TSTP Solution File: SCT007-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT007-1 : 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 : n008.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 : Sun May 5 09:00:22 EDT 2024
% Result : Unsatisfiable 0.22s 0.53s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 778
% Syntax : Number of formulae : 1283 ( 502 unt; 0 def)
% Number of atoms : 2559 ( 407 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 2160 ( 884 ~; 871 |; 0 &)
% ( 405 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 432 ( 430 usr; 406 prp; 0-4 aty)
% Number of functors : 50 ( 50 usr; 7 con; 0-5 aty)
% Number of variables : 2147 (2147 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5089,plain,
$false,
inference(avatar_sat_refutation,[],[f676,f681,f686,f691,f696,f701,f706,f711,f716,f721,f726,f731,f736,f741,f746,f751,f755,f760,f764,f768,f772,f776,f780,f784,f788,f792,f796,f800,f804,f808,f812,f816,f820,f824,f828,f832,f836,f840,f844,f848,f852,f856,f860,f864,f868,f872,f876,f880,f884,f888,f892,f896,f904,f908,f912,f916,f920,f924,f928,f933,f937,f941,f945,f949,f953,f957,f961,f965,f969,f973,f981,f985,f989,f993,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1029,f1033,f1037,f1041,f1045,f1049,f1053,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1085,f1089,f1093,f1097,f1101,f1105,f1109,f1113,f1117,f1121,f1139,f1189,f1193,f1197,f1201,f1205,f1209,f1213,f1217,f1221,f1225,f1229,f1233,f1237,f1241,f1245,f1262,f1267,f1271,f1275,f1279,f1283,f1287,f1291,f1295,f1299,f1304,f1308,f1312,f1316,f1320,f1324,f1328,f1332,f1336,f1340,f1344,f1348,f1352,f1356,f1360,f1364,f1368,f1372,f1376,f1380,f1384,f1389,f1393,f1397,f1401,f1405,f1409,f1413,f1417,f1421,f1428,f1484,f1512,f1525,f1529,f1533,f1538,f1542,f1546,f1550,f1554,f1558,f1562,f1566,f1570,f1574,f1579,f1721,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1846,f1851,f1855,f1859,f1863,f1867,f1871,f1875,f1879,f1883,f1887,f1891,f1900,f1904,f2272,f2276,f2280,f2284,f2288,f2292,f2296,f2311,f2315,f2319,f2323,f2328,f2332,f2336,f2340,f2344,f2348,f2365,f2371,f2378,f2382,f2386,f2390,f2394,f2398,f2402,f2407,f2411,f2415,f2419,f2423,f2427,f2431,f2435,f2439,f2443,f2447,f2451,f2456,f2460,f2670,f2901,f2905,f2909,f2913,f2917,f2921,f2925,f2929,f2933,f2937,f2941,f2954,f2958,f2962,f2966,f2970,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3002,f3006,f3010,f3014,f3018,f3022,f3026,f3030,f3034,f3038,f3213,f3273,f3344,f3348,f3352,f3356,f3360,f3364,f3368,f3372,f3376,f3380,f3384,f3388,f3392,f3396,f3400,f3404,f3408,f3412,f3416,f3420,f3424,f3440,f3555,f3686,f3690,f3694,f3698,f3702,f3706,f3710,f3714,f3718,f3722,f3726,f3730,f3734,f3749,f3753,f3757,f3761,f3765,f3769,f3773,f3777,f3781,f3785,f3801,f3805,f3809,f3813,f3817,f3821,f3825,f3829,f3833,f4313,f4317,f4321,f4325,f4329,f4333,f4337,f4341,f4345,f4355,f4359,f4363,f4367,f4371,f4375,f4379,f4383,f4387,f4397,f4749,f4753,f4757,f4761,f4765,f4769,f4773,f4777,f4781,f4785,f4789,f4793,f4797,f4801,f4805,f4809,f4813,f4819,f4823,f4895,f5045,f5049,f5053,f5057,f5061,f5065,f5069,f5073,f5077,f5081,f5085,f5088]) ).
fof(f5088,plain,
( ~ spl0_1
| ~ spl0_395 ),
inference(avatar_contradiction_clause,[],[f5086]) ).
fof(f5086,plain,
( $false
| ~ spl0_1
| ~ spl0_395 ),
inference(resolution,[],[f5044,f675]) ).
fof(f675,plain,
( hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f673]) ).
fof(f673,plain,
( spl0_1
<=> hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f5044,plain,
( ! [X0] : ~ hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_395 ),
inference(avatar_component_clause,[],[f5043]) ).
fof(f5043,plain,
( spl0_395
<=> ! [X0] : ~ hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f5085,plain,
spl0_405,
inference(avatar_split_clause,[],[f377,f5083]) ).
fof(f5083,plain,
( spl0_405
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Odistrib__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X6,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X24,X6,X1),c_Lattices_Oupper__semilattice__class_Osup(X25,X6,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f377,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Odistrib__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X6,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X24,X6,X1),c_Lattices_Oupper__semilattice__class_Osup(X25,X6,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f5081,plain,
spl0_404,
inference(avatar_split_clause,[],[f342,f5079]) ).
fof(f5079,plain,
( spl0_404
<=> ! [X2,X0,X1] :
( ~ c_Relation_Orefl__on(X2,X0,X1)
| c_lessequals(X0,c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f342,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Orefl__on(X2,X0,X1)
| c_lessequals(X0,c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
fof(f5077,plain,
spl0_403,
inference(avatar_split_clause,[],[f271,f5075]) ).
fof(f5075,plain,
( spl0_403
<=> ! [X4,X9,X5,X2,X1] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_lessequals(c_Set_Ovimage(X9,X2,X4,X1),c_Set_Ovimage(X9,X5,X4,X1),tc_fun(X4,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f271,axiom,
! [X2,X1,X9,X4,X5] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_lessequals(c_Set_Ovimage(X9,X2,X4,X1),c_Set_Ovimage(X9,X5,X4,X1),tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
fof(f5073,plain,
spl0_402,
inference(avatar_split_clause,[],[f205,f5071]) ).
fof(f5071,plain,
( spl0_402
<=> ! [X2,X1,X8] :
( ~ hBOOL(c_Wellfounded_Owf(X8,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| ~ c_lessequals(X2,c_Relation_OImage(X8,X2,X1,X1),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f205,axiom,
! [X2,X1,X8] :
( ~ hBOOL(c_Wellfounded_Owf(X8,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| ~ c_lessequals(X2,c_Relation_OImage(X8,X2,X1,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
fof(f5069,plain,
spl0_401,
inference(avatar_split_clause,[],[f179,f5067]) ).
fof(f5067,plain,
( spl0_401
<=> ! [X7,X5,X2,X1] :
( hBOOL(c_in(X7,X5,X1))
| hBOOL(c_in(X7,X2,X1))
| ~ hBOOL(c_in(X7,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f179,axiom,
! [X2,X1,X7,X5] :
( hBOOL(c_in(X7,X5,X1))
| hBOOL(c_in(X7,X2,X1))
| ~ hBOOL(c_in(X7,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f5065,plain,
spl0_400,
inference(avatar_split_clause,[],[f89,f5063]) ).
fof(f5063,plain,
( spl0_400
<=> ! [X4,X7,X2,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = X2
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X7,tc_fun(X1,tc_bool),X4),X4,tc_fun(X1,tc_bool)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f89,axiom,
! [X2,X1,X7,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = X2
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X7,tc_fun(X1,tc_bool),X4),X4,tc_fun(X1,tc_bool)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_1) ).
fof(f5061,plain,
spl0_399,
inference(avatar_split_clause,[],[f87,f5059]) ).
fof(f5059,plain,
( spl0_399
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Odistrib__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X6,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X24,X6,X1),c_Lattices_Olower__semilattice__class_Oinf(X25,X6,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f87,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Odistrib__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X6,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X24,X6,X1),c_Lattices_Olower__semilattice__class_Oinf(X25,X6,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f5057,plain,
spl0_398,
inference(avatar_split_clause,[],[f86,f5055]) ).
fof(f5055,plain,
( spl0_398
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Odistrib__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),c_Lattices_Olower__semilattice__class_Oinf(X6,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f86,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Odistrib__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),c_Lattices_Olower__semilattice__class_Oinf(X6,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f5053,plain,
spl0_397,
inference(avatar_split_clause,[],[f22,f5051]) ).
fof(f5051,plain,
( spl0_397
<=> ! [X2,X5,X1] :
( c_lessequals(X5,X2,tc_fun(X1,tc_bool))
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f22,axiom,
! [X2,X1,X5] :
( c_lessequals(X5,X2,tc_fun(X1,tc_bool))
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
fof(f5049,plain,
spl0_396,
inference(avatar_split_clause,[],[f21,f5047]) ).
fof(f5047,plain,
( spl0_396
<=> ! [X2,X5,X1] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f21,axiom,
! [X2,X1,X5] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
fof(f5045,plain,
( spl0_395
| ~ spl0_17
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5002,f4807,f753,f5043]) ).
fof(f753,plain,
( spl0_17
<=> ! [X6] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f4807,plain,
( spl0_390
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f5002,plain,
( ! [X0] : ~ hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_17
| ~ spl0_390 ),
inference(resolution,[],[f4808,f754]) ).
fof(f754,plain,
( ! [X6] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X6))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f4808,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool))))
| ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1)) )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f4807]) ).
fof(f4895,plain,
( spl0_394
| ~ spl0_13
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1422,f1265,f733,f4892]) ).
fof(f4892,plain,
( spl0_394
<=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f733,plain,
( spl0_13
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1265,plain,
( spl0_124
<=> ! [X4] :
( ~ class_Orderings_Obot(X4)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X4)),v_x) = c_Orderings_Obot__class_Obot(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1422,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_13
| ~ spl0_124 ),
inference(resolution,[],[f1266,f735]) ).
fof(f735,plain,
( class_Orderings_Obot(tc_bool)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f1266,plain,
( ! [X4] :
( ~ class_Orderings_Obot(X4)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X4)),v_x) = c_Orderings_Obot__class_Obot(X4) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1265]) ).
fof(f4823,plain,
spl0_393,
inference(avatar_split_clause,[],[f671,f4821]) ).
fof(f4821,plain,
( spl0_393
<=> ! [X14,X6,X2,X1] :
( hBOOL(c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X2,X14,tc_fun(X1,tc_bool)),X1))
| ~ hBOOL(hAPP(X14,X6))
| ~ hBOOL(c_in(X6,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f671,plain,
! [X2,X1,X6,X14] :
( hBOOL(c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X2,X14,tc_fun(X1,tc_bool)),X1))
| ~ hBOOL(hAPP(X14,X6))
| ~ hBOOL(c_in(X6,X2,X1)) ),
inference(forward_demodulation,[],[f438,f29]) ).
fof(f29,axiom,
! [X1,X14] : c_Collect(X14,X1) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f438,axiom,
! [X2,X1,X6,X14] :
( ~ hBOOL(hAPP(X14,X6))
| ~ hBOOL(c_in(X6,X2,X1))
| hBOOL(c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X2,c_Collect(X14,X1),tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
fof(f4819,plain,
spl0_392,
inference(avatar_split_clause,[],[f615,f4817]) ).
fof(f4817,plain,
( spl0_392
<=> ! [X1,X8] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f615,plain,
! [X1,X8] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1),
inference(definition_unfolding,[],[f244,f76]) ).
fof(f76,axiom,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
fof(f244,axiom,
! [X1,X8] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X8,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__rtrancl_0) ).
fof(f4813,plain,
spl0_391,
inference(avatar_split_clause,[],[f607,f4811]) ).
fof(f4811,plain,
( spl0_391
<=> ! [X1] : c_Relation_OId(X1) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f607,plain,
! [X1] : c_Relation_OId(X1) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(definition_unfolding,[],[f14,f76]) ).
fof(f14,axiom,
! [X1] : c_Relation_OId(X1) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).
fof(f4809,plain,
spl0_390,
inference(avatar_split_clause,[],[f569,f4807]) ).
fof(f569,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__diff__Id_0) ).
fof(f4805,plain,
( spl0_389
| ~ spl0_50
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1255,f1211,f886,f4803]) ).
fof(f4803,plain,
( spl0_389
<=> ! [X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f886,plain,
( spl0_50
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ hBOOL(c_Wellfounded_Owf(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1211,plain,
( spl0_114
<=> ! [X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1255,plain,
( ! [X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_50
| ~ spl0_114 ),
inference(resolution,[],[f1212,f887]) ).
fof(f887,plain,
( ! [X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f886]) ).
fof(f1212,plain,
( ! [X0,X1] :
( hBOOL(c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1))
| ~ hBOOL(c_Wellfounded_Owf(X0,X1)) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1211]) ).
fof(f4801,plain,
spl0_388,
inference(avatar_split_clause,[],[f549,f4799]) ).
fof(f4799,plain,
( spl0_388
<=> ! [X4,X5,X2] :
( ~ class_HOL_Ominus(X4)
| hAPP(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(t_a,X4)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),hAPP(X5,v_x),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f549,axiom,
! [X2,X4,X5] :
( ~ class_HOL_Ominus(X4)
| hAPP(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(t_a,X4)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),hAPP(X5,v_x),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
fof(f4797,plain,
spl0_387,
inference(avatar_split_clause,[],[f539,f4795]) ).
fof(f4795,plain,
( spl0_387
<=> ! [X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| ~ hBOOL(c_Relation_Otrans(X0,X1))
| hBOOL(c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f539,axiom,
! [X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| ~ hBOOL(c_Relation_Otrans(X0,X1))
| hBOOL(c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).
fof(f4793,plain,
spl0_386,
inference(avatar_split_clause,[],[f406,f4791]) ).
fof(f4791,plain,
( spl0_386
<=> ! [X4,X9,X23] :
( ~ class_Lattices_Olattice(X4)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X9,X23,tc_fun(t_a,X4)),v_x) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(X9,v_x),hAPP(X23,v_x),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f406,axiom,
! [X9,X4,X23] :
( ~ class_Lattices_Olattice(X4)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X9,X23,tc_fun(t_a,X4)),v_x) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(X9,v_x),hAPP(X23,v_x),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
fof(f4789,plain,
spl0_385,
inference(avatar_split_clause,[],[f394,f4787]) ).
fof(f4787,plain,
( spl0_385
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Relation_Oirrefl(X0,X1))
| ~ hBOOL(c_Relation_Otrans(X0,X1))
| ~ hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f394,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Relation_Oirrefl(X0,X1))
| ~ hBOOL(c_Relation_Otrans(X0,X1))
| ~ hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).
fof(f4785,plain,
spl0_384,
inference(avatar_split_clause,[],[f349,f4783]) ).
fof(f4783,plain,
( spl0_384
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f349,axiom,
! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
fof(f4781,plain,
spl0_383,
inference(avatar_split_clause,[],[f213,f4779]) ).
fof(f4779,plain,
( spl0_383
<=> ! [X0,X1,X17] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| ~ hBOOL(c_Relation_Otrans(X17,X1))
| hBOOL(c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f213,axiom,
! [X0,X1,X17] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| ~ hBOOL(c_Relation_Otrans(X17,X1))
| hBOOL(c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Int_0) ).
fof(f4777,plain,
spl0_382,
inference(avatar_split_clause,[],[f196,f4775]) ).
fof(f4775,plain,
( spl0_382
<=> ! [X4,X11,X5,X2,X1] :
( ~ hBOOL(c_in(X11,X2,X1))
| c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X5,X1,tc_fun(X4,tc_bool)),hAPP(X5,X11),tc_fun(X4,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f196,axiom,
! [X2,X11,X1,X4,X5] :
( ~ hBOOL(c_in(X11,X2,X1))
| c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X5,X1,tc_fun(X4,tc_bool)),hAPP(X5,X11),tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__lower_0) ).
fof(f4773,plain,
spl0_381,
inference(avatar_split_clause,[],[f168,f4771]) ).
fof(f4771,plain,
( spl0_381
<=> ! [X2,X4,X9,X1] : c_Set_Ovimage(X9,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X4,tc_bool)),X1,X4) = c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(X9,X2,X1,X4),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f168,axiom,
! [X2,X1,X9,X4] : c_Set_Ovimage(X9,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X4,tc_bool)),X1,X4) = c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(X9,X2,X1,X4),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
fof(f4769,plain,
spl0_380,
inference(avatar_split_clause,[],[f114,f4767]) ).
fof(f4767,plain,
( spl0_380
<=> ! [X31,X9,X6,X1] : hAPP(X9,hAPP(c_Nat_Ocompow(X31,X9,X1,X1),X6)) = hAPP(c_Nat_Ocompow(X31,X9,X1,X1),hAPP(X9,X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f114,axiom,
! [X31,X1,X6,X9] : hAPP(X9,hAPP(c_Nat_Ocompow(X31,X9,X1,X1),X6)) = hAPP(c_Nat_Ocompow(X31,X9,X1,X1),hAPP(X9,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funpow__swap1_0) ).
fof(f4765,plain,
spl0_379,
inference(avatar_split_clause,[],[f83,f4763]) ).
fof(f4763,plain,
( spl0_379
<=> ! [X4,X9,X23] :
( ~ class_Lattices_Olattice(X4)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X9,X23,tc_fun(t_a,X4)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,v_x),hAPP(X23,v_x),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f83,axiom,
! [X9,X4,X23] :
( ~ class_Lattices_Olattice(X4)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X9,X23,tc_fun(t_a,X4)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,v_x),hAPP(X23,v_x),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
fof(f4761,plain,
( spl0_378
| ~ spl0_27
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1172,f1079,f794,f4759]) ).
fof(f4759,plain,
( spl0_378
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f794,plain,
( spl0_27
<=> ! [X0,X1] : hBOOL(c_Relation_Otrans(c_Transitive__Closure_Otrancl(X0,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1079,plain,
( spl0_96
<=> ! [X0,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| c_Transitive__Closure_Otrancl(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1172,plain,
( ! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1)
| ~ spl0_27
| ~ spl0_96 ),
inference(resolution,[],[f1080,f795]) ).
fof(f795,plain,
( ! [X0,X1] : hBOOL(c_Relation_Otrans(c_Transitive__Closure_Otrancl(X0,X1),X1))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f1080,plain,
( ! [X0,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| c_Transitive__Closure_Otrancl(X0,X1) = X0 )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1079]) ).
fof(f4757,plain,
spl0_377,
inference(avatar_split_clause,[],[f82,f4755]) ).
fof(f4755,plain,
( spl0_377
<=> ! [X2,X5,X1] :
( c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f82,axiom,
! [X2,X1,X5] :
( c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
fof(f4753,plain,
spl0_376,
inference(avatar_split_clause,[],[f66,f4751]) ).
fof(f4751,plain,
( spl0_376
<=> ! [X2,X4,X19,X6,X1] :
( ~ hBOOL(c_in(X6,X19,X1))
| ~ c_Finite__Set_Ofinite(hAPP(X2,X6),X4)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X19,X2,X1,tc_fun(X4,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f66,axiom,
! [X2,X1,X6,X19,X4] :
( ~ hBOOL(c_in(X6,X19,X1))
| ~ c_Finite__Set_Ofinite(hAPP(X2,X6),X4)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X19,X2,X1,tc_fun(X4,tc_bool)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__INT_0) ).
fof(f4749,plain,
spl0_375,
inference(avatar_split_clause,[],[f28,f4747]) ).
fof(f4747,plain,
( spl0_375
<=> ! [X4,X9,X2,X1] :
( ~ c_Fun_Oinj__on(X9,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X4)
| c_Set_Ovimage(X9,c_Set_Oimage(X9,X2,X1,X4),X1,X4) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f28,axiom,
! [X2,X1,X9,X4] :
( ~ c_Fun_Oinj__on(X9,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X4)
| c_Set_Ovimage(X9,c_Set_Oimage(X9,X2,X1,X4),X1,X4) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
fof(f4397,plain,
( spl0_374
| ~ spl0_17
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f4347,f3552,f753,f4395]) ).
fof(f4395,plain,
( spl0_374
<=> ! [X0] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f3552,plain,
( spl0_323
<=> c_Arrow__Order__Mirabelle_OLin = c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f4347,plain,
( ! [X0] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X0))
| ~ spl0_17
| ~ spl0_323 ),
inference(superposition,[],[f754,f3554]) ).
fof(f3554,plain,
( c_Arrow__Order__Mirabelle_OLin = c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_323 ),
inference(avatar_component_clause,[],[f3552]) ).
fof(f4387,plain,
spl0_373,
inference(avatar_split_clause,[],[f566,f4385]) ).
fof(f4385,plain,
( spl0_373
<=> ! [X2,X5,X1] : c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f566,axiom,
! [X2,X1,X5] : c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f4383,plain,
spl0_372,
inference(avatar_split_clause,[],[f559,f4381]) ).
fof(f4381,plain,
( spl0_372
<=> ! [X2,X0,X1] :
( hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| ~ hBOOL(c_Relation_Ototal__on(X2,c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f559,axiom,
! [X2,X0,X1] :
( hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| ~ hBOOL(c_Relation_Ototal__on(X2,c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).
fof(f4379,plain,
spl0_371,
inference(avatar_split_clause,[],[f558,f4377]) ).
fof(f4377,plain,
( spl0_371
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| hBOOL(c_Relation_Ototal__on(X2,c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f558,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| hBOOL(c_Relation_Ototal__on(X2,c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).
fof(f4375,plain,
spl0_370,
inference(avatar_split_clause,[],[f508,f4373]) ).
fof(f4373,plain,
( spl0_370
<=> ! [X2,X5,X1] : c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ominus__class_Ominus(X5,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f508,axiom,
! [X2,X1,X5] : c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ominus__class_Ominus(X5,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
fof(f4371,plain,
spl0_369,
inference(avatar_split_clause,[],[f507,f4369]) ).
fof(f4369,plain,
( spl0_369
<=> ! [X2,X5,X1] : c_Lattices_Oupper__semilattice__class_Osup(X5,X2,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X2,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f507,axiom,
! [X2,X1,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X2,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X2,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
fof(f4367,plain,
spl0_368,
inference(avatar_split_clause,[],[f479,f4365]) ).
fof(f4365,plain,
( spl0_368
<=> ! [X24,X4,X9,X6,X1] :
( X6 = X24
| hAPP(X9,X6) != hAPP(X9,X24)
| ~ c_Fun_Oinj__on(X9,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f479,axiom,
! [X1,X6,X9,X4,X24] :
( X6 = X24
| hAPP(X9,X6) != hAPP(X9,X24)
| ~ c_Fun_Oinj__on(X9,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
fof(f4363,plain,
spl0_367,
inference(avatar_split_clause,[],[f454,f4361]) ).
fof(f4361,plain,
( spl0_367
<=> ! [X4,X7,X2,X1] :
( ~ hBOOL(c_in(X7,X2,X4))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Set_Ovimage(c_COMBK(X7,X4,X1),X2,X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f454,axiom,
! [X2,X1,X7,X4] :
( ~ hBOOL(c_in(X7,X2,X4))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Set_Ovimage(c_COMBK(X7,X4,X1),X2,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).
fof(f4359,plain,
spl0_366,
inference(avatar_split_clause,[],[f414,f4357]) ).
fof(f4357,plain,
( spl0_366
<=> ! [X3,X5,X2,X1] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| ~ c_lessequals(X5,X3,tc_fun(X1,tc_bool))
| c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f414,axiom,
! [X2,X3,X1,X5] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| ~ c_lessequals(X5,X3,tc_fun(X1,tc_bool))
| c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f4355,plain,
spl0_365,
inference(avatar_split_clause,[],[f387,f4352]) ).
fof(f4352,plain,
( spl0_365
<=> hAPP(c_Order__Relation_Ostrict__linear__order__on(v_A,t_a),v_r) = c_and(c_Relation_Otrans(v_r,t_a),c_and(c_Relation_Oirrefl(v_r,t_a),c_Relation_Ototal__on(v_A,v_r,t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f387,axiom,
hAPP(c_Order__Relation_Ostrict__linear__order__on(v_A,t_a),v_r) = c_and(c_Relation_Otrans(v_r,t_a),c_and(c_Relation_Oirrefl(v_r,t_a),c_Relation_Ototal__on(v_A,v_r,t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def__raw_0) ).
fof(f4345,plain,
spl0_364,
inference(avatar_split_clause,[],[f386,f4343]) ).
fof(f4343,plain,
( spl0_364
<=> ! [X2,X5,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f386,axiom,
! [X2,X1,X5] : c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f4341,plain,
spl0_363,
inference(avatar_split_clause,[],[f331,f4339]) ).
fof(f4339,plain,
( spl0_363
<=> ! [X2,X1,X9] :
( ~ c_Finite__Set_Ofinite(X2,X1)
| c_Fun_Oinj__on(X9,X2,X1,X1)
| ~ c_lessequals(X2,c_Set_Oimage(X9,X2,X1,X1),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f331,axiom,
! [X2,X1,X9] :
( ~ c_Finite__Set_Ofinite(X2,X1)
| c_Fun_Oinj__on(X9,X2,X1,X1)
| ~ c_lessequals(X2,c_Set_Oimage(X9,X2,X1,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
fof(f4337,plain,
spl0_362,
inference(avatar_split_clause,[],[f306,f4335]) ).
fof(f4335,plain,
( spl0_362
<=> ! [X2,X5,X1] : c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f306,axiom,
! [X2,X1,X5] : c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f4333,plain,
spl0_361,
inference(avatar_split_clause,[],[f246,f4331]) ).
fof(f4331,plain,
( spl0_361
<=> ! [X4,X7,X2,X1] :
( hBOOL(c_in(X7,X2,X4))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Ovimage(c_COMBK(X7,X4,X1),X2,X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f246,axiom,
! [X2,X1,X7,X4] :
( hBOOL(c_in(X7,X2,X4))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Ovimage(c_COMBK(X7,X4,X1),X2,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
fof(f4329,plain,
spl0_360,
inference(avatar_split_clause,[],[f231,f4327]) ).
fof(f4327,plain,
( spl0_360
<=> ! [X2,X5,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f231,axiom,
! [X2,X1,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
fof(f4325,plain,
spl0_359,
inference(avatar_split_clause,[],[f92,f4323]) ).
fof(f4323,plain,
( spl0_359
<=> ! [X4,X20,X27,X1] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X27,X20,X4,X1),X4)
| ~ c_Fun_Oinj__on(X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f92,axiom,
! [X1,X27,X4,X20] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X27,X20,X4,X1),X4)
| ~ c_Fun_Oinj__on(X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
fof(f4321,plain,
spl0_358,
inference(avatar_split_clause,[],[f90,f4319]) ).
fof(f4319,plain,
( spl0_358
<=> ! [X26,X4,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X26,X4,X1),X1,X4) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f90,axiom,
! [X2,X1,X26,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X26,X4,X1),X1,X4) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__const_0) ).
fof(f4317,plain,
spl0_357,
inference(avatar_split_clause,[],[f27,f4315]) ).
fof(f4315,plain,
( spl0_357
<=> ! [X4,X13,X8,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)) = c_Relation_Orel__comp(X8,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X13,X4),tc_bool)),X1,X13,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f27,axiom,
! [X1,X8,X4,X13] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)) = c_Relation_Orel__comp(X8,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X13,X4),tc_bool)),X1,X13,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).
fof(f4313,plain,
spl0_356,
inference(avatar_split_clause,[],[f26,f4311]) ).
fof(f4311,plain,
( spl0_356
<=> ! [X4,X13,X8,X1] : c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X13),tc_bool)),X8,X1,X13,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f26,axiom,
! [X1,X8,X4,X13] : c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X13),tc_bool)),X8,X1,X13,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).
fof(f3833,plain,
spl0_355,
inference(avatar_split_clause,[],[f623,f3831]) ).
fof(f3831,plain,
( spl0_355
<=> ! [X4,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),X1,X4),X4,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f623,plain,
! [X1,X4] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),X1,X4),X4,X1),
inference(definition_unfolding,[],[f102,f69]) ).
fof(f69,axiom,
! [X0,X1,X4] : c_Relation_ORange(c_Relation_Oconverse(X0,X1,X4),X4,X1) = c_Relation_ODomain(X0,X1,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
fof(f102,axiom,
! [X1,X4] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),X1,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty_0) ).
fof(f3829,plain,
spl0_354,
inference(avatar_split_clause,[],[f617,f3827]) ).
fof(f3827,plain,
( spl0_354
<=> ! [X0,X1] : c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f617,plain,
! [X0,X1] : c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1,X1),
inference(definition_unfolding,[],[f315,f69,f69]) ).
fof(f315,axiom,
! [X0,X1] : c_Relation_ODomain(X0,X1,X1) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
fof(f3825,plain,
spl0_353,
inference(avatar_split_clause,[],[f613,f3823]) ).
fof(f3823,plain,
( spl0_353
<=> ! [X0,X1] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f613,plain,
! [X0,X1] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),
inference(definition_unfolding,[],[f192,f76]) ).
fof(f192,axiom,
! [X0,X1] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Transitive__Closure_Ortrancl(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__rtrancl_0) ).
fof(f3821,plain,
spl0_352,
inference(avatar_split_clause,[],[f563,f3819]) ).
fof(f3819,plain,
( spl0_352
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Owell__order__on(X2,X0,X1))
| hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f563,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Owell__order__on(X2,X0,X1))
| hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_well__order__on__def_1) ).
fof(f3817,plain,
spl0_351,
inference(avatar_split_clause,[],[f464,f3815]) ).
fof(f3815,plain,
( spl0_351
<=> ! [X4,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X1),tc_bool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Relation_ORange(X0,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f464,axiom,
! [X0,X1,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X1),tc_bool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Relation_ORange(X0,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).
fof(f3813,plain,
spl0_350,
inference(avatar_split_clause,[],[f452,f3811]) ).
fof(f3811,plain,
( spl0_350
<=> ! [X5,X6,X2,X1] :
( ~ hBOOL(hAPP(X2,X6))
| ~ hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f452,axiom,
! [X2,X1,X6,X5] :
( ~ hBOOL(hAPP(X2,X6))
| ~ hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f3809,plain,
spl0_349,
inference(avatar_split_clause,[],[f404,f3807]) ).
fof(f3807,plain,
( spl0_349
<=> ! [X2,X5,X1,X3] :
( c_lessequals(X5,X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f404,axiom,
! [X2,X3,X1,X5] :
( c_lessequals(X5,X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f3805,plain,
spl0_348,
inference(avatar_split_clause,[],[f403,f3803]) ).
fof(f3803,plain,
( spl0_348
<=> ! [X3,X5,X2,X1] :
( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f403,axiom,
! [X2,X3,X1,X5] :
( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f3801,plain,
spl0_347,
inference(avatar_split_clause,[],[f327,f3799]) ).
fof(f3799,plain,
( spl0_347
<=> ! [X2,X5,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f327,axiom,
! [X2,X1,X5] : c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
fof(f3785,plain,
spl0_346,
inference(avatar_split_clause,[],[f326,f3783]) ).
fof(f3783,plain,
( spl0_346
<=> ! [X1,X8] :
( hBOOL(c_Wellfounded_Owf(X8,X1))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) != c_Relation_Orel__comp(X8,X8,X1,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f326,axiom,
! [X1,X8] :
( hBOOL(c_Wellfounded_Owf(X8,X1))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) != c_Relation_Orel__comp(X8,X8,X1,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).
fof(f3781,plain,
spl0_345,
inference(avatar_split_clause,[],[f312,f3779]) ).
fof(f3779,plain,
( spl0_345
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X6,X1),c_HOL_Ouminus__class_Ouminus(X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f312,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X6,X1),c_HOL_Ouminus__class_Ouminus(X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).
fof(f3777,plain,
spl0_344,
inference(avatar_split_clause,[],[f301,f3775]) ).
fof(f3775,plain,
( spl0_344
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X6,X1),c_HOL_Ouminus__class_Ouminus(X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f301,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X6,X1),c_HOL_Ouminus__class_Ouminus(X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).
fof(f3773,plain,
spl0_343,
inference(avatar_split_clause,[],[f281,f3771]) ).
fof(f3771,plain,
( spl0_343
<=> ! [X3,X5,X2,X1] :
( c_lessequals(X3,X2,tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f281,axiom,
! [X2,X3,X1,X5] :
( c_lessequals(X3,X2,tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f3769,plain,
spl0_342,
inference(avatar_split_clause,[],[f280,f3767]) ).
fof(f3767,plain,
( spl0_342
<=> ! [X3,X5,X2,X1] :
( c_lessequals(X3,X5,tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f280,axiom,
! [X2,X3,X1,X5] :
( c_lessequals(X3,X5,tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f3765,plain,
spl0_341,
inference(avatar_split_clause,[],[f274,f3763]) ).
fof(f3763,plain,
( spl0_341
<=> ! [X2,X5,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f274,axiom,
! [X2,X1,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f3761,plain,
spl0_340,
inference(avatar_split_clause,[],[f273,f3759]) ).
fof(f3759,plain,
( spl0_340
<=> ! [X2,X5,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f273,axiom,
! [X2,X1,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f3757,plain,
spl0_339,
inference(avatar_split_clause,[],[f266,f3755]) ).
fof(f3755,plain,
( spl0_339
<=> ! [X6,X11,X12,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X6,X11,X1)
| ~ c_lessequals(X6,X12,X1)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f266,axiom,
! [X11,X1,X6,X12] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X6,X11,X1)
| ~ c_lessequals(X6,X12,X1)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
fof(f3753,plain,
spl0_338,
inference(avatar_split_clause,[],[f195,f3751]) ).
fof(f3751,plain,
( spl0_338
<=> ! [X2,X18,X4,X1,X26] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| ~ hBOOL(c_in(X18,X2,X1))
| c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X26,X1,X4),hAPP(X26,X18),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f195,axiom,
! [X2,X18,X1,X26,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| ~ hBOOL(c_in(X18,X2,X1))
| c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X26,X1,X4),hAPP(X26,X18),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
fof(f3749,plain,
spl0_337,
inference(avatar_split_clause,[],[f189,f3747]) ).
fof(f3747,plain,
( spl0_337
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X25,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f189,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X25,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f3734,plain,
spl0_336,
inference(avatar_split_clause,[],[f188,f3732]) ).
fof(f3732,plain,
( spl0_336
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X24,c_Lattices_Olower__semilattice__class_Oinf(X6,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f188,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X24,c_Lattices_Olower__semilattice__class_Oinf(X6,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f3730,plain,
spl0_335,
inference(avatar_split_clause,[],[f187,f3728]) ).
fof(f3728,plain,
( spl0_335
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X24,c_Lattices_Olower__semilattice__class_Oinf(X6,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f187,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X24,c_Lattices_Olower__semilattice__class_Oinf(X6,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f3726,plain,
spl0_334,
inference(avatar_split_clause,[],[f186,f3724]) ).
fof(f3724,plain,
( spl0_334
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X25,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f186,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X25,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f3722,plain,
spl0_333,
inference(avatar_split_clause,[],[f182,f3720]) ).
fof(f3720,plain,
( spl0_333
<=> ! [X17,X4,X13,X0,X1] :
( ~ c_Relation_Osingle__valued(X0,X1,X4)
| ~ c_Relation_Osingle__valued(X17,X4,X13)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X0,X17,X1,X4,X13),X1,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f182,axiom,
! [X0,X1,X4,X17,X13] :
( ~ c_Relation_Osingle__valued(X0,X1,X4)
| ~ c_Relation_Osingle__valued(X17,X4,X13)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X0,X17,X1,X4,X13),X1,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
fof(f3718,plain,
spl0_332,
inference(avatar_split_clause,[],[f181,f3716]) ).
fof(f3716,plain,
( spl0_332
<=> ! [X0,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| c_lessequals(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f181,axiom,
! [X0,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| c_lessequals(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
fof(f3714,plain,
spl0_331,
inference(avatar_split_clause,[],[f173,f3712]) ).
fof(f3712,plain,
( spl0_331
<=> ! [X5,X6,X2,X1] :
( hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(X2,X6))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f173,axiom,
! [X2,X1,X6,X5] :
( hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(X2,X6))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f3710,plain,
spl0_330,
inference(avatar_split_clause,[],[f145,f3708]) ).
fof(f3708,plain,
( spl0_330
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X24,X6,X1)
| ~ c_lessequals(X25,X6,X1)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f145,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X24,X6,X1)
| ~ c_lessequals(X25,X6,X1)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
fof(f3706,plain,
spl0_329,
inference(avatar_split_clause,[],[f125,f3704]) ).
fof(f3704,plain,
( spl0_329
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X25,X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f125,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X25,X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f3702,plain,
spl0_328,
inference(avatar_split_clause,[],[f124,f3700]) ).
fof(f3700,plain,
( spl0_328
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X24,c_Lattices_Oupper__semilattice__class_Osup(X6,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f124,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X24,c_Lattices_Oupper__semilattice__class_Osup(X6,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f3698,plain,
spl0_327,
inference(avatar_split_clause,[],[f123,f3696]) ).
fof(f3696,plain,
( spl0_327
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X24,c_Lattices_Oupper__semilattice__class_Osup(X6,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f123,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X24,c_Lattices_Oupper__semilattice__class_Osup(X6,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f3694,plain,
spl0_326,
inference(avatar_split_clause,[],[f122,f3692]) ).
fof(f3692,plain,
( spl0_326
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X25,X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f122,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X25,X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X24,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f3690,plain,
spl0_325,
inference(avatar_split_clause,[],[f116,f3688]) ).
fof(f3688,plain,
( spl0_325
<=> ! [X2,X5,X1] : c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f116,axiom,
! [X2,X1,X5] : c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
fof(f3686,plain,
spl0_324,
inference(avatar_split_clause,[],[f49,f3684]) ).
fof(f3684,plain,
( spl0_324
<=> ! [X4,X8,X9,X1] : c_Relation_Oconverse(c_Relation_Oinv__image(X8,X9,X4,X1),X1,X1) = c_Relation_Oinv__image(c_Relation_Oconverse(X8,X4,X4),X9,X4,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f49,axiom,
! [X1,X8,X9,X4] : c_Relation_Oconverse(c_Relation_Oinv__image(X8,X9,X4,X1),X1,X1) = c_Relation_Oinv__image(c_Relation_Oconverse(X8,X4,X4),X9,X4,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
fof(f3555,plain,
( spl0_323
| ~ spl0_22
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2888,f2453,f774,f3552]) ).
fof(f774,plain,
( spl0_22
<=> ! [X1,X14] : c_Collect(X14,X1) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f2453,plain,
( spl0_263
<=> c_Arrow__Order__Mirabelle_OLin = c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2888,plain,
( c_Arrow__Order__Mirabelle_OLin = c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_22
| ~ spl0_263 ),
inference(superposition,[],[f2455,f775]) ).
fof(f775,plain,
( ! [X1,X14] : c_Collect(X14,X1) = X14
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f2455,plain,
( c_Arrow__Order__Mirabelle_OLin = c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f3440,plain,
( spl0_322
| ~ spl0_199
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f2876,f2433,f1796,f3438]) ).
fof(f3438,plain,
( spl0_322
<=> ! [X0] : c_Relation_Osym(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f1796,plain,
( spl0_199
<=> ! [X0,X1] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f2433,plain,
( spl0_258
<=> ! [X5,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2876,plain,
( ! [X0] : c_Relation_Osym(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_199
| ~ spl0_258 ),
inference(superposition,[],[f1797,f2434]) ).
fof(f2434,plain,
( ! [X1,X5] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool))
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f2433]) ).
fof(f1797,plain,
( ! [X0,X1] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1796]) ).
fof(f3424,plain,
spl0_321,
inference(avatar_split_clause,[],[f637,f3422]) ).
fof(f3422,plain,
( spl0_321
<=> ! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f637,plain,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ),
inference(definition_unfolding,[],[f153,f76]) ).
fof(f153,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
fof(f3420,plain,
spl0_320,
inference(avatar_split_clause,[],[f636,f3418]) ).
fof(f3418,plain,
( spl0_320
<=> ! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f636,plain,
! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| c_Relation_Oantisym(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ),
inference(definition_unfolding,[],[f215,f76]) ).
fof(f215,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
fof(f3416,plain,
spl0_319,
inference(avatar_split_clause,[],[f511,f3414]) ).
fof(f3414,plain,
( spl0_319
<=> ! [X48,X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(X48,X1))
| ~ c_lessequals(X48,X0,tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f511,axiom,
! [X48,X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(X48,X1))
| ~ c_lessequals(X48,X0,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
fof(f3412,plain,
spl0_318,
inference(avatar_split_clause,[],[f437,f3410]) ).
fof(f3410,plain,
( spl0_318
<=> ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f437,axiom,
! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
fof(f3408,plain,
spl0_317,
inference(avatar_split_clause,[],[f424,f3406]) ).
fof(f3406,plain,
( spl0_317
<=> ! [X17,X4,X0,X1] :
( ~ c_Relation_Osingle__valued(X17,X1,X4)
| c_Relation_Osingle__valued(X0,X1,X4)
| ~ c_lessequals(X0,X17,tc_fun(tc_prod(X1,X4),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f424,axiom,
! [X0,X1,X4,X17] :
( ~ c_Relation_Osingle__valued(X17,X1,X4)
| c_Relation_Osingle__valued(X0,X1,X4)
| ~ c_lessequals(X0,X17,tc_fun(tc_prod(X1,X4),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
fof(f3404,plain,
spl0_316,
inference(avatar_split_clause,[],[f415,f3402]) ).
fof(f3402,plain,
( spl0_316
<=> ! [X2,X4,X9,X5,X1] :
( ~ c_Fun_Oinj__on(X9,X5,X1,X4)
| c_Fun_Oinj__on(X9,X2,X1,X4)
| ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f415,axiom,
! [X2,X1,X9,X4,X5] :
( ~ c_Fun_Oinj__on(X9,X5,X1,X4)
| c_Fun_Oinj__on(X9,X2,X1,X4)
| ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
fof(f3400,plain,
spl0_315,
inference(avatar_split_clause,[],[f409,f3398]) ).
fof(f3398,plain,
( spl0_315
<=> ! [X7,X5,X2,X1] :
( ~ hBOOL(c_in(X7,X2,X1))
| hBOOL(c_in(X7,X5,X1))
| ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f409,axiom,
! [X2,X1,X7,X5] :
( ~ hBOOL(c_in(X7,X2,X1))
| hBOOL(c_in(X7,X5,X1))
| ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
fof(f3396,plain,
spl0_314,
inference(avatar_split_clause,[],[f359,f3394]) ).
fof(f3394,plain,
( spl0_314
<=> ! [X6,X4,X9,X23,X1] :
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X9,X23,tc_fun(X1,X4))
| c_lessequals(hAPP(X9,X6),hAPP(X23,X6),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f359,axiom,
! [X1,X6,X9,X4,X23] :
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X9,X23,tc_fun(X1,X4))
| c_lessequals(hAPP(X9,X6),hAPP(X23,X6),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f3392,plain,
( spl0_313
| ~ spl0_215
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2513,f2290,f1861,f3390]) ).
fof(f3390,plain,
( spl0_313
<=> ! [X0] : c_Relation_Osym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f1861,plain,
( spl0_215
<=> ! [X0,X1] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2290,plain,
( spl0_230
<=> ! [X5,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2513,plain,
( ! [X0] : c_Relation_Osym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_215
| ~ spl0_230 ),
inference(superposition,[],[f1862,f2291]) ).
fof(f2291,plain,
( ! [X1,X5] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool))
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2290]) ).
fof(f1862,plain,
( ! [X0,X1] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f1861]) ).
fof(f3388,plain,
spl0_312,
inference(avatar_split_clause,[],[f343,f3386]) ).
fof(f3386,plain,
( spl0_312
<=> ! [X42,X9,X6,X2,X1] :
( ~ hBOOL(c_in(X6,X2,X42))
| hBOOL(c_in(hAPP(X9,X6),c_Set_Oimage(X9,X2,X42,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f343,axiom,
! [X2,X1,X6,X9,X42] :
( ~ hBOOL(c_in(X6,X2,X42))
| hBOOL(c_in(hAPP(X9,X6),c_Set_Oimage(X9,X2,X42,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
fof(f3384,plain,
spl0_311,
inference(avatar_split_clause,[],[f338,f3382]) ).
fof(f3382,plain,
( spl0_311
<=> ! [X0,X1,X17] :
( ~ c_Relation_Osym(X0,X1)
| ~ c_Relation_Osym(X17,X1)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f338,axiom,
! [X0,X1,X17] :
( ~ c_Relation_Osym(X0,X1)
| ~ c_Relation_Osym(X17,X1)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).
fof(f3380,plain,
spl0_310,
inference(avatar_split_clause,[],[f314,f3378]) ).
fof(f3378,plain,
( spl0_310
<=> ! [X2,X5,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ominus__class_Ominus(X5,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f314,axiom,
! [X2,X1,X5] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ominus__class_Ominus(X5,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
fof(f3376,plain,
spl0_309,
inference(avatar_split_clause,[],[f292,f3374]) ).
fof(f3374,plain,
( spl0_309
<=> ! [X4,X11,X9,X2,X1] :
( hBOOL(c_in(hAPP(X9,X11),X2,X4))
| ~ hBOOL(c_in(X11,c_Set_Ovimage(X9,X2,X1,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f292,axiom,
! [X2,X11,X1,X9,X4] :
( hBOOL(c_in(hAPP(X9,X11),X2,X4))
| ~ hBOOL(c_in(X11,c_Set_Ovimage(X9,X2,X1,X4),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
fof(f3372,plain,
spl0_308,
inference(avatar_split_clause,[],[f288,f3370]) ).
fof(f3370,plain,
( spl0_308
<=> ! [X4,X9,X11,X5,X1] :
( ~ hBOOL(c_in(hAPP(X9,X11),X5,X4))
| hBOOL(c_in(X11,c_Set_Ovimage(X9,X5,X1,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f288,axiom,
! [X11,X1,X9,X4,X5] :
( ~ hBOOL(c_in(hAPP(X9,X11),X5,X4))
| hBOOL(c_in(X11,c_Set_Ovimage(X9,X5,X1,X4),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
fof(f3368,plain,
spl0_307,
inference(avatar_split_clause,[],[f247,f3366]) ).
fof(f3366,plain,
( spl0_307
<=> ! [X2,X1] :
( ~ c_Finite__Set_Ofinite(X2,X1)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f247,axiom,
! [X2,X1] :
( ~ c_Finite__Set_Ofinite(X2,X1)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_0) ).
fof(f3364,plain,
spl0_306,
inference(avatar_split_clause,[],[f172,f3362]) ).
fof(f3362,plain,
( spl0_306
<=> ! [X0,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| hBOOL(c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f172,axiom,
! [X0,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| hBOOL(c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
fof(f3360,plain,
spl0_305,
inference(avatar_split_clause,[],[f169,f3358]) ).
fof(f3358,plain,
( spl0_305
<=> ! [X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1))
| hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f169,axiom,
! [X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1))
| hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
fof(f3356,plain,
spl0_304,
inference(avatar_split_clause,[],[f77,f3354]) ).
fof(f3354,plain,
( spl0_304
<=> ! [X4,X9,X5,X2,X1] :
( ~ c_Finite__Set_Ofinite(X2,X1)
| c_Finite__Set_Ofinite(X5,X4)
| ~ c_lessequals(X5,c_Set_Oimage(X9,X2,X1,X4),tc_fun(X4,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f77,axiom,
! [X2,X1,X9,X4,X5] :
( ~ c_Finite__Set_Ofinite(X2,X1)
| c_Finite__Set_Ofinite(X5,X4)
| ~ c_lessequals(X5,c_Set_Oimage(X9,X2,X1,X4),tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
fof(f3352,plain,
spl0_303,
inference(avatar_split_clause,[],[f40,f3350]) ).
fof(f3350,plain,
( spl0_303
<=> ! [X0,X1,X17] :
( ~ c_Relation_Osym(X0,X1)
| ~ c_Relation_Osym(X17,X1)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f40,axiom,
! [X0,X1,X17] :
( ~ c_Relation_Osym(X0,X1)
| ~ c_Relation_Osym(X17,X1)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).
fof(f3348,plain,
( spl0_302
| ~ spl0_6
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1253,f1207,f698,f3346]) ).
fof(f3346,plain,
( spl0_302
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f698,plain,
( spl0_6
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1207,plain,
( spl0_113
<=> ! [X6,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1253,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ spl0_6
| ~ spl0_113 ),
inference(resolution,[],[f1208,f700]) ).
fof(f700,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f1208,plain,
( ! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(X1),X1) )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f3344,plain,
spl0_301,
inference(avatar_split_clause,[],[f16,f3342]) ).
fof(f3342,plain,
( spl0_301
<=> ! [X4,X9,X2,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X9,X2,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f16,axiom,
! [X2,X1,X9,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X9,X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
fof(f3273,plain,
( spl0_300
| ~ spl0_6
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1251,f1203,f698,f3271]) ).
fof(f3271,plain,
( spl0_300
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f1203,plain,
( spl0_112
<=> ! [X6,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1251,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool)
| ~ spl0_6
| ~ spl0_112 ),
inference(resolution,[],[f1204,f700]) ).
fof(f1204,plain,
( ! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X6,X1) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f3213,plain,
( spl0_299
| ~ spl0_6
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1249,f1195,f698,f3211]) ).
fof(f3211,plain,
( spl0_299
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f1195,plain,
( spl0_110
<=> ! [X6,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1249,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
| ~ spl0_6
| ~ spl0_110 ),
inference(resolution,[],[f1196,f700]) ).
fof(f1196,plain,
( ! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X6,X1) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f3038,plain,
( spl0_298
| ~ spl0_6
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1247,f1191,f698,f3036]) ).
fof(f3036,plain,
( spl0_298
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f1191,plain,
( spl0_109
<=> ! [X6,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1247,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| ~ spl0_6
| ~ spl0_109 ),
inference(resolution,[],[f1192,f700]) ).
fof(f1192,plain,
( ! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X1),X1) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f3034,plain,
spl0_297,
inference(avatar_split_clause,[],[f608,f3032]) ).
fof(f3032,plain,
( spl0_297
<=> ! [X4,X0,X1] : c_Relation_ORange(X0,X4,X1) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X0,X4,X1),X1,X4),X4,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f608,plain,
! [X0,X1,X4] : c_Relation_ORange(X0,X4,X1) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X0,X4,X1),X1,X4),X4,X1),
inference(definition_unfolding,[],[f405,f69]) ).
fof(f405,axiom,
! [X0,X1,X4] : c_Relation_ODomain(c_Relation_Oconverse(X0,X4,X1),X1,X4) = c_Relation_ORange(X0,X4,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
fof(f3030,plain,
spl0_296,
inference(avatar_split_clause,[],[f553,f3028]) ).
fof(f3028,plain,
( spl0_296
<=> ! [X2,X1] : c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f553,axiom,
! [X2,X1] : c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Diff__UNIV_0) ).
fof(f3026,plain,
spl0_295,
inference(avatar_split_clause,[],[f527,f3024]) ).
fof(f3024,plain,
( spl0_295
<=> ! [X0,X1] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f527,axiom,
! [X0,X1] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__reflcl_0) ).
fof(f3022,plain,
spl0_294,
inference(avatar_split_clause,[],[f526,f3020]) ).
fof(f3020,plain,
( spl0_294
<=> ! [X11,X0,X14,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(hAPP(X14,X11))
| ~ hBOOL(hAPP(X14,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X14,X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f526,axiom,
! [X0,X11,X1,X14] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(hAPP(X14,X11))
| ~ hBOOL(hAPP(X14,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X14,X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
fof(f3018,plain,
spl0_293,
inference(avatar_split_clause,[],[f521,f3016]) ).
fof(f3016,plain,
( spl0_293
<=> ! [X51,X14,X8,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X8,X1))
| hBOOL(hAPP(X14,X51))
| ~ hBOOL(hAPP(X14,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X14,X8,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f521,axiom,
! [X51,X1,X8,X14] :
( ~ hBOOL(c_Wellfounded_Owf(X8,X1))
| hBOOL(hAPP(X14,X51))
| ~ hBOOL(hAPP(X14,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X14,X8,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
fof(f3014,plain,
spl0_292,
inference(avatar_split_clause,[],[f519,f3012]) ).
fof(f3012,plain,
( spl0_292
<=> ! [X11,X0,X14,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(hAPP(X14,X11))
| ~ hBOOL(hAPP(X14,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X14,X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f519,axiom,
! [X0,X11,X1,X14] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(hAPP(X14,X11))
| ~ hBOOL(hAPP(X14,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X14,X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).
fof(f3010,plain,
spl0_291,
inference(avatar_split_clause,[],[f516,f3008]) ).
fof(f3008,plain,
( spl0_291
<=> ! [X0,X14,X50,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(hAPP(X14,X50))
| ~ hBOOL(hAPP(X14,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X14,X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f516,axiom,
! [X50,X0,X1,X14] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(hAPP(X14,X50))
| ~ hBOOL(hAPP(X14,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X14,X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).
fof(f3006,plain,
spl0_290,
inference(avatar_split_clause,[],[f513,f3004]) ).
fof(f3004,plain,
( spl0_290
<=> ! [X0,X1,X28] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X0,X28,tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f513,axiom,
! [X28,X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X0,X28,tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
fof(f3002,plain,
spl0_289,
inference(avatar_split_clause,[],[f512,f3000]) ).
fof(f3000,plain,
( spl0_289
<=> ! [X0,X1,X28] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X28,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f512,axiom,
! [X28,X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X28,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
fof(f2998,plain,
spl0_288,
inference(avatar_split_clause,[],[f502,f2996]) ).
fof(f2996,plain,
( spl0_288
<=> ! [X2,X4,X5,X9,X1] :
( ~ c_Fun_Oinj__on(X9,X2,X1,X4)
| c_Fun_Oinj__on(X9,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f502,axiom,
! [X2,X1,X9,X4,X5] :
( ~ c_Fun_Oinj__on(X9,X2,X1,X4)
| c_Fun_Oinj__on(X9,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
fof(f2994,plain,
( spl0_287
| ~ spl0_50
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1185,f1107,f886,f2992]) ).
fof(f2992,plain,
( spl0_287
<=> ! [X0] : c_Wellfounded_Oacyclic(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f1107,plain,
( spl0_103
<=> ! [X1] : hBOOL(c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1185,plain,
( ! [X0] : c_Wellfounded_Oacyclic(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_50
| ~ spl0_103 ),
inference(resolution,[],[f1108,f887]) ).
fof(f1108,plain,
( ! [X1] : hBOOL(c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1))
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1107]) ).
fof(f2990,plain,
spl0_286,
inference(avatar_split_clause,[],[f498,f2988]) ).
fof(f2988,plain,
( spl0_286
<=> ! [X7,X5,X2,X1] :
( hBOOL(c_in(X7,X2,X1))
| ~ hBOOL(c_in(X7,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f498,axiom,
! [X2,X1,X7,X5] :
( hBOOL(c_in(X7,X2,X1))
| ~ hBOOL(c_in(X7,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f2986,plain,
spl0_285,
inference(avatar_split_clause,[],[f497,f2984]) ).
fof(f2984,plain,
( spl0_285
<=> ! [X7,X5,X2,X1] :
( ~ hBOOL(c_in(X7,X5,X1))
| ~ hBOOL(c_in(X7,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f497,axiom,
! [X2,X1,X7,X5] :
( ~ hBOOL(c_in(X7,X5,X1))
| ~ hBOOL(c_in(X7,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f2982,plain,
spl0_284,
inference(avatar_split_clause,[],[f463,f2980]) ).
fof(f2980,plain,
( spl0_284
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) = c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f463,axiom,
! [X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) = c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__empty_0) ).
fof(f2978,plain,
spl0_283,
inference(avatar_split_clause,[],[f458,f2976]) ).
fof(f2976,plain,
( spl0_283
<=> ! [X4,X9,X2,X1] :
( c_Finite__Set_Ofinite(X2,X4)
| ~ c_Fun_Oinj__on(X9,X2,X4,X1)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X9,X2,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f458,axiom,
! [X2,X1,X9,X4] :
( c_Finite__Set_Ofinite(X2,X4)
| ~ c_Fun_Oinj__on(X9,X2,X4,X1)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X9,X2,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
fof(f2974,plain,
spl0_282,
inference(avatar_split_clause,[],[f392,f2972]) ).
fof(f2972,plain,
( spl0_282
<=> ! [X7,X5,X2,X1] :
( ~ hBOOL(c_in(X7,X2,X1))
| hBOOL(c_in(X7,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f392,axiom,
! [X2,X1,X7,X5] :
( ~ hBOOL(c_in(X7,X2,X1))
| hBOOL(c_in(X7,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f2970,plain,
spl0_281,
inference(avatar_split_clause,[],[f391,f2968]) ).
fof(f2968,plain,
( spl0_281
<=> ! [X7,X5,X2,X1] :
( ~ hBOOL(c_in(X7,X5,X1))
| hBOOL(c_in(X7,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f391,axiom,
! [X2,X1,X7,X5] :
( ~ hBOOL(c_in(X7,X5,X1))
| hBOOL(c_in(X7,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f2966,plain,
spl0_280,
inference(avatar_split_clause,[],[f375,f2964]) ).
fof(f2964,plain,
( spl0_280
<=> ! [X4,X2] :
( ~ class_HOL_Ouminus(X4)
| hAPP(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(t_a,X4)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X2,v_x),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f375,axiom,
! [X2,X4] :
( ~ class_HOL_Ouminus(X4)
| hAPP(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(t_a,X4)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X2,v_x),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
fof(f2962,plain,
spl0_279,
inference(avatar_split_clause,[],[f374,f2960]) ).
fof(f2960,plain,
( spl0_279
<=> ! [X4,X5,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5,X4,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f374,axiom,
! [X1,X4,X5] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5,X4,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__empty_0) ).
fof(f2958,plain,
spl0_278,
inference(avatar_split_clause,[],[f333,f2956]) ).
fof(f2956,plain,
( spl0_278
<=> ! [X2,X4,X5,X9,X1] :
( c_Fun_Oinj__on(X9,X2,X1,X4)
| ~ c_Fun_Oinj__on(X9,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f333,axiom,
! [X2,X1,X9,X4,X5] :
( c_Fun_Oinj__on(X9,X2,X1,X4)
| ~ c_Fun_Oinj__on(X9,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
fof(f2954,plain,
spl0_277,
inference(avatar_split_clause,[],[f332,f2952]) ).
fof(f2952,plain,
( spl0_277
<=> ! [X2,X4,X9,X5,X1] :
( c_Fun_Oinj__on(X9,X5,X1,X4)
| ~ c_Fun_Oinj__on(X9,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f332,axiom,
! [X2,X1,X9,X4,X5] :
( c_Fun_Oinj__on(X9,X5,X1,X4)
| ~ c_Fun_Oinj__on(X9,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
fof(f2941,plain,
spl0_276,
inference(avatar_split_clause,[],[f305,f2939]) ).
fof(f2939,plain,
( spl0_276
<=> ! [X4,X5,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)) = c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X5,X1,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f305,axiom,
! [X1,X4,X5] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)) = c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X5,X1,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).
fof(f2937,plain,
spl0_275,
inference(avatar_split_clause,[],[f250,f2935]) ).
fof(f2935,plain,
( spl0_275
<=> ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f250,axiom,
! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f2933,plain,
spl0_274,
inference(avatar_split_clause,[],[f225,f2931]) ).
fof(f2931,plain,
( spl0_274
<=> ! [X2,X5,X1] :
( X2 = X5
| ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f225,axiom,
! [X2,X1,X5] :
( X2 = X5
| ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
fof(f2929,plain,
spl0_273,
inference(avatar_split_clause,[],[f161,f2927]) ).
fof(f2927,plain,
( spl0_273
<=> ! [X2,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f161,axiom,
! [X2,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
fof(f2925,plain,
spl0_272,
inference(avatar_split_clause,[],[f160,f2923]) ).
fof(f2923,plain,
( spl0_272
<=> ! [X2,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f160,axiom,
! [X2,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).
fof(f2921,plain,
spl0_271,
inference(avatar_split_clause,[],[f127,f2919]) ).
fof(f2919,plain,
( spl0_271
<=> ! [X7,X5,X2,X1] :
( hBOOL(c_in(X7,X2,X1))
| ~ hBOOL(c_in(X7,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f127,axiom,
! [X2,X1,X7,X5] :
( hBOOL(c_in(X7,X2,X1))
| ~ hBOOL(c_in(X7,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f2917,plain,
spl0_270,
inference(avatar_split_clause,[],[f126,f2915]) ).
fof(f2915,plain,
( spl0_270
<=> ! [X7,X5,X2,X1] :
( hBOOL(c_in(X7,X5,X1))
| ~ hBOOL(c_in(X7,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f126,axiom,
! [X2,X1,X7,X5] :
( hBOOL(c_in(X7,X5,X1))
| ~ hBOOL(c_in(X7,c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f2913,plain,
spl0_269,
inference(avatar_split_clause,[],[f91,f2911]) ).
fof(f2911,plain,
( spl0_269
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1))
| ~ hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f91,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1))
| ~ hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__order__on__def_2) ).
fof(f2909,plain,
spl0_268,
inference(avatar_split_clause,[],[f11,f2907]) ).
fof(f2907,plain,
( spl0_268
<=> ! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f11,axiom,
! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
fof(f2905,plain,
spl0_267,
inference(avatar_split_clause,[],[f10,f2903]) ).
fof(f2903,plain,
( spl0_267
<=> ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f10,axiom,
! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
fof(f2901,plain,
( ~ spl0_10
| spl0_266
| ~ spl0_90
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2297,f1760,f1055,f2899,f718]) ).
fof(f718,plain,
( spl0_10
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f2899,plain,
( spl0_266
<=> ! [X0] : c_lessequals(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1055,plain,
( spl0_90
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1760,plain,
( spl0_190
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f2297,plain,
( ! [X0] :
( c_lessequals(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_90
| ~ spl0_190 ),
inference(superposition,[],[f1056,f1761]) ).
fof(f1761,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) = X0
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1760]) ).
fof(f1056,plain,
( ! [X1,X6,X24] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X6,X1)
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f2670,plain,
( ~ spl0_10
| spl0_265
| ~ spl0_80
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1894,f1482,f1015,f2668,f718]) ).
fof(f2668,plain,
( spl0_265
<=> ! [X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1015,plain,
( spl0_80
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X24,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1482,plain,
( spl0_164
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1894,plain,
( ! [X0] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_80
| ~ spl0_164 ),
inference(superposition,[],[f1016,f1483]) ).
fof(f1483,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1482]) ).
fof(f1016,plain,
( ! [X1,X6,X24] :
( c_lessequals(X24,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1)
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1015]) ).
fof(f2460,plain,
spl0_264,
inference(avatar_split_clause,[],[f665,f2458]) ).
fof(f2458,plain,
( spl0_264
<=> ! [X14,X6,X2,X1] :
( ~ hBOOL(c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X2,X14,tc_fun(X1,tc_bool)),X1))
| hBOOL(hAPP(X14,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f665,plain,
! [X2,X1,X6,X14] :
( ~ hBOOL(c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X2,X14,tc_fun(X1,tc_bool)),X1))
| hBOOL(hAPP(X14,X6)) ),
inference(forward_demodulation,[],[f88,f29]) ).
fof(f88,axiom,
! [X2,X1,X6,X14] :
( hBOOL(hAPP(X14,X6))
| ~ hBOOL(c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X2,c_Collect(X14,X1),tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
fof(f2456,plain,
spl0_263,
inference(avatar_split_clause,[],[f562,f2453]) ).
fof(f562,axiom,
c_Arrow__Order__Mirabelle_OLin = c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lin__def_0) ).
fof(f2451,plain,
spl0_262,
inference(avatar_split_clause,[],[f552,f2449]) ).
fof(f2449,plain,
( spl0_262
<=> ! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f552,axiom,
! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
fof(f2447,plain,
spl0_261,
inference(avatar_split_clause,[],[f514,f2445]) ).
fof(f2445,plain,
( spl0_261
<=> ! [X1,X8,X31] :
( hBOOL(c_Wellfounded_Owf(X8,X1))
| ~ hBOOL(c_Wellfounded_Owf(c_Nat_Ocompow(X31,X8,tc_prod(X1,X1),tc_bool),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f514,axiom,
! [X31,X1,X8] :
( hBOOL(c_Wellfounded_Owf(X8,X1))
| ~ hBOOL(c_Wellfounded_Owf(c_Nat_Ocompow(X31,X8,tc_prod(X1,X1),tc_bool),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__exp_0) ).
fof(f2443,plain,
spl0_260,
inference(avatar_split_clause,[],[f500,f2441]) ).
fof(f2441,plain,
( spl0_260
<=> ! [X2,X5,X1] :
( ~ c_Finite__Set_Ofinite(X5,X1)
| c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f500,axiom,
! [X2,X1,X5] :
( ~ c_Finite__Set_Ofinite(X5,X1)
| c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
fof(f2439,plain,
spl0_259,
inference(avatar_split_clause,[],[f494,f2437]) ).
fof(f2437,plain,
( spl0_259
<=> ! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f494,axiom,
! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f2435,plain,
spl0_258,
inference(avatar_split_clause,[],[f482,f2433]) ).
fof(f482,axiom,
! [X1,X5] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
fof(f2431,plain,
spl0_257,
inference(avatar_split_clause,[],[f481,f2429]) ).
fof(f2429,plain,
( spl0_257
<=> ! [X2,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f481,axiom,
! [X2,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
fof(f2427,plain,
spl0_256,
inference(avatar_split_clause,[],[f447,f2425]) ).
fof(f2425,plain,
( spl0_256
<=> ! [X4,X9,X6,X2,X1] :
( ~ hBOOL(hAPP(X2,hAPP(X9,X6)))
| hBOOL(hAPP(c_Set_Ovimage(X9,X2,X1,X4),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f447,axiom,
! [X2,X1,X6,X9,X4] :
( ~ hBOOL(hAPP(X2,hAPP(X9,X6)))
| hBOOL(hAPP(c_Set_Ovimage(X9,X2,X1,X4),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
fof(f2423,plain,
spl0_255,
inference(avatar_split_clause,[],[f446,f2421]) ).
fof(f2421,plain,
( spl0_255
<=> ! [X4,X9,X6,X2,X1] :
( hBOOL(hAPP(X2,hAPP(X9,X6)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X9,X2,X1,X4),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f446,axiom,
! [X2,X1,X6,X9,X4] :
( hBOOL(hAPP(X2,hAPP(X9,X6)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X9,X2,X1,X4),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
fof(f2419,plain,
spl0_254,
inference(avatar_split_clause,[],[f425,f2417]) ).
fof(f2417,plain,
( spl0_254
<=> ! [X24,X6,X25,X1] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X6,X24,X1)
| ~ c_lessequals(X24,X25,X1)
| c_lessequals(X6,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f425,axiom,
! [X1,X6,X24,X25] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X6,X24,X1)
| ~ c_lessequals(X24,X25,X1)
| c_lessequals(X6,X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f2415,plain,
spl0_253,
inference(avatar_split_clause,[],[f422,f2413]) ).
fof(f2413,plain,
( spl0_253
<=> ! [X0,X1,X17] :
( ~ c_Wellfounded_Oacyclic(X17,X1)
| c_Wellfounded_Oacyclic(X0,X1)
| ~ c_lessequals(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f422,axiom,
! [X0,X1,X17] :
( ~ c_Wellfounded_Oacyclic(X17,X1)
| c_Wellfounded_Oacyclic(X0,X1)
| ~ c_lessequals(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
fof(f2411,plain,
spl0_252,
inference(avatar_split_clause,[],[f419,f2409]) ).
fof(f2409,plain,
( spl0_252
<=> ! [X0,X1,X17] :
( ~ c_Relation_Oantisym(X17,X1)
| c_Relation_Oantisym(X0,X1)
| ~ c_lessequals(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f419,axiom,
! [X0,X1,X17] :
( ~ c_Relation_Oantisym(X17,X1)
| c_Relation_Oantisym(X0,X1)
| ~ c_lessequals(X0,X17,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
fof(f2407,plain,
( ~ spl0_251
| ~ spl0_59
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2372,f2368,f926,f2404]) ).
fof(f2404,plain,
( spl0_251
<=> hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f926,plain,
( spl0_59
<=> ! [X11,X1] : ~ hBOOL(c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f2368,plain,
( spl0_243
<=> c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2372,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
| ~ spl0_59
| ~ spl0_243 ),
inference(superposition,[],[f927,f2370]) ).
fof(f2370,plain,
( c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2368]) ).
fof(f927,plain,
( ! [X11,X1] : ~ hBOOL(c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f2402,plain,
spl0_250,
inference(avatar_split_clause,[],[f416,f2400]) ).
fof(f2400,plain,
( spl0_250
<=> ! [X14,X6,X1,X30] :
( ~ hBOOL(hAPP(X14,X6))
| hBOOL(hAPP(X30,X6))
| ~ c_lessequals(X14,X30,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f416,axiom,
! [X1,X6,X14,X30] :
( ~ hBOOL(hAPP(X14,X6))
| hBOOL(hAPP(X30,X6))
| ~ c_lessequals(X14,X30,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
fof(f2398,plain,
spl0_249,
inference(avatar_split_clause,[],[f407,f2396]) ).
fof(f2396,plain,
( spl0_249
<=> ! [X24,X6,X25,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X24,X6,X1)
| ~ c_lessequals(X25,X24,X1)
| c_lessequals(X25,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f407,axiom,
! [X1,X6,X24,X25] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X24,X6,X1)
| ~ c_lessequals(X25,X24,X1)
| c_lessequals(X25,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f2394,plain,
spl0_248,
inference(avatar_split_clause,[],[f385,f2392]) ).
fof(f2392,plain,
( spl0_248
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f385,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f2390,plain,
spl0_247,
inference(avatar_split_clause,[],[f384,f2388]) ).
fof(f2388,plain,
( spl0_247
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f384,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f2386,plain,
spl0_246,
inference(avatar_split_clause,[],[f308,f2384]) ).
fof(f2384,plain,
( spl0_246
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f308,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f2382,plain,
spl0_245,
inference(avatar_split_clause,[],[f307,f2380]) ).
fof(f2380,plain,
( spl0_245
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f307,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f2378,plain,
spl0_244,
inference(avatar_split_clause,[],[f279,f2376]) ).
fof(f2376,plain,
( spl0_244
<=> ! [X1,X8,X31] :
( ~ c_Relation_Osingle__valued(X8,X1,X1)
| c_Relation_Osingle__valued(c_Nat_Ocompow(X31,X8,tc_prod(X1,X1),tc_bool),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f279,axiom,
! [X31,X1,X8] :
( ~ c_Relation_Osingle__valued(X8,X1,X1)
| c_Relation_Osingle__valued(c_Nat_Ocompow(X31,X8,tc_prod(X1,X1),tc_bool),X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__pow_0) ).
fof(f2371,plain,
( spl0_243
| ~ spl0_13
| ~ spl0_124
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f2366,f2362,f1265,f733,f2368]) ).
fof(f2362,plain,
( spl0_242
<=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2366,plain,
( c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_13
| ~ spl0_124
| ~ spl0_242 ),
inference(forward_demodulation,[],[f2364,f1422]) ).
fof(f2364,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2362]) ).
fof(f2365,plain,
spl0_242,
inference(avatar_split_clause,[],[f243,f2362]) ).
fof(f243,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
fof(f2348,plain,
spl0_241,
inference(avatar_split_clause,[],[f241,f2346]) ).
fof(f2346,plain,
( spl0_241
<=> ! [X4,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X1),tc_bool)),X4,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f241,axiom,
! [X1,X4] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X1),tc_bool)),X4,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty_0) ).
fof(f2344,plain,
spl0_240,
inference(avatar_split_clause,[],[f237,f2342]) ).
fof(f2342,plain,
( spl0_240
<=> ! [X2,X5,X1] :
( c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f237,axiom,
! [X2,X1,X5] :
( c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f2340,plain,
spl0_239,
inference(avatar_split_clause,[],[f236,f2338]) ).
fof(f2338,plain,
( spl0_239
<=> ! [X2,X5,X1] :
( ~ c_lessequals(X5,X2,tc_fun(X1,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f236,axiom,
! [X2,X1,X5] :
( ~ c_lessequals(X5,X2,tc_fun(X1,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f2336,plain,
spl0_238,
inference(avatar_split_clause,[],[f235,f2334]) ).
fof(f2334,plain,
( spl0_238
<=> ! [X2,X5,X1] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f235,axiom,
! [X2,X1,X5] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f2332,plain,
spl0_237,
inference(avatar_split_clause,[],[f221,f2330]) ).
fof(f2330,plain,
( spl0_237
<=> ! [X2,X5,X1] :
( X2 = X5
| c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f221,axiom,
! [X2,X1,X5] :
( X2 = X5
| c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
fof(f2328,plain,
spl0_236,
inference(avatar_split_clause,[],[f202,f2325]) ).
fof(f2325,plain,
( spl0_236
<=> c_Order__Relation_Olinear__order__on(v_A,v_r,t_a) = c_and(c_Order__Relation_Opartial__order__on(v_A,v_r,t_a),c_Relation_Ototal__on(v_A,v_r,t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f202,axiom,
c_Order__Relation_Olinear__order__on(v_A,v_r,t_a) = c_and(c_Order__Relation_Opartial__order__on(v_A,v_r,t_a),c_Relation_Ototal__on(v_A,v_r,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__order__on__def__raw_0) ).
fof(f2323,plain,
spl0_235,
inference(avatar_split_clause,[],[f134,f2321]) ).
fof(f2321,plain,
( spl0_235
<=> ! [X2,X5,X1] :
( ~ c_lessequals(X5,X2,tc_fun(X1,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f134,axiom,
! [X2,X1,X5] :
( ~ c_lessequals(X5,X2,tc_fun(X1,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f2319,plain,
spl0_234,
inference(avatar_split_clause,[],[f133,f2317]) ).
fof(f2317,plain,
( spl0_234
<=> ! [X2,X5,X1] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f133,axiom,
! [X2,X1,X5] :
( ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f2315,plain,
spl0_233,
inference(avatar_split_clause,[],[f112,f2313]) ).
fof(f2313,plain,
( spl0_233
<=> ! [X4,X9,X6,X1] : hBOOL(c_in(hAPP(X9,X6),c_Set_Oimage(X9,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f112,axiom,
! [X1,X6,X9,X4] : hBOOL(c_in(hAPP(X9,X6),c_Set_Oimage(X9,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
fof(f2311,plain,
spl0_232,
inference(avatar_split_clause,[],[f62,f2309]) ).
fof(f2309,plain,
( spl0_232
<=> ! [X20,X21,X1] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| ~ c_Finite__Set_Ofinite(X21,X1)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X20,X21,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f62,axiom,
! [X21,X1,X20] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| ~ c_Finite__Set_Ofinite(X21,X1)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X20,X21,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
fof(f2296,plain,
spl0_231,
inference(avatar_split_clause,[],[f48,f2294]) ).
fof(f2294,plain,
( spl0_231
<=> ! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f48,axiom,
! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f2292,plain,
spl0_230,
inference(avatar_split_clause,[],[f47,f2290]) ).
fof(f47,axiom,
! [X1,X5] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f2288,plain,
spl0_229,
inference(avatar_split_clause,[],[f24,f2286]) ).
fof(f2286,plain,
( spl0_229
<=> ! [X4,X9,X2,X1] : c_lessequals(c_Set_Oimage(X9,c_Set_Ovimage(X9,X2,X4,X1),X4,X1),X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f24,axiom,
! [X2,X1,X9,X4] : c_lessequals(c_Set_Oimage(X9,c_Set_Ovimage(X9,X2,X4,X1),X4,X1),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
fof(f2284,plain,
spl0_228,
inference(avatar_split_clause,[],[f7,f2282]) ).
fof(f2282,plain,
( spl0_228
<=> ! [X2,X1,X7] :
( hBOOL(c_in(X7,X2,X1))
| hBOOL(c_in(X7,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f7,axiom,
! [X2,X1,X7] :
( hBOOL(c_in(X7,X2,X1))
| hBOOL(c_in(X7,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
fof(f2280,plain,
spl0_227,
inference(avatar_split_clause,[],[f6,f2278]) ).
fof(f2278,plain,
( spl0_227
<=> ! [X2,X1,X7] :
( ~ hBOOL(c_in(X7,X2,X1))
| ~ hBOOL(c_in(X7,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f6,axiom,
! [X2,X1,X7] :
( ~ hBOOL(c_in(X7,X2,X1))
| ~ hBOOL(c_in(X7,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
fof(f2276,plain,
spl0_226,
inference(avatar_split_clause,[],[f3,f2274]) ).
fof(f2274,plain,
( spl0_226
<=> ! [X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f3,axiom,
! [X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
fof(f2272,plain,
spl0_225,
inference(avatar_split_clause,[],[f2,f2270]) ).
fof(f2270,plain,
( spl0_225
<=> ! [X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2,axiom,
! [X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
fof(f1904,plain,
spl0_224,
inference(avatar_split_clause,[],[f541,f1902]) ).
fof(f1902,plain,
( spl0_224
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Olinear__order__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f541,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Olinear__order__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__order__on__converse_1) ).
fof(f1900,plain,
spl0_223,
inference(avatar_split_clause,[],[f540,f1898]) ).
fof(f1898,plain,
( spl0_223
<=> ! [X2,X0,X1] :
( hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f540,axiom,
! [X2,X0,X1] :
( hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__order__on__converse_0) ).
fof(f1891,plain,
spl0_222,
inference(avatar_split_clause,[],[f523,f1889]) ).
fof(f1889,plain,
( spl0_222
<=> ! [X1,X8] :
( ~ hBOOL(c_Wellfounded_Owf(X8,X1))
| hBOOL(c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X1,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f523,axiom,
! [X1,X8] :
( ~ hBOOL(c_Wellfounded_Owf(X8,X1))
| hBOOL(c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X1,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
fof(f1887,plain,
spl0_221,
inference(avatar_split_clause,[],[f522,f1885]) ).
fof(f1885,plain,
( spl0_221
<=> ! [X1,X8] :
( hBOOL(c_Wellfounded_Owf(X8,X1))
| ~ hBOOL(c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X1,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f522,axiom,
! [X1,X8] :
( hBOOL(c_Wellfounded_Owf(X8,X1))
| ~ hBOOL(c_Wellfounded_Owf(c_Relation_Orel__comp(X8,X8,X1,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
fof(f1883,plain,
spl0_220,
inference(avatar_split_clause,[],[f483,f1881]) ).
fof(f1881,plain,
( spl0_220
<=> ! [X4,X1,X9] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Set_Ovimage(X9,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X1,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f483,axiom,
! [X1,X9,X4] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Set_Ovimage(X9,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X1,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
fof(f1879,plain,
spl0_219,
inference(avatar_split_clause,[],[f471,f1877]) ).
fof(f1877,plain,
( spl0_219
<=> ! [X2,X5,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = X5
| c_Orderings_Otop__class_Otop(X1) != c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f471,axiom,
! [X2,X1,X5] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = X5
| c_Orderings_Otop__class_Otop(X1) != c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
fof(f1875,plain,
spl0_218,
inference(avatar_split_clause,[],[f470,f1873]) ).
fof(f1873,plain,
( spl0_218
<=> ! [X2,X5,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = X2
| c_Orderings_Otop__class_Otop(X1) != c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f470,axiom,
! [X2,X1,X5] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = X2
| c_Orderings_Otop__class_Otop(X1) != c_Lattices_Olower__semilattice__class_Oinf(X2,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
fof(f1871,plain,
spl0_217,
inference(avatar_split_clause,[],[f466,f1869]) ).
fof(f1869,plain,
( spl0_217
<=> ! [X6,X2,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X6,X2,X1))
| c_lessequals(X6,c_Complete__Lattice_OSup__class_OSup(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f466,axiom,
! [X2,X1,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X6,X2,X1))
| c_lessequals(X6,c_Complete__Lattice_OSup__class_OSup(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
fof(f1867,plain,
spl0_216,
inference(avatar_split_clause,[],[f462,f1865]) ).
fof(f1865,plain,
( spl0_216
<=> ! [X4,X1,X9] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Ovimage(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X1,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f462,axiom,
! [X1,X9,X4] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Ovimage(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X1,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
fof(f1863,plain,
spl0_215,
inference(avatar_split_clause,[],[f460,f1861]) ).
fof(f460,axiom,
! [X0,X1] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
fof(f1859,plain,
spl0_214,
inference(avatar_split_clause,[],[f457,f1857]) ).
fof(f1857,plain,
( spl0_214
<=> ! [X1] : hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f457,axiom,
! [X1] : hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lnear__order__on__empty_0) ).
fof(f1855,plain,
spl0_213,
inference(avatar_split_clause,[],[f449,f1853]) ).
fof(f1853,plain,
( spl0_213
<=> ! [X2,X0,X1] :
( hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1))
| ~ hBOOL(c_Order__Relation_Opartial__order__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f449,axiom,
! [X2,X0,X1] :
( hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1))
| ~ hBOOL(c_Order__Relation_Opartial__order__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_partial__order__on__converse_0) ).
fof(f1851,plain,
( spl0_212
| ~ spl0_7
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1179,f1095,f703,f1848]) ).
fof(f1848,plain,
( spl0_212
<=> c_Orderings_Otop__class_Otop(tc_bool) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f703,plain,
( spl0_7
<=> class_Lattices_Oboolean__algebra(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1095,plain,
( spl0_100
<=> ! [X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Otop__class_Otop(X1) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1179,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| ~ spl0_7
| ~ spl0_100 ),
inference(resolution,[],[f1096,f705]) ).
fof(f705,plain,
( class_Lattices_Oboolean__algebra(tc_bool)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f1096,plain,
( ! [X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Otop__class_Otop(X1) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1846,plain,
spl0_211,
inference(avatar_split_clause,[],[f448,f1844]) ).
fof(f1844,plain,
( spl0_211
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Opartial__order__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f448,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Opartial__order__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_partial__order__on__converse_1) ).
fof(f1842,plain,
spl0_210,
inference(avatar_split_clause,[],[f444,f1840]) ).
fof(f1840,plain,
( spl0_210
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| hBOOL(c_Relation_Ototal__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f444,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| hBOOL(c_Relation_Ototal__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
fof(f1838,plain,
spl0_209,
inference(avatar_split_clause,[],[f443,f1836]) ).
fof(f1836,plain,
( spl0_209
<=> ! [X2,X0,X1] :
( hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| ~ hBOOL(c_Relation_Ototal__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f443,axiom,
! [X2,X0,X1] :
( hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| ~ hBOOL(c_Relation_Ototal__on(X2,c_Relation_Oconverse(X0,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
fof(f1834,plain,
spl0_208,
inference(avatar_split_clause,[],[f402,f1832]) ).
fof(f1832,plain,
( spl0_208
<=> ! [X11,X12,X6,X1] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X11,X6,X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f402,axiom,
! [X11,X1,X6,X12] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X11,X6,X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
fof(f1830,plain,
spl0_207,
inference(avatar_split_clause,[],[f400,f1828]) ).
fof(f1828,plain,
( spl0_207
<=> ! [X6,X11,X12,X1] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X6,X11,X1)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f400,axiom,
! [X11,X1,X6,X12] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X6,X11,X1)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f1826,plain,
spl0_206,
inference(avatar_split_clause,[],[f399,f1824]) ).
fof(f1824,plain,
( spl0_206
<=> ! [X11,X12,X6,X1] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X6,X12,X1)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f399,axiom,
! [X11,X1,X6,X12] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X6,X12,X1)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f1822,plain,
spl0_205,
inference(avatar_split_clause,[],[f397,f1820]) ).
fof(f1820,plain,
( spl0_205
<=> ! [X6,X25,X1,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X24,X25,X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f397,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X24,X25,X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
fof(f1818,plain,
spl0_204,
inference(avatar_split_clause,[],[f383,f1816]) ).
fof(f1816,plain,
( spl0_204
<=> ! [X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f383,axiom,
! [X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
fof(f1814,plain,
spl0_203,
inference(avatar_split_clause,[],[f329,f1812]) ).
fof(f1812,plain,
( spl0_203
<=> ! [X5,X6,X2,X1] :
( hBOOL(hAPP(X2,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f329,axiom,
! [X2,X1,X6,X5] :
( hBOOL(hAPP(X2,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f1810,plain,
spl0_202,
inference(avatar_split_clause,[],[f328,f1808]) ).
fof(f1808,plain,
( spl0_202
<=> ! [X6,X2,X5,X1] :
( hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f328,axiom,
! [X2,X1,X6,X5] :
( hBOOL(hAPP(X5,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f1806,plain,
( spl0_201
| ~ spl0_6
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1177,f1091,f698,f1804]) ).
fof(f1804,plain,
( spl0_201
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1091,plain,
( spl0_99
<=> ! [X6,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(X1),X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1177,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0
| ~ spl0_6
| ~ spl0_99 ),
inference(resolution,[],[f1092,f700]) ).
fof(f1092,plain,
( ! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(X1),X1) = X6 )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f1802,plain,
spl0_200,
inference(avatar_split_clause,[],[f320,f1800]) ).
fof(f1800,plain,
( spl0_200
<=> ! [X1] : hBOOL(c_Order__Relation_Owell__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f320,axiom,
! [X1] : hBOOL(c_Order__Relation_Owell__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_well__order__on__empty_0) ).
fof(f1798,plain,
spl0_199,
inference(avatar_split_clause,[],[f319,f1796]) ).
fof(f319,axiom,
! [X0,X1] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
fof(f1794,plain,
spl0_198,
inference(avatar_split_clause,[],[f310,f1792]) ).
fof(f1792,plain,
( spl0_198
<=> ! [X4,X1,X9] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f310,axiom,
! [X1,X9,X4] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
fof(f1790,plain,
spl0_197,
inference(avatar_split_clause,[],[f297,f1788]) ).
fof(f1788,plain,
( spl0_197
<=> ! [X2,X5,X1] : c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f297,axiom,
! [X2,X1,X5] : c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f1786,plain,
spl0_196,
inference(avatar_split_clause,[],[f286,f1784]) ).
fof(f1784,plain,
( spl0_196
<=> ! [X24,X6,X25,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X6,X24,X1)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f286,axiom,
! [X1,X6,X24,X25] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X6,X24,X1)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f1782,plain,
spl0_195,
inference(avatar_split_clause,[],[f285,f1780]) ).
fof(f1780,plain,
( spl0_195
<=> ! [X6,X12,X1,X11] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X12,X6,X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f285,axiom,
! [X11,X1,X6,X12] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X12,X6,X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f1778,plain,
spl0_194,
inference(avatar_split_clause,[],[f284,f1776]) ).
fof(f1776,plain,
( spl0_194
<=> ! [X11,X12,X6,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X11,X6,X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f284,axiom,
! [X11,X1,X6,X12] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X11,X6,X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f1774,plain,
spl0_193,
inference(avatar_split_clause,[],[f283,f1772]) ).
fof(f1772,plain,
( spl0_193
<=> ! [X11,X12,X6,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X6,X12,X1)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f283,axiom,
! [X11,X1,X6,X12] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X6,X12,X1)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
fof(f1770,plain,
spl0_192,
inference(avatar_split_clause,[],[f276,f1768]) ).
fof(f1768,plain,
( spl0_192
<=> ! [X2,X5,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = X5
| c_Orderings_Obot__class_Obot(X1) != c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f276,axiom,
! [X2,X1,X5] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = X5
| c_Orderings_Obot__class_Obot(X1) != c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f1766,plain,
spl0_191,
inference(avatar_split_clause,[],[f275,f1764]) ).
fof(f1764,plain,
( spl0_191
<=> ! [X2,X5,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = X2
| c_Orderings_Obot__class_Obot(X1) != c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f275,axiom,
! [X2,X1,X5] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = X2
| c_Orderings_Obot__class_Obot(X1) != c_Lattices_Oupper__semilattice__class_Osup(X2,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f1762,plain,
( spl0_190
| ~ spl0_6
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1175,f1087,f698,f1760]) ).
fof(f1087,plain,
( spl0_98
<=> ! [X6,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X6,X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1175,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) = X0
| ~ spl0_6
| ~ spl0_98 ),
inference(resolution,[],[f1088,f700]) ).
fof(f1088,plain,
( ! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X6,X1) = X6 )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1087]) ).
fof(f1758,plain,
spl0_189,
inference(avatar_split_clause,[],[f227,f1756]) ).
fof(f1756,plain,
( spl0_189
<=> ! [X6,X1,X24] :
( ~ class_Orderings_Oorder(X1)
| X6 = X24
| ~ c_lessequals(X6,X24,X1)
| ~ c_lessequals(X24,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f227,axiom,
! [X1,X6,X24] :
( ~ class_Orderings_Oorder(X1)
| X6 = X24
| ~ c_lessequals(X6,X24,X1)
| ~ c_lessequals(X24,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f1754,plain,
spl0_188,
inference(avatar_split_clause,[],[f209,f1752]) ).
fof(f1752,plain,
( spl0_188
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f209,axiom,
! [X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
fof(f1750,plain,
spl0_187,
inference(avatar_split_clause,[],[f175,f1748]) ).
fof(f1748,plain,
( spl0_187
<=> ! [X5,X6,X2,X1] :
( ~ hBOOL(hAPP(X2,X6))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f175,axiom,
! [X2,X1,X6,X5] :
( ~ hBOOL(hAPP(X2,X6))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f1746,plain,
spl0_186,
inference(avatar_split_clause,[],[f174,f1744]) ).
fof(f1744,plain,
( spl0_186
<=> ! [X6,X2,X5,X1] :
( ~ hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f174,axiom,
! [X2,X1,X6,X5] :
( ~ hBOOL(hAPP(X5,X6))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f1742,plain,
spl0_185,
inference(avatar_split_clause,[],[f149,f1740]) ).
fof(f1740,plain,
( spl0_185
<=> ! [X2,X5,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f149,axiom,
! [X2,X1,X5] : c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f1738,plain,
spl0_184,
inference(avatar_split_clause,[],[f117,f1736]) ).
fof(f1736,plain,
( spl0_184
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ominus__class_Ominus(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ouminus__class_Ouminus(X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f117,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ominus__class_Ominus(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ouminus__class_Ouminus(X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
fof(f1734,plain,
spl0_183,
inference(avatar_split_clause,[],[f70,f1732]) ).
fof(f1732,plain,
( spl0_183
<=> ! [X1] : hBOOL(c_Order__Relation_Opartial__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f70,axiom,
! [X1] : hBOOL(c_Order__Relation_Opartial__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_partial__order__on__empty_0) ).
fof(f1730,plain,
spl0_182,
inference(avatar_split_clause,[],[f50,f1728]) ).
fof(f1728,plain,
( spl0_182
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f50,axiom,
! [X0,X1] : c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
fof(f1726,plain,
spl0_181,
inference(avatar_split_clause,[],[f36,f1724]) ).
fof(f1724,plain,
( spl0_181
<=> ! [X4,X1,X8] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_OImage(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f36,axiom,
! [X1,X8,X4] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_OImage(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
fof(f1721,plain,
( spl0_180
| ~ spl0_7
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1173,f1083,f703,f1719]) ).
fof(f1719,plain,
( spl0_180
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1083,plain,
( spl0_97
<=> ! [X6,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X1),X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1173,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),tc_bool) = X0
| ~ spl0_7
| ~ spl0_97 ),
inference(resolution,[],[f1084,f705]) ).
fof(f1084,plain,
( ! [X1,X6] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X1),X1) = X6 )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1083]) ).
fof(f1579,plain,
( spl0_179
| ~ spl0_24
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1171,f1079,f782,f1577]) ).
fof(f1577,plain,
( spl0_179
<=> ! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Otrancl(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f782,plain,
( spl0_24
<=> ! [X1] : hBOOL(c_Relation_Otrans(c_Relation_OId(X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1171,plain,
( ! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Otrancl(c_Relation_OId(X0),X0)
| ~ spl0_24
| ~ spl0_96 ),
inference(resolution,[],[f1080,f783]) ).
fof(f783,plain,
( ! [X1] : hBOOL(c_Relation_Otrans(c_Relation_OId(X1),X1))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f782]) ).
fof(f1574,plain,
spl0_178,
inference(avatar_split_clause,[],[f561,f1572]) ).
fof(f1572,plain,
( spl0_178
<=> ! [X0,X1] : hBOOL(c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f561,axiom,
! [X0,X1] : hBOOL(c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).
fof(f1570,plain,
spl0_177,
inference(avatar_split_clause,[],[f520,f1568]) ).
fof(f1568,plain,
( spl0_177
<=> ! [X4,X0,X9,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(c_Relation_Oinv__image(X0,X9,X1,X4),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f520,axiom,
! [X0,X1,X9,X4] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(c_Relation_Oinv__image(X0,X9,X1,X4),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
fof(f1566,plain,
spl0_176,
inference(avatar_split_clause,[],[f423,f1564]) ).
fof(f1564,plain,
( spl0_176
<=> ! [X2,X5,X1] :
( ~ c_Finite__Set_Ofinite(X5,X1)
| c_Finite__Set_Ofinite(X2,X1)
| ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f423,axiom,
! [X2,X1,X5] :
( ~ c_Finite__Set_Ofinite(X5,X1)
| c_Finite__Set_Ofinite(X2,X1)
| ~ c_lessequals(X2,X5,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
fof(f1562,plain,
spl0_175,
inference(avatar_split_clause,[],[f258,f1560]) ).
fof(f1560,plain,
( spl0_175
<=> ! [X1] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f258,axiom,
! [X1] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).
fof(f1558,plain,
spl0_174,
inference(avatar_split_clause,[],[f234,f1556]) ).
fof(f1556,plain,
( spl0_174
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X6,X24,X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f234,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X6,X24,X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f1554,plain,
spl0_173,
inference(avatar_split_clause,[],[f233,f1552]) ).
fof(f1552,plain,
( spl0_173
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X6,X24,X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) != X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f233,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X6,X24,X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) != X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f1550,plain,
spl0_172,
inference(avatar_split_clause,[],[f232,f1548]) ).
fof(f1548,plain,
( spl0_172
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X24,X6,X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f232,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X24,X6,X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f1546,plain,
spl0_171,
inference(avatar_split_clause,[],[f219,f1544]) ).
fof(f1544,plain,
( spl0_171
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oboolean__algebra(X1)
| X6 = X24
| c_HOL_Ouminus__class_Ouminus(X6,X1) != c_HOL_Ouminus__class_Ouminus(X24,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f219,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oboolean__algebra(X1)
| X6 = X24
| c_HOL_Ouminus__class_Ouminus(X6,X1) != c_HOL_Ouminus__class_Ouminus(X24,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
fof(f1542,plain,
spl0_170,
inference(avatar_split_clause,[],[f137,f1540]) ).
fof(f1540,plain,
( spl0_170
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X24,X6,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f137,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X24,X6,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f1538,plain,
( spl0_169
| ~ spl0_7
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1149,f1043,f703,f1535]) ).
fof(f1535,plain,
( spl0_169
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1043,plain,
( spl0_87
<=> ! [X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Obot__class_Obot(X1) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1149,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ spl0_7
| ~ spl0_87 ),
inference(resolution,[],[f1044,f705]) ).
fof(f1044,plain,
( ! [X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Obot__class_Obot(X1) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X1),X1) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f1533,plain,
spl0_168,
inference(avatar_split_clause,[],[f136,f1531]) ).
fof(f1531,plain,
( spl0_168
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X6,X24,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) != X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f136,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X6,X24,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) != X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f1529,plain,
spl0_167,
inference(avatar_split_clause,[],[f135,f1527]) ).
fof(f1527,plain,
( spl0_167
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X6,X24,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f135,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X6,X24,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f1525,plain,
spl0_166,
inference(avatar_split_clause,[],[f55,f1523]) ).
fof(f1523,plain,
( spl0_166
<=> ! [X4,X0,X9,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| hBOOL(c_Relation_Otrans(c_Relation_Oinv__image(X0,X9,X1,X4),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f55,axiom,
! [X0,X1,X9,X4] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| hBOOL(c_Relation_Otrans(c_Relation_Oinv__image(X0,X9,X1,X4),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
fof(f1512,plain,
( spl0_165
| ~ spl0_6
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f1142,f1031,f698,f1510]) ).
fof(f1510,plain,
( spl0_165
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1031,plain,
( spl0_84
<=> ! [X6,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X6,X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1142,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_6
| ~ spl0_84 ),
inference(resolution,[],[f1032,f700]) ).
fof(f1032,plain,
( ! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X6,X1) = X6 )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1484,plain,
( spl0_164
| ~ spl0_6
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f1140,f1027,f698,f1482]) ).
fof(f1027,plain,
( spl0_83
<=> ! [X6,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X1),X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1140,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_6
| ~ spl0_83 ),
inference(resolution,[],[f1028,f700]) ).
fof(f1028,plain,
( ! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X1),X1) = X6 )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1428,plain,
( spl0_163
| ~ spl0_57
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1385,f1301,f918,f1425]) ).
fof(f1425,plain,
( spl0_163
<=> c_Relation_Oantisym(v_r,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f918,plain,
( spl0_57
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1301,plain,
( spl0_133
<=> hBOOL(c_Order__Relation_Opartial__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1385,plain,
( c_Relation_Oantisym(v_r,tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_57
| ~ spl0_133 ),
inference(resolution,[],[f1303,f919]) ).
fof(f919,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1))
| c_Relation_Oantisym(X0,X1) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f1303,plain,
( hBOOL(c_Order__Relation_Opartial__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1301]) ).
fof(f1421,plain,
spl0_162,
inference(avatar_split_clause,[],[f551,f1419]) ).
fof(f1419,plain,
( spl0_162
<=> ! [X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f551,axiom,
! [X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
fof(f1417,plain,
spl0_161,
inference(avatar_split_clause,[],[f550,f1415]) ).
fof(f1415,plain,
( spl0_161
<=> ! [X4] :
( ~ class_Orderings_Otop(X4)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X4)),v_x) = c_Orderings_Otop__class_Otop(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f550,axiom,
! [X4] :
( ~ class_Orderings_Otop(X4)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X4)),v_x) = c_Orderings_Otop__class_Otop(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
fof(f1413,plain,
spl0_160,
inference(avatar_split_clause,[],[f547,f1411]) ).
fof(f1411,plain,
( spl0_160
<=> ! [X2,X0,X1] :
( hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f547,axiom,
! [X2,X0,X1] :
( hBOOL(c_Relation_Ototal__on(X2,X0,X1))
| ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).
fof(f1409,plain,
spl0_159,
inference(avatar_split_clause,[],[f517,f1407]) ).
fof(f1407,plain,
( spl0_159
<=> ! [X9,X1,X8] :
( ~ hBOOL(c_Wellfounded_Owf(X8,X1))
| hBOOL(c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X9,X8,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f517,axiom,
! [X1,X8,X9] :
( ~ hBOOL(c_Wellfounded_Owf(X8,X1))
| hBOOL(c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X9,X8,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__mlex_0) ).
fof(f1405,plain,
spl0_158,
inference(avatar_split_clause,[],[f504,f1403]) ).
fof(f1403,plain,
( spl0_158
<=> ! [X2,X5,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f504,axiom,
! [X2,X1,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f1401,plain,
spl0_157,
inference(avatar_split_clause,[],[f503,f1399]) ).
fof(f1399,plain,
( spl0_157
<=> ! [X2,X5,X1] :
( ~ c_Finite__Set_Ofinite(X2,X1)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f503,axiom,
! [X2,X1,X5] :
( ~ c_Finite__Set_Ofinite(X2,X1)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
fof(f1397,plain,
spl0_156,
inference(avatar_split_clause,[],[f496,f1395]) ).
fof(f1395,plain,
( spl0_156
<=> ! [X2,X1] : c_HOL_Ominus__class_Ominus(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f496,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f1393,plain,
spl0_155,
inference(avatar_split_clause,[],[f495,f1391]) ).
fof(f1391,plain,
( spl0_155
<=> ! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f495,axiom,
! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f1389,plain,
spl0_154,
inference(avatar_split_clause,[],[f477,f1387]) ).
fof(f1387,plain,
( spl0_154
<=> ! [X5,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f477,axiom,
! [X1,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
fof(f1384,plain,
spl0_153,
inference(avatar_split_clause,[],[f476,f1382]) ).
fof(f1382,plain,
( spl0_153
<=> ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f476,axiom,
! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
fof(f1380,plain,
spl0_152,
inference(avatar_split_clause,[],[f370,f1378]) ).
fof(f1378,plain,
( spl0_152
<=> ! [X2,X5,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f370,axiom,
! [X2,X1,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f1376,plain,
spl0_151,
inference(avatar_split_clause,[],[f358,f1374]) ).
fof(f1374,plain,
( spl0_151
<=> ! [X20,X21,X1] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f358,axiom,
! [X21,X1,X20] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
fof(f1372,plain,
spl0_150,
inference(avatar_split_clause,[],[f357,f1370]) ).
fof(f1370,plain,
( spl0_150
<=> ! [X20,X21,X1] :
( ~ c_Finite__Set_Ofinite(X21,X1)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f357,axiom,
! [X21,X1,X20] :
( ~ c_Finite__Set_Ofinite(X21,X1)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
fof(f1368,plain,
spl0_149,
inference(avatar_split_clause,[],[f350,f1366]) ).
fof(f1366,plain,
( spl0_149
<=> ! [X2,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f350,axiom,
! [X2,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
fof(f1364,plain,
spl0_148,
inference(avatar_split_clause,[],[f299,f1362]) ).
fof(f1362,plain,
( spl0_148
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = c_Lattices_Oupper__semilattice__class_Osup(X24,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f299,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = c_Lattices_Oupper__semilattice__class_Osup(X24,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f1360,plain,
spl0_147,
inference(avatar_split_clause,[],[f298,f1358]) ).
fof(f1358,plain,
( spl0_147
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = c_Lattices_Oupper__semilattice__class_Osup(X24,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f298,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1) = c_Lattices_Oupper__semilattice__class_Osup(X24,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f1356,plain,
spl0_146,
inference(avatar_split_clause,[],[f269,f1354]) ).
fof(f1354,plain,
( spl0_146
<=> ! [X2,X5,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f269,axiom,
! [X2,X1,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f1352,plain,
spl0_145,
inference(avatar_split_clause,[],[f230,f1350]) ).
fof(f1350,plain,
( spl0_145
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f230,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f1348,plain,
spl0_144,
inference(avatar_split_clause,[],[f216,f1346]) ).
fof(f1346,plain,
( spl0_144
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f216,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f1344,plain,
spl0_143,
inference(avatar_split_clause,[],[f200,f1342]) ).
fof(f1342,plain,
( spl0_143
<=> ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f200,axiom,
! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f1340,plain,
spl0_142,
inference(avatar_split_clause,[],[f199,f1338]) ).
fof(f1338,plain,
( spl0_142
<=> ! [X5,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f199,axiom,
! [X1,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X5,tc_fun(X1,tc_bool)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f1336,plain,
spl0_141,
inference(avatar_split_clause,[],[f194,f1334]) ).
fof(f1334,plain,
( spl0_141
<=> ! [X20,X21,X1] :
( c_Finite__Set_Ofinite(X21,X1)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X20,X21,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f194,axiom,
! [X21,X1,X20] :
( c_Finite__Set_Ofinite(X21,X1)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X20,X21,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
fof(f1332,plain,
spl0_140,
inference(avatar_split_clause,[],[f193,f1330]) ).
fof(f1330,plain,
( spl0_140
<=> ! [X20,X21,X1] :
( c_Finite__Set_Ofinite(X20,X1)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X20,X21,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f193,axiom,
! [X21,X1,X20] :
( c_Finite__Set_Ofinite(X20,X1)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X20,X21,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
fof(f1328,plain,
spl0_139,
inference(avatar_split_clause,[],[f167,f1326]) ).
fof(f1326,plain,
( spl0_139
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X0,X1)
| ~ c_Relation_Orefl__on(X2,c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f167,axiom,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X0,X1)
| ~ c_Relation_Orefl__on(X2,c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
fof(f1324,plain,
spl0_138,
inference(avatar_split_clause,[],[f166,f1322]) ).
fof(f1322,plain,
( spl0_138
<=> ! [X2,X0,X1] :
( ~ c_Relation_Orefl__on(X2,X0,X1)
| c_Relation_Orefl__on(X2,c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f166,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Orefl__on(X2,X0,X1)
| c_Relation_Orefl__on(X2,c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
fof(f1320,plain,
spl0_137,
inference(avatar_split_clause,[],[f163,f1318]) ).
fof(f1318,plain,
( spl0_137
<=> ! [X6,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_HOL_Ouminus__class_Ouminus(X6,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f163,axiom,
! [X1,X6] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_HOL_Ouminus__class_Ouminus(X6,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
fof(f1316,plain,
spl0_136,
inference(avatar_split_clause,[],[f162,f1314]) ).
fof(f1314,plain,
( spl0_136
<=> ! [X6,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X6,X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f162,axiom,
! [X1,X6] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X6,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
fof(f1312,plain,
spl0_135,
inference(avatar_split_clause,[],[f151,f1310]) ).
fof(f1310,plain,
( spl0_135
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X24,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f151,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X24,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f1308,plain,
spl0_134,
inference(avatar_split_clause,[],[f150,f1306]) ).
fof(f1306,plain,
( spl0_134
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X24,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f150,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X24,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f1304,plain,
( spl0_133
| ~ spl0_1
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1257,f1227,f673,f1301]) ).
fof(f1227,plain,
( spl0_118
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1257,plain,
( hBOOL(c_Order__Relation_Opartial__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_1
| ~ spl0_118 ),
inference(resolution,[],[f1228,f675]) ).
fof(f1228,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1)) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f1299,plain,
spl0_132,
inference(avatar_split_clause,[],[f140,f1297]) ).
fof(f1297,plain,
( spl0_132
<=> ! [X2,X5,X1] : c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f140,axiom,
! [X2,X1,X5] : c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f1295,plain,
spl0_131,
inference(avatar_split_clause,[],[f139,f1293]) ).
fof(f1293,plain,
( spl0_131
<=> ! [X2,X5,X1] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f139,axiom,
! [X2,X1,X5] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f1291,plain,
spl0_130,
inference(avatar_split_clause,[],[f101,f1289]) ).
fof(f1289,plain,
( spl0_130
<=> ! [X0,X1] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Relation_ORange(X0,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f101,axiom,
! [X0,X1] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Relation_ORange(X0,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
fof(f1287,plain,
spl0_129,
inference(avatar_split_clause,[],[f59,f1285]) ).
fof(f1285,plain,
( spl0_129
<=> ! [X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f59,axiom,
! [X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
fof(f1283,plain,
spl0_128,
inference(avatar_split_clause,[],[f34,f1281]) ).
fof(f1281,plain,
( spl0_128
<=> ! [X0,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| hBOOL(c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f34,axiom,
! [X0,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| hBOOL(c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).
fof(f1279,plain,
spl0_127,
inference(avatar_split_clause,[],[f33,f1277]) ).
fof(f1277,plain,
( spl0_127
<=> ! [X0,X1] :
( hBOOL(c_Relation_Otrans(X0,X1))
| ~ hBOOL(c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f33,axiom,
! [X0,X1] :
( hBOOL(c_Relation_Otrans(X0,X1))
| ~ hBOOL(c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).
fof(f1275,plain,
spl0_126,
inference(avatar_split_clause,[],[f9,f1273]) ).
fof(f1273,plain,
( spl0_126
<=> ! [X6,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X6,X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f9,axiom,
! [X1,X6] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X6,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
fof(f1271,plain,
spl0_125,
inference(avatar_split_clause,[],[f8,f1269]) ).
fof(f1269,plain,
( spl0_125
<=> ! [X6,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ouminus__class_Ouminus(X6,X1),X1) = c_Orderings_Obot__class_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f8,axiom,
! [X1,X6] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ouminus__class_Ouminus(X6,X1),X1) = c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
fof(f1267,plain,
spl0_124,
inference(avatar_split_clause,[],[f5,f1265]) ).
fof(f5,axiom,
! [X4] :
( ~ class_Orderings_Obot(X4)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X4)),v_x) = c_Orderings_Obot__class_Obot(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
fof(f1262,plain,
( spl0_123
| ~ spl0_1
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1256,f1223,f673,f1259]) ).
fof(f1259,plain,
( spl0_123
<=> hBOOL(c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1223,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(c_Relation_Ototal__on(X2,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1256,plain,
( hBOOL(c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_1
| ~ spl0_117 ),
inference(resolution,[],[f1224,f675]) ).
fof(f1224,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(c_Relation_Ototal__on(X2,X0,X1)) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1223]) ).
fof(f1245,plain,
spl0_122,
inference(avatar_split_clause,[],[f662,f1243]) ).
fof(f1243,plain,
( spl0_122
<=> ! [X6,X1,X14] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X14
| ~ hBOOL(hAPP(X14,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f662,plain,
! [X1,X6,X14] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X14
| ~ hBOOL(hAPP(X14,X6)) ),
inference(forward_demodulation,[],[f381,f29]) ).
fof(f381,axiom,
! [X1,X6,X14] :
( ~ hBOOL(hAPP(X14,X6))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Collect(X14,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
fof(f1241,plain,
spl0_121,
inference(avatar_split_clause,[],[f555,f1239]) ).
fof(f1239,plain,
( spl0_121
<=> ! [X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Relation_OId(X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f555,axiom,
! [X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Relation_OId(X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id_0) ).
fof(f1237,plain,
spl0_120,
inference(avatar_split_clause,[],[f546,f1235]) ).
fof(f1235,plain,
( spl0_120
<=> ! [X2,X0,X1] :
( hBOOL(c_Relation_Oirrefl(X0,X1))
| ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f546,axiom,
! [X2,X0,X1] :
( hBOOL(c_Relation_Oirrefl(X0,X1))
| ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).
fof(f1233,plain,
spl0_119,
inference(avatar_split_clause,[],[f545,f1231]) ).
fof(f1231,plain,
( spl0_119
<=> ! [X2,X0,X1] :
( hBOOL(c_Relation_Otrans(X0,X1))
| ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f545,axiom,
! [X2,X0,X1] :
( hBOOL(c_Relation_Otrans(X0,X1))
| ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X2,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).
fof(f1229,plain,
spl0_118,
inference(avatar_split_clause,[],[f544,f1227]) ).
fof(f544,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__order__on__def_0) ).
fof(f1225,plain,
spl0_117,
inference(avatar_split_clause,[],[f543,f1223]) ).
fof(f543,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1))
| hBOOL(c_Relation_Ototal__on(X2,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__order__on__def_1) ).
fof(f1221,plain,
spl0_116,
inference(avatar_split_clause,[],[f542,f1219]) ).
fof(f1219,plain,
( spl0_116
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Owell__order__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f542,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_Order__Relation_Owell__order__on(X2,X0,X1))
| hBOOL(c_Order__Relation_Olinear__order__on(X2,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_well__order__on__def_0) ).
fof(f1217,plain,
( ~ spl0_10
| spl0_115
| ~ spl0_81
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1159,f1119,f1019,f1215,f718]) ).
fof(f1215,plain,
( spl0_115
<=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1019,plain,
( spl0_81
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1119,plain,
( spl0_106
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1159,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_81
| ~ spl0_106 ),
inference(superposition,[],[f1020,f1120]) ).
fof(f1120,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1119]) ).
fof(f1020,plain,
( ! [X1,X6,X24] :
( c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1)
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1213,plain,
spl0_114,
inference(avatar_split_clause,[],[f518,f1211]) ).
fof(f518,axiom,
! [X0,X1] :
( ~ hBOOL(c_Wellfounded_Owf(X0,X1))
| hBOOL(c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
fof(f1209,plain,
spl0_113,
inference(avatar_split_clause,[],[f473,f1207]) ).
fof(f473,axiom,
! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
fof(f1205,plain,
spl0_112,
inference(avatar_split_clause,[],[f472,f1203]) ).
fof(f472,axiom,
! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
fof(f1201,plain,
spl0_111,
inference(avatar_split_clause,[],[f239,f1199]) ).
fof(f1199,plain,
( spl0_111
<=> ! [X20,X27,X1,X4] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Set_Oimage(X27,X20,X1,X4),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f239,axiom,
! [X1,X27,X4,X20] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Set_Oimage(X27,X20,X1,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
fof(f1197,plain,
spl0_110,
inference(avatar_split_clause,[],[f46,f1195]) ).
fof(f46,axiom,
! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f1193,plain,
spl0_109,
inference(avatar_split_clause,[],[f45,f1191]) ).
fof(f45,axiom,
! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f1189,plain,
spl0_108,
inference(avatar_split_clause,[],[f13,f1187]) ).
fof(f1187,plain,
( spl0_108
<=> ! [X4,X0,X9,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Relation_Oinv__image(X0,X9,X1,X4),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f13,axiom,
! [X0,X1,X9,X4] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Relation_Oinv__image(X0,X9,X1,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
fof(f1139,plain,
( spl0_107
| ~ spl0_4
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f976,f943,f688,f1137]) ).
fof(f1137,plain,
( spl0_107
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f688,plain,
( spl0_4
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f943,plain,
( spl0_63
<=> ! [X6,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f976,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
| ~ spl0_4
| ~ spl0_63 ),
inference(resolution,[],[f944,f690]) ).
fof(f690,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f944,plain,
( ! [X1,X6] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X1) = X6 )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f943]) ).
fof(f1121,plain,
( spl0_106
| ~ spl0_3
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f974,f906,f683,f1119]) ).
fof(f683,plain,
( spl0_3
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f906,plain,
( spl0_54
<=> ! [X6,X1] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f974,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_3
| ~ spl0_54 ),
inference(resolution,[],[f907,f685]) ).
fof(f685,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f907,plain,
( ! [X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X1) = X6 )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f1117,plain,
spl0_105,
inference(avatar_split_clause,[],[f537,f1115]) ).
fof(f1115,plain,
( spl0_105
<=> ! [X4,X1,X8] : c_Relation_Orel__comp(c_Relation_OId(X1),X8,X1,X1,X4) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f537,axiom,
! [X1,X8,X4] : c_Relation_Orel__comp(c_Relation_OId(X1),X8,X1,X1,X4) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
fof(f1113,plain,
spl0_104,
inference(avatar_split_clause,[],[f536,f1111]) ).
fof(f1111,plain,
( spl0_104
<=> ! [X4,X1,X8] : c_Relation_Orel__comp(X8,c_Relation_OId(X4),X1,X4,X4) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f536,axiom,
! [X1,X8,X4] : c_Relation_Orel__comp(X8,c_Relation_OId(X4),X1,X4,X4) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
fof(f1109,plain,
spl0_103,
inference(avatar_split_clause,[],[f525,f1107]) ).
fof(f525,axiom,
! [X1] : hBOOL(c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).
fof(f1105,plain,
spl0_102,
inference(avatar_split_clause,[],[f478,f1103]) ).
fof(f1103,plain,
( spl0_102
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f478,axiom,
! [X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
fof(f1101,plain,
spl0_101,
inference(avatar_split_clause,[],[f475,f1099]) ).
fof(f1099,plain,
( spl0_101
<=> ! [X2,X1] : c_lessequals(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f475,axiom,
! [X2,X1] : c_lessequals(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
fof(f1097,plain,
spl0_100,
inference(avatar_split_clause,[],[f382,f1095]) ).
fof(f382,axiom,
! [X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Otop__class_Otop(X1) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
fof(f1093,plain,
spl0_99,
inference(avatar_split_clause,[],[f369,f1091]) ).
fof(f369,axiom,
! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(X1),X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
fof(f1089,plain,
spl0_98,
inference(avatar_split_clause,[],[f368,f1087]) ).
fof(f368,axiom,
! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X6,X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
fof(f1085,plain,
spl0_97,
inference(avatar_split_clause,[],[f352,f1083]) ).
fof(f352,axiom,
! [X1,X6] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X1),X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
fof(f1081,plain,
spl0_96,
inference(avatar_split_clause,[],[f340,f1079]) ).
fof(f340,axiom,
! [X0,X1] :
( ~ hBOOL(c_Relation_Otrans(X0,X1))
| c_Transitive__Closure_Otrancl(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).
fof(f1077,plain,
spl0_95,
inference(avatar_split_clause,[],[f318,f1075]) ).
fof(f1075,plain,
( spl0_95
<=> ! [X0,X1] :
( c_Relation_Osym(X0,X1)
| ~ c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f318,axiom,
! [X0,X1] :
( c_Relation_Osym(X0,X1)
| ~ c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
fof(f1073,plain,
spl0_94,
inference(avatar_split_clause,[],[f317,f1071]) ).
fof(f1071,plain,
( spl0_94
<=> ! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f317,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
fof(f1069,plain,
spl0_93,
inference(avatar_split_clause,[],[f268,f1067]) ).
fof(f1067,plain,
( spl0_93
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f268,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f1065,plain,
spl0_92,
inference(avatar_split_clause,[],[f267,f1063]) ).
fof(f1063,plain,
( spl0_92
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X24,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f267,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X24,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f1061,plain,
spl0_91,
inference(avatar_split_clause,[],[f263,f1059]) ).
fof(f1059,plain,
( spl0_91
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X24,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f263,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X24,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f1057,plain,
spl0_90,
inference(avatar_split_clause,[],[f262,f1055]) ).
fof(f262,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X24,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f1053,plain,
spl0_89,
inference(avatar_split_clause,[],[f224,f1051]) ).
fof(f1051,plain,
( spl0_89
<=> ! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f224,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
fof(f1049,plain,
spl0_88,
inference(avatar_split_clause,[],[f223,f1047]) ).
fof(f1047,plain,
( spl0_88
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f223,axiom,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
fof(f1045,plain,
spl0_87,
inference(avatar_split_clause,[],[f208,f1043]) ).
fof(f208,axiom,
! [X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Orderings_Obot__class_Obot(X1) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
fof(f1041,plain,
spl0_86,
inference(avatar_split_clause,[],[f207,f1039]) ).
fof(f1039,plain,
( spl0_86
<=> ! [X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| c_Relation_Oantisym(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f207,axiom,
! [X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| c_Relation_Oantisym(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
fof(f1037,plain,
spl0_85,
inference(avatar_split_clause,[],[f206,f1035]) ).
fof(f1035,plain,
( spl0_85
<=> ! [X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f206,axiom,
! [X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
fof(f1033,plain,
spl0_84,
inference(avatar_split_clause,[],[f198,f1031]) ).
fof(f198,axiom,
! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X6,X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1029,plain,
spl0_83,
inference(avatar_split_clause,[],[f197,f1027]) ).
fof(f197,axiom,
! [X1,X6] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X1),X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1025,plain,
spl0_82,
inference(avatar_split_clause,[],[f184,f1023]) ).
fof(f1023,plain,
( spl0_82
<=> ! [X4,X0,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X4),X4,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f184,axiom,
! [X0,X1,X4] : c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X4),X4,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
fof(f1021,plain,
spl0_81,
inference(avatar_split_clause,[],[f148,f1019]) ).
fof(f148,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f1017,plain,
spl0_80,
inference(avatar_split_clause,[],[f147,f1015]) ).
fof(f147,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X24,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f1013,plain,
spl0_79,
inference(avatar_split_clause,[],[f144,f1011]) ).
fof(f1011,plain,
( spl0_79
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X24,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f144,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X24,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1009,plain,
spl0_78,
inference(avatar_split_clause,[],[f143,f1007]) ).
fof(f1007,plain,
( spl0_78
<=> ! [X6,X1,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f143,axiom,
! [X1,X6,X24] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X24,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1005,plain,
spl0_77,
inference(avatar_split_clause,[],[f108,f1003]) ).
fof(f1003,plain,
( spl0_77
<=> ! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Oconverse(X0,X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f108,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Oconverse(X0,X1,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
fof(f1001,plain,
spl0_76,
inference(avatar_split_clause,[],[f107,f999]) ).
fof(f999,plain,
( spl0_76
<=> ! [X0,X1] :
( c_Relation_Osym(X0,X1)
| c_Relation_Oconverse(X0,X1,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f107,axiom,
! [X0,X1] :
( c_Relation_Osym(X0,X1)
| c_Relation_Oconverse(X0,X1,X1) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
fof(f997,plain,
( spl0_75
| ~ spl0_32
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f899,f886,f814,f995]) ).
fof(f995,plain,
( spl0_75
<=> ! [X0,X1] : c_Wellfounded_Oacyclic(c_List_Omeasures(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f814,plain,
( spl0_32
<=> ! [X1,X49] : hBOOL(c_Wellfounded_Owf(c_List_Omeasures(X49,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f899,plain,
( ! [X0,X1] : c_Wellfounded_Oacyclic(c_List_Omeasures(X0,X1),X1)
| ~ spl0_32
| ~ spl0_50 ),
inference(resolution,[],[f887,f815]) ).
fof(f815,plain,
( ! [X49,X1] : hBOOL(c_Wellfounded_Owf(c_List_Omeasures(X49,X1),X1))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f993,plain,
spl0_74,
inference(avatar_split_clause,[],[f106,f991]) ).
fof(f991,plain,
( spl0_74
<=> ! [X6,X1,X10] :
( hBOOL(hAPP(X10,X6))
| ~ hBOOL(c_in(X6,X10,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f106,axiom,
! [X10,X1,X6] :
( hBOOL(hAPP(X10,X6))
| ~ hBOOL(c_in(X6,X10,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f989,plain,
spl0_73,
inference(avatar_split_clause,[],[f105,f987]) ).
fof(f987,plain,
( spl0_73
<=> ! [X6,X1,X10] :
( ~ hBOOL(hAPP(X10,X6))
| hBOOL(c_in(X6,X10,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f105,axiom,
! [X10,X1,X6] :
( ~ hBOOL(hAPP(X10,X6))
| hBOOL(c_in(X6,X10,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f985,plain,
spl0_72,
inference(avatar_split_clause,[],[f30,f983]) ).
fof(f983,plain,
( spl0_72
<=> ! [X2,X1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f30,axiom,
! [X2,X1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f981,plain,
( spl0_71
| ~ spl0_31
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f898,f886,f810,f979]) ).
fof(f979,plain,
( spl0_71
<=> ! [X0,X1] : c_Wellfounded_Oacyclic(c_Wellfounded_Omeasure(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f810,plain,
( spl0_31
<=> ! [X9,X1] : hBOOL(c_Wellfounded_Owf(c_Wellfounded_Omeasure(X9,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f898,plain,
( ! [X0,X1] : c_Wellfounded_Oacyclic(c_Wellfounded_Omeasure(X0,X1),X1)
| ~ spl0_31
| ~ spl0_50 ),
inference(resolution,[],[f887,f811]) ).
fof(f811,plain,
( ! [X1,X9] : hBOOL(c_Wellfounded_Owf(c_Wellfounded_Omeasure(X9,X1),X1))
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f973,plain,
spl0_70,
inference(avatar_split_clause,[],[f580,f971]) ).
fof(f971,plain,
( spl0_70
<=> ! [X52,X53] :
( ~ class_Finite__Set_Ofinite_Ofinite(X52)
| ~ class_Finite__Set_Ofinite_Ofinite(X53)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f580,axiom,
! [X52,X53] :
( ~ class_Finite__Set_Ofinite_Ofinite(X52)
| ~ class_Finite__Set_Ofinite_Ofinite(X53)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f969,plain,
spl0_69,
inference(avatar_split_clause,[],[f573,f967]) ).
fof(f967,plain,
( spl0_69
<=> ! [X52,X53] :
( ~ class_Finite__Set_Ofinite_Ofinite(X52)
| ~ class_Finite__Set_Ofinite_Ofinite(X53)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f573,axiom,
! [X52,X53] :
( ~ class_Finite__Set_Ofinite_Ofinite(X52)
| ~ class_Finite__Set_Ofinite_Ofinite(X53)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
fof(f965,plain,
spl0_68,
inference(avatar_split_clause,[],[f554,f963]) ).
fof(f963,plain,
( spl0_68
<=> ! [X1] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Relation_OId(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f554,axiom,
! [X1] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Relation_OId(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__Id_0) ).
fof(f961,plain,
spl0_67,
inference(avatar_split_clause,[],[f535,f959]) ).
fof(f959,plain,
( spl0_67
<=> ! [X2,X1] : c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f535,axiom,
! [X2,X1] : c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
fof(f957,plain,
spl0_66,
inference(avatar_split_clause,[],[f533,f955]) ).
fof(f955,plain,
( spl0_66
<=> ! [X1] : c_Relation_OId(X1) = c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f533,axiom,
! [X1] : c_Relation_OId(X1) = c_Relation_Oconverse(c_Relation_OId(X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
fof(f953,plain,
spl0_65,
inference(avatar_split_clause,[],[f480,f951]) ).
fof(f951,plain,
( spl0_65
<=> ! [X6,X1] : hBOOL(c_in(X6,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f480,axiom,
! [X1,X6] : hBOOL(c_in(X6,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f949,plain,
spl0_64,
inference(avatar_split_clause,[],[f396,f947]) ).
fof(f947,plain,
( spl0_64
<=> ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,X2,tc_fun(X1,tc_bool)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f396,axiom,
! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X2,X2,tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f945,plain,
spl0_63,
inference(avatar_split_clause,[],[f395,f943]) ).
fof(f395,axiom,
! [X1,X6] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f941,plain,
spl0_62,
inference(avatar_split_clause,[],[f341,f939]) ).
fof(f939,plain,
( spl0_62
<=> ! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f341,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
fof(f937,plain,
spl0_61,
inference(avatar_split_clause,[],[f259,f935]) ).
fof(f935,plain,
( spl0_61
<=> ! [X0,X1] : hBOOL(c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f259,axiom,
! [X0,X1] : hBOOL(c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
fof(f933,plain,
( spl0_60
| ~ spl0_18
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f897,f886,f757,f930]) ).
fof(f930,plain,
( spl0_60
<=> c_Wellfounded_Oacyclic(c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f757,plain,
( spl0_18
<=> hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f897,plain,
( c_Wellfounded_Oacyclic(c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_18
| ~ spl0_50 ),
inference(resolution,[],[f887,f759]) ).
fof(f759,plain,
( hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f928,plain,
spl0_59,
inference(avatar_split_clause,[],[f254,f926]) ).
fof(f254,axiom,
! [X11,X1] : ~ hBOOL(c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
fof(f924,plain,
spl0_58,
inference(avatar_split_clause,[],[f240,f922]) ).
fof(f922,plain,
( spl0_58
<=> ! [X1] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f240,axiom,
! [X1] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).
fof(f920,plain,
spl0_57,
inference(avatar_split_clause,[],[f183,f918]) ).
fof(f183,axiom,
! [X2,X0,X1] :
( c_Relation_Oantisym(X0,X1)
| ~ hBOOL(c_Order__Relation_Opartial__order__on(X2,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_partial__order__on__def_1) ).
fof(f916,plain,
spl0_56,
inference(avatar_split_clause,[],[f119,f914]) ).
fof(f914,plain,
( spl0_56
<=> ! [X4,X1,X9] : c_Fun_Oinj__on(X9,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f119,axiom,
! [X1,X9,X4] : c_Fun_Oinj__on(X9,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
fof(f912,plain,
spl0_55,
inference(avatar_split_clause,[],[f109,f910]) ).
fof(f910,plain,
( spl0_55
<=> ! [X4,X14,X30,X1] : hAPP(c_COMBK(X14,X1,X4),X30) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f109,axiom,
! [X1,X14,X4,X30] : hAPP(c_COMBK(X14,X1,X4),X30) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f908,plain,
spl0_54,
inference(avatar_split_clause,[],[f95,f906]) ).
fof(f95,axiom,
! [X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X1) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f904,plain,
spl0_53,
inference(avatar_split_clause,[],[f94,f902]) ).
fof(f902,plain,
( spl0_53
<=> ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X2,X2,tc_fun(X1,tc_bool)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f94,axiom,
! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X2,X2,tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f896,plain,
spl0_52,
inference(avatar_split_clause,[],[f605,f894]) ).
fof(f894,plain,
( spl0_52
<=> ! [X54,X1,X55] :
( X54 = X55
| ~ c_fequal(X54,X55,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f605,axiom,
! [X1,X54,X55] :
( X54 = X55
| ~ c_fequal(X54,X55,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f892,plain,
spl0_51,
inference(avatar_split_clause,[],[f565,f890]) ).
fof(f890,plain,
( spl0_51
<=> ! [X6,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f565,axiom,
! [X1,X6] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
fof(f888,plain,
spl0_50,
inference(avatar_split_clause,[],[f524,f886]) ).
fof(f524,axiom,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ hBOOL(c_Wellfounded_Owf(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
fof(f884,plain,
spl0_49,
inference(avatar_split_clause,[],[f367,f882]) ).
fof(f882,plain,
( spl0_49
<=> ! [X6,X1] :
( ~ class_Orderings_Otop(X1)
| c_lessequals(X6,c_Orderings_Otop__class_Otop(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f367,axiom,
! [X1,X6] :
( ~ class_Orderings_Otop(X1)
| c_lessequals(X6,c_Orderings_Otop__class_Otop(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
fof(f880,plain,
spl0_48,
inference(avatar_split_clause,[],[f210,f878]) ).
fof(f878,plain,
( spl0_48
<=> ! [X6,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f210,axiom,
! [X1,X6] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f876,plain,
spl0_47,
inference(avatar_split_clause,[],[f32,f874]) ).
fof(f874,plain,
( spl0_47
<=> ! [X6,X1] :
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f32,axiom,
! [X1,X6] :
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f872,plain,
spl0_46,
inference(avatar_split_clause,[],[f588,f870]) ).
fof(f870,plain,
( spl0_46
<=> ! [X52,X53] :
( ~ class_HOL_Oord(X53)
| class_HOL_Oord(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f588,axiom,
! [X52,X53] :
( ~ class_HOL_Oord(X53)
| class_HOL_Oord(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f868,plain,
spl0_45,
inference(avatar_split_clause,[],[f587,f866]) ).
fof(f866,plain,
( spl0_45
<=> ! [X52,X53] :
( ~ class_HOL_Ominus(X53)
| class_HOL_Ominus(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f587,axiom,
! [X52,X53] :
( ~ class_HOL_Ominus(X53)
| class_HOL_Ominus(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
fof(f864,plain,
spl0_44,
inference(avatar_split_clause,[],[f586,f862]) ).
fof(f862,plain,
( spl0_44
<=> ! [X52,X53] :
( ~ class_HOL_Ouminus(X53)
| class_HOL_Ouminus(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f586,axiom,
! [X52,X53] :
( ~ class_HOL_Ouminus(X53)
| class_HOL_Ouminus(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).
fof(f860,plain,
spl0_43,
inference(avatar_split_clause,[],[f585,f858]) ).
fof(f858,plain,
( spl0_43
<=> ! [X52,X53] :
( ~ class_Orderings_Obot(X53)
| class_Orderings_Obot(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f585,axiom,
! [X52,X53] :
( ~ class_Orderings_Obot(X53)
| class_Orderings_Obot(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f856,plain,
spl0_42,
inference(avatar_split_clause,[],[f584,f854]) ).
fof(f854,plain,
( spl0_42
<=> ! [X52,X53] :
( ~ class_Orderings_Otop(X53)
| class_Orderings_Otop(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f584,axiom,
! [X52,X53] :
( ~ class_Orderings_Otop(X53)
| class_Orderings_Otop(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
fof(f852,plain,
spl0_41,
inference(avatar_split_clause,[],[f583,f850]) ).
fof(f850,plain,
( spl0_41
<=> ! [X52,X53] :
( ~ class_Orderings_Oorder(X53)
| class_Orderings_Oorder(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f583,axiom,
! [X52,X53] :
( ~ class_Orderings_Oorder(X53)
| class_Orderings_Oorder(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f848,plain,
spl0_40,
inference(avatar_split_clause,[],[f582,f846]) ).
fof(f846,plain,
( spl0_40
<=> ! [X52,X53] :
( ~ class_Lattices_Olattice(X53)
| class_Lattices_Olattice(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f582,axiom,
! [X52,X53] :
( ~ class_Lattices_Olattice(X53)
| class_Lattices_Olattice(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f844,plain,
spl0_39,
inference(avatar_split_clause,[],[f581,f842]) ).
fof(f842,plain,
( spl0_39
<=> ! [X52,X53] :
( ~ class_Orderings_Opreorder(X53)
| class_Orderings_Opreorder(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f581,axiom,
! [X52,X53] :
( ~ class_Orderings_Opreorder(X53)
| class_Orderings_Opreorder(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f840,plain,
spl0_38,
inference(avatar_split_clause,[],[f579,f838]) ).
fof(f838,plain,
( spl0_38
<=> ! [X52,X53] :
( ~ class_Lattices_Oboolean__algebra(X53)
| class_Lattices_Oboolean__algebra(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f579,axiom,
! [X52,X53] :
( ~ class_Lattices_Oboolean__algebra(X53)
| class_Lattices_Oboolean__algebra(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(f836,plain,
spl0_37,
inference(avatar_split_clause,[],[f578,f834]) ).
fof(f834,plain,
( spl0_37
<=> ! [X52,X53] :
( ~ class_Lattices_Obounded__lattice(X53)
| class_Lattices_Obounded__lattice(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f578,axiom,
! [X52,X53] :
( ~ class_Lattices_Obounded__lattice(X53)
| class_Lattices_Obounded__lattice(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f832,plain,
spl0_36,
inference(avatar_split_clause,[],[f577,f830]) ).
fof(f830,plain,
( spl0_36
<=> ! [X52,X53] :
( ~ class_Lattices_Odistrib__lattice(X53)
| class_Lattices_Odistrib__lattice(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f577,axiom,
! [X52,X53] :
( ~ class_Lattices_Odistrib__lattice(X53)
| class_Lattices_Odistrib__lattice(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f828,plain,
spl0_35,
inference(avatar_split_clause,[],[f576,f826]) ).
fof(f826,plain,
( spl0_35
<=> ! [X52,X53] :
( ~ class_Lattices_Olattice(X53)
| class_Lattices_Olower__semilattice(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f576,axiom,
! [X52,X53] :
( ~ class_Lattices_Olattice(X53)
| class_Lattices_Olower__semilattice(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f824,plain,
spl0_34,
inference(avatar_split_clause,[],[f575,f822]) ).
fof(f822,plain,
( spl0_34
<=> ! [X52,X53] :
( ~ class_Lattices_Olattice(X53)
| class_Lattices_Oupper__semilattice(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f575,axiom,
! [X52,X53] :
( ~ class_Lattices_Olattice(X53)
| class_Lattices_Oupper__semilattice(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f820,plain,
spl0_33,
inference(avatar_split_clause,[],[f574,f818]) ).
fof(f818,plain,
( spl0_33
<=> ! [X52,X53] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X53)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X52,X53)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f574,axiom,
! [X52,X53] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X53)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f816,plain,
spl0_32,
inference(avatar_split_clause,[],[f515,f814]) ).
fof(f515,axiom,
! [X49,X1] : hBOOL(c_Wellfounded_Owf(c_List_Omeasures(X49,X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__measures_0) ).
fof(f812,plain,
spl0_31,
inference(avatar_split_clause,[],[f510,f810]) ).
fof(f510,axiom,
! [X1,X9] : hBOOL(c_Wellfounded_Owf(c_Wellfounded_Omeasure(X9,X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__measure_0) ).
fof(f808,plain,
spl0_30,
inference(avatar_split_clause,[],[f418,f806]) ).
fof(f806,plain,
( spl0_30
<=> ! [X6,X1] :
( ~ class_Orderings_Opreorder(X1)
| c_lessequals(X6,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f418,axiom,
! [X1,X6] :
( ~ class_Orderings_Opreorder(X1)
| c_lessequals(X6,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f804,plain,
spl0_29,
inference(avatar_split_clause,[],[f417,f802]) ).
fof(f802,plain,
( spl0_29
<=> ! [X6,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X6,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f417,axiom,
! [X1,X6] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X6,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f800,plain,
spl0_28,
inference(avatar_split_clause,[],[f413,f798]) ).
fof(f798,plain,
( spl0_28
<=> ! [X2,X1] : c_lessequals(X2,X2,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f413,axiom,
! [X2,X1] : c_lessequals(X2,X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
fof(f796,plain,
spl0_27,
inference(avatar_split_clause,[],[f97,f794]) ).
fof(f97,axiom,
! [X0,X1] : hBOOL(c_Relation_Otrans(c_Transitive__Closure_Otrancl(X0,X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
fof(f792,plain,
spl0_26,
inference(avatar_split_clause,[],[f54,f790]) ).
fof(f790,plain,
( spl0_26
<=> ! [X1] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f54,axiom,
! [X1] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
fof(f788,plain,
spl0_25,
inference(avatar_split_clause,[],[f534,f786]) ).
fof(f786,plain,
( spl0_25
<=> ! [X1] : c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f534,axiom,
! [X1] : c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
fof(f784,plain,
spl0_24,
inference(avatar_split_clause,[],[f531,f782]) ).
fof(f531,axiom,
! [X1] : hBOOL(c_Relation_Otrans(c_Relation_OId(X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).
fof(f780,plain,
spl0_23,
inference(avatar_split_clause,[],[f321,f778]) ).
fof(f778,plain,
( spl0_23
<=> ! [X2,X1] :
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f321,axiom,
! [X2,X1] :
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
fof(f776,plain,
spl0_22,
inference(avatar_split_clause,[],[f29,f774]) ).
fof(f772,plain,
spl0_21,
inference(avatar_split_clause,[],[f604,f770]) ).
fof(f770,plain,
( spl0_21
<=> ! [X6,X1] : c_fequal(X6,X6,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f604,axiom,
! [X1,X6] : c_fequal(X6,X6,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f768,plain,
spl0_20,
inference(avatar_split_clause,[],[f538,f766]) ).
fof(f766,plain,
( spl0_20
<=> ! [X1] : c_Relation_Osym(c_Relation_OId(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f538,axiom,
! [X1] : c_Relation_Osym(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
fof(f764,plain,
spl0_19,
inference(avatar_split_clause,[],[f532,f762]) ).
fof(f762,plain,
( spl0_19
<=> ! [X1] : c_Relation_Oantisym(c_Relation_OId(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f532,axiom,
! [X1] : c_Relation_Oantisym(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
fof(f760,plain,
spl0_18,
inference(avatar_split_clause,[],[f571,f757]) ).
fof(f571,axiom,
hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f755,plain,
spl0_17,
inference(avatar_split_clause,[],[f572,f753]) ).
fof(f572,axiom,
! [X6] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f751,plain,
spl0_16,
inference(avatar_split_clause,[],[f603,f748]) ).
fof(f748,plain,
( spl0_16
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f603,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f746,plain,
spl0_15,
inference(avatar_split_clause,[],[f602,f743]) ).
fof(f743,plain,
( spl0_15
<=> class_HOL_Ominus(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f602,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
fof(f741,plain,
spl0_14,
inference(avatar_split_clause,[],[f601,f738]) ).
fof(f738,plain,
( spl0_14
<=> class_HOL_Ouminus(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f601,axiom,
class_HOL_Ouminus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
fof(f736,plain,
spl0_13,
inference(avatar_split_clause,[],[f600,f733]) ).
fof(f600,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f731,plain,
spl0_12,
inference(avatar_split_clause,[],[f599,f728]) ).
fof(f728,plain,
( spl0_12
<=> class_Orderings_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f599,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
fof(f726,plain,
spl0_11,
inference(avatar_split_clause,[],[f598,f723]) ).
fof(f723,plain,
( spl0_11
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f598,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f721,plain,
spl0_10,
inference(avatar_split_clause,[],[f597,f718]) ).
fof(f597,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f716,plain,
spl0_9,
inference(avatar_split_clause,[],[f596,f713]) ).
fof(f713,plain,
( spl0_9
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f596,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f711,plain,
spl0_8,
inference(avatar_split_clause,[],[f595,f708]) ).
fof(f708,plain,
( spl0_8
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f595,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f706,plain,
spl0_7,
inference(avatar_split_clause,[],[f594,f703]) ).
fof(f594,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
fof(f701,plain,
spl0_6,
inference(avatar_split_clause,[],[f593,f698]) ).
fof(f593,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f696,plain,
spl0_5,
inference(avatar_split_clause,[],[f592,f693]) ).
fof(f693,plain,
( spl0_5
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f592,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f691,plain,
spl0_4,
inference(avatar_split_clause,[],[f591,f688]) ).
fof(f591,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f686,plain,
spl0_3,
inference(avatar_split_clause,[],[f590,f683]) ).
fof(f590,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f681,plain,
spl0_2,
inference(avatar_split_clause,[],[f589,f678]) ).
fof(f678,plain,
( spl0_2
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f589,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(f676,plain,
spl0_1,
inference(avatar_split_clause,[],[f570,f673]) ).
fof(f570,axiom,
hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SCT007-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 14:10:57 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (24604)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.40 % (24609)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.41 % (24607)WARNING: value z3 for option sas not known
% 0.14/0.41 % (24605)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.41 % (24606)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.41 % (24608)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.41 % (24607)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.41 % (24610)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.41 % (24611)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.52 % (24609)First to succeed.
% 0.22/0.53 % (24609)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-24604"
% 0.22/0.53 % (24609)Refutation found. Thanks to Tanya!
% 0.22/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.54 % (24609)------------------------------
% 0.22/0.54 % (24609)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.54 % (24609)Termination reason: Refutation
% 0.22/0.54
% 0.22/0.54 % (24609)Memory used [KB]: 3322
% 0.22/0.54 % (24609)Time elapsed: 0.127 s
% 0.22/0.54 % (24609)Instructions burned: 286 (million)
% 0.22/0.54 % (24604)Success in time 0.171 s
%------------------------------------------------------------------------------