TSTP Solution File: SWV880-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV880-1 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:07:20 EDT 2024
% Result : Unsatisfiable 2.54s 0.78s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 840
% Syntax : Number of formulae : 1390 ( 483 unt; 0 def)
% Number of atoms : 3281 ( 425 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 3244 (1353 ~;1447 |; 0 &)
% ( 444 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 466 ( 464 usr; 445 prp; 0-6 aty)
% Number of functors : 38 ( 38 usr; 8 con; 0-5 aty)
% Number of variables : 3053 (3053 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9122,plain,
$false,
inference(avatar_sat_refutation,[],[f515,f520,f525,f530,f535,f540,f545,f550,f555,f560,f565,f570,f575,f580,f585,f590,f595,f600,f605,f610,f615,f619,f623,f627,f631,f635,f639,f643,f647,f651,f655,f659,f663,f667,f671,f675,f679,f683,f687,f691,f695,f699,f703,f707,f711,f715,f719,f723,f727,f732,f736,f740,f744,f748,f752,f761,f766,f770,f774,f778,f782,f786,f790,f794,f798,f802,f806,f816,f820,f824,f828,f832,f836,f840,f844,f848,f852,f857,f861,f865,f869,f873,f877,f881,f885,f889,f893,f897,f951,f956,f960,f964,f968,f972,f976,f980,f984,f988,f992,f996,f1000,f1004,f1008,f1012,f1030,f1052,f1063,f1067,f1071,f1075,f1079,f1083,f1087,f1091,f1095,f1099,f1103,f1201,f1205,f1209,f1213,f1217,f1221,f1225,f1229,f1233,f1242,f1246,f1250,f1254,f1258,f1262,f1266,f1270,f1274,f1278,f1282,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1379,f1597,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1687,f1691,f1695,f1699,f1703,f1721,f1725,f1729,f1733,f1737,f1741,f1745,f1749,f1753,f1757,f1761,f1765,f1769,f1773,f1777,f1781,f1785,f1789,f1793,f1797,f1801,f1872,f2286,f2307,f2311,f2315,f2319,f2323,f2327,f2331,f2339,f2343,f2347,f2351,f2355,f2359,f2363,f2367,f2371,f2375,f2379,f2383,f2387,f2391,f2395,f2399,f2403,f2407,f2411,f2415,f2419,f2425,f2429,f2433,f2437,f2441,f2445,f2449,f2460,f2782,f3072,f3076,f3080,f3084,f3088,f3092,f3096,f3100,f3104,f3108,f3112,f3116,f3120,f3393,f3397,f3401,f3405,f3409,f3413,f3417,f3421,f3425,f3429,f3433,f3437,f3441,f3445,f3739,f3753,f3757,f3761,f3765,f3769,f3773,f3777,f3781,f3785,f3789,f3793,f3797,f3801,f3805,f3809,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4146,f4150,f4154,f4158,f4162,f4166,f4174,f4320,f4826,f4830,f4834,f4838,f4842,f4846,f4850,f4854,f4858,f4862,f4866,f4870,f4874,f4878,f4882,f4886,f4890,f4894,f5048,f5213,f5217,f5221,f5225,f5229,f5233,f5237,f5241,f5245,f5249,f5253,f5446,f5450,f5454,f5464,f5468,f5472,f5535,f5539,f5543,f5547,f5551,f5555,f5667,f5673,f5677,f5681,f5685,f5689,f5693,f5697,f5701,f5761,f5893,f5897,f5901,f5923,f5927,f5931,f5935,f5939,f5943,f5947,f5951,f5955,f5959,f5963,f5967,f5971,f5975,f5979,f6423,f6466,f6470,f6474,f6478,f6482,f6486,f6490,f6494,f6498,f6706,f6710,f6714,f6718,f6722,f6726,f6730,f6734,f6738,f6742,f6746,f6750,f7100,f7112,f7116,f7120,f7124,f7128,f7132,f7136,f7140,f7447,f7451,f7455,f7459,f7583,f7587,f7591,f7595,f7730,f7734,f8036,f8040,f8204,f8208,f8212,f8216,f8220,f8250,f8255,f8410,f8414,f8418,f8422,f8426,f8430,f8434,f8532,f8694,f8711,f8716,f8777,f8781,f8814,f8881,f8885,f8889,f8893,f9001,f9030,f9039,f9058,f9062,f9066,f9081,f9085,f9094,f9105,f9121]) ).
fof(f9121,plain,
( ~ spl0_67
| spl0_444 ),
inference(avatar_contradiction_clause,[],[f9116]) ).
fof(f9116,plain,
( $false
| ~ spl0_67
| spl0_444 ),
inference(resolution,[],[f9093,f805]) ).
fof(f805,plain,
( ! [X0,X8] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f804,plain,
( spl0_67
<=> ! [X0,X8] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f9093,plain,
( ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool))
| spl0_444 ),
inference(avatar_component_clause,[],[f9091]) ).
fof(f9091,plain,
( spl0_444
<=> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f9105,plain,
( ~ spl0_283
| spl0_443 ),
inference(avatar_contradiction_clause,[],[f9096]) ).
fof(f9096,plain,
( $false
| ~ spl0_283
| spl0_443 ),
inference(resolution,[],[f9089,f4125]) ).
fof(f4125,plain,
( ! [X0] : c_in(hAPP(v_mgt__call,v_pn),v_G,X0)
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f4124]) ).
fof(f4124,plain,
( spl0_283
<=> ! [X0] : c_in(hAPP(v_mgt__call,v_pn),v_G,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f9089,plain,
( ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| spl0_443 ),
inference(avatar_component_clause,[],[f9087]) ).
fof(f9087,plain,
( spl0_443
<=> c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f9094,plain,
( ~ spl0_443
| ~ spl0_444
| spl0_21
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4680,f4160,f612,f9091,f9087]) ).
fof(f612,plain,
( spl0_21
<=> c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),v_G,tc_fun(t_a,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f4160,plain,
( spl0_292
<=> ! [X3,X0,X9,X8] :
( ~ c_in(X3,X9,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f4680,plain,
( ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| spl0_21
| ~ spl0_292 ),
inference(resolution,[],[f4161,f614]) ).
fof(f614,plain,
( ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),v_G,tc_fun(t_a,tc_bool))
| spl0_21 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f4161,plain,
( ! [X3,X0,X8,X9] :
( c_lessequals(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_in(X3,X9,X0) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f4160]) ).
fof(f9085,plain,
( spl0_442
| ~ spl0_3
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4631,f4148,f522,f9083]) ).
fof(f9083,plain,
( spl0_442
<=> ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0,t_a,tc_Com_Opname) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f522,plain,
( spl0_3
<=> v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f4148,plain,
( spl0_289
<=> ! [X9,X0,X6,X8,X7] :
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X8,X6,X7,X0),X9,X0,X7)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f4631,plain,
( ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0,t_a,tc_Com_Opname) )
| ~ spl0_3
| ~ spl0_289 ),
inference(superposition,[],[f4149,f524]) ).
fof(f524,plain,
( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f4149,plain,
( ! [X0,X8,X6,X9,X7] :
( ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X8,X6,X7,X0),X9,X0,X7) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f4148]) ).
fof(f9081,plain,
( ~ spl0_1
| spl0_436
| ~ spl0_441
| ~ spl0_3
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4602,f4144,f522,f9078,f9032,f512]) ).
fof(f512,plain,
( spl0_1
<=> c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f9032,plain,
( spl0_436
<=> c_Fun_Oinj__on(v_mgt__call,v_U,tc_Com_Opname,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f9078,plain,
( spl0_441
<=> c_Finite__Set_Ocard(v_U,tc_Com_Opname) = c_Finite__Set_Ocard(v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f4144,plain,
( spl0_288
<=> ! [X0,X6,X8,X7] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Finite__Set_Ocard(X8,X0) != c_Finite__Set_Ocard(c_Set_Oimage(X6,X8,X0,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f4602,plain,
( c_Finite__Set_Ocard(v_U,tc_Com_Opname) != c_Finite__Set_Ocard(v_G,t_a)
| c_Fun_Oinj__on(v_mgt__call,v_U,tc_Com_Opname,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| ~ spl0_3
| ~ spl0_288 ),
inference(superposition,[],[f4145,f524]) ).
fof(f4145,plain,
( ! [X0,X8,X6,X7] :
( c_Finite__Set_Ocard(X8,X0) != c_Finite__Set_Ocard(c_Set_Oimage(X6,X8,X0,X7),X7)
| c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_Finite__Set_Ofinite(X8,X0) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f4144]) ).
fof(f9066,plain,
( spl0_440
| ~ spl0_3
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4599,f4140,f522,f9064]) ).
fof(f9064,plain,
( spl0_440
<=> ! [X0] :
( c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f4140,plain,
( spl0_287
<=> ! [X9,X0,X6,X8,X7] :
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X8,X9,X6,X7,X0),X8,X7)
| c_lessequals(c_Set_Oimage(X6,X8,X7,X0),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f4599,plain,
( ! [X0] :
( c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname) )
| ~ spl0_3
| ~ spl0_287 ),
inference(superposition,[],[f4141,f524]) ).
fof(f4141,plain,
( ! [X0,X8,X6,X9,X7] :
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X8,X9,X6,X7,X0),X8,X7)
| c_lessequals(c_Set_Oimage(X6,X8,X7,X0),X9,tc_fun(X0,tc_bool)) )
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f4140]) ).
fof(f9062,plain,
( spl0_439
| ~ spl0_3
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4537,f4136,f522,f9060]) ).
fof(f9060,plain,
( spl0_439
<=> ! [X0] :
( c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f4136,plain,
( spl0_286
<=> ! [X9,X0,X6,X8,X7] :
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X8,X9,X6,X0,X7),X8,X0)
| c_lessequals(c_Set_Oimage(X6,X8,X0,X7),X9,tc_fun(X7,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f4537,plain,
( ! [X0] :
( c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname) )
| ~ spl0_3
| ~ spl0_286 ),
inference(superposition,[],[f4137,f524]) ).
fof(f4137,plain,
( ! [X0,X8,X6,X9,X7] :
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X8,X9,X6,X0,X7),X8,X0)
| c_lessequals(c_Set_Oimage(X6,X8,X0,X7),X9,tc_fun(X7,tc_bool)) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f4136]) ).
fof(f9058,plain,
( spl0_438
| ~ spl0_3
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f4258,f4104,f522,f9056]) ).
fof(f9056,plain,
( spl0_438
<=> ! [X0] :
( ~ c_in(X0,v_G,t_a)
| hAPP(v_mgt__call,hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f4104,plain,
( spl0_278
<=> ! [X1,X0,X6,X8,X7] :
( ~ c_in(X1,c_Set_Oimage(X6,X8,X7,X0),X0)
| hAPP(X6,hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X7,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f4258,plain,
( ! [X0] :
( ~ c_in(X0,v_G,t_a)
| hAPP(v_mgt__call,hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0)) = X0 )
| ~ spl0_3
| ~ spl0_278 ),
inference(superposition,[],[f4105,f524]) ).
fof(f4105,plain,
( ! [X0,X1,X8,X6,X7] :
( ~ c_in(X1,c_Set_Oimage(X6,X8,X7,X0),X0)
| hAPP(X6,hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X7,X0),X1)) = X1 )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f4104]) ).
fof(f9039,plain,
( ~ spl0_436
| spl0_437
| ~ spl0_3
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3897,f3775,f522,f9036,f9032]) ).
fof(f9036,plain,
( spl0_437
<=> c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),v_G,t_a,tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f3775,plain,
( spl0_263
<=> ! [X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Fun_Oinj__on(c_Fun_Othe__inv__into(X8,X6,X0,X7),c_Set_Oimage(X6,X8,X0,X7),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f3897,plain,
( c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),v_G,t_a,tc_Com_Opname)
| ~ c_Fun_Oinj__on(v_mgt__call,v_U,tc_Com_Opname,t_a)
| ~ spl0_3
| ~ spl0_263 ),
inference(superposition,[],[f3776,f524]) ).
fof(f3776,plain,
( ! [X0,X8,X6,X7] :
( c_Fun_Oinj__on(c_Fun_Othe__inv__into(X8,X6,X0,X7),c_Set_Oimage(X6,X8,X0,X7),X7,X0)
| ~ c_Fun_Oinj__on(X6,X8,X0,X7) )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f3775]) ).
fof(f9030,plain,
( spl0_435
| ~ spl0_3
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f3858,f3767,f522,f9028]) ).
fof(f9028,plain,
( spl0_435
<=> ! [X0] :
( ~ c_in(X0,v_G,t_a)
| c_in(hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0),v_U,tc_Com_Opname) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f3767,plain,
( spl0_261
<=> ! [X3,X0,X6,X8,X7] :
( ~ c_in(X3,c_Set_Oimage(X6,X8,X7,X0),X0)
| c_in(hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X7,X0),X3),X8,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f3858,plain,
( ! [X0] :
( ~ c_in(X0,v_G,t_a)
| c_in(hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0),v_U,tc_Com_Opname) )
| ~ spl0_3
| ~ spl0_261 ),
inference(superposition,[],[f3768,f524]) ).
fof(f3768,plain,
( ! [X3,X0,X8,X6,X7] :
( ~ c_in(X3,c_Set_Oimage(X6,X8,X7,X0),X0)
| c_in(hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X7,X0),X3),X8,X7) )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f3767]) ).
fof(f9001,plain,
( spl0_434
| ~ spl0_158
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f3010,f2439,f1661,f8999]) ).
fof(f8999,plain,
( spl0_434
<=> ! [X2,X0,X1] :
( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
| c_in(v_pn,c_Set_Oinsert(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f1661,plain,
( spl0_158
<=> ! [X0,X1] :
( ~ c_lessequals(v_U,X1,tc_fun(X0,tc_bool))
| c_in(v_pn,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f2439,plain,
( spl0_224
<=> ! [X0,X14,X9,X8] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(X8,c_Set_Oinsert(X14,X9,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f3010,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
| c_in(v_pn,c_Set_Oinsert(X2,X0,X1),X1) )
| ~ spl0_158
| ~ spl0_224 ),
inference(resolution,[],[f2440,f1662]) ).
fof(f1662,plain,
( ! [X0,X1] :
( ~ c_lessequals(v_U,X1,tc_fun(X0,tc_bool))
| c_in(v_pn,X1,X0) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1661]) ).
fof(f2440,plain,
( ! [X0,X8,X9,X14] :
( c_lessequals(X8,c_Set_Oinsert(X14,X9,X0),tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2439]) ).
fof(f8893,plain,
spl0_433,
inference(avatar_split_clause,[],[f40,f8891]) ).
fof(f8891,plain,
( spl0_433
<=> ! [X15,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7)) = hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))
| hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7))) = hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f40,axiom,
! [X0,X8,X6,X7,X15] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7)) = hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))
| hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7))) = hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_4) ).
fof(f8889,plain,
spl0_432,
inference(avatar_split_clause,[],[f39,f8887]) ).
fof(f8887,plain,
( spl0_432
<=> ! [X15,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7)) = hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))
| hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7))) = hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f39,axiom,
! [X0,X8,X6,X7,X15] :
( ~ c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7)) = hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))
| hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7))) = hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_5) ).
fof(f8885,plain,
spl0_431,
inference(avatar_split_clause,[],[f38,f8883]) ).
fof(f8883,plain,
( spl0_431
<=> ! [X15,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7)) != hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))
| hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7))) != hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f38,axiom,
! [X0,X8,X6,X7,X15] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7)) != hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))
| hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7))) != hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_6) ).
fof(f8881,plain,
spl0_430,
inference(avatar_split_clause,[],[f37,f8879]) ).
fof(f8879,plain,
( spl0_430
<=> ! [X15,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| ~ c_Fun_Oinj__on(X15,X8,X0,X7)
| c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7)) != hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))
| hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7))) != hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f37,axiom,
! [X0,X8,X6,X7,X15] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| ~ c_Fun_Oinj__on(X15,X8,X0,X7)
| c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7)) != hAPP(X15,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))
| hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7))) != hAPP(X15,hAPP(X6,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_7) ).
fof(f8814,plain,
spl0_429,
inference(avatar_split_clause,[],[f296,f8812]) ).
fof(f8812,plain,
( spl0_429
<=> ! [X9,X0,X12,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X12,X0,X7)
| ~ c_lessequals(X8,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_Set_Oimage(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0,X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X7,tc_bool)),c_Set_Oimage(X6,X8,X0,X7)),c_Set_Oimage(X6,X9,X0,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f296,axiom,
! [X0,X8,X6,X9,X7,X12] :
( ~ c_Fun_Oinj__on(X6,X12,X0,X7)
| ~ c_lessequals(X8,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_Set_Oimage(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0,X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X7,tc_bool)),c_Set_Oimage(X6,X8,X0,X7)),c_Set_Oimage(X6,X9,X0,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
fof(f8781,plain,
spl0_428,
inference(avatar_split_clause,[],[f312,f8779]) ).
fof(f8779,plain,
( spl0_428
<=> ! [X15,X6,X0,X9,X8,X7] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_Finite__Set_Ofinite(X9,X7)
| ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,X9,X7,X0)
| c_Finite__Set_Ocard(X8,X0) = c_Finite__Set_Ocard(X9,X7)
| ~ c_lessequals(c_Set_Oimage(X6,X8,X0,X7),X9,tc_fun(X7,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X15,X9,X7,X0),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f312,axiom,
! [X0,X8,X6,X9,X7,X15] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_Finite__Set_Ofinite(X9,X7)
| ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,X9,X7,X0)
| c_Finite__Set_Ocard(X8,X0) = c_Finite__Set_Ocard(X9,X7)
| ~ c_lessequals(c_Set_Oimage(X6,X8,X0,X7),X9,tc_fun(X7,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X15,X9,X7,X0),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).
fof(f8777,plain,
( spl0_427
| ~ spl0_59
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1712,f1661,f772,f8775]) ).
fof(f8775,plain,
( spl0_427
<=> ! [X0,X1] :
( c_in(v_pn,c_Orderings_Oord__class_Omax(v_U,X0,tc_fun(X1,tc_bool)),X1)
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f772,plain,
( spl0_59
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1712,plain,
( ! [X0,X1] :
( c_in(v_pn,c_Orderings_Oord__class_Omax(v_U,X0,tc_fun(X1,tc_bool)),X1)
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool)) )
| ~ spl0_59
| ~ spl0_158 ),
inference(resolution,[],[f1662,f773]) ).
fof(f773,plain,
( ! [X3,X0,X1] :
( c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X1,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f8716,plain,
spl0_426,
inference(avatar_split_clause,[],[f347,f8714]) ).
fof(f8714,plain,
( spl0_426
<=> ! [X9,X0,X12,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X12,X0,X7)
| ~ c_lessequals(X8,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0,X7) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X6,X8,X0,X7),c_Set_Oimage(X6,X9,X0,X7),tc_fun(X7,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f347,axiom,
! [X0,X8,X6,X9,X7,X12] :
( ~ c_Fun_Oinj__on(X6,X12,X0,X7)
| ~ c_lessequals(X8,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0,X7) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X6,X8,X0,X7),c_Set_Oimage(X6,X9,X0,X7),tc_fun(X7,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
fof(f8711,plain,
spl0_425,
inference(avatar_split_clause,[],[f76,f8709]) ).
fof(f8709,plain,
( spl0_425
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Oimage(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0,X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X7,tc_bool)),c_Set_Oimage(X6,X8,X0,X7)),c_Set_Oimage(X6,X9,X0,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f76,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Oimage(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0,X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X7,tc_bool)),c_Set_Oimage(X6,X8,X0,X7)),c_Set_Oimage(X6,X9,X0,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
fof(f8694,plain,
spl0_424,
inference(avatar_split_clause,[],[f319,f8692]) ).
fof(f8692,plain,
( spl0_424
<=> ! [X3,X0,X9,X8] :
( c_in(X3,X9,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f319,axiom,
! [X3,X0,X8,X9] :
( c_in(X3,X9,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
fof(f8532,plain,
( spl0_423
| ~ spl0_58
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1711,f1661,f768,f8530]) ).
fof(f8530,plain,
( spl0_423
<=> ! [X0,X1] :
( c_in(v_pn,c_Orderings_Oord__class_Omax(X0,v_U,tc_fun(X1,tc_bool)),X1)
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f768,plain,
( spl0_58
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1711,plain,
( ! [X0,X1] :
( c_in(v_pn,c_Orderings_Oord__class_Omax(X0,v_U,tc_fun(X1,tc_bool)),X1)
| ~ class_Orderings_Olinorder(tc_fun(X1,tc_bool)) )
| ~ spl0_58
| ~ spl0_158 ),
inference(resolution,[],[f1662,f769]) ).
fof(f769,plain,
( ! [X3,X0,X1] :
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X3,X1,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f768]) ).
fof(f8434,plain,
spl0_422,
inference(avatar_split_clause,[],[f509,f8432]) ).
fof(f8432,plain,
( spl0_422
<=> ! [X0,X12,X9,X8] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X9),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X8),X9,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f509,plain,
! [X0,X8,X9,X12] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X9),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X8),X9,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f89,f124]) ).
fof(f124,axiom,
! [X0,X8,X9,X12] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X12,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_HOL_Ominus__class_Ominus(X9,X12,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
fof(f89,axiom,
! [X0,X8,X9,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X9),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
fof(f8430,plain,
spl0_421,
inference(avatar_split_clause,[],[f344,f8428]) ).
fof(f8428,plain,
( spl0_421
<=> ! [X0,X13,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Fun_Oinj__on(X6,c_Set_Oinsert(X13,X8,X0),X0,X7)
| c_in(hAPP(X6,X13),c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f344,axiom,
! [X0,X8,X6,X7,X13] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Fun_Oinj__on(X6,c_Set_Oinsert(X13,X8,X0),X0,X7)
| c_in(hAPP(X6,X13),c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X7),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
fof(f8426,plain,
spl0_420,
inference(avatar_split_clause,[],[f320,f8424]) ).
fof(f8424,plain,
( spl0_420
<=> ! [X1,X6,X0,X3,X8,X7] :
( ~ c_in(X3,X8,X7)
| c_Set_Oimage(c_Fun_Ofun__upd(X6,X3,X1,X7,X0),X8,X7,X0) = c_Set_Oinsert(X1,c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7),tc_fun(X7,tc_bool)),X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f320,axiom,
! [X3,X0,X1,X8,X6,X7] :
( ~ c_in(X3,X8,X7)
| c_Set_Oimage(c_Fun_Ofun__upd(X6,X3,X1,X7,X0),X8,X7,X0) = c_Set_Oinsert(X1,c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7),tc_fun(X7,tc_bool)),X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
fof(f8422,plain,
spl0_419,
inference(avatar_split_clause,[],[f305,f8420]) ).
fof(f8420,plain,
( spl0_419
<=> ! [X3,X0,X9,X8] :
( ~ c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f305,axiom,
! [X3,X0,X8,X9] :
( ~ c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
fof(f8418,plain,
spl0_418,
inference(avatar_split_clause,[],[f304,f8416]) ).
fof(f8416,plain,
( spl0_418
<=> ! [X3,X0,X9,X8] :
( ~ c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f304,axiom,
! [X3,X0,X8,X9] :
( ~ c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
fof(f8414,plain,
spl0_417,
inference(avatar_split_clause,[],[f154,f8412]) ).
fof(f8412,plain,
( spl0_417
<=> ! [X6,X0,X8,X3,X1,X7] :
( X1 = X3
| ~ c_in(X3,c_Set_Oimage(X6,X8,X0,X7),X7)
| ~ c_in(X1,c_Set_Oimage(X6,X8,X0,X7),X7)
| hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X0,X7),X3) != hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X0,X7),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f154,axiom,
! [X3,X0,X1,X8,X6,X7] :
( X1 = X3
| ~ c_in(X3,c_Set_Oimage(X6,X8,X0,X7),X7)
| ~ c_in(X1,c_Set_Oimage(X6,X8,X0,X7),X7)
| hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X0,X7),X3) != hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X0,X7),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).
fof(f8410,plain,
spl0_416,
inference(avatar_split_clause,[],[f97,f8408]) ).
fof(f8408,plain,
( spl0_416
<=> ! [X0,X12,X9,X8] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12),X9,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f97,axiom,
! [X0,X8,X9,X12] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12),X9,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
fof(f8255,plain,
( spl0_415
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f8251,f8248,f8253]) ).
fof(f8253,plain,
( spl0_415
<=> ! [X0,X12,X9,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool))),X12) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12),X9,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f8248,plain,
( spl0_414
<=> ! [X0,X12,X9,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool))),X12) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f8251,plain,
( ! [X0,X8,X9,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool))),X12) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12),X9,tc_fun(X0,tc_bool))
| ~ spl0_414 ),
inference(forward_demodulation,[],[f8249,f97]) ).
fof(f8249,plain,
( ! [X0,X8,X9,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool))),X12) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12),tc_fun(X0,tc_bool))
| ~ spl0_414 ),
inference(avatar_component_clause,[],[f8248]) ).
fof(f8250,plain,
spl0_414,
inference(avatar_split_clause,[],[f90,f8248]) ).
fof(f90,axiom,
! [X0,X8,X9,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool))),X12) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
fof(f8220,plain,
spl0_413,
inference(avatar_split_clause,[],[f322,f8218]) ).
fof(f8218,plain,
( spl0_413
<=> ! [X11,X0,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(X25,c_Set_Oinsert(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X8,X25,X0),c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X8,X25,X0),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f322,axiom,
! [X0,X11,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(X25,c_Set_Oinsert(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X8,X25,X0),c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X8,X25,X0),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_4) ).
fof(f8216,plain,
spl0_412,
inference(avatar_split_clause,[],[f308,f8214]) ).
fof(f8214,plain,
( spl0_412
<=> ! [X1,X6,X2,X0,X3,X8,X7] :
( ~ c_in(X3,X8,X0)
| c_Finite__Set_Ofold__graph(X6,X2,X8,hAPP(hAPP(X6,X3),X1),X0,X7)
| ~ c_Finite__Set_Ofold__graph(X6,X2,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X1,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f308,axiom,
! [X2,X3,X0,X1,X8,X6,X7] :
( ~ c_in(X3,X8,X0)
| c_Finite__Set_Ofold__graph(X6,X2,X8,hAPP(hAPP(X6,X3),X1),X0,X7)
| ~ c_Finite__Set_Ofold__graph(X6,X2,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X1,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
fof(f8212,plain,
spl0_411,
inference(avatar_split_clause,[],[f303,f8210]) ).
fof(f8210,plain,
( spl0_411
<=> ! [X1,X6,X2,X0,X3,X8,X7] :
( ~ c_in(X3,X8,X0)
| c_Nitpick_Ofold__graph_H(X6,X2,X8,hAPP(hAPP(X6,X3),X1),X0,X7)
| ~ c_Nitpick_Ofold__graph_H(X6,X2,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X1,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f303,axiom,
! [X2,X3,X0,X1,X8,X6,X7] :
( ~ c_in(X3,X8,X0)
| c_Nitpick_Ofold__graph_H(X6,X2,X8,hAPP(hAPP(X6,X3),X1),X0,X7)
| ~ c_Nitpick_Ofold__graph_H(X6,X2,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X1,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
fof(f8208,plain,
( spl0_410
| ~ spl0_68
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3579,f3415,f814,f8206]) ).
fof(f8206,plain,
( spl0_410
<=> ! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(v_pn,X1,X0),v_U,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f814,plain,
( spl0_68
<=> ! [X0] : c_in(v_pn,v_U,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f3415,plain,
( spl0_248
<=> ! [X17,X0,X8,X7] :
( ~ c_in(X17,X8,X7)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X17,X7,X0),X8,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3579,plain,
( ! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(v_pn,X1,X0),v_U,X0,X1)
| ~ spl0_68
| ~ spl0_248 ),
inference(resolution,[],[f3416,f815]) ).
fof(f815,plain,
( ! [X0] : c_in(v_pn,v_U,X0)
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f3416,plain,
( ! [X0,X8,X7,X17] :
( ~ c_in(X17,X8,X7)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X17,X7,X0),X8,X0,X7) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f3415]) ).
fof(f8204,plain,
spl0_409,
inference(avatar_split_clause,[],[f300,f8202]) ).
fof(f8202,plain,
( spl0_409
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0,X7) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X6,X8,X0,X7),c_Set_Oimage(X6,X9,X0,X7),tc_fun(X7,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f300,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0,X7) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X6,X8,X0,X7),c_Set_Oimage(X6,X9,X0,X7),tc_fun(X7,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
fof(f8040,plain,
spl0_408,
inference(avatar_split_clause,[],[f261,f8038]) ).
fof(f8038,plain,
( spl0_408
<=> ! [X24,X9,X0,X12,X8] :
( ~ c_lessequals(X8,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X24,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X24),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f261,axiom,
! [X0,X8,X9,X24,X12] :
( ~ c_lessequals(X8,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X24,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X24),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
fof(f8036,plain,
spl0_407,
inference(avatar_split_clause,[],[f162,f8034]) ).
fof(f8034,plain,
( spl0_407
<=> ! [X9,X0,X6,X8,X7] : c_lessequals(c_Set_Oimage(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X7,tc_bool)),X8),X9),X7,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oimage(X6,X8,X7,X0)),c_Set_Oimage(X6,X9,X7,X0)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f162,axiom,
! [X0,X8,X6,X9,X7] : c_lessequals(c_Set_Oimage(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X7,tc_bool)),X8),X9),X7,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oimage(X6,X8,X7,X0)),c_Set_Oimage(X6,X9,X7,X0)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
fof(f7734,plain,
spl0_406,
inference(avatar_split_clause,[],[f85,f7732]) ).
fof(f7732,plain,
( spl0_406
<=> ! [X0,X12,X9,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f85,axiom,
! [X0,X8,X9,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
fof(f7730,plain,
spl0_405,
inference(avatar_split_clause,[],[f84,f7728]) ).
fof(f7728,plain,
( spl0_405
<=> ! [X0,X12,X9,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f84,axiom,
! [X0,X8,X9,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
fof(f7595,plain,
spl0_404,
inference(avatar_split_clause,[],[f385,f7593]) ).
fof(f7593,plain,
( spl0_404
<=> ! [X3,X0,X9,X8] :
( ~ c_in(X3,X8,X0)
| ~ c_lessequals(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f385,axiom,
! [X3,X0,X8,X9] :
( ~ c_in(X3,X8,X0)
| ~ c_lessequals(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
fof(f7591,plain,
spl0_403,
inference(avatar_split_clause,[],[f384,f7589]) ).
fof(f7589,plain,
( spl0_403
<=> ! [X3,X0,X9,X8] :
( ~ c_in(X3,X8,X0)
| c_lessequals(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f384,axiom,
! [X3,X0,X8,X9] :
( ~ c_in(X3,X8,X0)
| c_lessequals(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
fof(f7587,plain,
spl0_402,
inference(avatar_split_clause,[],[f321,f7585]) ).
fof(f7585,plain,
( spl0_402
<=> ! [X11,X0,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| ~ c_in(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X8,X25,X0),c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X8,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f321,axiom,
! [X0,X11,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| ~ c_in(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X8,X25,X0),c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X8,X25,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_2) ).
fof(f7583,plain,
spl0_401,
inference(avatar_split_clause,[],[f281,f7581]) ).
fof(f7581,plain,
( spl0_401
<=> ! [X6,X13,X0,X16,X15,X7] :
( ~ c_in(X13,X16,X0)
| c_in(hAPP(X15,X13),c_Inductive_Ocomplete__lattice__class_Ogfp(X6,tc_fun(X7,tc_bool)),X7)
| ~ c_lessequals(c_Set_Oimage(X15,X16,X0,X7),hAPP(X6,c_Set_Oimage(X15,X16,X0,X7)),tc_fun(X7,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f281,axiom,
! [X0,X6,X16,X7,X15,X13] :
( ~ c_in(X13,X16,X0)
| c_in(hAPP(X15,X13),c_Inductive_Ocomplete__lattice__class_Ogfp(X6,tc_fun(X7,tc_bool)),X7)
| ~ c_lessequals(c_Set_Oimage(X15,X16,X0,X7),hAPP(X6,c_Set_Oimage(X15,X16,X0,X7)),tc_fun(X7,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct__image_0) ).
fof(f7459,plain,
( spl0_400
| ~ spl0_66
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f7184,f7098,f800,f7457]) ).
fof(f7457,plain,
( spl0_400
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X0,v_U,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f800,plain,
( spl0_66
<=> ! [X13,X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X13,X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f7098,plain,
( spl0_388
<=> ! [X2,X0,X1] : c_Set_Oinsert(X0,v_U,X1) = c_Set_Oinsert(v_pn,c_Set_Oinsert(X0,v_U,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f7184,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X0,v_U,X1)
| ~ spl0_66
| ~ spl0_388 ),
inference(superposition,[],[f801,f7099]) ).
fof(f7099,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X0,v_U,X1) = c_Set_Oinsert(v_pn,c_Set_Oinsert(X0,v_U,X1),X2)
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f7098]) ).
fof(f801,plain,
( ! [X0,X8,X13] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X13,X8,X0)
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f7455,plain,
spl0_399,
inference(avatar_split_clause,[],[f343,f7453]) ).
fof(f7453,plain,
( spl0_399
<=> ! [X13,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,c_Set_Oinsert(X13,X8,X0),X0,X7)
| ~ c_in(hAPP(X6,X13),c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f343,axiom,
! [X0,X8,X6,X7,X13] :
( ~ c_Fun_Oinj__on(X6,c_Set_Oinsert(X13,X8,X0),X0,X7)
| ~ c_in(hAPP(X6,X13),c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X7),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
fof(f7451,plain,
spl0_398,
inference(avatar_split_clause,[],[f310,f7449]) ).
fof(f7449,plain,
( spl0_398
<=> ! [X3,X9,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_in(X3,c_Set_Oimage(X6,X8,X0,X7),X7)
| c_in(hAPP(c_Fun_Othe__inv__into(X8,X6,X0,X7),X3),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f310,axiom,
! [X3,X0,X8,X6,X9,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_in(X3,c_Set_Oimage(X6,X8,X0,X7),X7)
| c_in(hAPP(c_Fun_Othe__inv__into(X8,X6,X0,X7),X3),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__into_0) ).
fof(f7447,plain,
spl0_397,
inference(avatar_split_clause,[],[f54,f7445]) ).
fof(f7445,plain,
( spl0_397
<=> ! [X9,X0,X6,X8,X7] : c_Set_Ovimage(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X7,tc_bool)),X8),X9),X0,X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Ovimage(X6,X8,X0,X7)),c_Set_Ovimage(X6,X9,X0,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f54,axiom,
! [X0,X8,X6,X9,X7] : c_Set_Ovimage(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X7,tc_bool)),X8),X9),X0,X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Ovimage(X6,X8,X0,X7)),c_Set_Ovimage(X6,X9,X0,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
fof(f7140,plain,
spl0_396,
inference(avatar_split_clause,[],[f349,f7138]) ).
fof(f7138,plain,
( spl0_396
<=> ! [X24,X0,X12,X9,X8] :
( ~ c_lessequals(X8,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X24,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X12,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f349,axiom,
! [X0,X8,X9,X24,X12] :
( ~ c_lessequals(X8,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X24,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X12,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
fof(f7136,plain,
spl0_395,
inference(avatar_split_clause,[],[f333,f7134]) ).
fof(f7134,plain,
( spl0_395
<=> ! [X6,X0,X9,X8,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X6,X8,X7,X0),c_Set_Oimage(X6,X9,X7,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X7,tc_bool)),X7,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f333,axiom,
! [X0,X8,X6,X9,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X6,X8,X7,X0),c_Set_Oimage(X6,X9,X7,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X7,tc_bool)),X7,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
fof(f7132,plain,
spl0_394,
inference(avatar_split_clause,[],[f297,f7130]) ).
fof(f7130,plain,
( spl0_394
<=> ! [X6,X0,X9,X8,X7] :
( c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| ~ c_lessequals(c_Set_Oimage(X6,X8,X0,X7),c_Set_Oimage(X6,X9,X0,X7),tc_fun(X7,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f297,axiom,
! [X0,X8,X6,X9,X7] :
( c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| ~ c_lessequals(c_Set_Oimage(X6,X8,X0,X7),c_Set_Oimage(X6,X9,X0,X7),tc_fun(X7,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
fof(f7128,plain,
spl0_393,
inference(avatar_split_clause,[],[f291,f7126]) ).
fof(f7126,plain,
( spl0_393
<=> ! [X15,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7),X8,X0)
| c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f291,axiom,
! [X0,X8,X6,X7,X15] :
( ~ c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7),X8,X0)
| c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_1) ).
fof(f7124,plain,
spl0_392,
inference(avatar_split_clause,[],[f290,f7122]) ).
fof(f7122,plain,
( spl0_392
<=> ! [X15,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f290,axiom,
! [X0,X8,X6,X7,X15] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(X8,X6,X15,X0,X7),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_0) ).
fof(f7120,plain,
spl0_391,
inference(avatar_split_clause,[],[f289,f7118]) ).
fof(f7118,plain,
( spl0_391
<=> ! [X15,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7),X8,X0)
| c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f289,axiom,
! [X0,X8,X6,X7,X15] :
( ~ c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7),X8,X0)
| c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_3) ).
fof(f7116,plain,
spl0_390,
inference(avatar_split_clause,[],[f288,f7114]) ).
fof(f7114,plain,
( spl0_390
<=> ! [X15,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f288,axiom,
! [X0,X8,X6,X7,X15] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Fun_Oinj__on(X15,X8,X0,X7)
| ~ c_Fun_Oinj__on(X15,c_Set_Oimage(X6,X8,X0,X0),X0,X7)
| c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(X8,X6,X15,X0,X7),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_2) ).
fof(f7112,plain,
spl0_389,
inference(avatar_split_clause,[],[f140,f7110]) ).
fof(f7110,plain,
( spl0_389
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X0,X7),tc_fun(X7,tc_bool))
| c_lessequals(c_Set_Ovimage(X6,X9,X0,X7),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f140,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X0,X7),tc_fun(X7,tc_bool))
| c_lessequals(c_Set_Ovimage(X6,X9,X0,X7),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
fof(f7100,plain,
( spl0_388
| ~ spl0_87
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2333,f2284,f891,f7098]) ).
fof(f891,plain,
( spl0_87
<=> ! [X13,X0,X8] :
( ~ c_in(X13,X8,X0)
| c_Set_Oinsert(X13,X8,X0) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f2284,plain,
( spl0_191
<=> ! [X2,X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2333,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X0,v_U,X1) = c_Set_Oinsert(v_pn,c_Set_Oinsert(X0,v_U,X1),X2)
| ~ spl0_87
| ~ spl0_191 ),
inference(resolution,[],[f2285,f892]) ).
fof(f892,plain,
( ! [X0,X8,X13] :
( ~ c_in(X13,X8,X0)
| c_Set_Oinsert(X13,X8,X0) = X8 )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f891]) ).
fof(f2285,plain,
( ! [X2,X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X2)
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f2284]) ).
fof(f6750,plain,
spl0_387,
inference(avatar_split_clause,[],[f423,f6748]) ).
fof(f6748,plain,
( spl0_387
<=> ! [X17,X13,X0,X14,X19] :
( X13 = X17
| X14 = X17
| c_Set_Oinsert(X13,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X17,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f423,axiom,
! [X0,X19,X14,X17,X13] :
( X13 = X17
| X14 = X17
| c_Set_Oinsert(X13,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X17,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
fof(f6746,plain,
spl0_386,
inference(avatar_split_clause,[],[f421,f6744]) ).
fof(f6744,plain,
( spl0_386
<=> ! [X17,X0,X14,X13,X19] :
( X14 = X19
| X14 = X17
| c_Set_Oinsert(X13,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X17,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f421,axiom,
! [X0,X19,X14,X17,X13] :
( X14 = X19
| X14 = X17
| c_Set_Oinsert(X13,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X17,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
fof(f6742,plain,
spl0_385,
inference(avatar_split_clause,[],[f391,f6740]) ).
fof(f6740,plain,
( spl0_385
<=> ! [X0,X8,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X8
| ~ c_lessequals(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f391,axiom,
! [X3,X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X8
| ~ c_lessequals(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f6738,plain,
spl0_384,
inference(avatar_split_clause,[],[f380,f6736]) ).
fof(f6736,plain,
( spl0_384
<=> ! [X11,X0,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| c_in(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X8,X25,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f380,axiom,
! [X0,X11,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| c_in(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X8,X25,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_1) ).
fof(f6734,plain,
spl0_383,
inference(avatar_split_clause,[],[f339,f6732]) ).
fof(f6732,plain,
( spl0_383
<=> ! [X13,X0,X9,X8] : c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f339,axiom,
! [X0,X8,X9,X13] : c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
fof(f6730,plain,
spl0_382,
inference(avatar_split_clause,[],[f338,f6728]) ).
fof(f6728,plain,
( spl0_382
<=> ! [X13,X0,X9,X8] : c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f338,axiom,
! [X0,X8,X9,X13] : c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
fof(f6726,plain,
spl0_381,
inference(avatar_split_clause,[],[f276,f6724]) ).
fof(f6724,plain,
( spl0_381
<=> ! [X11,X0,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X8,X25,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f276,axiom,
! [X0,X11,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X8,X25,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_3) ).
fof(f6722,plain,
spl0_380,
inference(avatar_split_clause,[],[f148,f6720]) ).
fof(f6720,plain,
( spl0_380
<=> ! [X13,X0,X9,X8] :
( ~ c_in(X13,X8,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X13,X9,X0)) = c_Set_Oinsert(X13,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f148,axiom,
! [X0,X8,X9,X13] :
( ~ c_in(X13,X8,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X13,X9,X0)) = c_Set_Oinsert(X13,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
fof(f6718,plain,
spl0_379,
inference(avatar_split_clause,[],[f147,f6716]) ).
fof(f6716,plain,
( spl0_379
<=> ! [X13,X0,X12,X9] :
( ~ c_in(X13,X12,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X13,X9,X0)),X12) = c_Set_Oinsert(X13,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f147,axiom,
! [X0,X9,X12,X13] :
( ~ c_in(X13,X12,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X13,X9,X0)),X12) = c_Set_Oinsert(X13,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
fof(f6714,plain,
spl0_378,
inference(avatar_split_clause,[],[f124,f6712]) ).
fof(f6712,plain,
( spl0_378
<=> ! [X0,X12,X9,X8] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X12,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_HOL_Ominus__class_Ominus(X9,X12,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f6710,plain,
( spl0_377
| ~ spl0_53
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f6499,f6421,f742,f6708]) ).
fof(f6708,plain,
( spl0_377
<=> ! [X2,X0,X1] : c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(X0,v_G,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f742,plain,
( spl0_53
<=> ! [X0,X3,X26] :
( ~ hBOOL(hAPP(X26,X3))
| c_in(X3,X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f6421,plain,
( spl0_366
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,v_G,X1),hAPP(v_mgt__call,v_pn))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f6499,plain,
( ! [X2,X0,X1] : c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(X0,v_G,X1),X2)
| ~ spl0_53
| ~ spl0_366 ),
inference(resolution,[],[f6422,f743]) ).
fof(f743,plain,
( ! [X3,X0,X26] :
( ~ hBOOL(hAPP(X26,X3))
| c_in(X3,X26,X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f6422,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,v_G,X1),hAPP(v_mgt__call,v_pn)))
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f6421]) ).
fof(f6706,plain,
spl0_376,
inference(avatar_split_clause,[],[f46,f6704]) ).
fof(f6704,plain,
( spl0_376
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X2),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),c_Orderings_Oord__class_Omax(X1,X2,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f46,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X2),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),c_Orderings_Oord__class_Omax(X1,X2,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
fof(f6498,plain,
spl0_375,
inference(avatar_split_clause,[],[f316,f6496]) ).
fof(f6496,plain,
( spl0_375
<=> ! [X0,X8,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X3,X8,X0),X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),c_Finite__Set_Olinorder__class_OMin(X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f316,axiom,
! [X3,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X3,X8,X0),X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),c_Finite__Set_Olinorder__class_OMin(X8,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__insert_0) ).
fof(f6494,plain,
spl0_374,
inference(avatar_split_clause,[],[f307,f6492]) ).
fof(f6492,plain,
( spl0_374
<=> ! [X13,X0,X6,X8] :
( c_in(X13,X8,X0)
| c_Finite__Set_Osetsum(X6,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,tc_nat) = c_Finite__Set_Osetsum(X6,X8,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f307,axiom,
! [X0,X8,X6,X13] :
( c_in(X13,X8,X0)
| c_Finite__Set_Osetsum(X6,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,tc_nat) = c_Finite__Set_Osetsum(X6,X8,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
fof(f6490,plain,
spl0_373,
inference(avatar_split_clause,[],[f295,f6488]) ).
fof(f6488,plain,
( spl0_373
<=> ! [X26,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_lessequals(X26,X8,tc_fun(X0,tc_bool))
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X8,X6,X0,X7),c_Set_Oimage(X6,X26,X0,X7),X7,X0) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f295,axiom,
! [X0,X8,X6,X26,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_lessequals(X26,X8,tc_fun(X0,tc_bool))
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X8,X6,X0,X7),c_Set_Oimage(X6,X26,X0,X7),X7,X0) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).
fof(f6486,plain,
spl0_372,
inference(avatar_split_clause,[],[f277,f6484]) ).
fof(f6484,plain,
( spl0_372
<=> ! [X11,X0,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X8,X25,X0),X0)
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f277,axiom,
! [X0,X11,X8,X25] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| hBOOL(hAPP(X25,X11))
| ~ c_lessequals(X11,X8,tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X8,X25,X0),X0)
| ~ hBOOL(hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_0) ).
fof(f6482,plain,
spl0_371,
inference(avatar_split_clause,[],[f255,f6480]) ).
fof(f6480,plain,
( spl0_371
<=> ! [X13,X0,X9,X8] : c_Set_Oinsert(X13,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X13,X8,X0)),c_Set_Oinsert(X13,X9,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f255,axiom,
! [X0,X8,X9,X13] : c_Set_Oinsert(X13,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X13,X8,X0)),c_Set_Oinsert(X13,X9,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
fof(f6478,plain,
spl0_370,
inference(avatar_split_clause,[],[f77,f6476]) ).
fof(f6476,plain,
( spl0_370
<=> ! [X17,X18,X13,X0,X14,X19,X7] :
( X13 = X17
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X18,X13,X14,X0,X7),X17,X19,X0,X7) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X18,X17,X19,X0,X7),X13,X14,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f77,axiom,
! [X0,X18,X19,X7,X14,X17,X13] :
( X13 = X17
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X18,X13,X14,X0,X7),X17,X19,X0,X7) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X18,X17,X19,X0,X7),X13,X14,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
fof(f6474,plain,
spl0_369,
inference(avatar_split_clause,[],[f75,f6472]) ).
fof(f6472,plain,
( spl0_369
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X2),X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),c_Orderings_Oord__class_Omax(X1,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f75,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X2),X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),c_Orderings_Oord__class_Omax(X1,X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
fof(f6470,plain,
spl0_368,
inference(avatar_split_clause,[],[f44,f6468]) ).
fof(f6468,plain,
( spl0_368
<=> ! [X0,X6,X16,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X6,X0,X7),c_Set_Oimage(X6,X16,X0,X7),X7,X0) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f44,axiom,
! [X0,X6,X7,X16] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X6,X0,X7),c_Set_Oimage(X6,X16,X0,X7),X7,X0) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).
fof(f6466,plain,
spl0_367,
inference(avatar_split_clause,[],[f1,f6464]) ).
fof(f6464,plain,
( spl0_367
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Oord__class_Omax(X1,X2,X0)),X3) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Oord__class_Omax(X1,X2,X0)),X3) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X3),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
fof(f6423,plain,
( spl0_366
| ~ spl0_54
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f6014,f5961,f746,f6421]) ).
fof(f746,plain,
( spl0_54
<=> ! [X0,X3,X26] :
( ~ c_in(X3,X26,X0)
| hBOOL(hAPP(X26,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f5961,plain,
( spl0_361
<=> ! [X0,X1] : c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(X0,v_G,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f6014,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,v_G,X1),hAPP(v_mgt__call,v_pn)))
| ~ spl0_54
| ~ spl0_361 ),
inference(resolution,[],[f5962,f747]) ).
fof(f747,plain,
( ! [X3,X0,X26] :
( ~ c_in(X3,X26,X0)
| hBOOL(hAPP(X26,X3)) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f746]) ).
fof(f5962,plain,
( ! [X0,X1] : c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(X0,v_G,X1),X1)
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f5961]) ).
fof(f5979,plain,
spl0_365,
inference(avatar_split_clause,[],[f382,f5977]) ).
fof(f5977,plain,
( spl0_365
<=> ! [X29,X0,X30] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X29,X0)
| ~ c_lessequals(X30,X29,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X30
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X30,X0),c_Finite__Set_Olinorder__class_OMax(X29,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f382,axiom,
! [X0,X29,X30] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X29,X0)
| ~ c_lessequals(X30,X29,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X30
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X30,X0),c_Finite__Set_Olinorder__class_OMax(X29,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).
fof(f5975,plain,
spl0_364,
inference(avatar_split_clause,[],[f381,f5973]) ).
fof(f5973,plain,
( spl0_364
<=> ! [X29,X0,X30] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X29,X0)
| ~ c_lessequals(X30,X29,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X30
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X29,X0),c_Finite__Set_Olinorder__class_OMin(X30,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f381,axiom,
! [X0,X29,X30] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X29,X0)
| ~ c_lessequals(X30,X29,tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X30
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X29,X0),c_Finite__Set_Olinorder__class_OMin(X30,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
fof(f5971,plain,
spl0_363,
inference(avatar_split_clause,[],[f378,f5969]) ).
fof(f5969,plain,
( spl0_363
<=> ! [X6,X0,X9,X8,X7] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool))
| c_Set_Oimage(X6,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X8,X9,X6,X7,X0),X7,X0) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f378,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool))
| c_Set_Oimage(X6,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X8,X9,X6,X7,X0),X7,X0) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_2) ).
fof(f5967,plain,
spl0_362,
inference(avatar_split_clause,[],[f376,f5965]) ).
fof(f5965,plain,
( spl0_362
<=> ! [X6,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Set_Oimage(X6,X8,X0,X0) = X8
| ~ c_lessequals(c_Set_Oimage(X6,X8,X0,X0),X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f376,axiom,
! [X0,X8,X6] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_Fun_Oinj__on(X6,X8,X0,X0)
| c_Set_Oimage(X6,X8,X0,X0) = X8
| ~ c_lessequals(c_Set_Oimage(X6,X8,X0,X0),X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
fof(f5963,plain,
( spl0_361
| ~ spl0_65
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f5917,f5759,f796,f5961]) ).
fof(f796,plain,
( spl0_65
<=> ! [X13,X9,X0] : c_lessequals(X9,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f5759,plain,
( spl0_347
<=> ! [X0,X1] :
( ~ c_lessequals(v_G,X1,tc_fun(X0,tc_bool))
| c_in(hAPP(v_mgt__call,v_pn),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f5917,plain,
( ! [X0,X1] : c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(X0,v_G,X1),X1)
| ~ spl0_65
| ~ spl0_347 ),
inference(resolution,[],[f5760,f797]) ).
fof(f797,plain,
( ! [X0,X9,X13] : c_lessequals(X9,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool))
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f5760,plain,
( ! [X0,X1] :
( ~ c_lessequals(v_G,X1,tc_fun(X0,tc_bool))
| c_in(hAPP(v_mgt__call,v_pn),X1,X0) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f5759]) ).
fof(f5959,plain,
spl0_360,
inference(avatar_split_clause,[],[f351,f5957]) ).
fof(f5957,plain,
( spl0_360
<=> ! [X0,X12,X9,X8] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X12,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f351,axiom,
! [X0,X8,X9,X12] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X12,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
fof(f5955,plain,
spl0_359,
inference(avatar_split_clause,[],[f318,f5953]) ).
fof(f5953,plain,
( spl0_359
<=> ! [X0,X8,X3] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_in(X3,X8,X0)
| c_Finite__Set_Ocard(X8,X0) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f318,axiom,
! [X3,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_in(X3,X8,X0)
| c_Finite__Set_Ocard(X8,X0) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).
fof(f5951,plain,
spl0_358,
inference(avatar_split_clause,[],[f266,f5949]) ).
fof(f5949,plain,
( spl0_358
<=> ! [X0,X12,X9,X8] :
( ~ c_lessequals(X12,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X12,X9,tc_fun(X0,tc_bool))
| c_lessequals(X12,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f266,axiom,
! [X0,X8,X9,X12] :
( ~ c_lessequals(X12,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X12,X9,tc_fun(X0,tc_bool))
| c_lessequals(X12,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
fof(f5947,plain,
spl0_357,
inference(avatar_split_clause,[],[f142,f5945]) ).
fof(f5945,plain,
( spl0_357
<=> ! [X1,X6,X2,X0,X3,X8,X7] :
( c_in(X3,X8,X0)
| ~ c_Finite__Set_Ofold__graph(X6,X2,X8,X1,X0,X7)
| c_Finite__Set_Ofold__graph(X6,X2,c_Set_Oinsert(X3,X8,X0),hAPP(hAPP(X6,X3),X1),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f142,axiom,
! [X2,X3,X0,X1,X8,X6,X7] :
( c_in(X3,X8,X0)
| ~ c_Finite__Set_Ofold__graph(X6,X2,X8,X1,X0,X7)
| c_Finite__Set_Ofold__graph(X6,X2,c_Set_Oinsert(X3,X8,X0),hAPP(hAPP(X6,X3),X1),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
fof(f5943,plain,
spl0_356,
inference(avatar_split_clause,[],[f130,f5941]) ).
fof(f5941,plain,
( spl0_356
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Oord__class_Omax(X3,X1,X0)),c_Orderings_Oord__class_Omax(X3,X2,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f130,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Oord__class_Omax(X3,X1,X0)),c_Orderings_Oord__class_Omax(X3,X2,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
fof(f5939,plain,
spl0_355,
inference(avatar_split_clause,[],[f96,f5937]) ).
fof(f5937,plain,
( spl0_355
<=> ! [X0,X6,X8,X7] : c_Set_Oimage(X6,c_Set_Ovimage(X6,X8,X7,X0),X7,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Set_Oimage(X6,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool)),X7,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f96,axiom,
! [X0,X8,X6,X7] : c_Set_Oimage(X6,c_Set_Ovimage(X6,X8,X7,X0),X7,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Set_Oimage(X6,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool)),X7,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
fof(f5935,plain,
spl0_354,
inference(avatar_split_clause,[],[f83,f5933]) ).
fof(f5933,plain,
( spl0_354
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f83,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f5931,plain,
spl0_353,
inference(avatar_split_clause,[],[f82,f5929]) ).
fof(f5929,plain,
( spl0_353
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f82,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f5927,plain,
spl0_352,
inference(avatar_split_clause,[],[f81,f5925]) ).
fof(f5925,plain,
( spl0_352
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f81,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f5923,plain,
spl0_351,
inference(avatar_split_clause,[],[f80,f5921]) ).
fof(f5921,plain,
( spl0_351
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f80,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f5901,plain,
spl0_350,
inference(avatar_split_clause,[],[f18,f5899]) ).
fof(f5899,plain,
( spl0_350
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
fof(f5897,plain,
spl0_349,
inference(avatar_split_clause,[],[f17,f5895]) ).
fof(f5895,plain,
( spl0_349
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1)),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f17,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1)),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
fof(f5893,plain,
spl0_348,
inference(avatar_split_clause,[],[f6,f5891]) ).
fof(f5891,plain,
( spl0_348
<=> ! [X9,X0,X6,X8,X7] : c_Set_Ovimage(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X7,tc_bool)),X0,X7) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X6,X8,X0,X7),c_Set_Ovimage(X6,X9,X0,X7),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f6,axiom,
! [X0,X8,X6,X9,X7] : c_Set_Ovimage(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X7,tc_bool)),X0,X7) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X6,X8,X0,X7),c_Set_Ovimage(X6,X9,X0,X7),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
fof(f5761,plain,
( spl0_347
| ~ spl0_151
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f3552,f3411,f1332,f5759]) ).
fof(f1332,plain,
( spl0_151
<=> ! [X3,X0,X9,X8] :
( c_in(X3,X9,X0)
| ~ c_lessequals(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f3411,plain,
( spl0_247
<=> ! [X0] : v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f3552,plain,
( ! [X0,X1] :
( ~ c_lessequals(v_G,X1,tc_fun(X0,tc_bool))
| c_in(hAPP(v_mgt__call,v_pn),X1,X0) )
| ~ spl0_151
| ~ spl0_247 ),
inference(superposition,[],[f1333,f3412]) ).
fof(f3412,plain,
( ! [X0] : v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,X0)
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f3411]) ).
fof(f1333,plain,
( ! [X3,X0,X8,X9] :
( ~ c_lessequals(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool))
| c_in(X3,X9,X0) )
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1332]) ).
fof(f5701,plain,
spl0_346,
inference(avatar_split_clause,[],[f375,f5699]) ).
fof(f5699,plain,
( spl0_346
<=> ! [X6,X0,X9,X8,X7] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool))
| c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X8,X9,X6,X7,X0),X8,tc_fun(X7,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f375,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool))
| c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X8,X9,X6,X7,X0),X8,tc_fun(X7,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_0) ).
fof(f5697,plain,
spl0_345,
inference(avatar_split_clause,[],[f315,f5695]) ).
fof(f5695,plain,
( spl0_345
<=> ! [X0,X8,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X3,X8,X0),X0) = c_Orderings_Oord__class_Omax(X3,c_Finite__Set_Olinorder__class_OMax(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f315,axiom,
! [X3,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X3,X8,X0),X0) = c_Orderings_Oord__class_Omax(X3,c_Finite__Set_Olinorder__class_OMax(X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__insert_0) ).
fof(f5693,plain,
spl0_344,
inference(avatar_split_clause,[],[f292,f5691]) ).
fof(f5691,plain,
( spl0_344
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),c_SetInterval_Oord__class_OlessThan(X5,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f292,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),c_SetInterval_Oord__class_OlessThan(X5,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).
fof(f5689,plain,
spl0_343,
inference(avatar_split_clause,[],[f286,f5687]) ).
fof(f5687,plain,
( spl0_343
<=> ! [X1,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_in(X1,c_Set_Oimage(X6,X8,X0,X7),X7)
| hAPP(X6,hAPP(c_Fun_Othe__inv__into(X8,X6,X0,X7),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f286,axiom,
! [X0,X1,X8,X6,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_in(X1,c_Set_Oimage(X6,X8,X0,X7),X7)
| hAPP(X6,hAPP(c_Fun_Othe__inv__into(X8,X6,X0,X7),X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__the__inv__into__f_0) ).
fof(f5685,plain,
spl0_342,
inference(avatar_split_clause,[],[f144,f5683]) ).
fof(f5683,plain,
( spl0_342
<=> ! [X13,X0,X9,X8] :
( c_in(X13,X8,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X13,X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f144,axiom,
! [X0,X8,X9,X13] :
( c_in(X13,X8,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X13,X9,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
fof(f5681,plain,
spl0_341,
inference(avatar_split_clause,[],[f143,f5679]) ).
fof(f5679,plain,
( spl0_341
<=> ! [X13,X0,X12,X9] :
( c_in(X13,X12,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X13,X9,X0)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f143,axiom,
! [X0,X9,X12,X13] :
( c_in(X13,X12,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X13,X9,X0)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
fof(f5677,plain,
spl0_340,
inference(avatar_split_clause,[],[f135,f5675]) ).
fof(f5675,plain,
( spl0_340
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Oord__class_Omax(X3,X1,X0)),c_Orderings_Oord__class_Omax(X3,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f135,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Oord__class_Omax(X3,X1,X0)),c_Orderings_Oord__class_Omax(X3,X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
fof(f5673,plain,
spl0_339,
inference(avatar_split_clause,[],[f134,f5671]) ).
fof(f5671,plain,
( spl0_339
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X3,X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Oord__class_Omax(X1,X3,X0)),c_Orderings_Oord__class_Omax(X2,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f134,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X3,X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Oord__class_Omax(X1,X3,X0)),c_Orderings_Oord__class_Omax(X2,X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
fof(f5667,plain,
spl0_338,
inference(avatar_split_clause,[],[f119,f5665]) ).
fof(f5665,plain,
( spl0_338
<=> ! [X9,X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f119,axiom,
! [X0,X8,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f5555,plain,
spl0_337,
inference(avatar_split_clause,[],[f366,f5553]) ).
fof(f5553,plain,
( spl0_337
<=> ! [X6,X0,X8,X3,X1,X7] :
( X1 = X3
| ~ c_in(X1,X8,X0)
| ~ c_in(X3,X8,X0)
| ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| hAPP(X6,X3) != hAPP(X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f366,axiom,
! [X3,X0,X1,X8,X6,X7] :
( X1 = X3
| ~ c_in(X1,X8,X0)
| ~ c_in(X3,X8,X0)
| ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| hAPP(X6,X3) != hAPP(X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
fof(f5551,plain,
spl0_336,
inference(avatar_split_clause,[],[f345,f5549]) ).
fof(f5549,plain,
( spl0_336
<=> ! [X3,X0,X9,X8] :
( c_in(X3,X9,X0)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f345,axiom,
! [X3,X0,X8,X9] :
( c_in(X3,X9,X0)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
fof(f5547,plain,
spl0_335,
inference(avatar_split_clause,[],[f287,f5545]) ).
fof(f5545,plain,
( spl0_335
<=> ! [X1,X3,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_in(X1,c_Set_Oimage(X6,X8,X0,X7),X7)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X6,X3,X1,X0,X7),X8,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f287,axiom,
! [X3,X0,X1,X8,X6,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_in(X1,c_Set_Oimage(X6,X8,X0,X7),X7)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X6,X3,X1,X0,X7),X8,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
fof(f5543,plain,
spl0_334,
inference(avatar_split_clause,[],[f174,f5541]) ).
fof(f5541,plain,
( spl0_334
<=> ! [X3,X0,X9,X8] :
( c_in(X3,X9,X0)
| c_in(X3,X8,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f174,axiom,
! [X3,X0,X8,X9] :
( c_in(X3,X9,X0)
| c_in(X3,X8,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
fof(f5539,plain,
( spl0_333
| ~ spl0_165
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4673,f4318,f1689,f5537]) ).
fof(f5537,plain,
( spl0_333
<=> ! [X0,X1] : c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,v_G,X1,t_a),X1,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f1689,plain,
( spl0_165
<=> ! [X0,X6,X8,X7] : c_lessequals(c_Set_Oimage(X6,c_Set_Ovimage(X6,X8,X7,X0),X7,X0),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f4318,plain,
( spl0_295
<=> ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Finite__Set_Ofinite(X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f4673,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,v_G,X1,t_a),X1,t_a),t_a)
| ~ spl0_165
| ~ spl0_295 ),
inference(resolution,[],[f4319,f1690]) ).
fof(f1690,plain,
( ! [X0,X8,X6,X7] : c_lessequals(c_Set_Oimage(X6,c_Set_Ovimage(X6,X8,X7,X0),X7,X0),X8,tc_fun(X0,tc_bool))
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1689]) ).
fof(f4319,plain,
( ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Finite__Set_Ofinite(X0,t_a) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f4318]) ).
fof(f5535,plain,
spl0_332,
inference(avatar_split_clause,[],[f173,f5533]) ).
fof(f5533,plain,
( spl0_332
<=> ! [X3,X0,X9,X8] :
( c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f173,axiom,
! [X3,X0,X8,X9] :
( c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
fof(f5472,plain,
spl0_331,
inference(avatar_split_clause,[],[f325,f5470]) ).
fof(f5470,plain,
( spl0_331
<=> ! [X17,X0,X8,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X8
| c_Set_Oimage(c_COMBK(X17,X0,X7),X8,X7,X0) = c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f325,axiom,
! [X0,X8,X7,X17] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X8
| c_Set_Oimage(c_COMBK(X17,X0,X7),X8,X7,X0) = c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
fof(f5468,plain,
spl0_330,
inference(avatar_split_clause,[],[f284,f5466]) ).
fof(f5466,plain,
( spl0_330
<=> ! [X13,X0,X6,X8,X7] :
( c_in(X13,X8,X0)
| ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| ~ c_in(hAPP(X6,X13),c_Set_Oimage(X6,X8,X0,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f284,axiom,
! [X0,X8,X6,X7,X13] :
( c_in(X13,X8,X0)
| ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| ~ c_in(hAPP(X6,X13),c_Set_Oimage(X6,X8,X0,X7),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
fof(f5464,plain,
spl0_329,
inference(avatar_split_clause,[],[f167,f5462]) ).
fof(f5462,plain,
( spl0_329
<=> ! [X6,X0,X9,X8,X7] :
( X8 = X9
| ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Oimage(X6,X8,X0,X7) != c_Set_Oimage(X6,X9,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f167,axiom,
! [X0,X8,X6,X9,X7] :
( X8 = X9
| ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Oimage(X6,X8,X0,X7) != c_Set_Oimage(X6,X9,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
fof(f5454,plain,
spl0_328,
inference(avatar_split_clause,[],[f122,f5452]) ).
fof(f5452,plain,
( spl0_328
<=> ! [X0,X6,X3,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X6,X0,X7),hAPP(X6,X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f122,axiom,
! [X3,X0,X6,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X6,X0,X7),hAPP(X6,X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__f_0) ).
fof(f5450,plain,
spl0_327,
inference(avatar_split_clause,[],[f42,f5448]) ).
fof(f5448,plain,
( spl0_327
<=> ! [X0,X8] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X8
| c_Finite__Set_Ocard(X8,X0) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f42,axiom,
! [X0,X8] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X8
| c_Finite__Set_Ocard(X8,X0) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
fof(f5446,plain,
spl0_326,
inference(avatar_split_clause,[],[f41,f5444]) ).
fof(f5444,plain,
( spl0_326
<=> ! [X0,X6,X3,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X6,X0,X7),hAPP(X6,X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f41,axiom,
! [X3,X0,X6,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X6,X0,X7),hAPP(X6,X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__f__f_0) ).
fof(f5253,plain,
spl0_325,
inference(avatar_split_clause,[],[f377,f5251]) ).
fof(f5251,plain,
( spl0_325
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X8,X9,X6,X7,X0),X7)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f377,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X8,X9,X6,X7,X0),X7)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_1) ).
fof(f5249,plain,
spl0_324,
inference(avatar_split_clause,[],[f327,f5247]) ).
fof(f5247,plain,
( spl0_324
<=> ! [X0,X8,X3] :
( c_in(X3,X8,X0)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X3,X8,X0),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f327,axiom,
! [X3,X0,X8] :
( c_in(X3,X8,X0)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X3,X8,X0),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
fof(f5245,plain,
spl0_323,
inference(avatar_split_clause,[],[f314,f5243]) ).
fof(f5243,plain,
( spl0_323
<=> ! [X0,X8,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Olinorder__class_OMin(X8,X0) = X3
| ~ c_lessequals(X3,c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X8,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f314,axiom,
! [X3,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Olinorder__class_OMin(X8,X0) = X3
| ~ c_lessequals(X3,c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X8,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_1) ).
fof(f5241,plain,
spl0_322,
inference(avatar_split_clause,[],[f313,f5239]) ).
fof(f5239,plain,
( spl0_322
<=> ! [X0,X8,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Olinorder__class_OMax(X8,X0) = X3
| ~ c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X8,X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f313,axiom,
! [X3,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Olinorder__class_OMax(X8,X0) = X3
| ~ c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X8,X3,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_1) ).
fof(f5237,plain,
spl0_321,
inference(avatar_split_clause,[],[f302,f5235]) ).
fof(f5235,plain,
( spl0_321
<=> ! [X0,X8,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Olinorder__class_OMin(X8,X0) = X3
| c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X8,X3,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f302,axiom,
! [X3,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Olinorder__class_OMin(X8,X0) = X3
| c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X8,X3,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_0) ).
fof(f5233,plain,
spl0_320,
inference(avatar_split_clause,[],[f301,f5231]) ).
fof(f5231,plain,
( spl0_320
<=> ! [X0,X8,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Olinorder__class_OMax(X8,X0) = X3
| c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X8,X3,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f301,axiom,
! [X3,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Olinorder__class_OMax(X8,X0) = X3
| c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X8,X3,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_0) ).
fof(f5229,plain,
spl0_319,
inference(avatar_split_clause,[],[f282,f5227]) ).
fof(f5227,plain,
( spl0_319
<=> ! [X6,X0,X9,X8,X7] :
( c_lessequals(c_Set_Oimage(X6,X8,X0,X7),X9,tc_fun(X7,tc_bool))
| ~ c_in(hAPP(X6,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X8,X9,X6,X0,X7)),X9,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f282,axiom,
! [X0,X8,X6,X9,X7] :
( c_lessequals(c_Set_Oimage(X6,X8,X0,X7),X9,tc_fun(X7,tc_bool))
| ~ c_in(hAPP(X6,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X8,X9,X6,X0,X7)),X9,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_1) ).
fof(f5225,plain,
( spl0_318
| ~ spl0_143
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4662,f4318,f1300,f5223]) ).
fof(f5223,plain,
( spl0_318
<=> ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),X0),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f1300,plain,
( spl0_143
<=> ! [X9,X0,X8] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f4662,plain,
( ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),X0),t_a)
| ~ spl0_143
| ~ spl0_295 ),
inference(resolution,[],[f4319,f1301]) ).
fof(f1301,plain,
( ! [X0,X8,X9] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X8,tc_fun(X0,tc_bool))
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1300]) ).
fof(f5221,plain,
spl0_317,
inference(avatar_split_clause,[],[f279,f5219]) ).
fof(f5219,plain,
( spl0_317
<=> ! [X6,X0,X9,X8,X7] :
( c_lessequals(c_Set_Oimage(X6,X8,X7,X0),X9,tc_fun(X0,tc_bool))
| ~ c_in(hAPP(X6,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X8,X9,X6,X7,X0)),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f279,axiom,
! [X0,X8,X6,X9,X7] :
( c_lessequals(c_Set_Oimage(X6,X8,X7,X0),X9,tc_fun(X0,tc_bool))
| ~ c_in(hAPP(X6,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X8,X9,X6,X7,X0)),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_2) ).
fof(f5217,plain,
spl0_316,
inference(avatar_split_clause,[],[f164,f5215]) ).
fof(f5215,plain,
( spl0_316
<=> ! [X9,X0,X8] :
( c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = X8
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f164,axiom,
! [X0,X8,X9] :
( c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = X8
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
fof(f5213,plain,
spl0_315,
inference(avatar_split_clause,[],[f141,f5211]) ).
fof(f5211,plain,
( spl0_315
<=> ! [X3,X0,X9,X8] :
( ~ c_in(X3,X9,X0)
| ~ c_in(X3,X8,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f141,axiom,
! [X3,X0,X8,X9] :
( ~ c_in(X3,X9,X0)
| ~ c_in(X3,X8,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f5048,plain,
( spl0_314
| ~ spl0_142
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4661,f4318,f1296,f5046]) ).
fof(f5046,plain,
( spl0_314
<=> ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),v_G),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f1296,plain,
( spl0_142
<=> ! [X9,X0,X8] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X9,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f4661,plain,
( ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),v_G),t_a)
| ~ spl0_142
| ~ spl0_295 ),
inference(resolution,[],[f4319,f1297]) ).
fof(f1297,plain,
( ! [X0,X8,X9] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X9,tc_fun(X0,tc_bool))
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1296]) ).
fof(f4894,plain,
spl0_313,
inference(avatar_split_clause,[],[f466,f4892]) ).
fof(f4892,plain,
( spl0_313
<=> ! [X3,X0,X9,X8] :
( X8 = X9
| c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| c_Set_Oinsert(X3,X8,X0) != c_Set_Oinsert(X3,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f466,axiom,
! [X3,X0,X8,X9] :
( X8 = X9
| c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| c_Set_Oinsert(X3,X8,X0) != c_Set_Oinsert(X3,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f4890,plain,
spl0_312,
inference(avatar_split_clause,[],[f461,f4888]) ).
fof(f4888,plain,
( spl0_312
<=> ! [X6,X0,X3,X8,X7] :
( ~ c_in(X3,X8,X0)
| c_Set_Oimage(X6,X8,X0,X7) = c_Set_Oinsert(hAPP(X6,X3),c_Set_Oimage(X6,X8,X0,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f461,axiom,
! [X3,X0,X8,X6,X7] :
( ~ c_in(X3,X8,X0)
| c_Set_Oimage(X6,X8,X0,X7) = c_Set_Oinsert(hAPP(X6,X3),c_Set_Oimage(X6,X8,X0,X7),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
fof(f4886,plain,
spl0_311,
inference(avatar_split_clause,[],[f446,f4884]) ).
fof(f4884,plain,
( spl0_311
<=> ! [X6,X9,X0,X3,X8,X7] :
( ~ c_in(X3,X8,X7)
| c_in(hAPP(X6,X3),X9,X0)
| ~ c_lessequals(c_Set_Oimage(X6,X8,X7,X0),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f446,axiom,
! [X3,X0,X8,X6,X9,X7] :
( ~ c_in(X3,X8,X7)
| c_in(hAPP(X6,X3),X9,X0)
| ~ c_lessequals(c_Set_Oimage(X6,X8,X7,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f4882,plain,
spl0_310,
inference(avatar_split_clause,[],[f389,f4880]) ).
fof(f4880,plain,
( spl0_310
<=> ! [X6,X0,X3,X8,X7] :
( ~ c_lessequals(X3,X8,tc_fun(X7,tc_bool))
| c_lessequals(c_Set_Oimage(X6,X3,X7,X0),c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f389,axiom,
! [X3,X0,X8,X6,X7] :
( ~ c_lessequals(X3,X8,tc_fun(X7,tc_bool))
| c_lessequals(c_Set_Oimage(X6,X3,X7,X0),c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
fof(f4878,plain,
spl0_309,
inference(avatar_split_clause,[],[f386,f4876]) ).
fof(f4876,plain,
( spl0_309
<=> ! [X17,X0,X3,X8,X7] :
( ~ c_in(X3,X8,X0)
| c_Set_Oimage(c_COMBK(X17,X7,X0),X8,X0,X7) = c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f386,axiom,
! [X3,X0,X8,X7,X17] :
( ~ c_in(X3,X8,X0)
| c_Set_Oimage(c_COMBK(X17,X7,X0),X8,X0,X7) = c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
fof(f4874,plain,
spl0_308,
inference(avatar_split_clause,[],[f346,f4872]) ).
fof(f4872,plain,
( spl0_308
<=> ! [X3,X0,X9,X8] :
( ~ c_in(X3,X9,X0)
| c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f346,axiom,
! [X3,X0,X8,X9] :
( ~ c_in(X3,X9,X0)
| c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
fof(f4870,plain,
spl0_307,
inference(avatar_split_clause,[],[f336,f4868]) ).
fof(f4868,plain,
( spl0_307
<=> ! [X13,X0,X8] : c_Set_Oinsert(X13,X8,X0) = c_Set_Oinsert(X13,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f336,axiom,
! [X0,X8,X13] : c_Set_Oinsert(X13,X8,X0) = c_Set_Oinsert(X13,c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
fof(f4866,plain,
spl0_306,
inference(avatar_split_clause,[],[f272,f4864]) ).
fof(f4864,plain,
( spl0_306
<=> ! [X6,X0,X9,X8,X7] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Ovimage(X6,X8,X7,X0),c_Set_Ovimage(X6,X9,X7,X0),tc_fun(X7,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f272,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Ovimage(X6,X8,X7,X0),c_Set_Ovimage(X6,X9,X7,X0),tc_fun(X7,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
fof(f4862,plain,
spl0_305,
inference(avatar_split_clause,[],[f257,f4860]) ).
fof(f4860,plain,
( spl0_305
<=> ! [X0,X6,X15,X7] :
( ~ class_HOL_Oord(X7)
| ~ c_lessequals(X6,X15,tc_fun(X0,X7))
| c_HOL_Oord__class_Oless(X6,X15,tc_fun(X0,X7))
| c_lessequals(X15,X6,tc_fun(X0,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f257,axiom,
! [X0,X6,X7,X15] :
( ~ class_HOL_Oord(X7)
| ~ c_lessequals(X6,X15,tc_fun(X0,X7))
| c_HOL_Oord__class_Oless(X6,X15,tc_fun(X0,X7))
| c_lessequals(X15,X6,tc_fun(X0,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
fof(f4858,plain,
spl0_304,
inference(avatar_split_clause,[],[f168,f4856]) ).
fof(f4856,plain,
( spl0_304
<=> ! [X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Set_Oimage(c_Fun_Othe__inv__into(X8,X6,X0,X7),c_Set_Oimage(X6,X8,X0,X7),X7,X0) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f168,axiom,
! [X0,X8,X6,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Set_Oimage(c_Fun_Othe__inv__into(X8,X6,X0,X7),c_Set_Oimage(X6,X8,X0,X7),X7,X0) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).
fof(f4854,plain,
( spl0_303
| ~ spl0_99
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4676,f4318,f990,f4852]) ).
fof(f4852,plain,
( spl0_303
<=> ! [X0] : c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v_G,X0,tc_fun(t_a,tc_bool)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f990,plain,
( spl0_99
<=> ! [X9,X0,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f4676,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v_G,X0,tc_fun(t_a,tc_bool)),t_a)
| ~ spl0_99
| ~ spl0_295 ),
inference(resolution,[],[f4319,f991]) ).
fof(f991,plain,
( ! [X0,X8,X9] : c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f990]) ).
fof(f4850,plain,
spl0_302,
inference(avatar_split_clause,[],[f159,f4848]) ).
fof(f4848,plain,
( spl0_302
<=> ! [X6,X0,X3,X8,X7] :
( ~ c_in(X3,X8,X0)
| ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| hAPP(c_Fun_Othe__inv__into(X8,X6,X0,X7),hAPP(X6,X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f159,axiom,
! [X3,X0,X8,X6,X7] :
( ~ c_in(X3,X8,X0)
| ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| hAPP(c_Fun_Othe__inv__into(X8,X6,X0,X7),hAPP(X6,X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__f_0) ).
fof(f4846,plain,
spl0_301,
inference(avatar_split_clause,[],[f157,f4844]) ).
fof(f4844,plain,
( spl0_301
<=> ! [X6,X0,X3,X8,X7] :
( ~ c_in(X3,X8,X0)
| ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X0,X7),hAPP(X6,X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f157,axiom,
! [X3,X0,X8,X6,X7] :
( ~ c_in(X3,X8,X0)
| ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X0,X7),hAPP(X6,X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).
fof(f4842,plain,
spl0_300,
inference(avatar_split_clause,[],[f156,f4840]) ).
fof(f4840,plain,
( spl0_300
<=> ! [X1,X6,X0,X3,X8,X7] :
( c_in(X3,X8,X7)
| c_Set_Oimage(X6,X8,X7,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X6,X3,X1,X7,X0),X8,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f156,axiom,
! [X3,X0,X1,X8,X6,X7] :
( c_in(X3,X8,X7)
| c_Set_Oimage(X6,X8,X7,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X6,X3,X1,X7,X0),X8,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
fof(f4838,plain,
spl0_299,
inference(avatar_split_clause,[],[f149,f4836]) ).
fof(f4836,plain,
( spl0_299
<=> ! [X6,X13,X0,X16] :
( ~ c_in(X13,X16,X0)
| ~ c_lessequals(X16,hAPP(X6,X16),tc_fun(X0,tc_bool))
| c_in(X13,c_Inductive_Ocomplete__lattice__class_Ogfp(X6,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f149,axiom,
! [X0,X6,X16,X13] :
( ~ c_in(X13,X16,X0)
| ~ c_lessequals(X16,hAPP(X6,X16),tc_fun(X0,tc_bool))
| c_in(X13,c_Inductive_Ocomplete__lattice__class_Ogfp(X6,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct_0) ).
fof(f4834,plain,
spl0_298,
inference(avatar_split_clause,[],[f118,f4832]) ).
fof(f4832,plain,
( spl0_298
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f118,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f4830,plain,
spl0_297,
inference(avatar_split_clause,[],[f117,f4828]) ).
fof(f4828,plain,
( spl0_297
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f117,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f4826,plain,
spl0_296,
inference(avatar_split_clause,[],[f10,f4824]) ).
fof(f4824,plain,
( spl0_296
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f10,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
fof(f4320,plain,
( ~ spl0_1
| spl0_295
| ~ spl0_3
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f3354,f3114,f522,f4318,f512]) ).
fof(f3114,plain,
( spl0_240
<=> ! [X6,X0,X9,X8,X7] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(X9,X7)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X0,X7),tc_fun(X7,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f3354,plain,
( ! [X0] :
( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
| c_Finite__Set_Ofinite(X0,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) )
| ~ spl0_3
| ~ spl0_240 ),
inference(superposition,[],[f3115,f524]) ).
fof(f3115,plain,
( ! [X0,X8,X6,X9,X7] :
( ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X0,X7),tc_fun(X7,tc_bool))
| c_Finite__Set_Ofinite(X9,X7)
| ~ c_Finite__Set_Ofinite(X8,X0) )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f3114]) ).
fof(f4174,plain,
spl0_294,
inference(avatar_split_clause,[],[f465,f4172]) ).
fof(f4172,plain,
( spl0_294
<=> ! [X3,X0,X9,X8] :
( c_in(X3,X8,X0)
| c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f465,axiom,
! [X3,X0,X8,X9] :
( c_in(X3,X8,X0)
| c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
fof(f4166,plain,
spl0_293,
inference(avatar_split_clause,[],[f413,f4164]) ).
fof(f4164,plain,
( spl0_293
<=> ! [X9,X0,X13,X6,X7] : c_Set_Oimage(X6,c_Set_Oinsert(X13,X9,X7),X7,X0) = c_Set_Oinsert(hAPP(X6,X13),c_Set_Oimage(X6,X9,X7,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f413,axiom,
! [X0,X6,X9,X7,X13] : c_Set_Oimage(X6,c_Set_Oinsert(X13,X9,X7),X7,X0) = c_Set_Oinsert(hAPP(X6,X13),c_Set_Oimage(X6,X9,X7,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f4162,plain,
spl0_292,
inference(avatar_split_clause,[],[f411,f4160]) ).
fof(f411,axiom,
! [X3,X0,X8,X9] :
( ~ c_in(X3,X9,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f4158,plain,
spl0_291,
inference(avatar_split_clause,[],[f342,f4156]) ).
fof(f4156,plain,
( spl0_291
<=> ! [X13,X0,X9,X8] :
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f342,axiom,
! [X0,X8,X9,X13] :
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
fof(f4154,plain,
spl0_290,
inference(avatar_split_clause,[],[f341,f4152]) ).
fof(f4152,plain,
( spl0_290
<=> ! [X13,X0,X9,X8] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f341,axiom,
! [X0,X8,X9,X13] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
fof(f4150,plain,
spl0_289,
inference(avatar_split_clause,[],[f299,f4148]) ).
fof(f299,axiom,
! [X0,X8,X6,X9,X7] :
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X8,X6,X7,X0),X9,X0,X7)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).
fof(f4146,plain,
spl0_288,
inference(avatar_split_clause,[],[f293,f4144]) ).
fof(f293,axiom,
! [X0,X8,X6,X7] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Finite__Set_Ocard(X8,X0) != c_Finite__Set_Ocard(c_Set_Oimage(X6,X8,X0,X7),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).
fof(f4142,plain,
spl0_287,
inference(avatar_split_clause,[],[f280,f4140]) ).
fof(f280,axiom,
! [X0,X8,X6,X9,X7] :
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X8,X9,X6,X7,X0),X8,X7)
| c_lessequals(c_Set_Oimage(X6,X8,X7,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_1) ).
fof(f4138,plain,
spl0_286,
inference(avatar_split_clause,[],[f278,f4136]) ).
fof(f278,axiom,
! [X0,X8,X6,X9,X7] :
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X8,X9,X6,X0,X7),X8,X0)
| c_lessequals(c_Set_Oimage(X6,X8,X0,X7),X9,tc_fun(X7,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_0) ).
fof(f4134,plain,
spl0_285,
inference(avatar_split_clause,[],[f274,f4132]) ).
fof(f4132,plain,
( spl0_285
<=> ! [X0,X12,X9,X8] :
( c_lessequals(X12,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X12,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f274,axiom,
! [X0,X8,X9,X12] :
( c_lessequals(X12,X8,tc_fun(X0,tc_bool))
| ~ c_lessequals(X12,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f4130,plain,
spl0_284,
inference(avatar_split_clause,[],[f273,f4128]) ).
fof(f4128,plain,
( spl0_284
<=> ! [X0,X12,X9,X8] :
( c_lessequals(X12,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X12,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f273,axiom,
! [X0,X8,X9,X12] :
( c_lessequals(X12,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X12,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f4126,plain,
( spl0_283
| ~ spl0_53
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f3860,f3736,f742,f4124]) ).
fof(f3736,plain,
( spl0_256
<=> hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_pn))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f3860,plain,
( ! [X0] : c_in(hAPP(v_mgt__call,v_pn),v_G,X0)
| ~ spl0_53
| ~ spl0_256 ),
inference(resolution,[],[f3738,f743]) ).
fof(f3738,plain,
( hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_pn)))
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f3736]) ).
fof(f4122,plain,
spl0_282,
inference(avatar_split_clause,[],[f215,f4120]) ).
fof(f4120,plain,
( spl0_282
<=> ! [X13,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X13,X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f215,axiom,
! [X3,X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X13,X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
fof(f4118,plain,
spl0_281,
inference(avatar_split_clause,[],[f198,f4116]) ).
fof(f4116,plain,
( spl0_281
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X2,X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f198,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X2,X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
fof(f4114,plain,
spl0_280,
inference(avatar_split_clause,[],[f182,f4112]) ).
fof(f4112,plain,
( spl0_280
<=> ! [X13,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X13,X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f182,axiom,
! [X3,X0,X14,X13] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X13,X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
fof(f4110,plain,
spl0_279,
inference(avatar_split_clause,[],[f172,f4108]) ).
fof(f4108,plain,
( spl0_279
<=> ! [X13,X0,X14,X6,X7] :
( hAPP(X6,X13) = X14
| ~ c_in(X13,c_Set_Ovimage(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7),X0,X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f172,axiom,
! [X0,X6,X7,X14,X13] :
( hAPP(X6,X13) = X14
| ~ c_in(X13,c_Set_Ovimage(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7),X0,X7),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
fof(f4106,plain,
spl0_278,
inference(avatar_split_clause,[],[f155,f4104]) ).
fof(f155,axiom,
! [X0,X1,X8,X6,X7] :
( ~ c_in(X1,c_Set_Oimage(X6,X8,X7,X0),X0)
| hAPP(X6,hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X7,X0),X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).
fof(f4102,plain,
spl0_277,
inference(avatar_split_clause,[],[f145,f4100]) ).
fof(f4100,plain,
( spl0_277
<=> ! [X3,X0,X9,X8] :
( ~ c_in(X3,X9,X0)
| c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f145,axiom,
! [X3,X0,X8,X9] :
( ~ c_in(X3,X9,X0)
| c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X8,c_Set_Oinsert(X3,X9,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
fof(f4098,plain,
spl0_276,
inference(avatar_split_clause,[],[f127,f4096]) ).
fof(f4096,plain,
( spl0_276
<=> ! [X9,X0,X8,X3] :
( ~ hBOOL(hAPP(X8,X3))
| ~ hBOOL(hAPP(X9,X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f127,axiom,
! [X3,X0,X8,X9] :
( ~ hBOOL(hAPP(X8,X3))
| ~ hBOOL(hAPP(X9,X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f4094,plain,
spl0_275,
inference(avatar_split_clause,[],[f86,f4092]) ).
fof(f4092,plain,
( spl0_275
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f86,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
fof(f4090,plain,
spl0_274,
inference(avatar_split_clause,[],[f56,f4088]) ).
fof(f4088,plain,
( spl0_274
<=> ! [X17,X0,X9,X8] :
( ~ c_in(X17,X8,X0)
| ~ c_in(X17,X9,X0)
| c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f56,axiom,
! [X0,X8,X9,X17] :
( ~ c_in(X17,X8,X0)
| ~ c_in(X17,X9,X0)
| c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
fof(f4086,plain,
spl0_273,
inference(avatar_split_clause,[],[f9,f4084]) ).
fof(f4084,plain,
( spl0_273
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
fof(f4082,plain,
spl0_272,
inference(avatar_split_clause,[],[f5,f4080]) ).
fof(f4080,plain,
( spl0_272
<=> ! [X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Ovimage(X6,c_Set_Oimage(X6,X8,X0,X7),X0,X7) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f5,axiom,
! [X0,X8,X6,X7] :
( ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7)
| c_Set_Ovimage(X6,c_Set_Oimage(X6,X8,X0,X7),X0,X7) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
fof(f3809,plain,
spl0_271,
inference(avatar_split_clause,[],[f456,f3807]) ).
fof(f3807,plain,
( spl0_271
<=> ! [X13,X0,X14] :
( X13 = X14
| c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f456,axiom,
! [X0,X14,X13] :
( X13 = X14
| c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f3805,plain,
spl0_270,
inference(avatar_split_clause,[],[f402,f3803]) ).
fof(f3803,plain,
( spl0_270
<=> ! [X0,X12,X9,X8] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_lessequals(X8,X12,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f402,axiom,
! [X0,X8,X9,X12] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_lessequals(X8,X12,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f3801,plain,
spl0_269,
inference(avatar_split_clause,[],[f388,f3799]) ).
fof(f3799,plain,
( spl0_269
<=> ! [X24,X13,X0,X12] :
( ~ c_lessequals(X12,X24,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X13,X12,X0),c_Set_Oinsert(X13,X24,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f388,axiom,
! [X0,X24,X12,X13] :
( ~ c_lessequals(X12,X24,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X13,X12,X0),c_Set_Oinsert(X13,X24,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f3797,plain,
spl0_268,
inference(avatar_split_clause,[],[f379,f3795]) ).
fof(f3795,plain,
( spl0_268
<=> ! [X6,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Fun_Oinj__on(X6,X8,X0,X0)
| ~ c_lessequals(X8,c_Set_Oimage(X6,X8,X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f379,axiom,
! [X0,X8,X6] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Fun_Oinj__on(X6,X8,X0,X0)
| ~ c_lessequals(X8,c_Set_Oimage(X6,X8,X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
fof(f3793,plain,
spl0_267,
inference(avatar_split_clause,[],[f372,f3791]) ).
fof(f3791,plain,
( spl0_267
<=> ! [X9,X0,X8] : c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f372,axiom,
! [X0,X8,X9] : c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f3789,plain,
( spl0_266
| ~ spl0_66
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f3547,f3411,f800,f3787]) ).
fof(f3787,plain,
( spl0_266
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != v_G ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f3547,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != v_G
| ~ spl0_66
| ~ spl0_247 ),
inference(superposition,[],[f801,f3412]) ).
fof(f3785,plain,
spl0_265,
inference(avatar_split_clause,[],[f263,f3783]) ).
fof(f3783,plain,
( spl0_265
<=> ! [X0,X12,X9,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,X12,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f263,axiom,
! [X0,X8,X9,X12] :
( ~ c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X12,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,X12,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
fof(f3781,plain,
spl0_264,
inference(avatar_split_clause,[],[f262,f3779]) ).
fof(f3779,plain,
( spl0_264
<=> ! [X0,X12,X9,X8] :
( ~ c_HOL_Oord__class_Oless(X9,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,X12,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f262,axiom,
! [X0,X8,X9,X12] :
( ~ c_HOL_Oord__class_Oless(X9,X12,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,X12,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
fof(f3777,plain,
spl0_263,
inference(avatar_split_clause,[],[f166,f3775]) ).
fof(f166,axiom,
! [X0,X8,X6,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Fun_Oinj__on(c_Fun_Othe__inv__into(X8,X6,X0,X7),c_Set_Oimage(X6,X8,X0,X7),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).
fof(f3773,plain,
spl0_262,
inference(avatar_split_clause,[],[f163,f3771]) ).
fof(f3771,plain,
( spl0_262
<=> ! [X9,X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f163,axiom,
! [X0,X8,X9] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
fof(f3769,plain,
spl0_261,
inference(avatar_split_clause,[],[f153,f3767]) ).
fof(f153,axiom,
! [X3,X0,X8,X6,X7] :
( ~ c_in(X3,c_Set_Oimage(X6,X8,X7,X0),X0)
| c_in(hAPP(c_Hilbert__Choice_Oinv__into(X8,X6,X7,X0),X3),X8,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).
fof(f3765,plain,
spl0_260,
inference(avatar_split_clause,[],[f91,f3763]) ).
fof(f3763,plain,
( spl0_260
<=> ! [X1,X6,X0,X3,X2,X7] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X6,X3,X1,X0,X7),X3,X2,X0,X7) = c_Fun_Ofun__upd(X6,X3,X2,X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f91,axiom,
! [X2,X3,X0,X1,X6,X7] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X6,X3,X1,X0,X7),X3,X2,X0,X7) = c_Fun_Ofun__upd(X6,X3,X2,X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
fof(f3761,plain,
spl0_259,
inference(avatar_split_clause,[],[f78,f3759]) ).
fof(f3759,plain,
( spl0_259
<=> ! [X3,X7,X0,X6,X1] :
( X1 = X3
| hAPP(X6,X3) != hAPP(X6,X1)
| ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f78,axiom,
! [X3,X0,X1,X6,X7] :
( X1 = X3
| hAPP(X6,X3) != hAPP(X6,X1)
| ~ c_Fun_Oinj__on(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
fof(f3757,plain,
spl0_258,
inference(avatar_split_clause,[],[f13,f3755]) ).
fof(f3755,plain,
( spl0_258
<=> ! [X0,X12,X9,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X9,X12,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,X12,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f13,axiom,
! [X0,X8,X9,X12] :
( ~ c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool))
| ~ c_HOL_Oord__class_Oless(X9,X12,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,X12,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
fof(f3753,plain,
spl0_257,
inference(avatar_split_clause,[],[f11,f3751]) ).
fof(f3751,plain,
( spl0_257
<=> ! [X11,X0,X10,X7] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X10,X11,X7,X0),X7)
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool)),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f11,axiom,
! [X10,X0,X11,X7] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X10,X11,X7,X0),X7)
| ~ c_Fun_Oinj__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool)),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
fof(f3739,plain,
( spl0_256
| ~ spl0_44
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f3543,f3411,f705,f3736]) ).
fof(f705,plain,
( spl0_44
<=> ! [X0,X8,X3] : hBOOL(hAPP(c_Set_Oinsert(X3,X8,X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f3543,plain,
( hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_pn)))
| ~ spl0_44
| ~ spl0_247 ),
inference(superposition,[],[f706,f3412]) ).
fof(f706,plain,
( ! [X3,X0,X8] : hBOOL(hAPP(c_Set_Oinsert(X3,X8,X0),X3))
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f3445,plain,
spl0_255,
inference(avatar_split_clause,[],[f363,f3443]) ).
fof(f3443,plain,
( spl0_255
<=> ! [X17,X0,X9,X8] :
( ~ c_in(X17,X8,X0)
| c_in(X17,X9,X0)
| c_in(X17,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f363,axiom,
! [X0,X8,X9,X17] :
( ~ c_in(X17,X8,X0)
| c_in(X17,X9,X0)
| c_in(X17,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
fof(f3441,plain,
spl0_254,
inference(avatar_split_clause,[],[f330,f3439]) ).
fof(f3439,plain,
( spl0_254
<=> ! [X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_in(c_Finite__Set_Olinorder__class_OMin(X8,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f330,axiom,
! [X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_in(c_Finite__Set_Olinorder__class_OMin(X8,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).
fof(f3437,plain,
spl0_253,
inference(avatar_split_clause,[],[f329,f3435]) ).
fof(f3435,plain,
( spl0_253
<=> ! [X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_in(c_Finite__Set_Olinorder__class_OMax(X8,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f329,axiom,
! [X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_in(c_Finite__Set_Olinorder__class_OMax(X8,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).
fof(f3433,plain,
spl0_252,
inference(avatar_split_clause,[],[f283,f3431]) ).
fof(f3431,plain,
( spl0_252
<=> ! [X17,X0,X8,X7] :
( c_in(X17,X8,X7)
| c_Set_Ovimage(c_COMBK(X17,X7,X0),X8,X0,X7) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f283,axiom,
! [X0,X8,X7,X17] :
( c_in(X17,X8,X7)
| c_Set_Ovimage(c_COMBK(X17,X7,X0),X8,X0,X7) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
fof(f3429,plain,
spl0_251,
inference(avatar_split_clause,[],[f210,f3427]) ).
fof(f3427,plain,
( spl0_251
<=> ! [X13,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X3,X0)
| ~ c_lessequals(X14,X3,X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X13,X14,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f210,axiom,
! [X3,X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X3,X0)
| ~ c_lessequals(X14,X3,X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X13,X14,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
fof(f3425,plain,
spl0_250,
inference(avatar_split_clause,[],[f207,f3423]) ).
fof(f3423,plain,
( spl0_250
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X3,X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f207,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X3,X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
fof(f3421,plain,
spl0_249,
inference(avatar_split_clause,[],[f170,f3419]) ).
fof(f3419,plain,
( spl0_249
<=> ! [X0,X8,X3] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Ocard(X8,X0) = c_Finite__Set_Ocard(c_Set_Oinsert(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f170,axiom,
! [X3,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_Finite__Set_Ocard(X8,X0) = c_Finite__Set_Ocard(c_Set_Oinsert(X3,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).
fof(f3417,plain,
spl0_248,
inference(avatar_split_clause,[],[f131,f3415]) ).
fof(f131,axiom,
! [X0,X8,X7,X17] :
( ~ c_in(X17,X8,X7)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X17,X7,X0),X8,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).
fof(f3413,plain,
( spl0_247
| ~ spl0_68
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f3257,f3106,f814,f3411]) ).
fof(f3106,plain,
( spl0_238
<=> ! [X0,X1] :
( ~ c_in(X0,v_U,tc_Com_Opname)
| v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f3257,plain,
( ! [X0] : v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,X0)
| ~ spl0_68
| ~ spl0_238 ),
inference(resolution,[],[f3107,f815]) ).
fof(f3107,plain,
( ! [X0,X1] :
( ~ c_in(X0,v_U,tc_Com_Opname)
| v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,X1) )
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f3106]) ).
fof(f3409,plain,
spl0_246,
inference(avatar_split_clause,[],[f79,f3407]) ).
fof(f3407,plain,
( spl0_246
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f79,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
fof(f3405,plain,
spl0_245,
inference(avatar_split_clause,[],[f49,f3403]) ).
fof(f3403,plain,
( spl0_245
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f49,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X3,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
fof(f3401,plain,
spl0_244,
inference(avatar_split_clause,[],[f48,f3399]) ).
fof(f3399,plain,
( spl0_244
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f48,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
fof(f3397,plain,
spl0_243,
inference(avatar_split_clause,[],[f26,f3395]) ).
fof(f3395,plain,
( spl0_243
<=> ! [X9,X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f26,axiom,
! [X0,X8,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f3393,plain,
spl0_242,
inference(avatar_split_clause,[],[f8,f3391]) ).
fof(f3391,plain,
( spl0_242
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
fof(f3120,plain,
spl0_241,
inference(avatar_split_clause,[],[f474,f3118]) ).
fof(f3118,plain,
( spl0_241
<=> ! [X3,X0,X6,X15,X7] :
( ~ class_HOL_Oord(X7)
| ~ c_lessequals(X6,X15,tc_fun(X0,X7))
| c_lessequals(hAPP(X6,X3),hAPP(X15,X3),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f474,axiom,
! [X3,X0,X6,X7,X15] :
( ~ class_HOL_Oord(X7)
| ~ c_lessequals(X6,X15,tc_fun(X0,X7))
| c_lessequals(hAPP(X6,X3),hAPP(X15,X3),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f3116,plain,
spl0_240,
inference(avatar_split_clause,[],[f445,f3114]) ).
fof(f445,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(X9,X7)
| ~ c_lessequals(X9,c_Set_Oimage(X6,X8,X0,X7),tc_fun(X7,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
fof(f3112,plain,
spl0_239,
inference(avatar_split_clause,[],[f442,f3110]) ).
fof(f3110,plain,
( spl0_239
<=> ! [X0,X6,X8,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X6,X8,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f442,axiom,
! [X0,X8,X6,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X6,X8,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
fof(f3108,plain,
( spl0_238
| ~ spl0_87
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f3031,f2780,f891,f3106]) ).
fof(f2780,plain,
( spl0_228
<=> ! [X0,X1] :
( ~ c_in(X0,v_U,tc_Com_Opname)
| c_in(hAPP(v_mgt__call,X0),v_G,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f3031,plain,
( ! [X0,X1] :
( ~ c_in(X0,v_U,tc_Com_Opname)
| v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,X1) )
| ~ spl0_87
| ~ spl0_228 ),
inference(resolution,[],[f2781,f892]) ).
fof(f2781,plain,
( ! [X0,X1] :
( c_in(hAPP(v_mgt__call,X0),v_G,X1)
| ~ c_in(X0,v_U,tc_Com_Opname) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2780]) ).
fof(f3104,plain,
spl0_237,
inference(avatar_split_clause,[],[f350,f3102]) ).
fof(f3102,plain,
( spl0_237
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X9,X0,X7)
| c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f350,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Fun_Oinj__on(X6,X9,X0,X7)
| c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
fof(f3100,plain,
spl0_236,
inference(avatar_split_clause,[],[f271,f3098]) ).
fof(f3098,plain,
( spl0_236
<=> ! [X9,X0,X8] :
( ~ c_lessequals(X9,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f271,axiom,
! [X0,X8,X9] :
( ~ c_lessequals(X9,X8,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f3096,plain,
spl0_235,
inference(avatar_split_clause,[],[f270,f3094]) ).
fof(f3094,plain,
( spl0_235
<=> ! [X9,X0,X8] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f270,axiom,
! [X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f3092,plain,
spl0_234,
inference(avatar_split_clause,[],[f252,f3090]) ).
fof(f3090,plain,
( spl0_234
<=> ! [X9,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f252,axiom,
! [X0,X9] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f3088,plain,
spl0_233,
inference(avatar_split_clause,[],[f251,f3086]) ).
fof(f3086,plain,
( spl0_233
<=> ! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f251,axiom,
! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f3084,plain,
spl0_232,
inference(avatar_split_clause,[],[f171,f3082]) ).
fof(f3082,plain,
( spl0_232
<=> ! [X13,X0,X6,X20] : c_in(X13,c_Set_Ovimage(X6,c_Set_Oinsert(hAPP(X6,X13),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X20,X0),X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f171,axiom,
! [X0,X6,X13,X20] : c_in(X13,c_Set_Ovimage(X6,c_Set_Oinsert(hAPP(X6,X13),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X20,X0),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
fof(f3080,plain,
spl0_231,
inference(avatar_split_clause,[],[f169,f3078]) ).
fof(f3078,plain,
( spl0_231
<=> ! [X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Finite__Set_Ocard(X8,X0) = c_Finite__Set_Ocard(c_Set_Oimage(X6,X8,X0,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f169,axiom,
! [X0,X8,X6,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Finite__Set_Ocard(X8,X0) = c_Finite__Set_Ocard(c_Set_Oimage(X6,X8,X0,X7),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).
fof(f3076,plain,
spl0_230,
inference(avatar_split_clause,[],[f151,f3074]) ).
fof(f3074,plain,
( spl0_230
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_SetInterval_Oord__class_OlessThan(X3,X0),c_SetInterval_Oord__class_OlessThan(X1,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f151,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_SetInterval_Oord__class_OlessThan(X3,X0),c_SetInterval_Oord__class_OlessThan(X1,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).
fof(f3072,plain,
spl0_229,
inference(avatar_split_clause,[],[f150,f3070]) ).
fof(f3070,plain,
( spl0_229
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X3,X0),c_SetInterval_Oord__class_OlessThan(X1,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f150,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X3,X0),c_SetInterval_Oord__class_OlessThan(X1,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).
fof(f2782,plain,
( spl0_228
| ~ spl0_53
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2529,f2458,f742,f2780]) ).
fof(f2458,plain,
( spl0_227
<=> ! [X0] :
( ~ c_in(X0,v_U,tc_Com_Opname)
| hBOOL(hAPP(v_G,hAPP(v_mgt__call,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f2529,plain,
( ! [X0,X1] :
( ~ c_in(X0,v_U,tc_Com_Opname)
| c_in(hAPP(v_mgt__call,X0),v_G,X1) )
| ~ spl0_53
| ~ spl0_227 ),
inference(resolution,[],[f2459,f743]) ).
fof(f2459,plain,
( ! [X0] :
( hBOOL(hAPP(v_G,hAPP(v_mgt__call,X0)))
| ~ c_in(X0,v_U,tc_Com_Opname) )
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2458]) ).
fof(f2460,plain,
( spl0_227
| ~ spl0_54
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2421,f2377,f746,f2458]) ).
fof(f2377,plain,
( spl0_209
<=> ! [X0] :
( c_in(hAPP(v_mgt__call,X0),v_G,t_a)
| ~ c_in(X0,v_U,tc_Com_Opname) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f2421,plain,
( ! [X0] :
( ~ c_in(X0,v_U,tc_Com_Opname)
| hBOOL(hAPP(v_G,hAPP(v_mgt__call,X0))) )
| ~ spl0_54
| ~ spl0_209 ),
inference(resolution,[],[f2378,f747]) ).
fof(f2378,plain,
( ! [X0] :
( c_in(hAPP(v_mgt__call,X0),v_G,t_a)
| ~ c_in(X0,v_U,tc_Com_Opname) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f2377]) ).
fof(f2449,plain,
spl0_226,
inference(avatar_split_clause,[],[f451,f2447]) ).
fof(f2447,plain,
( spl0_226
<=> ! [X0,X8,X3,X1] : c_Set_Oinsert(X3,c_Set_Oinsert(X1,X8,X0),X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X3,X8,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f451,axiom,
! [X3,X0,X1,X8] : c_Set_Oinsert(X3,c_Set_Oinsert(X1,X8,X0),X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X3,X8,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f2445,plain,
spl0_225,
inference(avatar_split_clause,[],[f444,f2443]) ).
fof(f2443,plain,
( spl0_225
<=> ! [X9,X0,X8,X3] :
( c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f444,axiom,
! [X3,X0,X8,X9] :
( c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
fof(f2441,plain,
spl0_224,
inference(avatar_split_clause,[],[f443,f2439]) ).
fof(f443,axiom,
! [X0,X8,X9,X14] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(X8,c_Set_Oinsert(X14,X9,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
fof(f2437,plain,
spl0_223,
inference(avatar_split_clause,[],[f429,f2435]) ).
fof(f2435,plain,
( spl0_223
<=> ! [X9,X0,X8] :
( X8 = X9
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f429,axiom,
! [X0,X8,X9] :
( X8 = X9
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
fof(f2433,plain,
spl0_222,
inference(avatar_split_clause,[],[f420,f2431]) ).
fof(f2431,plain,
( spl0_222
<=> ! [X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| ~ c_lessequals(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f420,axiom,
! [X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| ~ c_lessequals(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f2429,plain,
spl0_221,
inference(avatar_split_clause,[],[f374,f2427]) ).
fof(f2427,plain,
( spl0_221
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Fun_Oinj__on(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f374,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Fun_Oinj__on(X6,X8,X0,X7)
| c_Fun_Oinj__on(X6,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
fof(f2425,plain,
spl0_220,
inference(avatar_split_clause,[],[f335,f2423]) ).
fof(f2423,plain,
( spl0_220
<=> ! [X0,X6,X8,X7] :
( c_Finite__Set_Ofinite(X8,X7)
| ~ c_Fun_Oinj__on(X6,X8,X7,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X6,X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f335,axiom,
! [X0,X8,X6,X7] :
( c_Finite__Set_Ofinite(X8,X7)
| ~ c_Fun_Oinj__on(X6,X8,X7,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X6,X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
fof(f2419,plain,
spl0_219,
inference(avatar_split_clause,[],[f332,f2417]) ).
fof(f2417,plain,
( spl0_219
<=> ! [X0,X8,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f332,axiom,
! [X3,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).
fof(f2415,plain,
spl0_218,
inference(avatar_split_clause,[],[f331,f2413]) ).
fof(f2413,plain,
( spl0_218
<=> ! [X0,X8,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X8,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f331,axiom,
! [X3,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Finite__Set_Ofinite(X8,X0)
| ~ c_in(X3,X8,X0)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X8,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).
fof(f2411,plain,
spl0_217,
inference(avatar_split_clause,[],[f260,f2409]) ).
fof(f2409,plain,
( spl0_217
<=> ! [X9,X0,X8] :
( X8 = X9
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f260,axiom,
! [X0,X8,X9] :
( X8 = X9
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
fof(f2407,plain,
spl0_216,
inference(avatar_split_clause,[],[f238,f2405]) ).
fof(f2405,plain,
( spl0_216
<=> ! [X13,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X14,X3,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f238,axiom,
! [X3,X0,X14,X13] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X14,X3,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f2403,plain,
spl0_215,
inference(avatar_split_clause,[],[f237,f2401]) ).
fof(f2401,plain,
( spl0_215
<=> ! [X13,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X13,X3,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f237,axiom,
! [X3,X0,X14,X13] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X13,X3,X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f2399,plain,
spl0_214,
inference(avatar_split_clause,[],[f236,f2397]) ).
fof(f2397,plain,
( spl0_214
<=> ! [X13,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X14,X0)
| ~ c_lessequals(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f236,axiom,
! [X3,X0,X14,X13] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X14,X0)
| ~ c_lessequals(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
fof(f2395,plain,
spl0_213,
inference(avatar_split_clause,[],[f235,f2393]) ).
fof(f2393,plain,
( spl0_213
<=> ! [X13,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X13,X0)
| ~ c_lessequals(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f235,axiom,
! [X3,X0,X14,X13] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X13,X0)
| ~ c_lessequals(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
fof(f2391,plain,
spl0_212,
inference(avatar_split_clause,[],[f204,f2389]) ).
fof(f2389,plain,
( spl0_212
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f204,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
fof(f2387,plain,
spl0_211,
inference(avatar_split_clause,[],[f201,f2385]) ).
fof(f2385,plain,
( spl0_211
<=> ! [X13,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X3,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f201,axiom,
! [X3,X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X3,X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
fof(f2383,plain,
spl0_210,
inference(avatar_split_clause,[],[f200,f2381]) ).
fof(f2381,plain,
( spl0_210
<=> ! [X13,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X14,X0)
| ~ c_lessequals(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f200,axiom,
! [X3,X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X14,X0)
| ~ c_lessequals(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
fof(f2379,plain,
( spl0_209
| ~ spl0_3
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2302,f1799,f522,f2377]) ).
fof(f1799,plain,
( spl0_189
<=> ! [X6,X0,X3,X8,X7] :
( ~ c_in(X3,X8,X0)
| c_in(hAPP(X6,X3),c_Set_Oimage(X6,X8,X0,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f2302,plain,
( ! [X0] :
( c_in(hAPP(v_mgt__call,X0),v_G,t_a)
| ~ c_in(X0,v_U,tc_Com_Opname) )
| ~ spl0_3
| ~ spl0_189 ),
inference(superposition,[],[f1800,f524]) ).
fof(f1800,plain,
( ! [X3,X0,X8,X6,X7] :
( c_in(hAPP(X6,X3),c_Set_Oimage(X6,X8,X0,X7),X7)
| ~ c_in(X3,X8,X0) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1799]) ).
fof(f2375,plain,
spl0_208,
inference(avatar_split_clause,[],[f199,f2373]) ).
fof(f2373,plain,
( spl0_208
<=> ! [X13,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X13,X0)
| ~ c_lessequals(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f199,axiom,
! [X3,X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X13,X0)
| ~ c_lessequals(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
fof(f2371,plain,
spl0_207,
inference(avatar_split_clause,[],[f129,f2369]) ).
fof(f2369,plain,
( spl0_207
<=> ! [X1,X6,X0,X3,X2,X7] :
( X2 = X3
| hAPP(X6,X2) = hAPP(c_Fun_Ofun__upd(X6,X3,X1,X0,X7),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f129,axiom,
! [X2,X3,X0,X1,X6,X7] :
( X2 = X3
| hAPP(X6,X2) = hAPP(c_Fun_Ofun__upd(X6,X3,X1,X0,X7),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
fof(f2367,plain,
spl0_206,
inference(avatar_split_clause,[],[f111,f2365]) ).
fof(f2365,plain,
( spl0_206
<=> ! [X13,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X13,X3,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f111,axiom,
! [X3,X0,X14,X13] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X13,X3,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
fof(f2363,plain,
spl0_205,
inference(avatar_split_clause,[],[f110,f2361]) ).
fof(f2361,plain,
( spl0_205
<=> ! [X13,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X14,X3,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f110,axiom,
! [X3,X0,X14,X13] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X14,X3,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X13),X14),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
fof(f2359,plain,
spl0_204,
inference(avatar_split_clause,[],[f88,f2357]) ).
fof(f2357,plain,
( spl0_204
<=> ! [X9,X0,X8] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X8
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),X9) != c_Orderings_Otop__class_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f88,axiom,
! [X0,X8,X9] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X8
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),X9) != c_Orderings_Otop__class_Otop(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
fof(f2355,plain,
spl0_203,
inference(avatar_split_clause,[],[f87,f2353]) ).
fof(f2353,plain,
( spl0_203
<=> ! [X9,X0,X8] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X9
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),X9) != c_Orderings_Otop__class_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f87,axiom,
! [X0,X8,X9] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X9
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),X9) != c_Orderings_Otop__class_Otop(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
fof(f2351,plain,
spl0_202,
inference(avatar_split_clause,[],[f60,f2349]) ).
fof(f2349,plain,
( spl0_202
<=> ! [X17,X0,X9,X8] :
( c_in(X17,X8,X0)
| ~ c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f60,axiom,
! [X0,X8,X9,X17] :
( c_in(X17,X8,X0)
| ~ c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f2347,plain,
spl0_201,
inference(avatar_split_clause,[],[f59,f2345]) ).
fof(f2345,plain,
( spl0_201
<=> ! [X17,X0,X9,X8] :
( c_in(X17,X9,X0)
| ~ c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f59,axiom,
! [X0,X8,X9,X17] :
( c_in(X17,X9,X0)
| ~ c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f2343,plain,
spl0_200,
inference(avatar_split_clause,[],[f51,f2341]) ).
fof(f2341,plain,
( spl0_200
<=> ! [X9,X0,X8,X3] :
( hBOOL(hAPP(X8,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f51,axiom,
! [X3,X0,X8,X9] :
( hBOOL(hAPP(X8,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f2339,plain,
spl0_199,
inference(avatar_split_clause,[],[f50,f2337]) ).
fof(f2337,plain,
( spl0_199
<=> ! [X9,X0,X8,X3] :
( hBOOL(hAPP(X9,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f50,axiom,
! [X3,X0,X8,X9] :
( hBOOL(hAPP(X9,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f2331,plain,
spl0_198,
inference(avatar_split_clause,[],[f35,f2329]) ).
fof(f2329,plain,
( spl0_198
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f35,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
fof(f2327,plain,
spl0_197,
inference(avatar_split_clause,[],[f34,f2325]) ).
fof(f2325,plain,
( spl0_197
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f34,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
fof(f2323,plain,
spl0_196,
inference(avatar_split_clause,[],[f33,f2321]) ).
fof(f2321,plain,
( spl0_196
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f33,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
fof(f2319,plain,
spl0_195,
inference(avatar_split_clause,[],[f32,f2317]) ).
fof(f2317,plain,
( spl0_195
<=> ! [X13,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X3,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f32,axiom,
! [X3,X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X3,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X13),X14),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
fof(f2315,plain,
spl0_194,
inference(avatar_split_clause,[],[f29,f2313]) ).
fof(f2313,plain,
( spl0_194
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f29,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f2311,plain,
spl0_193,
inference(avatar_split_clause,[],[f28,f2309]) ).
fof(f2309,plain,
( spl0_193
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f28,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f2307,plain,
spl0_192,
inference(avatar_split_clause,[],[f27,f2305]) ).
fof(f2305,plain,
( spl0_192
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f27,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f2286,plain,
( spl0_191
| ~ spl0_53
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2100,f1870,f742,f2284]) ).
fof(f1870,plain,
( spl0_190
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,X1),v_pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f2100,plain,
( ! [X2,X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X2)
| ~ spl0_53
| ~ spl0_190 ),
inference(resolution,[],[f1871,f743]) ).
fof(f1871,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,X1),v_pn))
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1870]) ).
fof(f1872,plain,
( spl0_190
| ~ spl0_54
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1803,f1759,f746,f1870]) ).
fof(f1759,plain,
( spl0_179
<=> ! [X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1803,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,X1),v_pn))
| ~ spl0_54
| ~ spl0_179 ),
inference(resolution,[],[f1760,f747]) ).
fof(f1760,plain,
( ! [X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X1)
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1759]) ).
fof(f1801,plain,
spl0_189,
inference(avatar_split_clause,[],[f473,f1799]) ).
fof(f473,axiom,
! [X3,X0,X8,X6,X7] :
( ~ c_in(X3,X8,X0)
| c_in(hAPP(X6,X3),c_Set_Oimage(X6,X8,X0,X7),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
fof(f1797,plain,
spl0_188,
inference(avatar_split_clause,[],[f437,f1795]) ).
fof(f1795,plain,
( spl0_188
<=> ! [X0,X8,X3,X1] :
( X1 = X3
| hBOOL(hAPP(X8,X3))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X8,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f437,axiom,
! [X3,X0,X1,X8] :
( X1 = X3
| hBOOL(hAPP(X8,X3))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X8,X0),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f1793,plain,
spl0_187,
inference(avatar_split_clause,[],[f431,f1791]) ).
fof(f1791,plain,
( spl0_187
<=> ! [X13,X0,X14,X8] :
( X13 = X14
| c_in(X13,X8,X0)
| ~ c_in(X13,c_Set_Oinsert(X14,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f431,axiom,
! [X0,X8,X14,X13] :
( X13 = X14
| c_in(X13,X8,X0)
| ~ c_in(X13,c_Set_Oinsert(X14,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f1789,plain,
spl0_186,
inference(avatar_split_clause,[],[f410,f1787]) ).
fof(f1787,plain,
( spl0_186
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f410,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f1785,plain,
spl0_185,
inference(avatar_split_clause,[],[f409,f1783]) ).
fof(f1783,plain,
( spl0_185
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f409,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f1781,plain,
spl0_184,
inference(avatar_split_clause,[],[f408,f1779]) ).
fof(f1779,plain,
( spl0_184
<=> ! [X3,X0,X9,X8] :
( ~ c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f408,axiom,
! [X3,X0,X8,X9] :
( ~ c_in(X3,X8,X0)
| c_in(X3,X9,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
fof(f1777,plain,
spl0_183,
inference(avatar_split_clause,[],[f401,f1775]) ).
fof(f1775,plain,
( spl0_183
<=> ! [X28,X0,X3,X25] :
( ~ hBOOL(hAPP(X25,X3))
| hBOOL(hAPP(X28,X3))
| ~ c_lessequals(X25,X28,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f401,axiom,
! [X3,X28,X0,X25] :
( ~ hBOOL(hAPP(X25,X3))
| hBOOL(hAPP(X28,X3))
| ~ c_lessequals(X25,X28,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
fof(f1773,plain,
spl0_182,
inference(avatar_split_clause,[],[f358,f1771]) ).
fof(f1771,plain,
( spl0_182
<=> ! [X9,X0,X8] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(X8,X0)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f358,axiom,
! [X0,X8,X9] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(X8,X0)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
fof(f1769,plain,
spl0_181,
inference(avatar_split_clause,[],[f356,f1767]) ).
fof(f1767,plain,
( spl0_181
<=> ! [X0,X8] : 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)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f356,axiom,
! [X0,X8] : 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)),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f1765,plain,
spl0_180,
inference(avatar_split_clause,[],[f258,f1763]) ).
fof(f1763,plain,
( spl0_180
<=> ! [X0,X6,X15,X7] :
( ~ class_HOL_Oord(X7)
| ~ c_HOL_Oord__class_Oless(X6,X15,tc_fun(X0,X7))
| ~ c_lessequals(X15,X6,tc_fun(X0,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f258,axiom,
! [X0,X6,X7,X15] :
( ~ class_HOL_Oord(X7)
| ~ c_HOL_Oord__class_Oless(X6,X15,tc_fun(X0,X7))
| ~ c_lessequals(X15,X6,tc_fun(X0,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
fof(f1761,plain,
( spl0_179
| ~ spl0_65
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1717,f1661,f796,f1759]) ).
fof(f1717,plain,
( ! [X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X1)
| ~ spl0_65
| ~ spl0_158 ),
inference(resolution,[],[f1662,f797]) ).
fof(f1757,plain,
spl0_178,
inference(avatar_split_clause,[],[f256,f1755]) ).
fof(f1755,plain,
( spl0_178
<=> ! [X0,X6,X15,X7] :
( ~ class_HOL_Oord(X7)
| ~ c_HOL_Oord__class_Oless(X6,X15,tc_fun(X0,X7))
| c_lessequals(X6,X15,tc_fun(X0,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f256,axiom,
! [X0,X6,X7,X15] :
( ~ class_HOL_Oord(X7)
| ~ c_HOL_Oord__class_Oless(X6,X15,tc_fun(X0,X7))
| c_lessequals(X6,X15,tc_fun(X0,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
fof(f1753,plain,
spl0_177,
inference(avatar_split_clause,[],[f234,f1751]) ).
fof(f1751,plain,
( spl0_177
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f234,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f1749,plain,
spl0_176,
inference(avatar_split_clause,[],[f233,f1747]) ).
fof(f1747,plain,
( spl0_176
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X1,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f233,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X1,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f1745,plain,
spl0_175,
inference(avatar_split_clause,[],[f232,f1743]) ).
fof(f1743,plain,
( spl0_175
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X1,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f232,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X1,X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f1741,plain,
spl0_174,
inference(avatar_split_clause,[],[f223,f1739]) ).
fof(f1739,plain,
( spl0_174
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X3,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f223,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X3,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f1737,plain,
spl0_173,
inference(avatar_split_clause,[],[f222,f1735]) ).
fof(f1735,plain,
( spl0_173
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f222,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f1733,plain,
spl0_172,
inference(avatar_split_clause,[],[f221,f1731]) ).
fof(f1731,plain,
( spl0_172
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X1,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f221,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X1,X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f1729,plain,
spl0_171,
inference(avatar_split_clause,[],[f189,f1727]) ).
fof(f1727,plain,
( spl0_171
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_lessequals(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f189,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_lessequals(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f1725,plain,
spl0_170,
inference(avatar_split_clause,[],[f178,f1723]) ).
fof(f1723,plain,
( spl0_170
<=> ! [X6,X0,X16] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_lessequals(X16,hAPP(X6,X16),X0)
| c_lessequals(X16,c_Inductive_Ocomplete__lattice__class_Ogfp(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f178,axiom,
! [X0,X6,X16] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ c_lessequals(X16,hAPP(X6,X16),X0)
| c_lessequals(X16,c_Inductive_Ocomplete__lattice__class_Ogfp(X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gfp__upperbound_0) ).
fof(f1721,plain,
spl0_169,
inference(avatar_split_clause,[],[f177,f1719]) ).
fof(f1719,plain,
( spl0_169
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f177,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f1703,plain,
spl0_168,
inference(avatar_split_clause,[],[f176,f1701]) ).
fof(f1701,plain,
( spl0_168
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X3,X0)
| c_HOL_Oord__class_Oless(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f176,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X3,X0)
| c_HOL_Oord__class_Oless(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f1699,plain,
spl0_167,
inference(avatar_split_clause,[],[f175,f1697]) ).
fof(f1697,plain,
( spl0_167
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f175,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f1695,plain,
spl0_166,
inference(avatar_split_clause,[],[f165,f1693]) ).
fof(f1693,plain,
( spl0_166
<=> ! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f165,axiom,
! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
fof(f1691,plain,
spl0_165,
inference(avatar_split_clause,[],[f161,f1689]) ).
fof(f161,axiom,
! [X0,X8,X6,X7] : c_lessequals(c_Set_Oimage(X6,c_Set_Ovimage(X6,X8,X7,X0),X7,X0),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
fof(f1687,plain,
spl0_164,
inference(avatar_split_clause,[],[f126,f1685]) ).
fof(f1685,plain,
( spl0_164
<=> ! [X3,X7,X0,X6,X8] :
( ~ hBOOL(hAPP(X8,hAPP(X6,X3)))
| hBOOL(hAPP(c_Set_Ovimage(X6,X8,X0,X7),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f126,axiom,
! [X3,X0,X8,X6,X7] :
( ~ hBOOL(hAPP(X8,hAPP(X6,X3)))
| hBOOL(hAPP(c_Set_Ovimage(X6,X8,X0,X7),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
fof(f1683,plain,
spl0_163,
inference(avatar_split_clause,[],[f125,f1681]) ).
fof(f1681,plain,
( spl0_163
<=> ! [X3,X7,X0,X6,X8] :
( hBOOL(hAPP(X8,hAPP(X6,X3)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X6,X8,X0,X7),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f125,axiom,
! [X3,X0,X8,X6,X7] :
( hBOOL(hAPP(X8,hAPP(X6,X3)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X6,X8,X0,X7),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
fof(f1679,plain,
spl0_162,
inference(avatar_split_clause,[],[f74,f1677]) ).
fof(f1677,plain,
( spl0_162
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f74,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f1675,plain,
spl0_161,
inference(avatar_split_clause,[],[f65,f1673]) ).
fof(f1673,plain,
( spl0_161
<=> ! [X13,X0,X6,X8,X7] :
( c_in(hAPP(X6,X13),X8,X7)
| ~ c_in(X13,c_Set_Ovimage(X6,X8,X0,X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f65,axiom,
! [X0,X8,X6,X7,X13] :
( c_in(hAPP(X6,X13),X8,X7)
| ~ c_in(X13,c_Set_Ovimage(X6,X8,X0,X7),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
fof(f1671,plain,
spl0_160,
inference(avatar_split_clause,[],[f62,f1669]) ).
fof(f1669,plain,
( spl0_160
<=> ! [X13,X0,X6,X8,X7] :
( ~ c_in(hAPP(X6,X13),X8,X0)
| c_in(X13,c_Set_Ovimage(X6,X8,X7,X0),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f62,axiom,
! [X0,X8,X6,X7,X13] :
( ~ c_in(hAPP(X6,X13),X8,X0)
| c_in(X13,c_Set_Ovimage(X6,X8,X7,X0),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
fof(f1667,plain,
spl0_159,
inference(avatar_split_clause,[],[f58,f1665]) ).
fof(f1665,plain,
( spl0_159
<=> ! [X17,X0,X9,X8] :
( ~ c_in(X17,X8,X0)
| c_in(X17,X9,X0)
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f58,axiom,
! [X0,X8,X9,X17] :
( ~ c_in(X17,X8,X0)
| c_in(X17,X9,X0)
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
fof(f1663,plain,
( spl0_158
| ~ spl0_105
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1645,f1332,f1028,f1661]) ).
fof(f1028,plain,
( spl0_105
<=> ! [X0] : v_U = c_Set_Oinsert(v_pn,v_U,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1645,plain,
( ! [X0,X1] :
( ~ c_lessequals(v_U,X1,tc_fun(X0,tc_bool))
| c_in(v_pn,X1,X0) )
| ~ spl0_105
| ~ spl0_151 ),
inference(superposition,[],[f1333,f1029]) ).
fof(f1029,plain,
( ! [X0] : v_U = c_Set_Oinsert(v_pn,v_U,X0)
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1028]) ).
fof(f1659,plain,
spl0_157,
inference(avatar_split_clause,[],[f53,f1657]) ).
fof(f1657,plain,
( spl0_157
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f53,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
fof(f1655,plain,
spl0_156,
inference(avatar_split_clause,[],[f14,f1653]) ).
fof(f1653,plain,
( spl0_156
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f1651,plain,
spl0_155,
inference(avatar_split_clause,[],[f12,f1649]) ).
fof(f1649,plain,
( spl0_155
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f1597,plain,
( spl0_154
| ~ spl0_42
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f754,f742,f697,f1595]) ).
fof(f1595,plain,
( spl0_154
<=> ! [X2,X0,X1] : c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f697,plain,
( spl0_42
<=> ! [X0,X3] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f754,plain,
( ! [X2,X0,X1] : c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)
| ~ spl0_42
| ~ spl0_53 ),
inference(resolution,[],[f743,f698]) ).
fof(f698,plain,
( ! [X3,X0] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f1379,plain,
( spl0_153
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f943,f883,f1377]) ).
fof(f1377,plain,
( spl0_153
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f883,plain,
( spl0_85
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| c_lessequals(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f943,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_85 ),
inference(factoring,[],[f884]) ).
fof(f884,plain,
( ! [X3,X0,X1] :
( c_lessequals(X3,X1,X0)
| c_lessequals(X1,X3,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f1338,plain,
spl0_152,
inference(avatar_split_clause,[],[f468,f1336]) ).
fof(f1336,plain,
( spl0_152
<=> ! [X6,X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X6,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f468,axiom,
! [X0,X6,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X6,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
fof(f1334,plain,
spl0_151,
inference(avatar_split_clause,[],[f459,f1332]) ).
fof(f459,axiom,
! [X3,X0,X8,X9] :
( c_in(X3,X9,X0)
| ~ c_lessequals(c_Set_Oinsert(X3,X8,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f1330,plain,
spl0_150,
inference(avatar_split_clause,[],[f447,f1328]) ).
fof(f1328,plain,
( spl0_150
<=> ! [X13,X0,X14] :
( X13 = X14
| ~ c_in(X14,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f447,axiom,
! [X0,X14,X13] :
( X13 = X14
| ~ c_in(X14,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f1326,plain,
spl0_149,
inference(avatar_split_clause,[],[f426,f1324]) ).
fof(f1324,plain,
( spl0_149
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X0)
| X1 = X3
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f426,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X3
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X3,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f1322,plain,
spl0_148,
inference(avatar_split_clause,[],[f369,f1320]) ).
fof(f1320,plain,
( spl0_148
<=> ! [X17,X0,X9,X8] :
( ~ c_in(X17,X9,X0)
| ~ c_in(X17,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f369,axiom,
! [X0,X8,X9,X17] :
( ~ c_in(X17,X9,X0)
| ~ c_in(X17,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f1318,plain,
spl0_147,
inference(avatar_split_clause,[],[f368,f1316]) ).
fof(f1316,plain,
( spl0_147
<=> ! [X17,X0,X9,X8] :
( c_in(X17,X8,X0)
| ~ c_in(X17,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f368,axiom,
! [X0,X8,X9,X17] :
( c_in(X17,X8,X0)
| ~ c_in(X17,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f1314,plain,
spl0_146,
inference(avatar_split_clause,[],[f352,f1312]) ).
fof(f1312,plain,
( spl0_146
<=> ! [X0,X13,X6,X8,X7] :
( c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_Fun_Oinj__on(X6,c_Set_Oinsert(X13,X8,X0),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f352,axiom,
! [X0,X8,X6,X7,X13] :
( c_Fun_Oinj__on(X6,X8,X0,X7)
| ~ c_Fun_Oinj__on(X6,c_Set_Oinsert(X13,X8,X0),X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
fof(f1310,plain,
spl0_145,
inference(avatar_split_clause,[],[f340,f1308]) ).
fof(f1308,plain,
( spl0_145
<=> ! [X13,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f340,axiom,
! [X0,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
fof(f1306,plain,
spl0_144,
inference(avatar_split_clause,[],[f337,f1304]) ).
fof(f1304,plain,
( spl0_144
<=> ! [X13,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f337,axiom,
! [X0,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
fof(f1302,plain,
spl0_143,
inference(avatar_split_clause,[],[f268,f1300]) ).
fof(f268,axiom,
! [X0,X8,X9] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f1298,plain,
spl0_142,
inference(avatar_split_clause,[],[f267,f1296]) ).
fof(f267,axiom,
! [X0,X8,X9] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X9),X9,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f1294,plain,
spl0_141,
inference(avatar_split_clause,[],[f250,f1292]) ).
fof(f1292,plain,
( spl0_141
<=> ! [X6,X0,X3,X2,X7] :
( X2 = X3
| ~ c_Finite__Set_Ofold__graph(X6,X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f250,axiom,
! [X2,X3,X0,X6,X7] :
( X2 = X3
| ~ c_Finite__Set_Ofold__graph(X6,X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
fof(f1290,plain,
spl0_140,
inference(avatar_split_clause,[],[f247,f1288]) ).
fof(f1288,plain,
( spl0_140
<=> ! [X6,X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X6,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f247,axiom,
! [X0,X6,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X6,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
fof(f1286,plain,
spl0_139,
inference(avatar_split_clause,[],[f244,f1284]) ).
fof(f1284,plain,
( spl0_139
<=> ! [X0,X11,X23] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X11),X23),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f244,axiom,
! [X0,X11,X23] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X11),X23),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
fof(f1282,plain,
spl0_138,
inference(avatar_split_clause,[],[f243,f1280]) ).
fof(f1280,plain,
( spl0_138
<=> ! [X0,X11,X23] :
( ~ c_Finite__Set_Ofinite(X23,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X11),X23),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f243,axiom,
! [X0,X11,X23] :
( ~ c_Finite__Set_Ofinite(X23,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X11),X23),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
fof(f1278,plain,
spl0_137,
inference(avatar_split_clause,[],[f196,f1276]) ).
fof(f1276,plain,
( spl0_137
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X2,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f196,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X2,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
fof(f1274,plain,
spl0_136,
inference(avatar_split_clause,[],[f194,f1272]) ).
fof(f1272,plain,
( spl0_136
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f194,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
fof(f1270,plain,
spl0_135,
inference(avatar_split_clause,[],[f193,f1268]) ).
fof(f1268,plain,
( spl0_135
<=> ! [X13,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f193,axiom,
! [X3,X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
fof(f1266,plain,
spl0_134,
inference(avatar_split_clause,[],[f191,f1264]) ).
fof(f1264,plain,
( spl0_134
<=> ! [X13,X0,X3,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X3,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X13,X14,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f191,axiom,
! [X3,X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X3,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X13,X14,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
fof(f1262,plain,
spl0_133,
inference(avatar_split_clause,[],[f152,f1260]) ).
fof(f1260,plain,
( spl0_133
<=> ! [X0,X6,X3,X7] : c_in(hAPP(X6,X3),c_Set_Oimage(X6,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool)),X7,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f152,axiom,
! [X3,X0,X6,X7] : c_in(hAPP(X6,X3),c_Set_Oimage(X6,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool)),X7,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
fof(f1258,plain,
spl0_132,
inference(avatar_split_clause,[],[f105,f1256]) ).
fof(f1256,plain,
( spl0_132
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f105,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
fof(f1254,plain,
spl0_131,
inference(avatar_split_clause,[],[f95,f1252]) ).
fof(f1252,plain,
( spl0_131
<=> ! [X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f95,axiom,
! [X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
fof(f1250,plain,
spl0_130,
inference(avatar_split_clause,[],[f94,f1248]) ).
fof(f1248,plain,
( spl0_130
<=> ! [X9,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X9) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f94,axiom,
! [X0,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X9) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
fof(f1246,plain,
spl0_129,
inference(avatar_split_clause,[],[f70,f1244]) ).
fof(f1244,plain,
( spl0_129
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X0)
| X1 = X3
| ~ c_lessequals(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f70,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X3
| ~ c_lessequals(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
fof(f1242,plain,
( ~ spl0_127
| spl0_128
| spl0_21
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f921,f863,f612,f1239,f1235]) ).
fof(f1235,plain,
( spl0_127
<=> class_Orderings_Olinorder(tc_fun(t_a,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1239,plain,
( spl0_128
<=> c_HOL_Oord__class_Oless(v_G,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f863,plain,
( spl0_80
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_lessequals(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f921,plain,
( c_HOL_Oord__class_Oless(v_G,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool))
| ~ class_Orderings_Olinorder(tc_fun(t_a,tc_bool))
| spl0_21
| ~ spl0_80 ),
inference(resolution,[],[f864,f614]) ).
fof(f864,plain,
( ! [X3,X0,X1] :
( c_lessequals(X3,X1,X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f863]) ).
fof(f1233,plain,
spl0_126,
inference(avatar_split_clause,[],[f66,f1231]) ).
fof(f1231,plain,
( spl0_126
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X3
| ~ c_lessequals(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f66,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X3
| ~ c_lessequals(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f1229,plain,
spl0_125,
inference(avatar_split_clause,[],[f52,f1227]) ).
fof(f1227,plain,
( spl0_125
<=> ! [X3,X7,X0,X6,X1] :
( hAPP(X6,X3) = X1
| c_Fun_Ofun__upd(X6,X3,X1,X0,X7) != X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f52,axiom,
! [X3,X0,X1,X6,X7] :
( hAPP(X6,X3) = X1
| c_Fun_Ofun__upd(X6,X3,X1,X0,X7) != X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
fof(f1225,plain,
spl0_124,
inference(avatar_split_clause,[],[f47,f1223]) ).
fof(f1223,plain,
( spl0_124
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f47,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
fof(f1221,plain,
spl0_123,
inference(avatar_split_clause,[],[f25,f1219]) ).
fof(f1219,plain,
( spl0_123
<=> ! [X2,X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f25,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
fof(f1217,plain,
spl0_122,
inference(avatar_split_clause,[],[f24,f1215]) ).
fof(f1215,plain,
( spl0_122
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
fof(f1213,plain,
spl0_121,
inference(avatar_split_clause,[],[f23,f1211]) ).
fof(f1211,plain,
( spl0_121
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
fof(f1209,plain,
spl0_120,
inference(avatar_split_clause,[],[f22,f1207]) ).
fof(f1207,plain,
( spl0_120
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
fof(f1205,plain,
spl0_119,
inference(avatar_split_clause,[],[f19,f1203]) ).
fof(f1203,plain,
( spl0_119
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),c_Orderings_Oord__class_Omax(X3,X1,X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f19,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),c_Orderings_Oord__class_Omax(X3,X1,X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
fof(f1201,plain,
spl0_118,
inference(avatar_split_clause,[],[f4,f1199]) ).
fof(f1199,plain,
( spl0_118
<=> ! [X6,X0,X7] : c_Set_Ovimage(X6,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool)),X0,X7) = c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f4,axiom,
! [X0,X6,X7] : c_Set_Ovimage(X6,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_bool)),X0,X7) = c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
fof(f1103,plain,
( spl0_117
| ~ spl0_66
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1057,f1028,f800,f1101]) ).
fof(f1101,plain,
( spl0_117
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != v_U ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1057,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != v_U
| ~ spl0_66
| ~ spl0_105 ),
inference(superposition,[],[f801,f1029]) ).
fof(f1099,plain,
spl0_116,
inference(avatar_split_clause,[],[f438,f1097]) ).
fof(f1097,plain,
( spl0_116
<=> ! [X0,X8,X3] : c_Set_Oinsert(X3,X8,X0) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X8,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f438,axiom,
! [X3,X0,X8] : c_Set_Oinsert(X3,X8,X0) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X8,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f1095,plain,
spl0_115,
inference(avatar_split_clause,[],[f398,f1093]) ).
fof(f1093,plain,
( spl0_115
<=> ! [X9,X0,X8] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(X8,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f398,axiom,
! [X0,X8,X9] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(X8,X0)
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
fof(f1091,plain,
spl0_114,
inference(avatar_split_clause,[],[f269,f1089]) ).
fof(f1089,plain,
( spl0_114
<=> ! [X9,X0,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f269,axiom,
! [X0,X8,X9] :
( ~ c_HOL_Oord__class_Oless(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
fof(f1087,plain,
spl0_113,
inference(avatar_split_clause,[],[f246,f1085]) ).
fof(f1085,plain,
( spl0_113
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Obot__class_Obot(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f246,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Obot__class_Obot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f1083,plain,
spl0_112,
inference(avatar_split_clause,[],[f245,f1081]) ).
fof(f1081,plain,
( spl0_112
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f245,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f1079,plain,
spl0_111,
inference(avatar_split_clause,[],[f220,f1077]) ).
fof(f1077,plain,
( spl0_111
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X3,X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f220,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X3,X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f1075,plain,
spl0_110,
inference(avatar_split_clause,[],[f219,f1073]) ).
fof(f1073,plain,
( spl0_110
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f219,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f1071,plain,
spl0_109,
inference(avatar_split_clause,[],[f218,f1069]) ).
fof(f1069,plain,
( spl0_109
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X1,X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f218,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X1,X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f1067,plain,
spl0_108,
inference(avatar_split_clause,[],[f30,f1065]) ).
fof(f1065,plain,
( spl0_108
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X3
| c_SetInterval_Oord__class_OlessThan(X3,X0) != c_SetInterval_Oord__class_OlessThan(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f30,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X3
| c_SetInterval_Oord__class_OlessThan(X3,X0) != c_SetInterval_Oord__class_OlessThan(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).
fof(f1063,plain,
spl0_107,
inference(avatar_split_clause,[],[f3,f1061]) ).
fof(f1061,plain,
( spl0_107
<=> ! [X5,X4,X0] :
( ~ class_HOL_Oord(X0)
| c_HOL_Oord__class_Oless(X4,X5,X0)
| ~ c_in(X4,c_SetInterval_Oord__class_OlessThan(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f3,axiom,
! [X0,X4,X5] :
( ~ class_HOL_Oord(X0)
| c_HOL_Oord__class_Oless(X4,X5,X0)
| ~ c_in(X4,c_SetInterval_Oord__class_OlessThan(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__iff_0) ).
fof(f1052,plain,
spl0_106,
inference(avatar_split_clause,[],[f2,f1050]) ).
fof(f1050,plain,
( spl0_106
<=> ! [X5,X4,X0] :
( ~ class_HOL_Oord(X0)
| ~ c_HOL_Oord__class_Oless(X4,X5,X0)
| c_in(X4,c_SetInterval_Oord__class_OlessThan(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2,axiom,
! [X0,X4,X5] :
( ~ class_HOL_Oord(X0)
| ~ c_HOL_Oord__class_Oless(X4,X5,X0)
| c_in(X4,c_SetInterval_Oord__class_OlessThan(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__iff_1) ).
fof(f1030,plain,
( spl0_105
| ~ spl0_68
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f947,f891,f814,f1028]) ).
fof(f947,plain,
( ! [X0] : v_U = c_Set_Oinsert(v_pn,v_U,X0)
| ~ spl0_68
| ~ spl0_87 ),
inference(resolution,[],[f892,f815]) ).
fof(f1012,plain,
spl0_104,
inference(avatar_split_clause,[],[f460,f1010]) ).
fof(f1010,plain,
( spl0_104
<=> ! [X0,X1,X8,X3] :
( ~ hBOOL(hAPP(X8,X3))
| hBOOL(hAPP(c_Set_Oinsert(X1,X8,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f460,axiom,
! [X3,X0,X1,X8] :
( ~ hBOOL(hAPP(X8,X3))
| hBOOL(hAPP(c_Set_Oinsert(X1,X8,X0),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f1008,plain,
spl0_103,
inference(avatar_split_clause,[],[f394,f1006]) ).
fof(f1006,plain,
( spl0_103
<=> ! [X13,X0,X14,X8] :
( ~ c_in(X13,X8,X0)
| c_in(X13,c_Set_Oinsert(X14,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f394,axiom,
! [X0,X8,X14,X13] :
( ~ c_in(X13,X8,X0)
| c_in(X13,c_Set_Oinsert(X14,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
fof(f1004,plain,
spl0_102,
inference(avatar_split_clause,[],[f357,f1002]) ).
fof(f1002,plain,
( spl0_102
<=> ! [X9,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f357,axiom,
! [X0,X8,X9] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
fof(f1000,plain,
spl0_101,
inference(avatar_split_clause,[],[f355,f998]) ).
fof(f998,plain,
( spl0_101
<=> ! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X8,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f355,axiom,
! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X8,X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f996,plain,
spl0_100,
inference(avatar_split_clause,[],[f354,f994]) ).
fof(f994,plain,
( spl0_100
<=> ! [X0,X8] : c_HOL_Ominus__class_Ominus(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f354,axiom,
! [X0,X8] : c_HOL_Ominus__class_Ominus(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f992,plain,
spl0_99,
inference(avatar_split_clause,[],[f348,f990]) ).
fof(f348,axiom,
! [X0,X8,X9] : c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f988,plain,
spl0_98,
inference(avatar_split_clause,[],[f214,f986]) ).
fof(f986,plain,
( spl0_98
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f214,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f984,plain,
spl0_97,
inference(avatar_split_clause,[],[f213,f982]) ).
fof(f982,plain,
( spl0_97
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f213,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X1),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f980,plain,
spl0_96,
inference(avatar_split_clause,[],[f186,f978]) ).
fof(f978,plain,
( spl0_96
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f186,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f976,plain,
spl0_95,
inference(avatar_split_clause,[],[f185,f974]) ).
fof(f974,plain,
( spl0_95
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f185,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f972,plain,
spl0_94,
inference(avatar_split_clause,[],[f181,f970]) ).
fof(f970,plain,
( spl0_94
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f181,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f968,plain,
spl0_93,
inference(avatar_split_clause,[],[f180,f966]) ).
fof(f966,plain,
( spl0_93
<=> ! [X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f180,axiom,
! [X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f964,plain,
spl0_92,
inference(avatar_split_clause,[],[f93,f962]) ).
fof(f962,plain,
( spl0_92
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f93,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
fof(f960,plain,
spl0_91,
inference(avatar_split_clause,[],[f92,f958]) ).
fof(f958,plain,
( spl0_91
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Otop__class_Otop(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f92,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Otop__class_Otop(X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
fof(f956,plain,
( ~ spl0_1
| spl0_90
| ~ spl0_3
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f946,f887,f522,f953,f512]) ).
fof(f953,plain,
( spl0_90
<=> c_Finite__Set_Ofinite(v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f887,plain,
( spl0_86
<=> ! [X0,X11,X7,X10] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Set_Oimage(X10,X11,X0,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f946,plain,
( c_Finite__Set_Ofinite(v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| ~ spl0_3
| ~ spl0_86 ),
inference(superposition,[],[f888,f524]) ).
fof(f888,plain,
( ! [X10,X0,X11,X7] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X10,X11,X0,X7),X7)
| ~ c_Finite__Set_Ofinite(X11,X0) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f951,plain,
spl0_89,
inference(avatar_split_clause,[],[f43,f949]) ).
fof(f949,plain,
( spl0_89
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) = c_Orderings_Oord__class_Omax(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f43,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X1,X0) = c_Orderings_Oord__class_Omax(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f897,plain,
( spl0_88
| ~ spl0_6
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f753,f730,f537,f895]) ).
fof(f895,plain,
( spl0_88
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f537,plain,
( spl0_6
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f730,plain,
( spl0_50
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f753,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0
| ~ spl0_6
| ~ spl0_50 ),
inference(resolution,[],[f731,f539]) ).
fof(f539,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f731,plain,
( ! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X3,X0) = X3 )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f893,plain,
spl0_87,
inference(avatar_split_clause,[],[f467,f891]) ).
fof(f467,axiom,
! [X0,X8,X13] :
( ~ c_in(X13,X8,X0)
| c_Set_Oinsert(X13,X8,X0) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f889,plain,
spl0_86,
inference(avatar_split_clause,[],[f425,f887]) ).
fof(f425,axiom,
! [X10,X0,X11,X7] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Set_Oimage(X10,X11,X0,X7),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
fof(f885,plain,
spl0_85,
inference(avatar_split_clause,[],[f387,f883]) ).
fof(f387,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| c_lessequals(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f881,plain,
spl0_84,
inference(avatar_split_clause,[],[f254,f879]) ).
fof(f879,plain,
( spl0_84
<=> ! [X6,X2,X0,X7] : c_Nitpick_Ofold__graph_H(X6,X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X2,X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f254,axiom,
! [X2,X0,X6,X7] : c_Nitpick_Ofold__graph_H(X6,X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X2,X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
fof(f877,plain,
spl0_83,
inference(avatar_split_clause,[],[f253,f875]) ).
fof(f875,plain,
( spl0_83
<=> ! [X6,X2,X0,X7] : c_Finite__Set_Ofold__graph(X6,X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X2,X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f253,axiom,
! [X2,X0,X6,X7] : c_Finite__Set_Ofold__graph(X6,X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X2,X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
fof(f873,plain,
spl0_82,
inference(avatar_split_clause,[],[f242,f871]) ).
fof(f871,plain,
( spl0_82
<=> ! [X2,X6,X0,X3,X8,X7] :
( c_Finite__Set_Ofinite(X8,X0)
| ~ c_Finite__Set_Ofold__graph(X6,X2,X8,X3,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f242,axiom,
! [X2,X3,X0,X8,X6,X7] :
( c_Finite__Set_Ofinite(X8,X0)
| ~ c_Finite__Set_Ofold__graph(X6,X2,X8,X3,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
fof(f869,plain,
spl0_81,
inference(avatar_split_clause,[],[f231,f867]) ).
fof(f867,plain,
( spl0_81
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_lessequals(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f231,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_lessequals(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f865,plain,
spl0_80,
inference(avatar_split_clause,[],[f230,f863]) ).
fof(f230,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_lessequals(X3,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
fof(f861,plain,
spl0_79,
inference(avatar_split_clause,[],[f229,f859]) ).
fof(f859,plain,
( spl0_79
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f229,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(X3,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f857,plain,
spl0_78,
inference(avatar_split_clause,[],[f188,f855]) ).
fof(f855,plain,
( spl0_78
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| c_lessequals(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f188,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| c_lessequals(X3,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f852,plain,
spl0_77,
inference(avatar_split_clause,[],[f187,f850]) ).
fof(f850,plain,
( spl0_77
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| c_lessequals(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f187,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| c_lessequals(X3,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f848,plain,
spl0_76,
inference(avatar_split_clause,[],[f139,f846]) ).
fof(f846,plain,
( spl0_76
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f139,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f844,plain,
spl0_75,
inference(avatar_split_clause,[],[f137,f842]) ).
fof(f842,plain,
( spl0_75
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f137,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f840,plain,
spl0_74,
inference(avatar_split_clause,[],[f136,f838]) ).
fof(f838,plain,
( spl0_74
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f136,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f836,plain,
spl0_73,
inference(avatar_split_clause,[],[f121,f834]) ).
fof(f834,plain,
( spl0_73
<=> ! [X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X8) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f121,axiom,
! [X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f832,plain,
spl0_72,
inference(avatar_split_clause,[],[f120,f830]) ).
fof(f830,plain,
( spl0_72
<=> ! [X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f120,axiom,
! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f828,plain,
spl0_71,
inference(avatar_split_clause,[],[f114,f826]) ).
fof(f826,plain,
( spl0_71
<=> ! [X0,X6,X3,X7] : c_Fun_Ofun__upd(X6,X3,hAPP(X6,X3),X0,X7) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f114,axiom,
! [X3,X0,X6,X7] : c_Fun_Ofun__upd(X6,X3,hAPP(X6,X3),X0,X7) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
fof(f824,plain,
spl0_70,
inference(avatar_split_clause,[],[f113,f822]) ).
fof(f822,plain,
( spl0_70
<=> ! [X6,X0,X3,X1,X7] : hAPP(c_Fun_Ofun__upd(X6,X3,X1,X7,X0),X3) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f113,axiom,
! [X3,X0,X1,X6,X7] : hAPP(c_Fun_Ofun__upd(X6,X3,X1,X7,X0),X3) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
fof(f820,plain,
spl0_69,
inference(avatar_split_clause,[],[f102,f818]) ).
fof(f818,plain,
( spl0_69
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f102,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f816,plain,
( spl0_68
| ~ spl0_53
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f807,f763,f742,f814]) ).
fof(f763,plain,
( spl0_57
<=> hBOOL(hAPP(v_U,v_pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f807,plain,
( ! [X0] : c_in(v_pn,v_U,X0)
| ~ spl0_53
| ~ spl0_57 ),
inference(resolution,[],[f765,f743]) ).
fof(f765,plain,
( hBOOL(hAPP(v_U,v_pn))
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f806,plain,
spl0_67,
inference(avatar_split_clause,[],[f441,f804]) ).
fof(f441,axiom,
! [X0,X8] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f802,plain,
spl0_66,
inference(avatar_split_clause,[],[f439,f800]) ).
fof(f439,axiom,
! [X0,X8,X13] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X13,X8,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
fof(f798,plain,
spl0_65,
inference(avatar_split_clause,[],[f436,f796]) ).
fof(f436,axiom,
! [X0,X9,X13] : c_lessequals(X9,c_Set_Oinsert(X13,X9,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f794,plain,
spl0_64,
inference(avatar_split_clause,[],[f435,f792]) ).
fof(f792,plain,
( spl0_64
<=> ! [X13,X0,X8] :
( c_Finite__Set_Ofinite(X8,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X13,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f435,axiom,
! [X0,X8,X13] :
( c_Finite__Set_Ofinite(X8,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X13,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
fof(f790,plain,
spl0_63,
inference(avatar_split_clause,[],[f434,f788]) ).
fof(f788,plain,
( spl0_63
<=> ! [X13,X0,X8] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X13,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f434,axiom,
! [X0,X8,X13] :
( ~ c_Finite__Set_Ofinite(X8,X0)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X13,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
fof(f786,plain,
spl0_62,
inference(avatar_split_clause,[],[f264,f784]) ).
fof(f784,plain,
( spl0_62
<=> ! [X0,X8] : c_lessequals(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f264,axiom,
! [X0,X8] : c_lessequals(X8,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
fof(f782,plain,
spl0_61,
inference(avatar_split_clause,[],[f249,f780]) ).
fof(f780,plain,
( spl0_61
<=> ! [X0,X8] : ~ c_HOL_Oord__class_Oless(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f249,axiom,
! [X0,X8] : ~ c_HOL_Oord__class_Oless(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
fof(f778,plain,
spl0_60,
inference(avatar_split_clause,[],[f248,f776]) ).
fof(f776,plain,
( spl0_60
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f248,axiom,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
fof(f774,plain,
spl0_59,
inference(avatar_split_clause,[],[f209,f772]) ).
fof(f209,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f770,plain,
spl0_58,
inference(avatar_split_clause,[],[f208,f768]) ).
fof(f208,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f766,plain,
( spl0_57
| ~ spl0_2
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f757,f746,f517,f763]) ).
fof(f517,plain,
( spl0_2
<=> c_in(v_pn,v_U,tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f757,plain,
( hBOOL(hAPP(v_U,v_pn))
| ~ spl0_2
| ~ spl0_54 ),
inference(resolution,[],[f747,f519]) ).
fof(f519,plain,
( c_in(v_pn,v_U,tc_Com_Opname)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f761,plain,
spl0_56,
inference(avatar_split_clause,[],[f15,f759]) ).
fof(f759,plain,
( spl0_56
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Oord__class_Omin(X0) = c_Lattices_Olower__semilattice__class_Oinf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f15,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Oord__class_Omin(X0) = c_Lattices_Olower__semilattice__class_Oinf(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__min_0) ).
fof(f752,plain,
spl0_55,
inference(avatar_split_clause,[],[f482,f750]) ).
fof(f750,plain,
( spl0_55
<=> ! [X32,X33] :
( ~ class_Finite__Set_Ofinite_Ofinite(X32)
| ~ class_Finite__Set_Ofinite_Ofinite(X33)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f482,axiom,
! [X32,X33] :
( ~ class_Finite__Set_Ofinite_Ofinite(X32)
| ~ class_Finite__Set_Ofinite_Ofinite(X33)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f748,plain,
spl0_54,
inference(avatar_split_clause,[],[f453,f746]) ).
fof(f453,axiom,
! [X3,X0,X26] :
( ~ c_in(X3,X26,X0)
| hBOOL(hAPP(X26,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f744,plain,
spl0_53,
inference(avatar_split_clause,[],[f452,f742]) ).
fof(f452,axiom,
! [X3,X0,X26] :
( ~ hBOOL(hAPP(X26,X3))
| c_in(X3,X26,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f740,plain,
spl0_52,
inference(avatar_split_clause,[],[f373,f738]) ).
fof(f738,plain,
( spl0_52
<=> ! [X28,X0,X25,X7] : hAPP(c_COMBK(X25,X0,X7),X28) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f373,axiom,
! [X28,X0,X7,X25] : hAPP(c_COMBK(X25,X0,X7),X28) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f736,plain,
spl0_51,
inference(avatar_split_clause,[],[f353,f734]) ).
fof(f734,plain,
( spl0_51
<=> ! [X6,X0,X7] : c_Fun_Oinj__on(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f353,axiom,
! [X0,X6,X7] : c_Fun_Oinj__on(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
fof(f732,plain,
spl0_50,
inference(avatar_split_clause,[],[f109,f730]) ).
fof(f109,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f727,plain,
spl0_49,
inference(avatar_split_clause,[],[f507,f725]) ).
fof(f725,plain,
( spl0_49
<=> ! [X34,X16,X0] :
( X16 = X34
| ~ c_fequal(X16,X34,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f507,axiom,
! [X0,X16,X34] :
( X16 = X34
| ~ c_fequal(X16,X34,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f723,plain,
spl0_48,
inference(avatar_split_clause,[],[f450,f721]) ).
fof(f721,plain,
( spl0_48
<=> ! [X9,X0,X3] : c_in(X3,c_Set_Oinsert(X3,X9,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f450,axiom,
! [X3,X0,X9] : c_in(X3,c_Set_Oinsert(X3,X9,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f719,plain,
spl0_47,
inference(avatar_split_clause,[],[f440,f717]) ).
fof(f717,plain,
( spl0_47
<=> ! [X0,X3] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f440,axiom,
! [X3,X0] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f715,plain,
spl0_46,
inference(avatar_split_clause,[],[f432,f713]) ).
fof(f713,plain,
( spl0_46
<=> ! [X0,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f432,axiom,
! [X3,X0] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f711,plain,
spl0_45,
inference(avatar_split_clause,[],[f414,f709]) ).
fof(f709,plain,
( spl0_45
<=> ! [X0,X3] : ~ c_in(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f414,axiom,
! [X3,X0] : ~ c_in(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
fof(f707,plain,
spl0_44,
inference(avatar_split_clause,[],[f412,f705]) ).
fof(f412,axiom,
! [X3,X0,X8] : hBOOL(hAPP(c_Set_Oinsert(X3,X8,X0),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f703,plain,
spl0_43,
inference(avatar_split_clause,[],[f179,f701]) ).
fof(f701,plain,
( spl0_43
<=> ! [X0,X3] :
( ~ class_Orderings_Otop(X0)
| c_lessequals(X3,c_Orderings_Otop__class_Otop(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f179,axiom,
! [X3,X0] :
( ~ class_Orderings_Otop(X0)
| c_lessequals(X3,c_Orderings_Otop__class_Otop(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
fof(f699,plain,
spl0_42,
inference(avatar_split_clause,[],[f103,f697]) ).
fof(f103,axiom,
! [X3,X0] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
fof(f695,plain,
spl0_41,
inference(avatar_split_clause,[],[f57,f693]) ).
fof(f693,plain,
( spl0_41
<=> ! [X0,X3] : c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f57,axiom,
! [X3,X0] : c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f691,plain,
spl0_40,
inference(avatar_split_clause,[],[f488,f689]) ).
fof(f689,plain,
( spl0_40
<=> ! [X32,X33] :
( ~ class_HOL_Oord(X33)
| class_HOL_Oord(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f488,axiom,
! [X32,X33] :
( ~ class_HOL_Oord(X33)
| class_HOL_Oord(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f687,plain,
spl0_39,
inference(avatar_split_clause,[],[f487,f685]) ).
fof(f685,plain,
( spl0_39
<=> ! [X32,X33] :
( ~ class_Orderings_Obot(X33)
| class_Orderings_Obot(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f487,axiom,
! [X32,X33] :
( ~ class_Orderings_Obot(X33)
| class_Orderings_Obot(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f683,plain,
spl0_38,
inference(avatar_split_clause,[],[f486,f681]) ).
fof(f681,plain,
( spl0_38
<=> ! [X32,X33] :
( ~ class_Orderings_Otop(X33)
| class_Orderings_Otop(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f486,axiom,
! [X32,X33] :
( ~ class_Orderings_Otop(X33)
| class_Orderings_Otop(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
fof(f679,plain,
spl0_37,
inference(avatar_split_clause,[],[f485,f677]) ).
fof(f677,plain,
( spl0_37
<=> ! [X32,X33] :
( ~ class_Orderings_Oorder(X33)
| class_Orderings_Oorder(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f485,axiom,
! [X32,X33] :
( ~ class_Orderings_Oorder(X33)
| class_Orderings_Oorder(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f675,plain,
spl0_36,
inference(avatar_split_clause,[],[f484,f673]) ).
fof(f673,plain,
( spl0_36
<=> ! [X32,X33] :
( ~ class_Lattices_Olattice(X33)
| class_Lattices_Olattice(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f484,axiom,
! [X32,X33] :
( ~ class_Lattices_Olattice(X33)
| class_Lattices_Olattice(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f671,plain,
spl0_35,
inference(avatar_split_clause,[],[f483,f669]) ).
fof(f669,plain,
( spl0_35
<=> ! [X32,X33] :
( ~ class_Orderings_Opreorder(X33)
| class_Orderings_Opreorder(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f483,axiom,
! [X32,X33] :
( ~ class_Orderings_Opreorder(X33)
| class_Orderings_Opreorder(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f667,plain,
spl0_34,
inference(avatar_split_clause,[],[f481,f665]) ).
fof(f665,plain,
( spl0_34
<=> ! [X32,X33] :
( ~ class_Lattices_Obounded__lattice(X33)
| class_Lattices_Obounded__lattice(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f481,axiom,
! [X32,X33] :
( ~ class_Lattices_Obounded__lattice(X33)
| class_Lattices_Obounded__lattice(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f663,plain,
spl0_33,
inference(avatar_split_clause,[],[f480,f661]) ).
fof(f661,plain,
( spl0_33
<=> ! [X32,X33] :
( ~ class_Lattices_Olattice(X33)
| class_Lattices_Olower__semilattice(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f480,axiom,
! [X32,X33] :
( ~ class_Lattices_Olattice(X33)
| class_Lattices_Olower__semilattice(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f659,plain,
spl0_32,
inference(avatar_split_clause,[],[f479,f657]) ).
fof(f657,plain,
( spl0_32
<=> ! [X32,X33] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f479,axiom,
! [X32,X33] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X32,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f655,plain,
spl0_31,
inference(avatar_split_clause,[],[f433,f653]) ).
fof(f653,plain,
( spl0_31
<=> ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f433,axiom,
! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
fof(f651,plain,
spl0_30,
inference(avatar_split_clause,[],[f406,f649]) ).
fof(f649,plain,
( spl0_30
<=> ! [X0,X3] : c_lessequals(X3,X3,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f406,axiom,
! [X3,X0] : c_lessequals(X3,X3,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
fof(f647,plain,
spl0_29,
inference(avatar_split_clause,[],[f400,f645]) ).
fof(f645,plain,
( spl0_29
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f400,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f643,plain,
spl0_28,
inference(avatar_split_clause,[],[f399,f641]) ).
fof(f641,plain,
( spl0_28
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f399,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f639,plain,
spl0_27,
inference(avatar_split_clause,[],[f101,f637]) ).
fof(f637,plain,
( spl0_27
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f101,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f635,plain,
spl0_26,
inference(avatar_split_clause,[],[f100,f633]) ).
fof(f633,plain,
( spl0_26
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f100,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f631,plain,
spl0_25,
inference(avatar_split_clause,[],[f99,f629]) ).
fof(f629,plain,
( spl0_25
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f99,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f627,plain,
spl0_24,
inference(avatar_split_clause,[],[f98,f625]) ).
fof(f625,plain,
( spl0_24
<=> ! [X0,X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f98,axiom,
! [X3,X0] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
fof(f623,plain,
spl0_23,
inference(avatar_split_clause,[],[f469,f621]) ).
fof(f621,plain,
( spl0_23
<=> ! [X0,X8] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f469,axiom,
! [X0,X8] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
fof(f619,plain,
spl0_22,
inference(avatar_split_clause,[],[f506,f617]) ).
fof(f617,plain,
( spl0_22
<=> ! [X0,X3] : c_fequal(X3,X3,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f506,axiom,
! [X3,X0] : c_fequal(X3,X3,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f615,plain,
~ spl0_21,
inference(avatar_split_clause,[],[f508,f612]) ).
fof(f508,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),v_G,tc_fun(t_a,tc_bool)),
inference(forward_demodulation,[],[f478,f476]) ).
fof(f476,axiom,
v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f478,axiom,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f610,plain,
spl0_20,
inference(avatar_split_clause,[],[f505,f607]) ).
fof(f607,plain,
( spl0_20
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f505,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f605,plain,
spl0_19,
inference(avatar_split_clause,[],[f504,f602]) ).
fof(f602,plain,
( spl0_19
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f504,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f600,plain,
spl0_18,
inference(avatar_split_clause,[],[f503,f597]) ).
fof(f597,plain,
( spl0_18
<=> class_Orderings_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f503,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
fof(f595,plain,
spl0_17,
inference(avatar_split_clause,[],[f502,f592]) ).
fof(f592,plain,
( spl0_17
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f502,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f590,plain,
spl0_16,
inference(avatar_split_clause,[],[f501,f587]) ).
fof(f587,plain,
( spl0_16
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f501,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f585,plain,
spl0_15,
inference(avatar_split_clause,[],[f500,f582]) ).
fof(f582,plain,
( spl0_15
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f500,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f580,plain,
spl0_14,
inference(avatar_split_clause,[],[f499,f577]) ).
fof(f577,plain,
( spl0_14
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f499,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f575,plain,
spl0_13,
inference(avatar_split_clause,[],[f498,f572]) ).
fof(f572,plain,
( spl0_13
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f498,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f570,plain,
spl0_12,
inference(avatar_split_clause,[],[f497,f567]) ).
fof(f567,plain,
( spl0_12
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f497,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f565,plain,
spl0_11,
inference(avatar_split_clause,[],[f496,f562]) ).
fof(f562,plain,
( spl0_11
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f496,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(f560,plain,
spl0_10,
inference(avatar_split_clause,[],[f495,f557]) ).
fof(f557,plain,
( spl0_10
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f495,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
fof(f555,plain,
spl0_9,
inference(avatar_split_clause,[],[f494,f552]) ).
fof(f552,plain,
( spl0_9
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f494,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f550,plain,
spl0_8,
inference(avatar_split_clause,[],[f493,f547]) ).
fof(f547,plain,
( spl0_8
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f493,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f545,plain,
spl0_7,
inference(avatar_split_clause,[],[f492,f542]) ).
fof(f542,plain,
( spl0_7
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f492,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f540,plain,
spl0_6,
inference(avatar_split_clause,[],[f491,f537]) ).
fof(f491,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f535,plain,
spl0_5,
inference(avatar_split_clause,[],[f490,f532]) ).
fof(f532,plain,
( spl0_5
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f490,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f530,plain,
spl0_4,
inference(avatar_split_clause,[],[f489,f527]) ).
fof(f527,plain,
( spl0_4
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f489,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f525,plain,
spl0_3,
inference(avatar_split_clause,[],[f476,f522]) ).
fof(f520,plain,
spl0_2,
inference(avatar_split_clause,[],[f477,f517]) ).
fof(f477,axiom,
c_in(v_pn,v_U,tc_Com_Opname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f515,plain,
spl0_1,
inference(avatar_split_clause,[],[f475,f512]) ).
fof(f475,axiom,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV880-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 04:52:11 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (16871)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (16874)WARNING: value z3 for option sas not known
% 0.14/0.39 % (16873)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (16875)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (16872)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (16877)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39 % (16874)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39 % (16876)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.39 % (16878)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)
% 0.20/0.48 TRYING [1]
% 0.20/0.50 TRYING [2]
% 1.85/0.67 TRYING [3]
% 1.85/0.70 TRYING [1]
% 1.85/0.71 TRYING [2]
% 2.54/0.72 TRYING [1]
% 2.54/0.76 % (16876)First to succeed.
% 2.54/0.77 TRYING [2]
% 2.54/0.78 % (16876)Refutation found. Thanks to Tanya!
% 2.54/0.78 % SZS status Unsatisfiable for theBenchmark
% 2.54/0.78 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/0.79 % (16876)------------------------------
% 2.54/0.79 % (16876)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.54/0.79 % (16876)Termination reason: Refutation
% 2.54/0.79
% 2.54/0.79 % (16876)Memory used [KB]: 6654
% 2.54/0.79 % (16876)Time elapsed: 0.383 s
% 2.54/0.79 % (16876)Instructions burned: 903 (million)
% 2.54/0.79 % (16876)------------------------------
% 2.54/0.79 % (16876)------------------------------
% 2.54/0.79 % (16871)Success in time 0.42 s
%------------------------------------------------------------------------------