar_split_clause,[],[f134,f4462]) ).
fof(f4462,plain,
( spl0_334
<=> ! [X4,X0,X5,X1] :
( hBOOL(c_in(X1,X4,X0))
| c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X4,c_Set_Oinsert(X1,X5,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f134,axiom,
! [X0,X1,X4,X5] :
( hBOOL(c_in(X1,X4,X0))
| c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X4,c_Set_Oinsert(X1,X5,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
fof(f4460,plain,
spl0_333,
inference(avatar_split_clause,[],[f127,f4458]) ).
fof(f4458,plain,
( spl0_333
<=> ! [X4,X0,X23] : c_Set_Oinsert(X23,X4,X0) = c_Set_Oinsert(X23,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f127,axiom,
! [X0,X4,X23] : c_Set_Oinsert(X23,X4,X0) = c_Set_Oinsert(X23,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
fof(f4456,plain,
spl0_332,
inference(avatar_split_clause,[],[f52,f4454]) ).
fof(f4454,plain,
( spl0_332
<=> ! [X20,X0,X19] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X19,X0),c_Transitive__Closure_Ortrancl(X20,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f52,axiom,
! [X0,X19,X20] :
( ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X19,X0),c_Transitive__Closure_Ortrancl(X20,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
fof(f4452,plain,
spl0_331,
inference(avatar_split_clause,[],[f27,f4450]) ).
fof(f4450,plain,
( spl0_331
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f27,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f4448,plain,
spl0_330,
inference(avatar_split_clause,[],[f26,f4446]) ).
fof(f4446,plain,
( spl0_330
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f26,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f4420,plain,
( spl0_103
| ~ spl0_54
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1467,f1390,f958,f1219]) ).
fof(f4183,plain,
spl0_329,
inference(avatar_split_clause,[],[f580,f4181]) ).
fof(f580,axiom,
! [X0,X8,X19,X22,X23] :
( hBOOL(c_in(X23,c_Relation_ODomain(X19,X0,X8),X0))
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X8),X19,tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainI_0) ).
fof(f4179,plain,
spl0_328,
inference(avatar_split_clause,[],[f491,f4177]) ).
fof(f491,axiom,
! [X0,X19] :
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X19,X0,X0),X19,X0)
| c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),X19,X0,X0,X0) != X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
fof(f4175,plain,
spl0_327,
inference(avatar_split_clause,[],[f463,f4173]) ).
fof(f4173,plain,
( spl0_327
<=> ! [X4,X19,X0,X22,X8] :
( ~ hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X8,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X4,X22,X19,X8,X0),X4,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f463,axiom,
! [X0,X8,X19,X4,X22] :
( ~ hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X8,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X4,X22,X19,X8,X0),X4,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_0) ).
fof(f4171,plain,
spl0_326,
inference(avatar_split_clause,[],[f431,f4169]) ).
fof(f4169,plain,
( spl0_326
<=> ! [X0,X14,X8,X7] : hAPP(c_Relation_Oconverse(X0,X0),c_Relation_Oinv__image(X14,X7,X8,X0)) = c_Relation_Oinv__image(hAPP(c_Relation_Oconverse(X8,X8),X14),X7,X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f431,axiom,
! [X0,X8,X7,X14] : hAPP(c_Relation_Oconverse(X0,X0),c_Relation_Oinv__image(X14,X7,X8,X0)) = c_Relation_Oinv__image(hAPP(c_Relation_Oconverse(X8,X8),X14),X7,X8,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
fof(f4167,plain,
spl0_325,
inference(avatar_split_clause,[],[f340,f4165]) ).
fof(f4165,plain,
( spl0_325
<=> ! [X4,X0,X14] :
( ~ c_Wellfounded_Owf(X14,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
| ~ c_lessequals(X4,c_Relation_OImage(X14,X4,X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f340,axiom,
! [X0,X14,X4] :
( ~ c_Wellfounded_Owf(X14,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
| ~ c_lessequals(X4,c_Relation_OImage(X14,X4,X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
fof(f4163,plain,
spl0_324,
inference(avatar_split_clause,[],[f338,f4161]) ).
fof(f4161,plain,
( spl0_324
<=> ! [X0,X35] :
( ~ hBOOL(c_in(X35,c_Relation_OId(X0),tc_prod(X0,X0)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X0),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X0),X0,X0) = X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f338,axiom,
! [X0,X35] :
( ~ hBOOL(c_in(X35,c_Relation_OId(X0),tc_prod(X0,X0)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X0),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X0),X0,X0) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IdE_0) ).
fof(f4159,plain,
spl0_323,
inference(avatar_split_clause,[],[f282,f4157]) ).
fof(f4157,plain,
( spl0_323
<=> ! [X4,X19,X0,X22,X8] :
( ~ hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X8,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X22,X19,X8,X0),X4,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f282,axiom,
! [X0,X8,X19,X4,X22] :
( ~ hBOOL(c_in(X22,c_Relation_OImage(X19,X4,X8,X0),X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X22,X19,X8,X0),X4,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_1) ).
fof(f4155,plain,
spl0_322,
inference(avatar_split_clause,[],[f241,f4153]) ).
fof(f4153,plain,
( spl0_322
<=> ! [X21,X8,X7] :
( ~ class_Lattices_Olattice(X8)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(t_a,X8)),v_x) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(X7,v_x),hAPP(X21,v_x),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f241,axiom,
! [X21,X8,X7] :
( ~ class_Lattices_Olattice(X8)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(t_a,X8)),v_x) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(X7,v_x),hAPP(X21,v_x),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
fof(f4151,plain,
spl0_321,
inference(avatar_split_clause,[],[f149,f4149]) ).
fof(f4149,plain,
( spl0_321
<=> ! [X4,X5,X8] :
( ~ class_HOL_Ominus(X8)
| hAPP(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(t_a,X8)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X4,v_x),hAPP(X5,v_x),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f149,axiom,
! [X8,X4,X5] :
( ~ class_HOL_Ominus(X8)
| hAPP(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(t_a,X8)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X4,v_x),hAPP(X5,v_x),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
fof(f4147,plain,
spl0_320,
inference(avatar_split_clause,[],[f106,f4145]) ).
fof(f4145,plain,
( spl0_320
<=> ! [X23,X0,X5,X8,X7] : c_Set_Oimage(X7,c_Set_Oinsert(X23,X5,X8),X8,X0) = c_Set_Oinsert(hAPP(X7,X23),c_Set_Oimage(X7,X5,X8,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f106,axiom,
! [X0,X8,X7,X5,X23] : c_Set_Oimage(X7,c_Set_Oinsert(X23,X5,X8),X8,X0) = c_Set_Oinsert(hAPP(X7,X23),c_Set_Oimage(X7,X5,X8,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f4143,plain,
spl0_319,
inference(avatar_split_clause,[],[f45,f4141]) ).
fof(f4141,plain,
( spl0_319
<=> ! [X4,X0,X5,X23] : c_Lattices_Oupper__semilattice__class_Osup(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f45,axiom,
! [X0,X4,X5,X23] : c_Lattices_Oupper__semilattice__class_Osup(X4,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X23,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
fof(f4139,plain,
spl0_318,
inference(avatar_split_clause,[],[f44,f4137]) ).
fof(f4135,plain,
spl0_317,
inference(avatar_split_clause,[],[f32,f4133]) ).
fof(f4133,plain,
( spl0_317
<=> ! [X5,X4,X0] :
( c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)) = X4
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f32,axiom,
! [X0,X4,X5] :
( c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)) = X4
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
fof(f4131,plain,
spl0_316,
inference(avatar_split_clause,[],[f31,f4129]) ).
fof(f4129,plain,
( spl0_316
<=> ! [X21,X8,X7] :
( ~ class_Lattices_Olattice(X8)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(t_a,X8)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,v_x),hAPP(X21,v_x),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f31,axiom,
! [X21,X8,X7] :
( ~ class_Lattices_Olattice(X8)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(t_a,X8)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,v_x),hAPP(X21,v_x),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
fof(f4111,plain,
( spl0_109
| ~ spl0_42
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1468,f1390,f909,f1249]) ).
fof(f3907,plain,
( spl0_315
| ~ spl0_104
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3668,f3367,f1226,f3904]) ).
fof(f3668,plain,
( c_FunDef_Oin__rel(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_104
| ~ spl0_293 ),
inference(resolution,[],[f3368,f1227]) ).
fof(f3777,plain,
spl0_314,
inference(avatar_split_clause,[],[f574,f3775]) ).
fof(f574,axiom,
! [X0,X1,X4] :
( ~ hBOOL(c_in(X1,X4,X0))
| hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
fof(f3773,plain,
spl0_313,
inference(avatar_split_clause,[],[f573,f3771]) ).
fof(f573,axiom,
! [X2,X0,X1,X4] :
( hBOOL(c_in(X1,X4,X0))
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
fof(f3769,plain,
spl0_312,
inference(avatar_split_clause,[],[f401,f3767]) ).
fof(f3767,plain,
( spl0_312
<=> ! [X22,X0,X23] :
( X22 = X23
| c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f401,axiom,
! [X0,X22,X23] :
( X22 = X23
| c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f3765,plain,
spl0_311,
inference(avatar_split_clause,[],[f356,f3763]) ).
fof(f356,axiom,
! [X0,X19] :
( c_Nitpick_Orefl_H(X19,X0)
| ~ hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X19,X0),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
fof(f3761,plain,
spl0_310,
inference(avatar_split_clause,[],[f353,f3759]) ).
fof(f353,axiom,
! [X0,X19] :
( c_Relation_Oirrefl(X19,X0)
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X19,X0),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X19,X0),X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
fof(f3757,plain,
spl0_309,
inference(avatar_split_clause,[],[f291,f3755]) ).
fof(f3755,plain,
( spl0_309
<=> ! [X23,X0,X12,X19] :
( hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X12,X19,X0)))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f291,axiom,
! [X0,X19,X12,X23] :
( hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X12,X19,X0)))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
fof(f3753,plain,
spl0_308,
inference(avatar_split_clause,[],[f287,f3751]) ).
fof(f3751,plain,
( spl0_308
<=> ! [X23,X0,X12,X19] :
( hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X12,X19,X0)))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f287,axiom,
! [X0,X19,X12,X23] :
( hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X12,X19,X0)))
| ~ hBOOL(c_in(X23,c_Wellfounded_Oacc(X19,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_2) ).
fof(f3749,plain,
spl0_307,
inference(avatar_split_clause,[],[f268,f3747]) ).
fof(f3747,plain,
( spl0_307
<=> ! [X23,X0,X6,X26] :
( ~ c_lessequals(X6,X26,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X23,X6,X0),c_Set_Oinsert(X23,X26,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f268,axiom,
! [X0,X6,X26,X23] :
( ~ c_lessequals(X6,X26,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X23,X6,X0),c_Set_Oinsert(X23,X26,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f3745,plain,
spl0_306,
inference(avatar_split_clause,[],[f246,f3743]) ).
fof(f3743,plain,
( spl0_306
<=> ! [X6,X4,X0,X5] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X0,tc_bool))
| c_lessequals(X4,X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f246,axiom,
! [X0,X6,X4,X5] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X0,tc_bool))
| c_lessequals(X4,X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f3741,plain,
spl0_305,
inference(avatar_split_clause,[],[f227,f3739]) ).
fof(f3739,plain,
( spl0_305
<=> ! [X5,X4,X0] : c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f227,axiom,
! [X0,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f3737,plain,
spl0_304,
inference(avatar_split_clause,[],[f166,f3735]) ).
fof(f3735,plain,
( spl0_304
<=> ! [X5,X4,X0] : c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f166,axiom,
! [X0,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f3733,plain,
spl0_303,
inference(avatar_split_clause,[],[f165,f3731]) ).
fof(f3731,plain,
( spl0_303
<=> ! [X29,X0,X30] :
( ~ c_lessequals(X30,X29,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X29,X0),c_Wellfounded_Oacc(X30,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f165,axiom,
! [X29,X0,X30] :
( ~ c_lessequals(X30,X29,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X29,X0),c_Wellfounded_Oacc(X30,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__subset_0) ).
fof(f3729,plain,
spl0_302,
inference(avatar_split_clause,[],[f145,f3727]) ).
fof(f3727,plain,
( spl0_302
<=> ! [X5,X4,X0] : c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f145,axiom,
! [X0,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
fof(f3725,plain,
spl0_301,
inference(avatar_split_clause,[],[f144,f3723]) ).
fof(f3723,plain,
( spl0_301
<=> ! [X5,X4,X0] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f144,axiom,
! [X0,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
fof(f3721,plain,
spl0_300,
inference(avatar_split_clause,[],[f94,f3719]) ).
fof(f3719,plain,
( spl0_300
<=> ! [X5,X4,X0] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f94,axiom,
! [X0,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
fof(f3717,plain,
spl0_299,
inference(avatar_split_clause,[],[f19,f3715]) ).
fof(f3715,plain,
( spl0_299
<=> ! [X5,X4,X0] : c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f19,axiom,
! [X0,X4,X5] : c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f3713,plain,
( ~ spl0_298
| spl0_103
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3683,f3371,f1219,f3710]) ).
fof(f3683,plain,
( ~ c_FunDef_Oin__rel(hAPP(v_P_H____,v_x),v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| spl0_103
| ~ spl0_294 ),
inference(resolution,[],[f3372,f1220]) ).
fof(f3385,plain,
( spl0_297
| ~ spl0_171
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2600,f2176,f1730,f3383]) ).
fof(f3383,plain,
( spl0_297
<=> ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2600,plain,
( ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_171
| ~ spl0_214 ),
inference(resolution,[],[f2177,f1731]) ).
fof(f3381,plain,
spl0_296,
inference(avatar_split_clause,[],[f652,f3379]) ).
fof(f3377,plain,
spl0_295,
inference(avatar_split_clause,[],[f644,f3375]) ).
fof(f3375,plain,
( spl0_295
<=> ! [X0,X8,X19] : c_Relation_ODomain(X19,X0,X8) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),hAPP(c_Relation_Oconverse(X0,X8),X19)),X0,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f644,plain,
! [X0,X8,X19] : c_Relation_ODomain(X19,X0,X8) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X0),hAPP(c_Relation_Oconverse(X0,X8),X19)),X0,X8),
inference(definition_unfolding,[],[f493,f507]) ).
fof(f493,axiom,
! [X0,X8,X19] : c_Relation_ODomain(X19,X0,X8) = c_Relation_ORange(hAPP(c_Relation_Oconverse(X0,X8),X19),X8,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__converse_0) ).
fof(f3373,plain,
spl0_294,
inference(avatar_split_clause,[],[f522,f3371]) ).
fof(f522,axiom,
! [X2,X0,X1,X8,X14] :
( ~ c_FunDef_Oin__rel(X14,X1,X2,X0,X8)
| hBOOL(c_in(c_Pair(X1,X2,X0,X8),X14,tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rel__def_0) ).
fof(f3369,plain,
spl0_293,
inference(avatar_split_clause,[],[f521,f3367]) ).
fof(f521,axiom,
! [X2,X0,X1,X8,X14] :
( c_FunDef_Oin__rel(X14,X1,X2,X0,X8)
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X8),X14,tc_prod(X0,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rel__def_1) ).
fof(f3365,plain,
spl0_292,
inference(avatar_split_clause,[],[f495,f3363]) ).
fof(f3363,plain,
( spl0_292
<=> ! [X18,X19,X0,X8,X20] :
( ~ c_Relation_Osingle__valued(X19,X0,X8)
| ~ c_Relation_Osingle__valued(X20,X8,X18)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X19,X20,X0,X8,X18),X0,X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f495,axiom,
! [X0,X18,X8,X19,X20] :
( ~ c_Relation_Osingle__valued(X19,X0,X8)
| ~ c_Relation_Osingle__valued(X20,X8,X18)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X19,X20,X0,X8,X18),X0,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
fof(f3361,plain,
spl0_291,
inference(avatar_split_clause,[],[f450,f3359]) ).
fof(f3359,plain,
( spl0_291
<=> ! [X18,X0,X8,X23,X22,X7] : hAPP(hAPP(X7,X23),X22) = hAPP(c_split(X7,X8,X18,X0),c_Pair(X23,X22,X8,X18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f450,axiom,
! [X0,X18,X8,X7,X22,X23] : hAPP(hAPP(X7,X23),X22) = hAPP(c_split(X7,X8,X18,X0),c_Pair(X23,X22,X8,X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).
fof(f3357,plain,
spl0_290,
inference(avatar_split_clause,[],[f355,f3355]) ).
fof(f3355,plain,
( spl0_290
<=> ! [X0,X19] :
( ~ c_Relation_Oantisym(X19,X0)
| ~ c_Relation_Otrans(X19,X0)
| c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f355,axiom,
! [X0,X19] :
( ~ c_Relation_Oantisym(X19,X0)
| ~ c_Relation_Otrans(X19,X0)
| c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).
fof(f3353,plain,
spl0_289,
inference(avatar_split_clause,[],[f344,f3351]) ).
fof(f3351,plain,
( spl0_289
<=> ! [X4,X0,X31] :
( hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X31,X0),X4,X0))
| ~ hBOOL(c_in(X31,c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f344,axiom,
! [X31,X0,X4] :
( hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X31,X0),X4,X0))
| ~ hBOOL(c_in(X31,c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__onE_0) ).
fof(f3349,plain,
spl0_288,
inference(avatar_split_clause,[],[f293,f3347]) ).
fof(f3347,plain,
( spl0_288
<=> ! [X0,X1,X19] :
( hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X19,X1,X0),c_Wellfounded_Oacc(X19,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f293,axiom,
! [X0,X1,X19] :
( hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,X0),X0))
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X19,X1,X0),c_Wellfounded_Oacc(X19,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
fof(f3345,plain,
spl0_287,
inference(avatar_split_clause,[],[f292,f3343]) ).
fof(f3343,plain,
( spl0_287
<=> ! [X12,X1,X19] :
( hBOOL(hAPP(X12,X1))
| ~ hBOOL(hAPP(X12,v_sko__Wellfounded__Xacc__Xinduct__1(X12,X19)))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f292,axiom,
! [X1,X19,X12] :
( hBOOL(hAPP(X12,X1))
| ~ hBOOL(hAPP(X12,v_sko__Wellfounded__Xacc__Xinduct__1(X12,X19)))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
fof(f3341,plain,
( spl0_286
| ~ spl0_173
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2593,f2172,f1738,f3339]) ).
fof(f3339,plain,
( spl0_286
<=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2593,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_173
| ~ spl0_213 ),
inference(resolution,[],[f2173,f1739]) ).
fof(f3337,plain,
spl0_285,
inference(avatar_split_clause,[],[f290,f3335]) ).
fof(f3335,plain,
( spl0_285
<=> ! [X0,X1,X14] :
( hBOOL(c_in(X1,c_Wellfounded_Oacc(X14,X0),X0))
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X14,X1,X0),c_Wellfounded_Oacc(X14,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f290,axiom,
! [X0,X1,X14] :
( hBOOL(c_in(X1,c_Wellfounded_Oacc(X14,X0),X0))
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X14,X1,X0),c_Wellfounded_Oacc(X14,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
fof(f3333,plain,
spl0_284,
inference(avatar_split_clause,[],[f288,f3331]) ).
fof(f3331,plain,
( spl0_284
<=> ! [X12,X1,X19] :
( hBOOL(hAPP(X12,X1))
| ~ hBOOL(hAPP(X12,v_sko__Wellfounded__Xacc__Xinducts__1(X12,X19)))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f288,axiom,
! [X1,X19,X12] :
( hBOOL(hAPP(X12,X1))
| ~ hBOOL(hAPP(X12,v_sko__Wellfounded__Xacc__Xinducts__1(X12,X19)))
| ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,t_a),t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
fof(f3329,plain,
spl0_283,
inference(avatar_split_clause,[],[f262,f3327]) ).
fof(f3327,plain,
( spl0_283
<=> ! [X4,X0,X5,X1] :
( ~ hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f262,axiom,
! [X0,X1,X4,X5] :
( ~ hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f3325,plain,
spl0_282,
inference(avatar_split_clause,[],[f240,f3323]) ).
fof(f3323,plain,
( spl0_282
<=> ! [X6,X4,X0,X5] :
( c_lessequals(X5,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f240,axiom,
! [X0,X6,X4,X5] :
( c_lessequals(X5,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f3321,plain,
spl0_281,
inference(avatar_split_clause,[],[f239,f3319]) ).
fof(f3319,plain,
( spl0_281
<=> ! [X5,X4,X0,X6] :
( c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f239,axiom,
! [X0,X6,X4,X5] :
( c_lessequals(X4,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f3317,plain,
spl0_280,
inference(avatar_split_clause,[],[f164,f3315]) ).
fof(f3315,plain,
( spl0_280
<=> ! [X4,X0,X23] : c_Set_Oinsert(X23,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f3313,plain,
spl0_279,
inference(avatar_split_clause,[],[f151,f3311]) ).
fof(f3311,plain,
( spl0_279
<=> ! [X5,X4,X0,X6] :
( c_lessequals(X6,X4,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f151,axiom,
! [X0,X6,X4,X5] :
( c_lessequals(X6,X4,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f3309,plain,
spl0_278,
inference(avatar_split_clause,[],[f150,f3307]) ).
fof(f3307,plain,
( spl0_278
<=> ! [X6,X4,X0,X5] :
( c_lessequals(X6,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f150,axiom,
! [X0,X6,X4,X5] :
( c_lessequals(X6,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f3305,plain,
spl0_277,
inference(avatar_split_clause,[],[f141,f3303]) ).
fof(f3303,plain,
( spl0_277
<=> ! [X5,X4,X0] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f141,axiom,
! [X0,X4,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f3301,plain,
spl0_276,
inference(avatar_split_clause,[],[f140,f3299]) ).
fof(f3299,plain,
( spl0_276
<=> ! [X4,X5,X0] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f140,axiom,
! [X0,X4,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f3297,plain,
( spl0_275
| ~ spl0_174
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2592,f2172,f1742,f3295]) ).
fof(f3295,plain,
( spl0_275
<=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2592,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_174
| ~ spl0_213 ),
inference(resolution,[],[f2173,f1743]) ).
fof(f3293,plain,
spl0_274,
inference(avatar_split_clause,[],[f112,f3291]) ).
fof(f3291,plain,
( spl0_274
<=> ! [X0,X23,X22,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X23,X1,X0)
| ~ c_lessequals(X22,X1,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f112,axiom,
! [X0,X1,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X23,X1,X0)
| ~ c_lessequals(X22,X1,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
fof(f3289,plain,
spl0_273,
inference(avatar_split_clause,[],[f110,f3287]) ).
fof(f3287,plain,
( spl0_273
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f110,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
fof(f3285,plain,
spl0_272,
inference(avatar_split_clause,[],[f73,f3283]) ).
fof(f3283,plain,
( spl0_272
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f73,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f3281,plain,
spl0_271,
inference(avatar_split_clause,[],[f72,f3279]) ).
fof(f3279,plain,
( spl0_271
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f72,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f3277,plain,
spl0_270,
inference(avatar_split_clause,[],[f71,f3275]) ).
fof(f3275,plain,
( spl0_270
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f71,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f3273,plain,
spl0_269,
inference(avatar_split_clause,[],[f70,f3271]) ).
fof(f3271,plain,
( spl0_269
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f70,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f3269,plain,
spl0_268,
inference(avatar_split_clause,[],[f66,f3267]) ).
fof(f3267,plain,
( spl0_268
<=> ! [X4,X0,X5,X1] :
( hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f66,axiom,
! [X0,X1,X4,X5] :
( hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f3265,plain,
spl0_267,
inference(avatar_split_clause,[],[f12,f3263]) ).
fof(f3263,plain,
( spl0_267
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f3261,plain,
spl0_266,
inference(avatar_split_clause,[],[f11,f3259]) ).
fof(f3259,plain,
( spl0_266
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f3257,plain,
spl0_265,
inference(avatar_split_clause,[],[f2,f3255]) ).
fof(f3255,plain,
( spl0_265
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f3253,plain,
( spl0_264
| ~ spl0_171
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2586,f2168,f1730,f3251]) ).
fof(f3251,plain,
( spl0_264
<=> ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2586,plain,
( ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_171
| ~ spl0_212 ),
inference(resolution,[],[f2169,f1731]) ).
fof(f3249,plain,
spl0_263,
inference(avatar_split_clause,[],[f1,f3247]) ).
fof(f3247,plain,
( spl0_263
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f3027,plain,
spl0_262,
inference(avatar_split_clause,[],[f706,f3025]) ).
fof(f706,plain,
! [X50,X2,X1] :
( X1 = X2
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(duplicate_literal_removal,[],[f559]) ).
fof(f559,axiom,
! [X50,X2,X1] :
( X1 = X2
| X1 = X2
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
fof(f3023,plain,
spl0_261,
inference(avatar_split_clause,[],[f705,f3021]) ).
fof(f705,plain,
! [X50,X11,X1] :
( X1 = X11
| hBOOL(c_in(c_Pair(X11,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(duplicate_literal_removal,[],[f564]) ).
fof(f564,axiom,
! [X50,X11,X1] :
( X1 = X11
| X1 = X11
| hBOOL(c_in(c_Pair(X11,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_4) ).
fof(f3019,plain,
spl0_260,
inference(avatar_split_clause,[],[f651,f3017]) ).
fof(f3017,plain,
( spl0_260
<=> ! [X0,X19] : c_Relation_ODomain(X19,X0,X0) = c_Relation_ODomain(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f651,plain,
! [X0,X19] : c_Relation_ODomain(X19,X0,X0) = c_Relation_ODomain(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X0,X0),
inference(definition_unfolding,[],[f462,f506]) ).
fof(f462,axiom,
! [X0,X19] : c_Relation_ODomain(X19,X0,X0) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X19,X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
fof(f3014,plain,
spl0_259,
inference(avatar_split_clause,[],[f647,f3012]) ).
fof(f3012,plain,
( spl0_259
<=> ! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X14,X0),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X14,X0),X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f647,plain,
! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X14,X0),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X14,X0),X0),X0,X0,X0),
inference(definition_unfolding,[],[f485,f506]) ).
fof(f485,axiom,
! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X14,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
fof(f3010,plain,
spl0_258,
inference(avatar_split_clause,[],[f566,f3008]) ).
fof(f566,axiom,
! [X22,X23] :
( X22 = X23
| hBOOL(c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X23,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
fof(f3006,plain,
spl0_257,
inference(avatar_split_clause,[],[f538,f3004]) ).
fof(f538,axiom,
! [X2,X0,X1,X4] :
( X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
fof(f3002,plain,
spl0_256,
inference(avatar_split_clause,[],[f497,f3000]) ).
fof(f3000,plain,
( spl0_256
<=> ! [X4,X0,X19] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),X19,X0,X0,X0) = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f497,axiom,
! [X0,X19,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X0,X0),X19),X19,X0,X0,X0) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
fof(f2998,plain,
spl0_255,
inference(avatar_split_clause,[],[f439,f2996]) ).
fof(f2996,plain,
( spl0_255
<=> ! [X0,X19,X35] :
( ~ hBOOL(c_in(X35,X19,tc_prod(X0,X0)))
| hBOOL(c_in(X35,c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f439,axiom,
! [X0,X19,X35] :
( ~ hBOOL(c_in(X35,X19,tc_prod(X0,X0)))
| hBOOL(c_in(X35,c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
fof(f2994,plain,
spl0_254,
inference(avatar_split_clause,[],[f405,f2992]) ).
fof(f2992,plain,
( spl0_254
<=> ! [X4,X0,X23,X22] :
( X22 = X23
| hBOOL(c_in(X23,X4,X0))
| ~ hBOOL(c_in(X23,c_Set_Oinsert(X22,X4,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f405,axiom,
! [X0,X4,X22,X23] :
( X22 = X23
| hBOOL(c_in(X23,X4,X0))
| ~ hBOOL(c_in(X23,c_Set_Oinsert(X22,X4,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f2990,plain,
( spl0_253
| ~ spl0_146
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2601,f2176,f1486,f2988]) ).
fof(f2988,plain,
( spl0_253
<=> ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2601,plain,
( ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0)
| ~ spl0_146
| ~ spl0_214 ),
inference(resolution,[],[f2177,f1487]) ).
fof(f2986,plain,
spl0_252,
inference(avatar_split_clause,[],[f310,f2984]) ).
fof(f2984,plain,
( spl0_252
<=> ! [X4,X0,X19] :
( ~ c_Relation_Ototal__on(X4,X19,X0)
| c_Relation_Ototal__on(X4,c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f310,axiom,
! [X0,X19,X4] :
( ~ c_Relation_Ototal__on(X4,X19,X0)
| c_Relation_Ototal__on(X4,c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).
fof(f2982,plain,
spl0_251,
inference(avatar_split_clause,[],[f309,f2980]) ).
fof(f2980,plain,
( spl0_251
<=> ! [X4,X0,X19] :
( c_Relation_Ototal__on(X4,X19,X0)
| ~ c_Relation_Ototal__on(X4,c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f309,axiom,
! [X0,X19,X4] :
( c_Relation_Ototal__on(X4,X19,X0)
| ~ c_Relation_Ototal__on(X4,c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).
fof(f2978,plain,
spl0_250,
inference(avatar_split_clause,[],[f303,f2976]) ).
fof(f2976,plain,
( spl0_250
<=> ! [X0,X19] :
( ~ c_Relation_Otrans(X19,X0)
| c_lessequals(c_Relation_Orel__comp(X19,X19,X0,X0,X0),X19,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f303,axiom,
! [X0,X19] :
( ~ c_Relation_Otrans(X19,X0)
| c_lessequals(c_Relation_Orel__comp(X19,X19,X0,X0,X0),X19,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
fof(f2974,plain,
spl0_249,
inference(avatar_split_clause,[],[f280,f2972]) ).
fof(f280,axiom,
! [X0,X1,X14,X34] :
( ~ c_Wellfounded_Owf(X14,X0)
| ~ hBOOL(c_in(X1,X34,X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X34,X14,X0),X34,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_0) ).
fof(f2970,plain,
spl0_248,
inference(avatar_split_clause,[],[f279,f2968]) ).
fof(f279,axiom,
! [X0,X11,X19,X34] :
( ~ c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(X11,X34,X0))
| hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X34,X19,X0),X34,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
fof(f2966,plain,
spl0_247,
inference(avatar_split_clause,[],[f255,f2964]) ).
fof(f2964,plain,
( spl0_247
<=> ! [X4,X0,X8,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X4
| c_Set_Oimage(X7,X4,X8,X0) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f255,axiom,
! [X0,X8,X7,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X4
| c_Set_Oimage(X7,X4,X8,X0) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
fof(f2962,plain,
spl0_246,
inference(avatar_split_clause,[],[f254,f2960]) ).
fof(f2960,plain,
( spl0_246
<=> ! [X19,X20,X0,X8] :
( ~ c_Relation_Osingle__valued(X20,X0,X8)
| c_Relation_Osingle__valued(X19,X0,X8)
| ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X8),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f254,axiom,
! [X0,X8,X19,X20] :
( ~ c_Relation_Osingle__valued(X20,X0,X8)
| c_Relation_Osingle__valued(X19,X0,X8)
| ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X8),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
fof(f2958,plain,
spl0_245,
inference(avatar_split_clause,[],[f197,f2956]) ).
fof(f2956,plain,
( spl0_245
<=> ! [X4,X0,X33,X1,X7] :
( ~ hBOOL(c_in(X1,X4,X33))
| hBOOL(c_in(hAPP(X7,X1),c_Set_Oimage(X7,X4,X33,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f197,axiom,
! [X0,X1,X7,X4,X33] :
( ~ hBOOL(c_in(X1,X4,X33))
| hBOOL(c_in(hAPP(X7,X1),c_Set_Oimage(X7,X4,X33,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
fof(f2954,plain,
spl0_244,
inference(avatar_split_clause,[],[f184,f2952]) ).
fof(f2952,plain,
( spl0_244
<=> ! [X4,X0,X5,X32] :
( ~ hBOOL(c_in(X32,X4,X0))
| hBOOL(c_in(X32,X5,X0))
| ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f184,axiom,
! [X0,X4,X5,X32] :
( ~ hBOOL(c_in(X32,X4,X0))
| hBOOL(c_in(X32,X5,X0))
| ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
fof(f2950,plain,
spl0_243,
inference(avatar_split_clause,[],[f181,f2948]) ).
fof(f2948,plain,
( spl0_243
<=> ! [X1,X0,X8,X21,X7] :
( ~ class_HOL_Oord(X8)
| ~ c_lessequals(X7,X21,tc_fun(X0,X8))
| c_lessequals(hAPP(X7,X1),hAPP(X21,X1),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f181,axiom,
! [X21,X0,X1,X8,X7] :
( ~ class_HOL_Oord(X8)
| ~ c_lessequals(X7,X21,tc_fun(X0,X8))
| c_lessequals(hAPP(X7,X1),hAPP(X21,X1),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f2946,plain,
( spl0_242
| ~ spl0_146
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2587,f2168,f1486,f2944]) ).
fof(f2944,plain,
( spl0_242
<=> ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2587,plain,
( ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0)
| ~ spl0_146
| ~ spl0_212 ),
inference(resolution,[],[f2169,f1487]) ).
fof(f2942,plain,
spl0_241,
inference(avatar_split_clause,[],[f170,f2940]) ).
fof(f2940,plain,
( spl0_241
<=> ! [X5,X4,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f170,axiom,
! [X0,X4,X5] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
fof(f2938,plain,
spl0_240,
inference(avatar_split_clause,[],[f51,f2936]) ).
fof(f2936,plain,
( spl0_240
<=> ! [X20,X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| ~ c_Relation_Osym(X20,X0)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f51,axiom,
! [X0,X19,X20] :
( ~ c_Relation_Osym(X19,X0)
| ~ c_Relation_Osym(X20,X0)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un_0) ).
fof(f2703,plain,
spl0_239,
inference(avatar_split_clause,[],[f540,f2701]) ).
fof(f540,axiom,
! [X0,X22,X23] :
( X22 = X23
| ~ hBOOL(c_in(c_Pair(X23,X22,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
fof(f2699,plain,
spl0_238,
inference(avatar_split_clause,[],[f436,f2697]) ).
fof(f436,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Transitive__Closure_Ortrancl(X19,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
fof(f2695,plain,
spl0_237,
inference(avatar_split_clause,[],[f399,f2693]) ).
fof(f399,axiom,
! [X2,X0,X1,X4] : c_Set_Oinsert(X1,c_Set_Oinsert(X2,X4,X0),X0) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X4,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f2691,plain,
spl0_236,
inference(avatar_split_clause,[],[f301,f2689]) ).
fof(f2689,plain,
( spl0_236
<=> ! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f301,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).
fof(f2687,plain,
spl0_235,
inference(avatar_split_clause,[],[f300,f2685]) ).
fof(f300,axiom,
! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
fof(f2683,plain,
spl0_234,
inference(avatar_split_clause,[],[f299,f2681]) ).
fof(f299,axiom,
! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X14,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
fof(f2679,plain,
spl0_233,
inference(avatar_split_clause,[],[f194,f2677]) ).
fof(f2677,plain,
( spl0_233
<=> ! [X31,X4,X0,X5] :
( hBOOL(c_in(X31,X4,X0))
| ~ hBOOL(c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f194,axiom,
! [X31,X0,X4,X5] :
( hBOOL(c_in(X31,X4,X0))
| ~ hBOOL(c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f2675,plain,
spl0_232,
inference(avatar_split_clause,[],[f193,f2673]) ).
fof(f2673,plain,
( spl0_232
<=> ! [X31,X4,X0,X5] :
( hBOOL(c_in(X31,X5,X0))
| ~ hBOOL(c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f193,axiom,
! [X31,X0,X4,X5] :
( hBOOL(c_in(X31,X5,X0))
| ~ hBOOL(c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f2671,plain,
spl0_231,
inference(avatar_split_clause,[],[f192,f2669]) ).
fof(f2669,plain,
( spl0_231
<=> ! [X31,X4,X0,X5] :
( hBOOL(c_in(X31,X4,X0))
| ~ hBOOL(c_in(X31,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f192,axiom,
! [X31,X0,X4,X5] :
( hBOOL(c_in(X31,X4,X0))
| ~ hBOOL(c_in(X31,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f2667,plain,
spl0_230,
inference(avatar_split_clause,[],[f191,f2665]) ).
fof(f2665,plain,
( spl0_230
<=> ! [X31,X4,X0,X5] :
( ~ hBOOL(c_in(X31,X5,X0))
| ~ hBOOL(c_in(X31,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f191,axiom,
! [X31,X0,X4,X5] :
( ~ hBOOL(c_in(X31,X5,X0))
| ~ hBOOL(c_in(X31,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f2663,plain,
spl0_229,
inference(avatar_split_clause,[],[f189,f2661]) ).
fof(f2661,plain,
( spl0_229
<=> ! [X31,X4,X0,X5] :
( ~ hBOOL(c_in(X31,X5,X0))
| hBOOL(c_in(X31,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f189,axiom,
! [X31,X0,X4,X5] :
( ~ hBOOL(c_in(X31,X5,X0))
| hBOOL(c_in(X31,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f2659,plain,
spl0_228,
inference(avatar_split_clause,[],[f188,f2657]) ).
fof(f2657,plain,
( spl0_228
<=> ! [X31,X4,X0,X5] :
( ~ hBOOL(c_in(X31,X4,X0))
| hBOOL(c_in(X31,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f188,axiom,
! [X31,X0,X4,X5] :
( ~ hBOOL(c_in(X31,X4,X0))
| hBOOL(c_in(X31,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f2655,plain,
( spl0_130
| ~ spl0_81
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1398,f1226,f1070,f1335]) ).
fof(f1335,plain,
( spl0_130
<=> hBOOL(hAPP(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1398,plain,
( hBOOL(hAPP(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_81
| ~ spl0_104 ),
inference(resolution,[],[f1227,f1071]) ).
fof(f2654,plain,
spl0_227,
inference(avatar_split_clause,[],[f102,f2652]) ).
fof(f2652,plain,
( spl0_227
<=> ! [X4,X0] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
| ~ c_lessequals(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f102,axiom,
! [X0,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
| ~ c_lessequals(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f2650,plain,
spl0_226,
inference(avatar_split_clause,[],[f88,f2648]) ).
fof(f2648,plain,
( spl0_226
<=> ! [X4,X5,X0] :
( X4 = X5
| ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X4,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f88,axiom,
! [X0,X4,X5] :
( X4 = X5
| ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(X5,X4,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
fof(f2646,plain,
spl0_225,
inference(avatar_split_clause,[],[f39,f2644]) ).
fof(f2644,plain,
( spl0_225
<=> ! [X4,X0,X5,X22] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_lessequals(X4,c_Set_Oinsert(X22,X5,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f39,axiom,
! [X0,X4,X5,X22] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_lessequals(X4,c_Set_Oinsert(X22,X5,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
fof(f2642,plain,
spl0_224,
inference(avatar_split_clause,[],[f38,f2640]) ).
fof(f2640,plain,
( spl0_224
<=> ! [X5,X4,X0,X1] :
( c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f38,axiom,
! [X0,X1,X4,X5] :
( c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
fof(f2558,plain,
( spl0_223
| ~ spl0_132
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2382,f2073,f1390,f2556]) ).
fof(f2556,plain,
( spl0_223
<=> ! [X0] :
( ~ c_lessequals(hAPP(v_P_H____,v_x),X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2382,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(v_P_H____,v_x),X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_132
| ~ spl0_190 ),
inference(superposition,[],[f2074,f1392]) ).
fof(f2274,plain,
( ~ spl0_222
| ~ spl0_55
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2194,f2190,f962,f2271]) ).
fof(f2271,plain,
( spl0_222
<=> hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2190,plain,
( spl0_217
<=> 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_217])]) ).
fof(f2194,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
| ~ spl0_55
| ~ spl0_217 ),
inference(superposition,[],[f963,f2192]) ).
fof(f2192,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_217 ),
inference(avatar_component_clause,[],[f2190]) ).
fof(f2213,plain,
spl0_221,
inference(avatar_split_clause,[],[f648,f2211]) ).
fof(f2211,plain,
( spl0_221
<=> ! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f648,plain,
! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X14,c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),X0),
inference(definition_unfolding,[],[f509,f506]) ).
fof(f509,axiom,
! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X14,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
fof(f2209,plain,
spl0_220,
inference(avatar_split_clause,[],[f607,f2207]) ).
fof(f2207,plain,
( spl0_220
<=> ! [X18,X0,X8,X21,X1,X7] : hAPP(X7,hAPP(X21,X1)) = hAPP(c_Fun_Ocomp(X7,X21,X8,X0,X18),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f607,axiom,
! [X21,X0,X1,X8,X18,X7] : hAPP(X7,hAPP(X21,X1)) = hAPP(c_Fun_Ocomp(X7,X21,X8,X0,X18),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__apply_0) ).
fof(f2205,plain,
spl0_219,
inference(avatar_split_clause,[],[f596,f2203]) ).
fof(f2203,plain,
( spl0_219
<=> ! [X55,X22,X0,X56,X23,X8] :
( X23 = X55
| c_Pair(X23,X22,X0,X8) != c_Pair(X55,X56,X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f596,axiom,
! [X0,X56,X8,X55,X22,X23] :
( X23 = X55
| c_Pair(X23,X22,X0,X8) != c_Pair(X55,X56,X0,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
fof(f2201,plain,
spl0_218,
inference(avatar_split_clause,[],[f595,f2199]) ).
fof(f2199,plain,
( spl0_218
<=> ! [X55,X0,X8,X56,X23,X22] :
( X22 = X56
| c_Pair(X23,X22,X0,X8) != c_Pair(X55,X56,X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f595,axiom,
! [X0,X56,X8,X55,X22,X23] :
( X22 = X56
| c_Pair(X23,X22,X0,X8) != c_Pair(X55,X56,X0,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
fof(f2193,plain,
( spl0_217
| ~ spl0_8
| ~ spl0_127
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2184,f2180,f1322,f767,f2190]) ).
fof(f2180,plain,
( spl0_215
<=> 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_215])]) ).
fof(f2184,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_8
| ~ spl0_127
| ~ spl0_215 ),
inference(forward_demodulation,[],[f2182,f1405]) ).
fof(f2182,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_215 ),
inference(avatar_component_clause,[],[f2180]) ).
fof(f2188,plain,
( spl0_216
| ~ spl0_4
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f1178,f1109,f747,f2186]) ).
fof(f2186,plain,
( spl0_216
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f747,plain,
( spl0_4
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1109,plain,
( spl0_84
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1178,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
| ~ spl0_4
| ~ spl0_84 ),
inference(resolution,[],[f1110,f749]) ).
fof(f749,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f747]) ).
fof(f1110,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1109]) ).
fof(f2183,plain,
spl0_215,
inference(avatar_split_clause,[],[f552,f2180]) ).
fof(f552,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/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
fof(f2178,plain,
spl0_214,
inference(avatar_split_clause,[],[f542,f2176]) ).
fof(f542,axiom,
! [X0,X19,X23] :
( ~ c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(c_Pair(X23,X23,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
fof(f2174,plain,
spl0_213,
inference(avatar_split_clause,[],[f541,f2172]) ).
fof(f541,axiom,
! [X0,X1,X19] :
( ~ c_Nitpick_Orefl_H(X19,X0)
| hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
fof(f2170,plain,
spl0_212,
inference(avatar_split_clause,[],[f525,f2168]) ).
fof(f525,axiom,
! [X0,X1,X19] :
( ~ c_Relation_Oirrefl(X19,X0)
| ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X19,tc_prod(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
fof(f2166,plain,
spl0_211,
inference(avatar_split_clause,[],[f498,f2164]) ).
fof(f2164,plain,
( spl0_211
<=> ! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X14,X0),c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f498,axiom,
! [X0,X14] : c_Transitive__Closure_Ortrancl(X14,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X14,X0),c_Transitive__Closure_Ortrancl(X14,X0),X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
fof(f2162,plain,
spl0_210,
inference(avatar_split_clause,[],[f396,f2160]) ).
fof(f2160,plain,
( spl0_210
<=> ! [X4,X0,X2,X1] :
( X1 = X2
| hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,X4,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f396,axiom,
! [X2,X0,X1,X4] :
( X1 = X2
| hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,X4,X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f2158,plain,
spl0_209,
inference(avatar_split_clause,[],[f388,f2156]) ).
fof(f2156,plain,
( spl0_209
<=> ! [X22,X0,X23] :
( X22 = X23
| ~ hBOOL(c_in(X22,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f388,axiom,
! [X0,X22,X23] :
( X22 = X23
| ~ hBOOL(c_in(X22,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f2154,plain,
spl0_208,
inference(avatar_split_clause,[],[f357,f2152]) ).
fof(f2152,plain,
( spl0_208
<=> ! [X4,X0,X19] :
( ~ c_Relation_Oirrefl(X19,X0)
| ~ c_Relation_Otrans(X19,X0)
| ~ c_Relation_Ototal__on(X4,X19,X0)
| c_Order__Relation_Ostrict__linear__order__on(X4,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f357,axiom,
! [X0,X19,X4] :
( ~ c_Relation_Oirrefl(X19,X0)
| ~ c_Relation_Otrans(X19,X0)
| ~ c_Relation_Ototal__on(X4,X19,X0)
| c_Order__Relation_Ostrict__linear__order__on(X4,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).
fof(f2150,plain,
spl0_207,
inference(avatar_split_clause,[],[f308,f2148]) ).
fof(f2148,plain,
( spl0_207
<=> ! [X0,X19] :
( ~ c_Relation_Oantisym(X19,X0)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f308,axiom,
! [X0,X19] :
( ~ c_Relation_Oantisym(X19,X0)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
fof(f2146,plain,
spl0_206,
inference(avatar_split_clause,[],[f307,f2144]) ).
fof(f2144,plain,
( spl0_206
<=> ! [X0,X19] :
( c_Relation_Oantisym(X19,X0)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f307,axiom,
! [X0,X19] :
( c_Relation_Oantisym(X19,X0)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
fof(f2142,plain,
( spl0_205
| ~ spl0_4
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f1176,f1105,f747,f2140]) ).
fof(f2140,plain,
( spl0_205
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1105,plain,
( spl0_83
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1176,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| ~ spl0_4
| ~ spl0_83 ),
inference(resolution,[],[f1106,f749]) ).
fof(f1106,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1105]) ).
fof(f2138,plain,
spl0_204,
inference(avatar_split_clause,[],[f306,f2136]) ).
fof(f2136,plain,
( spl0_204
<=> ! [X5,X4,X0] : c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X4,X0),X5,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f306,axiom,
! [X0,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X4,X0),X5,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
fof(f2134,plain,
spl0_203,
inference(avatar_split_clause,[],[f305,f2132]) ).
fof(f2132,plain,
( spl0_203
<=> ! [X0,X19] :
( ~ c_Relation_Otrans(X19,X0)
| c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f305,axiom,
! [X0,X19] :
( ~ c_Relation_Otrans(X19,X0)
| c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
fof(f2130,plain,
spl0_202,
inference(avatar_split_clause,[],[f304,f2128]) ).
fof(f2128,plain,
( spl0_202
<=> ! [X0,X19] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f304,axiom,
! [X0,X19] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X19,hAPP(c_Relation_Oconverse(X0,X0),X19),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
fof(f2126,plain,
spl0_201,
inference(avatar_split_clause,[],[f253,f2124]) ).
fof(f253,axiom,
! [X0,X19,X20] :
( ~ c_Wellfounded_Oacyclic(X20,X0)
| c_Wellfounded_Oacyclic(X19,X0)
| ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
fof(f2122,plain,
spl0_200,
inference(avatar_split_clause,[],[f252,f2120]) ).
fof(f2120,plain,
( spl0_200
<=> ! [X34,X0,X12,X1] :
( ~ hBOOL(hAPP(X12,X1))
| hBOOL(hAPP(X34,X1))
| ~ c_lessequals(X12,X34,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f252,axiom,
! [X0,X1,X34,X12] :
( ~ hBOOL(hAPP(X12,X1))
| hBOOL(hAPP(X34,X1))
| ~ c_lessequals(X12,X34,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
fof(f2118,plain,
spl0_199,
inference(avatar_split_clause,[],[f251,f2116]) ).
fof(f251,axiom,
! [X0,X19,X20] :
( ~ c_Relation_Oantisym(X20,X0)
| c_Relation_Oantisym(X19,X0)
| ~ c_lessequals(X19,X20,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
fof(f2114,plain,
spl0_198,
inference(avatar_split_clause,[],[f248,f2112]) ).
fof(f248,axiom,
! [X0,X19,X35] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(X35,X0)
| ~ c_lessequals(X35,X19,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__subset_0) ).
fof(f2110,plain,
spl0_197,
inference(avatar_split_clause,[],[f243,f2108]) ).
fof(f2108,plain,
( spl0_197
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f243,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(X1,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f2106,plain,
spl0_196,
inference(avatar_split_clause,[],[f242,f2104]) ).
fof(f2104,plain,
( spl0_196
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f242,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(X3,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f2102,plain,
spl0_195,
inference(avatar_split_clause,[],[f226,f2100]) ).
fof(f2100,plain,
( spl0_195
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f226,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f2091,plain,
spl0_194,
inference(avatar_split_clause,[],[f225,f2089]) ).
fof(f2089,plain,
( spl0_194
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f225,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f2087,plain,
spl0_193,
inference(avatar_split_clause,[],[f171,f2085]) ).
fof(f2085,plain,
( spl0_193
<=> ! [X23,X0,X12,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X12,X19,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f171,axiom,
! [X0,X19,X12,X23] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X12,X19,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
fof(f2083,plain,
spl0_192,
inference(avatar_split_clause,[],[f168,f2081]) ).
fof(f2081,plain,
( spl0_192
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f168,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f2079,plain,
spl0_191,
inference(avatar_split_clause,[],[f167,f2077]) ).
fof(f2077,plain,
( spl0_191
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f167,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f2075,plain,
spl0_190,
inference(avatar_split_clause,[],[f130,f2073]) ).
fof(f130,axiom,
! [X0,X1,X4,X5] :
( hBOOL(c_in(X1,X5,X0))
| ~ c_lessequals(c_Set_Oinsert(X1,X4,X0),X5,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f2071,plain,
spl0_189,
inference(avatar_split_clause,[],[f100,f2069]) ).
fof(f2069,plain,
( spl0_189
<=> ! [X5,X4,X0] :
( c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f100,axiom,
! [X0,X4,X5] :
( c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f2067,plain,
spl0_188,
inference(avatar_split_clause,[],[f99,f2065]) ).
fof(f2065,plain,
( spl0_188
<=> ! [X5,X4,X0] :
( ~ c_lessequals(X5,X4,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f99,axiom,
! [X0,X4,X5] :
( ~ c_lessequals(X5,X4,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f2063,plain,
spl0_187,
inference(avatar_split_clause,[],[f98,f2061]) ).
fof(f2061,plain,
( spl0_187
<=> ! [X5,X4,X0] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f98,axiom,
! [X0,X4,X5] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f2059,plain,
spl0_186,
inference(avatar_split_clause,[],[f87,f2057]) ).
fof(f2057,plain,
( spl0_186
<=> ! [X0,X12,X27,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X27))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X12,X19,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f87,axiom,
! [X0,X19,X27,X12] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X27))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X12,X19,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__def_1) ).
fof(f2055,plain,
spl0_185,
inference(avatar_split_clause,[],[f80,f2053]) ).
fof(f2053,plain,
( spl0_185
<=> ! [X4,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)),X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f80,axiom,
! [X0,X4] : 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)),X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f2051,plain,
( ~ spl0_6
| spl0_184
| ~ spl0_71
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1208,f1157,f1030,f2049,f757]) ).
fof(f2049,plain,
( spl0_184
<=> ! [X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1030,plain,
( spl0_71
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1157,plain,
( spl0_96
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1208,plain,
( ! [X0] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_71
| ~ spl0_96 ),
inference(superposition,[],[f1031,f1158]) ).
fof(f1158,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1157]) ).
fof(f1031,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f2047,plain,
spl0_183,
inference(avatar_split_clause,[],[f56,f2045]) ).
fof(f2045,plain,
( spl0_183
<=> ! [X4,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f56,axiom,
! [X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f2043,plain,
spl0_182,
inference(avatar_split_clause,[],[f55,f2041]) ).
fof(f2041,plain,
( spl0_182
<=> ! [X5,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f55,axiom,
! [X0,X5] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f2039,plain,
spl0_181,
inference(avatar_split_clause,[],[f41,f2037]) ).
fof(f2037,plain,
( spl0_181
<=> ! [X23,X0,X12,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X12,X19,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f41,axiom,
! [X0,X19,X12,X23] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(hAPP(X12,X23))
| ~ hBOOL(hAPP(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X12,X19,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct_1) ).
fof(f2035,plain,
spl0_180,
inference(avatar_split_clause,[],[f20,f2033]) ).
fof(f2033,plain,
( spl0_180
<=> ! [X13,X0,X14,X12] :
( ~ c_Wellfounded_Owf(X14,X0)
| hBOOL(hAPP(X12,X13))
| ~ hBOOL(hAPP(X12,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X12,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f20,axiom,
! [X0,X14,X12,X13] :
( ~ c_Wellfounded_Owf(X14,X0)
| hBOOL(hAPP(X12,X13))
| ~ hBOOL(hAPP(X12,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X12,X14,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
fof(f2031,plain,
spl0_179,
inference(avatar_split_clause,[],[f4,f2029]) ).
fof(f4,axiom,
! [X0,X4,X5] :
( ~ c_lessequals(X5,X4,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f2027,plain,
spl0_178,
inference(avatar_split_clause,[],[f3,f2025]) ).
fof(f3,axiom,
! [X0,X4,X5] :
( ~ c_lessequals(X4,X5,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f1756,plain,
spl0_177,
inference(avatar_split_clause,[],[f668,f1754]) ).
fof(f1754,plain,
( spl0_177
<=> ! [X0,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f668,plain,
! [X0,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X0) ),
inference(definition_unfolding,[],[f487,f506]) ).
fof(f487,axiom,
! [X0,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
fof(f1752,plain,
spl0_176,
inference(avatar_split_clause,[],[f667,f1750]) ).
fof(f1750,plain,
( spl0_176
<=> ! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| c_Relation_Osym(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f667,plain,
! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| c_Relation_Osym(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X0) ),
inference(definition_unfolding,[],[f460,f506]) ).
fof(f460,axiom,
! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
fof(f1748,plain,
spl0_175,
inference(avatar_split_clause,[],[f666,f1746]) ).
fof(f1746,plain,
( spl0_175
<=> ! [X0,X19] :
( ~ c_Relation_Otrans(X19,X0)
| c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0) = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f666,plain,
! [X0,X19] :
( ~ c_Relation_Otrans(X19,X0)
| c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0) = X19 ),
inference(definition_unfolding,[],[f461,f506]) ).
fof(f461,axiom,
! [X0,X19] :
( ~ c_Relation_Otrans(X19,X0)
| c_Transitive__Closure_Otrancl(X19,X0) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__id_0) ).
fof(f1744,plain,
spl0_174,
inference(avatar_split_clause,[],[f561,f1742]) ).
fof(f561,axiom,
! [X50,X11,X1] : ~ hBOOL(c_in(c_Pair(X11,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
fof(f1740,plain,
spl0_173,
inference(avatar_split_clause,[],[f557,f1738]) ).
fof(f557,axiom,
! [X50,X2,X1] : ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X50,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).
fof(f1736,plain,
spl0_172,
inference(avatar_split_clause,[],[f553,f1734]) ).
fof(f1734,plain,
( spl0_172
<=> ! [X18,X7,X31,X8] : hAPP(c_Fun_Ocomp(c_COMBK(X31,X8,X18),X7,X18,X8,t_a),v_x) = X31 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f553,axiom,
! [X31,X18,X8,X7] : hAPP(c_Fun_Ocomp(c_COMBK(X31,X8,X18),X7,X18,X8,t_a),v_x) = X31,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
fof(f1732,plain,
spl0_171,
inference(avatar_split_clause,[],[f533,f1730]) ).
fof(f533,axiom,
! [X0,X1,X14] : hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Transitive__Closure_Ortrancl(X14,X0),tc_prod(X0,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
fof(f1728,plain,
( spl0_170
| ~ spl0_81
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1422,f1340,f1070,f1725]) ).
fof(f1725,plain,
( spl0_170
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1340,plain,
( spl0_131
<=> hBOOL(c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1422,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____))
| ~ spl0_81
| ~ spl0_131 ),
inference(resolution,[],[f1342,f1071]) ).
fof(f1342,plain,
( hBOOL(c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1723,plain,
spl0_169,
inference(avatar_split_clause,[],[f488,f1721]) ).
fof(f1721,plain,
( spl0_169
<=> ! [X0,X8,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Relation_OImage(X14,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f488,axiom,
! [X0,X8,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Relation_OImage(X14,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__empty_0) ).
fof(f1719,plain,
spl0_168,
inference(avatar_split_clause,[],[f404,f1717]) ).
fof(f1717,plain,
( spl0_168
<=> ! [X23,X0,X5,X22] :
( ~ hBOOL(c_in(X23,X5,X0))
| hBOOL(c_in(X23,c_Set_Oinsert(X22,X5,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f404,axiom,
! [X0,X5,X22,X23] :
( ~ hBOOL(c_in(X23,X5,X0))
| hBOOL(c_in(X23,c_Set_Oinsert(X22,X5,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
fof(f1715,plain,
spl0_167,
inference(avatar_split_clause,[],[f238,f1713]) ).
fof(f1713,plain,
( spl0_167
<=> ! [X0,X23,X22,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X23,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f238,axiom,
! [X0,X1,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X23,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
fof(f1711,plain,
spl0_166,
inference(avatar_split_clause,[],[f236,f1709]) ).
fof(f1709,plain,
( spl0_166
<=> ! [X0,X23,X22,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X23,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f236,axiom,
! [X0,X1,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X23,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f1707,plain,
spl0_165,
inference(avatar_split_clause,[],[f235,f1705]) ).
fof(f1705,plain,
( spl0_165
<=> ! [X0,X23,X22,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X22,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f235,axiom,
! [X0,X1,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X22,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f1703,plain,
spl0_164,
inference(avatar_split_clause,[],[f233,f1701]) ).
fof(f1701,plain,
( spl0_164
<=> ! [X2,X0,X1,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f233,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
fof(f1699,plain,
spl0_163,
inference(avatar_split_clause,[],[f176,f1697]) ).
fof(f1697,plain,
( spl0_163
<=> ! [X4,X0,X5,X1] :
( hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f176,axiom,
! [X0,X1,X4,X5] :
( hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f1695,plain,
spl0_162,
inference(avatar_split_clause,[],[f175,f1693]) ).
fof(f1693,plain,
( spl0_162
<=> ! [X4,X5,X1,X0] :
( hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f175,axiom,
! [X0,X1,X4,X5] :
( hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f1691,plain,
spl0_161,
inference(avatar_split_clause,[],[f160,f1689]) ).
fof(f1687,plain,
spl0_160,
inference(avatar_split_clause,[],[f156,f1685]) ).
fof(f1685,plain,
( spl0_160
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f156,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f1683,plain,
( spl0_159
| ~ spl0_81
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1420,f1330,f1070,f1680]) ).
fof(f1680,plain,
( spl0_159
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P_H____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1330,plain,
( spl0_129
<=> hBOOL(c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1420,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P_H____))
| ~ spl0_81
| ~ spl0_129 ),
inference(resolution,[],[f1332,f1071]) ).
fof(f1332,plain,
( hBOOL(c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1330]) ).
fof(f1678,plain,
spl0_158,
inference(avatar_split_clause,[],[f155,f1676]) ).
fof(f1676,plain,
( spl0_158
<=> ! [X22,X0,X1,X23] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X22,X1,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f155,axiom,
! [X0,X1,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X22,X1,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f1674,plain,
spl0_157,
inference(avatar_split_clause,[],[f154,f1672]) ).
fof(f1672,plain,
( spl0_157
<=> ! [X0,X23,X22,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X23,X1,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f154,axiom,
! [X0,X1,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X23,X1,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f1670,plain,
spl0_156,
inference(avatar_split_clause,[],[f153,f1668]) ).
fof(f153,axiom,
! [X0,X1,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X22,X0)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
fof(f1666,plain,
spl0_155,
inference(avatar_split_clause,[],[f143,f1664]) ).
fof(f1664,plain,
( spl0_155
<=> ! [X5,X4,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X5
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f143,axiom,
! [X0,X4,X5] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X5
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f1662,plain,
spl0_154,
inference(avatar_split_clause,[],[f142,f1660]) ).
fof(f1660,plain,
( spl0_154
<=> ! [X5,X4,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X4
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f142,axiom,
! [X0,X4,X5] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X4
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f1658,plain,
spl0_153,
inference(avatar_split_clause,[],[f119,f1656]) ).
fof(f1654,plain,
spl0_152,
inference(avatar_split_clause,[],[f90,f1652]) ).
fof(f1652,plain,
( spl0_152
<=> ! [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_152])]) ).
fof(f90,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f1650,plain,
spl0_151,
inference(avatar_split_clause,[],[f68,f1648]) ).
fof(f1648,plain,
( spl0_151
<=> ! [X4,X0,X5,X1] :
( ~ hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f68,axiom,
! [X0,X1,X4,X5] :
( ~ hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f1646,plain,
spl0_150,
inference(avatar_split_clause,[],[f67,f1644]) ).
fof(f67,axiom,
! [X0,X1,X4,X5] :
( ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f1642,plain,
spl0_149,
inference(avatar_split_clause,[],[f16,f1640]) ).
fof(f1640,plain,
( spl0_149
<=> ! [X0,X8,X7] : c_Set_Oimage(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8,X0) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f16,axiom,
! [X0,X8,X7] : c_Set_Oimage(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8,X0) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
fof(f1576,plain,
( ~ spl0_148
| ~ spl0_75
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1465,f1390,f1046,f1573]) ).
fof(f1573,plain,
( spl0_148
<=> hAPP(v_P_H____,v_x) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1046,plain,
( spl0_75
<=> ! [X4,X0,X23] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X23,X4,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1465,plain,
( hAPP(v_P_H____,v_x) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_75
| ~ spl0_132 ),
inference(superposition,[],[f1047,f1392]) ).
fof(f1047,plain,
( ! [X0,X4,X23] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X23,X4,X0)
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1046]) ).
fof(f1492,plain,
spl0_147,
inference(avatar_split_clause,[],[f646,f1490]) ).
fof(f1490,plain,
( spl0_147
<=> ! [X4,X0] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId__on(X4,X0)),X0,X0) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f646,plain,
! [X0,X4] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId__on(X4,X0)),X0,X0) = X4,
inference(definition_unfolding,[],[f494,f507]) ).
fof(f494,axiom,
! [X0,X4] : c_Relation_ORange(c_Relation_OId__on(X4,X0),X0,X0) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
fof(f1488,plain,
spl0_146,
inference(avatar_split_clause,[],[f550,f1486]) ).
fof(f550,axiom,
! [X0,X1] : hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
fof(f1484,plain,
spl0_145,
inference(avatar_split_clause,[],[f438,f1482]) ).
fof(f1482,plain,
( spl0_145
<=> ! [X4,X0,X19] :
( ~ c_Relation_Ototal__on(X4,X19,X0)
| c_Relation_Ototal__on(X4,hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f438,axiom,
! [X0,X19,X4] :
( ~ c_Relation_Ototal__on(X4,X19,X0)
| c_Relation_Ototal__on(X4,hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
fof(f1480,plain,
spl0_144,
inference(avatar_split_clause,[],[f437,f1478]) ).
fof(f1478,plain,
( spl0_144
<=> ! [X4,X0,X19] :
( c_Relation_Ototal__on(X4,X19,X0)
| ~ c_Relation_Ototal__on(X4,hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f437,axiom,
! [X0,X19,X4] :
( c_Relation_Ototal__on(X4,X19,X0)
| ~ c_Relation_Ototal__on(X4,hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
fof(f1476,plain,
spl0_143,
inference(avatar_split_clause,[],[f424,f1474]) ).
fof(f1474,plain,
( spl0_143
<=> ! [X4,X0,X19] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| c_Relation_Orefl__on(X4,hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f424,axiom,
! [X0,X19,X4] :
( ~ c_Relation_Orefl__on(X4,X19,X0)
| c_Relation_Orefl__on(X4,hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
fof(f1472,plain,
spl0_142,
inference(avatar_split_clause,[],[f423,f1470]) ).
fof(f1470,plain,
( spl0_142
<=> ! [X4,X0,X19] :
( c_Relation_Orefl__on(X4,X19,X0)
| ~ c_Relation_Orefl__on(X4,hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f423,axiom,
! [X0,X19,X4] :
( c_Relation_Orefl__on(X4,X19,X0)
| ~ c_Relation_Orefl__on(X4,hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
fof(f1463,plain,
spl0_141,
inference(avatar_split_clause,[],[f397,f1461]) ).
fof(f1461,plain,
( spl0_141
<=> ! [X4,X0,X1] : c_Set_Oinsert(X1,X4,X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X1,X4,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f397,axiom,
! [X0,X1,X4] : c_Set_Oinsert(X1,X4,X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X1,X4,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f1459,plain,
spl0_140,
inference(avatar_split_clause,[],[f343,f1457]) ).
fof(f343,axiom,
! [X0,X19] :
( c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X19,X0),c_Wellfounded_Oacc(X19,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
fof(f1455,plain,
spl0_139,
inference(avatar_split_clause,[],[f342,f1453]) ).
fof(f342,axiom,
! [X0,X19] :
( c_Wellfounded_Owf(X19,X0)
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X19,X0),c_Wellfounded_Oacc(X19,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
fof(f1451,plain,
spl0_138,
inference(avatar_split_clause,[],[f97,f1449]) ).
fof(f97,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f1447,plain,
spl0_137,
inference(avatar_split_clause,[],[f96,f1445]) ).
fof(f1445,plain,
( spl0_137
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f96,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f1443,plain,
spl0_136,
inference(avatar_split_clause,[],[f95,f1441]) ).
fof(f95,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f1439,plain,
spl0_135,
inference(avatar_split_clause,[],[f7,f1437]) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f1435,plain,
spl0_134,
inference(avatar_split_clause,[],[f6,f1433]) ).
fof(f1433,plain,
( spl0_134
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f1427,plain,
( ~ spl0_109
| ~ spl0_80
| spl0_103 ),
inference(avatar_split_clause,[],[f1395,f1219,f1066,f1249]) ).
fof(f1395,plain,
( ~ hBOOL(hAPP(hAPP(v_P_H____,v_x),c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_80
| spl0_103 ),
inference(resolution,[],[f1220,f1067]) ).
fof(f1426,plain,
spl0_133,
inference(avatar_split_clause,[],[f5,f1424]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f1396,plain,
( spl0_104
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1394,f1215,f1226]) ).
fof(f1215,plain,
( spl0_102
<=> hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1394,plain,
( hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_102 ),
inference(forward_demodulation,[],[f1217,f607]) ).
fof(f1217,plain,
( hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f1393,plain,
( spl0_132
| ~ spl0_103
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1378,f1306,f1219,f1390]) ).
fof(f1378,plain,
( hAPP(v_P_H____,v_x) = c_Set_Oinsert(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_103
| ~ spl0_123 ),
inference(resolution,[],[f1307,f1221]) ).
fof(f1343,plain,
spl0_131,
inference(avatar_split_clause,[],[f614,f1340]) ).
fof(f614,axiom,
hBOOL(c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
fof(f1338,plain,
( ~ spl0_130
| ~ spl0_80
| spl0_104 ),
inference(avatar_split_clause,[],[f1230,f1226,f1066,f1335]) ).
fof(f1230,plain,
( ~ hBOOL(hAPP(hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_80
| spl0_104 ),
inference(resolution,[],[f1228,f1067]) ).
fof(f1333,plain,
spl0_129,
inference(avatar_split_clause,[],[f613,f1330]) ).
fof(f613,axiom,
hBOOL(c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f1328,plain,
spl0_128,
inference(avatar_split_clause,[],[f605,f1326]) ).
fof(f605,axiom,
! [X0,X8,X19] : hAPP(c_Relation_Oconverse(X8,X0),hAPP(c_Relation_Oconverse(X0,X8),X19)) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__converse_0) ).
fof(f1324,plain,
spl0_127,
inference(avatar_split_clause,[],[f483,f1322]) ).
fof(f483,axiom,
! [X8] :
( ~ class_Orderings_Obot(X8)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X8)),v_x) = c_Orderings_Obot__class_Obot(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
fof(f1320,plain,
spl0_126,
inference(avatar_split_clause,[],[f472,f1318]) ).
fof(f1318,plain,
( spl0_126
<=> ! [X0,X14] :
( c_Wellfounded_Owf(X14,X0)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X14,X14,X0,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f472,axiom,
! [X0,X14] :
( c_Wellfounded_Owf(X14,X0)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X14,X14,X0,X0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
fof(f1316,plain,
spl0_125,
inference(avatar_split_clause,[],[f471,f1314]) ).
fof(f471,axiom,
! [X0,X14] :
( ~ c_Wellfounded_Owf(X14,X0)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X14,X14,X0,X0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
fof(f1312,plain,
spl0_124,
inference(avatar_split_clause,[],[f433,f1310]) ).
fof(f1310,plain,
( spl0_124
<=> ! [X4,X0] : c_Relation_OId__on(X4,X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId__on(X4,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f433,axiom,
! [X0,X4] : c_Relation_OId__on(X4,X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId__on(X4,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
fof(f1308,plain,
spl0_123,
inference(avatar_split_clause,[],[f410,f1306]) ).
fof(f410,axiom,
! [X0,X4,X23] :
( ~ hBOOL(c_in(X23,X4,X0))
| c_Set_Oinsert(X23,X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f1304,plain,
spl0_122,
inference(avatar_split_clause,[],[f402,f1302]) ).
fof(f1302,plain,
( spl0_122
<=> ! [X4,X0,X1,X2] :
( ~ hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(c_Set_Oinsert(X2,X4,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f402,axiom,
! [X2,X0,X1,X4] :
( ~ hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(c_Set_Oinsert(X2,X4,X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f1300,plain,
spl0_121,
inference(avatar_split_clause,[],[f216,f1298]) ).
fof(f1298,plain,
( spl0_121
<=> ! [X5,X4,X0] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f216,axiom,
! [X0,X4,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f1296,plain,
spl0_120,
inference(avatar_split_clause,[],[f215,f1294]) ).
fof(f1294,plain,
( spl0_120
<=> ! [X5,X4,X0] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f215,axiom,
! [X0,X4,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f1292,plain,
spl0_119,
inference(avatar_split_clause,[],[f206,f1290]) ).
fof(f206,axiom,
! [X0,X19] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X19,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).
fof(f1288,plain,
spl0_118,
inference(avatar_split_clause,[],[f162,f1286]) ).
fof(f1286,plain,
( spl0_118
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f162,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f1284,plain,
spl0_117,
inference(avatar_split_clause,[],[f161,f1282]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f1280,plain,
spl0_116,
inference(avatar_split_clause,[],[f126,f1278]) ).
fof(f1278,plain,
( spl0_116
<=> ! [X5,X4,X0] : c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f126,axiom,
! [X0,X4,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f1276,plain,
spl0_115,
inference(avatar_split_clause,[],[f121,f1274]) ).
fof(f1274,plain,
( spl0_115
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f121,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f1272,plain,
spl0_114,
inference(avatar_split_clause,[],[f120,f1270]) ).
fof(f120,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f1268,plain,
spl0_113,
inference(avatar_split_clause,[],[f93,f1266]) ).
fof(f93,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f1264,plain,
spl0_112,
inference(avatar_split_clause,[],[f86,f1262]) ).
fof(f86,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f1260,plain,
spl0_111,
inference(avatar_split_clause,[],[f79,f1258]) ).
fof(f1258,plain,
( spl0_111
<=> ! [X4,X0] : c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f79,axiom,
! [X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f1256,plain,
spl0_110,
inference(avatar_split_clause,[],[f78,f1254]) ).
fof(f78,axiom,
! [X0,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,tc_fun(X0,tc_bool)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f1252,plain,
( spl0_109
| ~ spl0_81
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1224,f1219,f1070,f1249]) ).
fof(f1224,plain,
( hBOOL(hAPP(hAPP(v_P_H____,v_x),c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_81
| ~ spl0_103 ),
inference(resolution,[],[f1221,f1071]) ).
fof(f1247,plain,
spl0_108,
inference(avatar_split_clause,[],[f64,f1245]) ).
fof(f64,axiom,
! [X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f1243,plain,
spl0_107,
inference(avatar_split_clause,[],[f63,f1241]) ).
fof(f1241,plain,
( spl0_107
<=> ! [X4,X0] : c_HOL_Ominus__class_Ominus(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f63,axiom,
! [X0,X4] : c_HOL_Ominus__class_Ominus(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f1239,plain,
spl0_106,
inference(avatar_split_clause,[],[f10,f1237]) ).
fof(f1237,plain,
( spl0_106
<=> ! [X5,X4,X0] : c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f10,axiom,
! [X0,X4,X5] : c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f1235,plain,
spl0_105,
inference(avatar_split_clause,[],[f9,f1233]) ).
fof(f9,axiom,
! [X0,X4,X5] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f1231,plain,
( ~ spl0_102
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f619,f1219,f1215]) ).
fof(f619,axiom,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1229,plain,
( ~ spl0_104
| spl0_102 ),
inference(avatar_split_clause,[],[f1223,f1215,f1226]) ).
fof(f1223,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| spl0_102 ),
inference(forward_demodulation,[],[f1216,f607]) ).
fof(f1216,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| spl0_102 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f1222,plain,
( spl0_102
| spl0_103 ),
inference(avatar_split_clause,[],[f618,f1219,f1215]) ).
fof(f618,axiom,
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1189,plain,
( spl0_101
| ~ spl0_4
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1075,f1010,f747,f1187]) ).
fof(f1187,plain,
( spl0_101
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1010,plain,
( spl0_66
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1075,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_4
| ~ spl0_66 ),
inference(resolution,[],[f1011,f749]) ).
fof(f1011,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f1175,plain,
spl0_100,
inference(avatar_split_clause,[],[f645,f1173]) ).
fof(f1173,plain,
( spl0_100
<=> ! [X0,X19] : c_Relation_Otrans(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f645,plain,
! [X0,X19] : c_Relation_Otrans(c_Relation_Orel__comp(X19,c_Transitive__Closure_Ortrancl(X19,X0),X0,X0,X0),X0),
inference(definition_unfolding,[],[f478,f506]) ).
fof(f478,axiom,
! [X0,X19] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X19,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
fof(f1171,plain,
spl0_99,
inference(avatar_split_clause,[],[f490,f1169]) ).
fof(f1169,plain,
( spl0_99
<=> ! [X19,X0,X8,X7] :
( ~ c_Relation_Otrans(X19,X0)
| c_Relation_Otrans(c_Relation_Oinv__image(X19,X7,X0,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f490,axiom,
! [X0,X8,X19,X7] :
( ~ c_Relation_Otrans(X19,X0)
| c_Relation_Otrans(c_Relation_Oinv__image(X19,X7,X0,X8),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
fof(f1167,plain,
spl0_98,
inference(avatar_split_clause,[],[f484,f1165]) ).
fof(f1165,plain,
( spl0_98
<=> ! [X19,X0,X8,X7] :
( ~ c_Relation_Osym(X19,X0)
| c_Relation_Osym(c_Relation_Oinv__image(X19,X7,X0,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f484,axiom,
! [X0,X8,X19,X7] :
( ~ c_Relation_Osym(X19,X0)
| c_Relation_Osym(c_Relation_Oinv__image(X19,X7,X0,X8),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
fof(f1163,plain,
spl0_97,
inference(avatar_split_clause,[],[f481,f1161]) ).
fof(f481,axiom,
! [X0,X8,X19,X7] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X19,X7,X0,X8),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
fof(f1159,plain,
( spl0_96
| ~ spl0_4
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f1073,f1006,f747,f1157]) ).
fof(f1006,plain,
( spl0_65
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1073,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_4
| ~ spl0_65 ),
inference(resolution,[],[f1007,f749]) ).
fof(f1007,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1155,plain,
spl0_95,
inference(avatar_split_clause,[],[f458,f1153]) ).
fof(f458,axiom,
! [X0,X1,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| hBOOL(c_in(X1,c_Wellfounded_Oacc(X19,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
fof(f1151,plain,
spl0_94,
inference(avatar_split_clause,[],[f435,f1149]) ).
fof(f1149,plain,
( spl0_94
<=> ! [X0,X19] :
( ~ c_Relation_Oantisym(X19,X0)
| c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f435,axiom,
! [X0,X19] :
( ~ c_Relation_Oantisym(X19,X0)
| c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
fof(f1147,plain,
spl0_93,
inference(avatar_split_clause,[],[f434,f1145]) ).
fof(f1145,plain,
( spl0_93
<=> ! [X0,X19] :
( c_Relation_Oantisym(X19,X0)
| ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f434,axiom,
! [X0,X19] :
( c_Relation_Oantisym(X19,X0)
| ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
fof(f1143,plain,
spl0_92,
inference(avatar_split_clause,[],[f429,f1141]) ).
fof(f429,axiom,
! [X0,X19] :
( ~ c_Relation_Otrans(X19,X0)
| c_Relation_Otrans(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_1) ).
fof(f1139,plain,
spl0_91,
inference(avatar_split_clause,[],[f428,f1137]) ).
fof(f1137,plain,
( spl0_91
<=> ! [X0,X19] :
( c_Relation_Otrans(X19,X0)
| ~ c_Relation_Otrans(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f428,axiom,
! [X0,X19] :
( c_Relation_Otrans(X19,X0)
| ~ c_Relation_Otrans(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_0) ).
fof(f1135,plain,
spl0_90,
inference(avatar_split_clause,[],[f426,f1133]) ).
fof(f1133,plain,
( spl0_90
<=> ! [X0,X19] :
( c_Relation_Osym(X19,X0)
| hAPP(c_Relation_Oconverse(X0,X0),X19) != X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f426,axiom,
! [X0,X19] :
( c_Relation_Osym(X19,X0)
| hAPP(c_Relation_Oconverse(X0,X0),X19) != X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
fof(f1131,plain,
spl0_89,
inference(avatar_split_clause,[],[f425,f1129]) ).
fof(f1129,plain,
( spl0_89
<=> ! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| hAPP(c_Relation_Oconverse(X0,X0),X19) = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f425,axiom,
! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| hAPP(c_Relation_Oconverse(X0,X0),X19) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
fof(f1127,plain,
spl0_88,
inference(avatar_split_clause,[],[f422,f1125]) ).
fof(f422,axiom,
! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| c_Relation_Osym(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_1) ).
fof(f1123,plain,
spl0_87,
inference(avatar_split_clause,[],[f421,f1121]) ).
fof(f1121,plain,
( spl0_87
<=> ! [X0,X19] :
( c_Relation_Osym(X19,X0)
| ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f421,axiom,
! [X0,X19] :
( c_Relation_Osym(X19,X0)
| ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_0) ).
fof(f1119,plain,
spl0_86,
inference(avatar_split_clause,[],[f204,f1117]) ).
fof(f1117,plain,
( spl0_86
<=> ! [X0,X19] :
( c_Wellfounded_Oacyclic(X19,X0)
| ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f204,axiom,
! [X0,X19] :
( c_Wellfounded_Oacyclic(X19,X0)
| ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
fof(f1115,plain,
spl0_85,
inference(avatar_split_clause,[],[f203,f1113]) ).
fof(f1113,plain,
( spl0_85
<=> ! [X0,X19] :
( ~ c_Wellfounded_Oacyclic(X19,X0)
| c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f203,axiom,
! [X0,X19] :
( ~ c_Wellfounded_Oacyclic(X19,X0)
| c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X0,X0),X19),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
fof(f1111,plain,
spl0_84,
inference(avatar_split_clause,[],[f54,f1109]) ).
fof(f54,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f1107,plain,
spl0_83,
inference(avatar_split_clause,[],[f53,f1105]) ).
fof(f53,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f1096,plain,
( ~ spl0_6
| spl0_82
| ~ spl0_63
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1078,f1014,f998,f1094,f757]) ).
fof(f1094,plain,
( spl0_82
<=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f998,plain,
( spl0_63
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1014,plain,
( spl0_67
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1078,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_63
| ~ spl0_67 ),
inference(superposition,[],[f1015,f999]) ).
fof(f999,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f998]) ).
fof(f1015,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f1072,plain,
spl0_81,
inference(avatar_split_clause,[],[f609,f1070]) ).
fof(f609,axiom,
! [X0,X1,X15] :
( hBOOL(hAPP(X15,X1))
| ~ hBOOL(c_in(X1,X15,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1068,plain,
spl0_80,
inference(avatar_split_clause,[],[f608,f1066]) ).
fof(f608,axiom,
! [X0,X1,X15] :
( ~ hBOOL(hAPP(X15,X1))
| hBOOL(c_in(X1,X15,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1064,plain,
spl0_79,
inference(avatar_split_clause,[],[f510,f1062]) ).
fof(f510,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X19,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
fof(f1060,plain,
spl0_78,
inference(avatar_split_clause,[],[f467,f1058]) ).
fof(f467,axiom,
! [X0,X8,X14] : c_Relation_Orel__comp(X14,c_Relation_OId(X8),X0,X8,X8) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
fof(f1056,plain,
spl0_77,
inference(avatar_split_clause,[],[f466,f1054]) ).
fof(f1054,plain,
( spl0_77
<=> ! [X0,X8,X14] : c_Relation_Orel__comp(c_Relation_OId(X0),X14,X0,X0,X8) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f466,axiom,
! [X0,X8,X14] : c_Relation_Orel__comp(c_Relation_OId(X0),X14,X0,X0,X8) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
fof(f1052,plain,
spl0_76,
inference(avatar_split_clause,[],[f430,f1050]) ).
fof(f430,axiom,
! [X0] : c_Relation_OId(X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id_0) ).
fof(f1048,plain,
spl0_75,
inference(avatar_split_clause,[],[f398,f1046]) ).
fof(f398,axiom,
! [X0,X4,X23] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X23,X4,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
fof(f1044,plain,
spl0_74,
inference(avatar_split_clause,[],[f214,f1042]) ).
fof(f1042,plain,
( spl0_74
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f214,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f1040,plain,
spl0_73,
inference(avatar_split_clause,[],[f213,f1038]) ).
fof(f213,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f1036,plain,
spl0_72,
inference(avatar_split_clause,[],[f118,f1034]) ).
fof(f1034,plain,
( spl0_72
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f118,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f1032,plain,
spl0_71,
inference(avatar_split_clause,[],[f117,f1030]) ).
fof(f117,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f1028,plain,
spl0_70,
inference(avatar_split_clause,[],[f114,f1026]) ).
fof(f1026,plain,
( spl0_70
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f114,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1024,plain,
spl0_69,
inference(avatar_split_clause,[],[f113,f1022]) ).
fof(f1022,plain,
( spl0_69
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f113,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1020,plain,
spl0_68,
inference(avatar_split_clause,[],[f109,f1018]) ).
fof(f1018,plain,
( spl0_68
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f109,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f1016,plain,
spl0_67,
inference(avatar_split_clause,[],[f108,f1014]) ).
fof(f108,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f1012,plain,
spl0_66,
inference(avatar_split_clause,[],[f77,f1010]) ).
fof(f77,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1008,plain,
spl0_65,
inference(avatar_split_clause,[],[f76,f1006]) ).
fof(f76,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1004,plain,
spl0_64,
inference(avatar_split_clause,[],[f57,f1002]) ).
fof(f57,axiom,
! [X0,X5,X23] : c_lessequals(X5,c_Set_Oinsert(X23,X5,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f1000,plain,
( spl0_63
| ~ spl0_2
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f987,f946,f737,f998]) ).
fof(f987,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
| ~ spl0_2
| ~ spl0_51 ),
inference(resolution,[],[f947,f739]) ).
fof(f996,plain,
spl0_62,
inference(avatar_split_clause,[],[f46,f994]) ).
fof(f46,axiom,
! [X0,X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f992,plain,
( spl0_61
| ~ spl0_1
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f985,f934,f732,f990]) ).
fof(f990,plain,
( spl0_61
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f985,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_1
| ~ spl0_48 ),
inference(resolution,[],[f935,f734]) ).
fof(f984,plain,
spl0_60,
inference(avatar_split_clause,[],[f500,f982]) ).
fof(f982,plain,
( spl0_60
<=> ! [X4,X0,X19] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| c_Relation_Orefl__on(X4,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f500,axiom,
! [X0,X19,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X19,X0)
| c_Relation_Orefl__on(X4,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
fof(f980,plain,
spl0_59,
inference(avatar_split_clause,[],[f476,f978]) ).
fof(f978,plain,
( spl0_59
<=> ! [X4,X0] : c_Relation_ODomain(c_Relation_OId__on(X4,X0),X0,X0) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f476,axiom,
! [X0,X4] : c_Relation_ODomain(c_Relation_OId__on(X4,X0),X0,X0) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
fof(f976,plain,
spl0_58,
inference(avatar_split_clause,[],[f475,f974]) ).
fof(f974,plain,
( spl0_58
<=> ! [X34,X0,X12,X8] : hAPP(c_COMBK(X12,X0,X8),X34) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f475,axiom,
! [X0,X8,X34,X12] : hAPP(c_COMBK(X12,X0,X8),X34) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f972,plain,
spl0_57,
inference(avatar_split_clause,[],[f473,f970]) ).
fof(f970,plain,
( spl0_57
<=> ! [X4,X0] : c_Relation_OImage(c_Relation_OId(X0),X4,X0,X0) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f473,axiom,
! [X0,X4] : c_Relation_OImage(c_Relation_OId(X0),X4,X0,X0) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id_0) ).
fof(f968,plain,
spl0_56,
inference(avatar_split_clause,[],[f470,f966]) ).
fof(f966,plain,
( spl0_56
<=> ! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f470,axiom,
! [X0,X19] :
( ~ c_Relation_Osym(X19,X0)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
fof(f964,plain,
spl0_55,
inference(avatar_split_clause,[],[f455,f962]) ).
fof(f455,axiom,
! [X31,X0] : ~ hBOOL(c_in(X31,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f960,plain,
spl0_54,
inference(avatar_split_clause,[],[f408,f958]) ).
fof(f408,axiom,
! [X0,X1,X5] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X5,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f956,plain,
spl0_53,
inference(avatar_split_clause,[],[f302,f954]) ).
fof(f302,axiom,
! [X0,X19] :
( ~ c_Wellfounded_Oacyclic(X19,X0)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
fof(f952,plain,
spl0_52,
inference(avatar_split_clause,[],[f231,f950]) ).
fof(f231,axiom,
! [X0,X4] : c_Lattices_Olower__semilattice__class_Oinf(X4,X4,tc_fun(X0,tc_bool)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f948,plain,
spl0_51,
inference(avatar_split_clause,[],[f230,f946]) ).
fof(f230,axiom,
! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f944,plain,
spl0_50,
inference(avatar_split_clause,[],[f139,f942]) ).
fof(f942,plain,
( spl0_50
<=> ! [X4,X0,X19] :
( ~ c_Order__Relation_Ostrict__linear__order__on(X4,X19,X0)
| c_Relation_Ototal__on(X4,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f139,axiom,
! [X0,X19,X4] :
( ~ c_Order__Relation_Ostrict__linear__order__on(X4,X19,X0)
| c_Relation_Ototal__on(X4,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).
fof(f940,plain,
spl0_49,
inference(avatar_split_clause,[],[f25,f938]) ).
fof(f938,plain,
( spl0_49
<=> ! [X4,X0] : c_Lattices_Oupper__semilattice__class_Osup(X4,X4,tc_fun(X0,tc_bool)) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f25,axiom,
! [X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(X4,X4,tc_fun(X0,tc_bool)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f936,plain,
spl0_48,
inference(avatar_split_clause,[],[f24,f934]) ).
fof(f24,axiom,
! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f931,plain,
spl0_47,
inference(avatar_split_clause,[],[f641,f929]) ).
fof(f929,plain,
( spl0_47
<=> ! [X61,X0,X62] :
( X61 = X62
| ~ c_fequal(X61,X62,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f641,axiom,
! [X0,X62,X61] :
( X61 = X62
| ~ c_fequal(X61,X62,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f927,plain,
spl0_46,
inference(avatar_split_clause,[],[f508,f925]) ).
fof(f925,plain,
( spl0_46
<=> ! [X4,X0,X19] :
( c_Relation_Otrans(X19,X0)
| ~ c_Equiv__Relations_Oequiv(X4,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f508,axiom,
! [X0,X19,X4] :
( c_Relation_Otrans(X19,X0)
| ~ c_Equiv__Relations_Oequiv(X4,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
fof(f923,plain,
spl0_45,
inference(avatar_split_clause,[],[f502,f921]) ).
fof(f921,plain,
( spl0_45
<=> ! [X4,X0,X19] :
( c_Relation_Osym(X19,X0)
| ~ c_Equiv__Relations_Oequiv(X4,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f502,axiom,
! [X0,X19,X4] :
( c_Relation_Osym(X19,X0)
| ~ c_Equiv__Relations_Oequiv(X4,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
fof(f919,plain,
spl0_44,
inference(avatar_split_clause,[],[f501,f917]) ).
fof(f917,plain,
( spl0_44
<=> ! [X0,X19] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X19,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f501,axiom,
! [X0,X19] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X19,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
fof(f915,plain,
spl0_43,
inference(avatar_split_clause,[],[f499,f913]) ).
fof(f913,plain,
( spl0_43
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f499,axiom,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f911,plain,
spl0_42,
inference(avatar_split_clause,[],[f390,f909]) ).
fof(f390,axiom,
! [X0,X1,X4] : hBOOL(hAPP(c_Set_Oinsert(X1,X4,X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f907,plain,
spl0_41,
inference(avatar_split_clause,[],[f273,f905]) ).
fof(f905,plain,
( spl0_41
<=> ! [X4,X0,X19] :
( c_Relation_Oirrefl(X19,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X4,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f273,axiom,
! [X0,X19,X4] :
( c_Relation_Oirrefl(X19,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X4,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).
fof(f903,plain,
spl0_40,
inference(avatar_split_clause,[],[f223,f901]) ).
fof(f901,plain,
( spl0_40
<=> ! [X4,X0,X19] :
( c_Relation_Otrans(X19,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X4,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f223,axiom,
! [X0,X19,X4] :
( c_Relation_Otrans(X19,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X4,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).
fof(f899,plain,
spl0_39,
inference(avatar_split_clause,[],[f47,f897]) ).
fof(f47,axiom,
! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f895,plain,
spl0_38,
inference(avatar_split_clause,[],[f629,f893]) ).
fof(f893,plain,
( spl0_38
<=> ! [X60,X59] :
( ~ class_HOL_Oord(X60)
| class_HOL_Oord(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f629,axiom,
! [X59,X60] :
( ~ class_HOL_Oord(X60)
| class_HOL_Oord(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f891,plain,
spl0_37,
inference(avatar_split_clause,[],[f628,f889]) ).
fof(f889,plain,
( spl0_37
<=> ! [X60,X59] :
( ~ class_HOL_Ominus(X60)
| class_HOL_Ominus(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f628,axiom,
! [X59,X60] :
( ~ class_HOL_Ominus(X60)
| class_HOL_Ominus(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
fof(f887,plain,
spl0_36,
inference(avatar_split_clause,[],[f627,f885]) ).
fof(f885,plain,
( spl0_36
<=> ! [X60,X59] :
( ~ class_Orderings_Obot(X60)
| class_Orderings_Obot(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f627,axiom,
! [X59,X60] :
( ~ class_Orderings_Obot(X60)
| class_Orderings_Obot(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f883,plain,
spl0_35,
inference(avatar_split_clause,[],[f626,f881]) ).
fof(f881,plain,
( spl0_35
<=> ! [X60,X59] :
( ~ class_Orderings_Oorder(X60)
| class_Orderings_Oorder(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f626,axiom,
! [X59,X60] :
( ~ class_Orderings_Oorder(X60)
| class_Orderings_Oorder(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f879,plain,
spl0_34,
inference(avatar_split_clause,[],[f625,f877]) ).
fof(f877,plain,
( spl0_34
<=> ! [X60,X59] :
( ~ class_Lattices_Olattice(X60)
| class_Lattices_Olattice(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f625,axiom,
! [X59,X60] :
( ~ class_Lattices_Olattice(X60)
| class_Lattices_Olattice(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f875,plain,
spl0_33,
inference(avatar_split_clause,[],[f624,f873]) ).
fof(f873,plain,
( spl0_33
<=> ! [X60,X59] :
( ~ class_Orderings_Opreorder(X60)
| class_Orderings_Opreorder(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f624,axiom,
! [X59,X60] :
( ~ class_Orderings_Opreorder(X60)
| class_Orderings_Opreorder(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f871,plain,
spl0_32,
inference(avatar_split_clause,[],[f623,f869]) ).
fof(f869,plain,
( spl0_32
<=> ! [X60,X59] :
( ~ class_Lattices_Obounded__lattice(X60)
| class_Lattices_Obounded__lattice(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f623,axiom,
! [X59,X60] :
( ~ class_Lattices_Obounded__lattice(X60)
| class_Lattices_Obounded__lattice(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f867,plain,
spl0_31,
inference(avatar_split_clause,[],[f622,f865]) ).
fof(f865,plain,
( spl0_31
<=> ! [X60,X59] :
( ~ class_Lattices_Odistrib__lattice(X60)
| class_Lattices_Odistrib__lattice(tc_fun(X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f622,axiom,
! [X59,X60] :
( ~ class_Lattices_Odistrib__lattice(X60)
| class_Lattices_Odistrib__lattice(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f863,plain,
spl0_30,
inference(avatar_split_clause,[],[f621,f861]) ).
fof(f621,axiom,
! [X59,X60] :
( ~ class_Lattices_Olattice(X60)
| class_Lattices_Olower__semilattice(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f859,plain,
spl0_29,
inference(avatar_split_clause,[],[f620,f857]) ).
fof(f620,axiom,
! [X59,X60] :
( ~ class_Lattices_Olattice(X60)
| class_Lattices_Oupper__semilattice(tc_fun(X59,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f855,plain,
spl0_28,
inference(avatar_split_clause,[],[f480,f853]) ).
fof(f853,plain,
( spl0_28
<=> ! [X4,X0] : c_Relation_Orefl__on(X4,c_Relation_OId__on(X4,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f480,axiom,
! [X0,X4] : c_Relation_Orefl__on(X4,c_Relation_OId__on(X4,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
fof(f851,plain,
spl0_27,
inference(avatar_split_clause,[],[f459,f849]) ).
fof(f849,plain,
( spl0_27
<=> ! [X4,X0] : c_Relation_Osingle__valued(c_Relation_OId__on(X4,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f459,axiom,
! [X0,X4] : c_Relation_Osingle__valued(c_Relation_OId__on(X4,X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
fof(f847,plain,
spl0_26,
inference(avatar_split_clause,[],[f250,f845]) ).
fof(f845,plain,
( spl0_26
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f250,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f843,plain,
spl0_25,
inference(avatar_split_clause,[],[f249,f841]) ).
fof(f841,plain,
( spl0_25
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f249,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f839,plain,
spl0_24,
inference(avatar_split_clause,[],[f245,f837]) ).
fof(f245,axiom,
! [X0,X4] : c_lessequals(X4,X4,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
fof(f835,plain,
spl0_23,
inference(avatar_split_clause,[],[f122,f833]) ).
fof(f122,axiom,
! [X0,X19] :
( ~ c_Wellfounded_Owf(X19,X0)
| c_Wellfounded_Oacyclic(X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
fof(f831,plain,
spl0_22,
inference(avatar_split_clause,[],[f486,f829]) ).
fof(f829,plain,
( spl0_22
<=> ! [X0,X19] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X19,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f486,axiom,
! [X0,X19] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X19,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
fof(f827,plain,
spl0_21,
inference(avatar_split_clause,[],[f479,f825]) ).
fof(f825,plain,
( spl0_21
<=> ! [X4,X0] : c_Relation_Osym(c_Relation_OId__on(X4,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f479,axiom,
! [X0,X4] : c_Relation_Osym(c_Relation_OId__on(X4,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
fof(f823,plain,
spl0_20,
inference(avatar_split_clause,[],[f474,f821]) ).
fof(f821,plain,
( spl0_20
<=> ! [X0] : c_Relation_Osingle__valued(c_Relation_OId(X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f474,axiom,
! [X0] : c_Relation_Osingle__valued(c_Relation_OId(X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
fof(f819,plain,
spl0_19,
inference(avatar_split_clause,[],[f468,f817]) ).
fof(f817,plain,
( spl0_19
<=> ! [X4,X0] : c_Relation_Oantisym(c_Relation_OId__on(X4,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f468,axiom,
! [X0,X4] : c_Relation_Oantisym(c_Relation_OId__on(X4,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
fof(f815,plain,
spl0_18,
inference(avatar_split_clause,[],[f465,f813]) ).
fof(f813,plain,
( spl0_18
<=> ! [X4,X0] : c_Relation_Otrans(c_Relation_OId__on(X4,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f465,axiom,
! [X0,X4] : c_Relation_Otrans(c_Relation_OId__on(X4,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
fof(f811,plain,
spl0_17,
inference(avatar_split_clause,[],[f640,f809]) ).
fof(f809,plain,
( spl0_17
<=> ! [X0,X1] : c_fequal(X1,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f640,axiom,
! [X0,X1] : c_fequal(X1,X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f807,plain,
spl0_16,
inference(avatar_split_clause,[],[f496,f805]) ).
fof(f805,plain,
( spl0_16
<=> ! [X0] : c_Relation_Otrans(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f496,axiom,
! [X0] : c_Relation_Otrans(c_Relation_OId(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id_0) ).
fof(f803,plain,
spl0_15,
inference(avatar_split_clause,[],[f492,f801]) ).
fof(f801,plain,
( spl0_15
<=> ! [X0] : c_Relation_Oantisym(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f492,axiom,
! [X0] : c_Relation_Oantisym(c_Relation_OId(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
fof(f799,plain,
spl0_14,
inference(avatar_split_clause,[],[f464,f797]) ).
fof(f797,plain,
( spl0_14
<=> ! [X0] : c_Relation_Osym(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f464,axiom,
! [X0] : c_Relation_Osym(c_Relation_OId(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id_0) ).
fof(f795,plain,
~ spl0_13,
inference(avatar_split_clause,[],[f617,f792]) ).
fof(f792,plain,
( spl0_13
<=> v_a____ = v_b____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f617,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_05) ).
fof(f790,plain,
~ spl0_12,
inference(avatar_split_clause,[],[f610,f787]) ).
fof(f787,plain,
( spl0_12
<=> v_a____ = v_c____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f610,axiom,
v_a____ != v_c____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A_I3_J_0) ).
fof(f785,plain,
~ spl0_11,
inference(avatar_split_clause,[],[f604,f782]) ).
fof(f782,plain,
( spl0_11
<=> v_b____ = v_c____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f604,axiom,
v_b____ != v_c____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A_I2_J_0) ).
fof(f780,plain,
spl0_10,
inference(avatar_split_clause,[],[f639,f777]) ).
fof(f777,plain,
( spl0_10
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f639,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f775,plain,
spl0_9,
inference(avatar_split_clause,[],[f638,f772]) ).
fof(f772,plain,
( spl0_9
<=> class_HOL_Ominus(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f638,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
fof(f770,plain,
spl0_8,
inference(avatar_split_clause,[],[f637,f767]) ).
fof(f637,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f765,plain,
spl0_7,
inference(avatar_split_clause,[],[f636,f762]) ).
fof(f762,plain,
( spl0_7
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f636,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f760,plain,
spl0_6,
inference(avatar_split_clause,[],[f635,f757]) ).
fof(f635,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f755,plain,
spl0_5,
inference(avatar_split_clause,[],[f634,f752]) ).
fof(f752,plain,
( spl0_5
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f634,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f750,plain,
spl0_4,
inference(avatar_split_clause,[],[f633,f747]) ).
fof(f633,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f745,plain,
spl0_3,
inference(avatar_split_clause,[],[f632,f742]) ).
fof(f742,plain,
( spl0_3
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f632,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f740,plain,
spl0_2,
inference(avatar_split_clause,[],[f631,f737]) ).
fof(f631,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f735,plain,
spl0_1,
inference(avatar_split_clause,[],[f630,f732]) ).
fof(f630,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SCT058-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n009.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Apr 29 22:15:41 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.31 % (19017)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.36 % (19024)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.36 % (19021)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.36 % (19020)WARNING: value z3 for option sas not known
% 0.15/0.36 % (19019)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.36 % (19020)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)
% 0.15/0.36 % (19022)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)
% 0.15/0.36 % (19023)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)
% 0.15/0.36 % (19018)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.51 Detected minimum model sizes of [3]
% 0.15/0.51 Detected maximum model sizes of [max]
% 1.78/0.60 TRYING [3]
% 5.22/1.12 Detected minimum model sizes of [3]
% 5.22/1.12 Detected maximum model sizes of [max]
% 8.37/1.60 Detected minimum model sizes of [3]
% 8.37/1.60 Detected maximum model sizes of [max]
% 9.02/1.68 TRYING [3]
% 9.60/1.77 % (19022)First to succeed.
% 10.36/1.81 % (19022)Refutation found. Thanks to Tanya!
% 10.36/1.81 % SZS status Unsatisfiable for theBenchmark
% 10.36/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 10.36/1.83 % (19022)------------------------------
% 10.36/1.83 % (19022)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 10.36/1.83 % (19022)Termination reason: Refutation
% 10.36/1.83
% 10.36/1.83 % (19022)Memory used [KB]: 13939
% 10.36/1.83 % (19022)Time elapsed: 1.441 s
% 10.36/1.83 % (19022)Instructions burned: 2781 (million)
% 10.36/1.83 % (19022)------------------------------
% 10.36/1.83 % (19022)------------------------------
% 10.36/1.83 % (19017)Success in time 1.498 s
%------------------------------------------------------------------------------