TSTP Solution File: SWV906-1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV906-1 : 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 : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 17:07:54 EDT 2024

% Result   : Unsatisfiable 0.23s 0.56s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  756
% Syntax   : Number of formulae    : 1303 ( 499 unt;   0 def)
%            Number of atoms       : 2637 ( 576 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 2294 ( 960   ~; 933   |;   0   &)
%                                         ( 401 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :  423 ( 421 usr; 404 prp; 0-3 aty)
%            Number of functors    :   57 (  57 usr;  14 con; 0-5 aty)
%            Number of variables   : 2599 (2599   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4771,plain,
    $false,
    inference(avatar_sat_refutation,[],[f600,f605,f610,f615,f620,f625,f630,f635,f640,f645,f650,f655,f660,f665,f670,f675,f680,f685,f690,f695,f700,f705,f710,f715,f719,f724,f730,f734,f738,f742,f746,f750,f754,f758,f762,f767,f773,f777,f781,f785,f789,f793,f797,f801,f805,f809,f813,f817,f821,f826,f830,f834,f838,f842,f846,f850,f854,f858,f862,f866,f871,f875,f879,f883,f887,f891,f895,f899,f903,f907,f911,f915,f919,f923,f927,f931,f935,f940,f944,f948,f952,f956,f960,f964,f968,f972,f976,f980,f984,f988,f992,f996,f1000,f1004,f1008,f1012,f1016,f1020,f1024,f1028,f1032,f1039,f1047,f1052,f1056,f1060,f1064,f1068,f1072,f1076,f1080,f1084,f1088,f1092,f1096,f1100,f1104,f1108,f1112,f1116,f1120,f1124,f1128,f1132,f1136,f1140,f1144,f1181,f1185,f1189,f1193,f1197,f1201,f1205,f1209,f1213,f1217,f1221,f1225,f1229,f1234,f1238,f1242,f1246,f1251,f1255,f1259,f1263,f1268,f1294,f1298,f1303,f1307,f1311,f1315,f1319,f1323,f1327,f1331,f1335,f1339,f1343,f1347,f1351,f1355,f1359,f1363,f1367,f1371,f1375,f1379,f1383,f1388,f1392,f1396,f1401,f1405,f1409,f1413,f1417,f1421,f1426,f1442,f1499,f1516,f1520,f1525,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1557,f1561,f1565,f1569,f1573,f1577,f1581,f1585,f1589,f1593,f1597,f1601,f1605,f1717,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1760,f1764,f1768,f1772,f1776,f1780,f1784,f1788,f1793,f1806,f1810,f1814,f1995,f1999,f2003,f2007,f2011,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2063,f2067,f2071,f2075,f2079,f2083,f2087,f2091,f2095,f2099,f2104,f2109,f2115,f2125,f2135,f2141,f2146,f2151,f2156,f2186,f2269,f2409,f2420,f2424,f2428,f2432,f2436,f2440,f2444,f2448,f2454,f2458,f2462,f2466,f2470,f2474,f2478,f2482,f2486,f2490,f2494,f2498,f2502,f2507,f2780,f2784,f2788,f2792,f2796,f2800,f2804,f2808,f2812,f2816,f2820,f2824,f2899,f2966,f2970,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3002,f3006,f3010,f3014,f3018,f3022,f3027,f3031,f3036,f3042,f3097,f3336,f3340,f3344,f3348,f3352,f3356,f3360,f3364,f3368,f3372,f3376,f3380,f3384,f3388,f3392,f3396,f3401,f3424,f3429,f3658,f3718,f3722,f3726,f3730,f3734,f3738,f3742,f3746,f3750,f3754,f3758,f3764,f3769,f4026,f4030,f4034,f4062,f4066,f4070,f4074,f4079,f4098,f4103,f4120,f4125,f4129,f4286,f4290,f4295,f4299,f4303,f4307,f4311,f4315,f4319,f4323,f4327,f4426,f4430,f4435,f4439,f4443,f4447,f4451,f4455,f4459,f4463,f4467,f4471,f4475,f4498,f4683,f4717,f4721,f4725,f4729,f4733,f4737,f4741,f4768]) ).

fof(f4768,plain,
    ( ~ spl0_40
    | ~ spl0_394 ),
    inference(avatar_contradiction_clause,[],[f4767]) ).

fof(f4767,plain,
    ( $false
    | ~ spl0_40
    | ~ spl0_394 ),
    inference(trivial_inequality_removal,[],[f4750]) ).

fof(f4750,plain,
    ( c_Option_Ooption_ONone(tc_Com_Ocom) != c_Option_Ooption_ONone(tc_Com_Ocom)
    | ~ spl0_40
    | ~ spl0_394 ),
    inference(superposition,[],[f784,f4682]) ).

fof(f4682,plain,
    ( c_Option_Ooption_ONone(tc_Com_Ocom) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom)
    | ~ spl0_394 ),
    inference(avatar_component_clause,[],[f4680]) ).

fof(f4680,plain,
    ( spl0_394
  <=> c_Option_Ooption_ONone(tc_Com_Ocom) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f784,plain,
    ( ! [X3,X6] : c_Option_Ooption_ONone(X3) != c_Option_Ooption_OSome(X6,X3)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f783]) ).

fof(f783,plain,
    ( spl0_40
  <=> ! [X6,X3] : c_Option_Ooption_ONone(X3) != c_Option_Ooption_OSome(X6,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f4741,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f526,f4739]) ).

fof(f4739,plain,
    ( spl0_401
  <=> ! [X4,X47,X0,X3] : c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3) = c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3),X4,c_Option_Ooption_OSome(X47,X0),X3,tc_Option_Ooption(X0)),X3,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f526,plain,
    ! [X3,X0,X47,X4] : c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3) = c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3),X4,c_Option_Ooption_OSome(X47,X0),X3,tc_Option_Ooption(X0)),X3,X0),
    inference(forward_demodulation,[],[f390,f435]) ).

fof(f435,axiom,
    ! [X3,X4] : c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Option_Oset_Osimps_I2_J_0) ).

fof(f390,axiom,
    ! [X3,X0,X47,X4] : c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3),X4,c_Option_Ooption_OSome(X47,X0),X3,tc_Option_Ooption(X0)),X3,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_1) ).

fof(f4737,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f75,f4735]) ).

fof(f4735,plain,
    ( spl0_400
  <=> ! [X38,X40,X36,X39,X37] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X36),X38),X40))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X37),X40),X39))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X36,X37)),X38),X39)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f75,axiom,
    ! [X40,X38,X39,X36,X37] :
      ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X36),X38),X40))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X37),X40),X39))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X36,X37)),X38),X39)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).

fof(f4733,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f74,f4731]) ).

fof(f4731,plain,
    ( spl0_399
  <=> ! [X5,X10,X9,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f74,axiom,
    ! [X3,X10,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

fof(f4729,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f44,f4727]) ).

fof(f4727,plain,
    ( spl0_398
  <=> ! [X4,X9,X0,X12,X5,X3] :
        ( ~ hBOOL(c_in(X4,X5,X0))
        | ~ hBOOL(c_in(X12,hAPP(X9,X4),X3))
        | hBOOL(c_in(X12,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X3,tc_bool)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f44,axiom,
    ! [X3,X0,X9,X4,X5,X12] :
      ( ~ hBOOL(c_in(X4,X5,X0))
      | ~ hBOOL(c_in(X12,hAPP(X9,X4),X3))
      | hBOOL(c_in(X12,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).

fof(f4725,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f16,f4723]) ).

fof(f4723,plain,
    ( spl0_397
  <=> ! [X5,X10,X9,X3] :
        ( ~ c_lessequals(X5,X10,tc_fun(X3,tc_bool))
        | ~ c_lessequals(X9,X10,tc_fun(X3,tc_bool))
        | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f16,axiom,
    ! [X3,X10,X9,X5] :
      ( ~ c_lessequals(X5,X10,tc_fun(X3,tc_bool))
      | ~ c_lessequals(X9,X10,tc_fun(X3,tc_bool))
      | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

fof(f4721,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f11,f4719]) ).

fof(f4719,plain,
    ( spl0_396
  <=> ! [X5,X10,X9,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f11,axiom,
    ! [X3,X10,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

fof(f4717,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f2,f4715]) ).

fof(f4715,plain,
    ( spl0_395
  <=> ! [X2,X4,X0,X3,X1] :
        ( hBOOL(c_in(X4,X1,X3))
        | c_Map_Orestrict__map(X2,X1,X3,X0) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X2,X1,X3,X0),X4,c_Option_Ooption_ONone(X0),X3,tc_Option_Ooption(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( hBOOL(c_in(X4,X1,X3))
      | c_Map_Orestrict__map(X2,X1,X3,X0) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X2,X1,X3,X0),X4,c_Option_Ooption_ONone(X0),X3,tc_Option_Ooption(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_1) ).

fof(f4683,plain,
    ( spl0_394
    | ~ spl0_4
    | ~ spl0_382 ),
    inference(avatar_split_clause,[],[f4477,f4432,f612,f4680]) ).

fof(f612,plain,
    ( spl0_4
  <=> hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f4432,plain,
    ( spl0_382
  <=> c_Option_Ooption_ONone(tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f4477,plain,
    ( c_Option_Ooption_ONone(tc_Com_Ocom) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom)
    | ~ spl0_4
    | ~ spl0_382 ),
    inference(superposition,[],[f4434,f614]) ).

fof(f614,plain,
    ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f612]) ).

fof(f4434,plain,
    ( c_Option_Ooption_ONone(tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn)
    | ~ spl0_382 ),
    inference(avatar_component_clause,[],[f4432]) ).

fof(f4498,plain,
    ( spl0_393
    | ~ spl0_225
    | ~ spl0_392 ),
    inference(avatar_split_clause,[],[f4476,f4473,f1791,f4496]) ).

fof(f4496,plain,
    ( spl0_393
  <=> ! [X42,X58,X3,X65] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X3)),X42),X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f1791,plain,
    ( spl0_225
  <=> ! [X4,X3] : c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3) = hAPP(c_fequal(X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f4473,plain,
    ( spl0_392
  <=> ! [X42,X58,X3,X65] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Option_Oset(c_Option_Ooption_OSome(X42,tc_Hoare__Mirabelle_Otriple(X3)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f4476,plain,
    ( ! [X65,X58,X3,X42] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X3)),X42),X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) )
    | ~ spl0_225
    | ~ spl0_392 ),
    inference(forward_demodulation,[],[f4474,f1792]) ).

fof(f1792,plain,
    ( ! [X3,X4] : c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3) = hAPP(c_fequal(X3),X4)
    | ~ spl0_225 ),
    inference(avatar_component_clause,[],[f1791]) ).

fof(f4474,plain,
    ( ! [X65,X58,X3,X42] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Option_Oset(c_Option_Ooption_OSome(X42,tc_Hoare__Mirabelle_Otriple(X3)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) )
    | ~ spl0_392 ),
    inference(avatar_component_clause,[],[f4473]) ).

fof(f4475,plain,
    spl0_392,
    inference(avatar_split_clause,[],[f577,f4473]) ).

fof(f577,plain,
    ! [X65,X58,X3,X42] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Option_Oset(c_Option_Ooption_OSome(X42,tc_Hoare__Mirabelle_Otriple(X3)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
      | c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    inference(forward_demodulation,[],[f442,f435]) ).

fof(f442,axiom,
    ! [X65,X58,X3,X42] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
      | c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).

fof(f4471,plain,
    spl0_391,
    inference(avatar_split_clause,[],[f243,f4469]) ).

fof(f4469,plain,
    ( spl0_391
  <=> ! [X2,X4,X0,X8,X63,X6,X3] :
        ( X4 = X6
        | c_Fun_Ofun__upd(X2,X8,c_Option_Ooption_OSome(X4,X0),X3,tc_Option_Ooption(X0)) != c_Fun_Ofun__upd(X63,X8,c_Option_Ooption_OSome(X6,X0),X3,tc_Option_Ooption(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f243,axiom,
    ! [X2,X3,X0,X8,X6,X4,X63] :
      ( X4 = X6
      | c_Fun_Ofun__upd(X2,X8,c_Option_Ooption_OSome(X4,X0),X3,tc_Option_Ooption(X0)) != c_Fun_Ofun__upd(X63,X8,c_Option_Ooption_OSome(X6,X0),X3,tc_Option_Ooption(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).

fof(f4467,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f242,f4465]) ).

fof(f4465,plain,
    ( spl0_390
  <=> ! [X4,X0,X6,X3,X7] :
        ( c_Option_Ooption_ONone(X0) = X6
        | c_Map_Odom(c_Fun_Ofun__upd(X7,X4,X6,X3,tc_Option_Ooption(X0)),X3,X0) = c_Set_Oinsert(X4,c_Map_Odom(X7,X3,X0),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f242,axiom,
    ! [X3,X0,X6,X7,X4] :
      ( c_Option_Ooption_ONone(X0) = X6
      | c_Map_Odom(c_Fun_Ofun__upd(X7,X4,X6,X3,tc_Option_Ooption(X0)),X3,X0) = c_Set_Oinsert(X4,c_Map_Odom(X7,X3,X0),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__fun__upd_1) ).

fof(f4463,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f227,f4461]) ).

fof(f4461,plain,
    ( spl0_389
  <=> ! [X5,X4,X9,X3] :
        ( X5 = X9
        | hBOOL(c_in(X4,X5,X3))
        | hBOOL(c_in(X4,X9,X3))
        | c_Set_Oinsert(X4,X5,X3) != c_Set_Oinsert(X4,X9,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f227,axiom,
    ! [X3,X9,X4,X5] :
      ( X5 = X9
      | hBOOL(c_in(X4,X5,X3))
      | hBOOL(c_in(X4,X9,X3))
      | c_Set_Oinsert(X4,X5,X3) != c_Set_Oinsert(X4,X9,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

fof(f4459,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f175,f4457]) ).

fof(f4457,plain,
    ( spl0_388
  <=> ! [X5,X10,X9,X3] :
        ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool))
        | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f175,axiom,
    ! [X3,X10,X9,X5] :
      ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool))
      | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

fof(f4455,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f174,f4453]) ).

fof(f4453,plain,
    ( spl0_387
  <=> ! [X5,X10,X9,X3] :
        ( ~ c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
        | c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f174,axiom,
    ! [X3,X10,X9,X5] :
      ( ~ c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
      | c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

fof(f4451,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f146,f4449]) ).

fof(f4449,plain,
    ( spl0_386
  <=> ! [X3,X59,X8,X12,X21] :
        ( ~ class_Orderings_Oorder(X3)
        | ~ c_lessequals(X8,X12,X3)
        | c_lessequals(X21,X8,X3)
        | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3),c_SetInterval_Oord__class_OatLeastAtMost(X21,X59,X3),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f146,axiom,
    ! [X21,X3,X59,X8,X12] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(X8,X12,X3)
      | c_lessequals(X21,X8,X3)
      | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3),c_SetInterval_Oord__class_OatLeastAtMost(X21,X59,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

fof(f4447,plain,
    spl0_385,
    inference(avatar_split_clause,[],[f145,f4445]) ).

fof(f4445,plain,
    ( spl0_385
  <=> ! [X3,X59,X21,X12,X8] :
        ( ~ class_Orderings_Oorder(X3)
        | ~ c_lessequals(X8,X12,X3)
        | c_lessequals(X12,X59,X3)
        | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3),c_SetInterval_Oord__class_OatLeastAtMost(X21,X59,X3),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f145,axiom,
    ! [X21,X3,X59,X8,X12] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(X8,X12,X3)
      | c_lessequals(X12,X59,X3)
      | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3),c_SetInterval_Oord__class_OatLeastAtMost(X21,X59,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

fof(f4443,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f144,f4441]) ).

fof(f4441,plain,
    ( spl0_384
  <=> ! [X59,X8,X12,X3,X21] :
        ( ~ class_Orderings_Oorder(X3)
        | ~ c_lessequals(X21,X8,X3)
        | ~ c_lessequals(X12,X59,X3)
        | c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3),c_SetInterval_Oord__class_OatLeastAtMost(X21,X59,X3),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f144,axiom,
    ! [X21,X3,X59,X8,X12] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(X21,X8,X3)
      | ~ c_lessequals(X12,X59,X3)
      | c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3),c_SetInterval_Oord__class_OatLeastAtMost(X21,X59,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

fof(f4439,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f94,f4437]) ).

fof(f4437,plain,
    ( spl0_383
  <=> ! [X4,X9,X0,X5,X3,X7] :
        ( ~ hBOOL(c_in(X4,X5,X0))
        | hBOOL(c_in(hAPP(X7,X4),X9,X3))
        | ~ c_lessequals(c_Set_Oimage(X7,X5,X0,X3),X9,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f94,axiom,
    ! [X3,X0,X9,X7,X4,X5] :
      ( ~ hBOOL(c_in(X4,X5,X0))
      | hBOOL(c_in(hAPP(X7,X4),X9,X3))
      | ~ c_lessequals(c_Set_Oimage(X7,X5,X0,X3),X9,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

fof(f4435,plain,
    ( spl0_382
    | ~ spl0_143
    | spl0_371 ),
    inference(avatar_split_clause,[],[f4341,f4292,f1240,f4432]) ).

fof(f1240,plain,
    ( spl0_143
  <=> ! [X73] :
        ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X73))
        | hAPP(c_Com_Obody,X73) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f4292,plain,
    ( spl0_371
  <=> c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f4341,plain,
    ( c_Option_Ooption_ONone(tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn)
    | ~ spl0_143
    | spl0_371 ),
    inference(resolution,[],[f4294,f1241]) ).

fof(f1241,plain,
    ( ! [X73] :
        ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X73))
        | hAPP(c_Com_Obody,X73) = c_Option_Ooption_ONone(tc_Com_Ocom) )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1240]) ).

fof(f4294,plain,
    ( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
    | spl0_371 ),
    inference(avatar_component_clause,[],[f4292]) ).

fof(f4430,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f7,f4428]) ).

fof(f4428,plain,
    ( spl0_381
  <=> ! [X5,X0,X3,X8,X7] : c_Map_Orestrict__map(X7,c_Set_Oinsert(X8,X5,X3),X3,X0) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X7,X5,X3,X0),X8,hAPP(X7,X8),X3,tc_Option_Ooption(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f7,axiom,
    ! [X3,X0,X8,X7,X5] : c_Map_Orestrict__map(X7,c_Set_Oinsert(X8,X5,X3),X3,X0) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X7,X5,X3,X0),X8,hAPP(X7,X8),X3,tc_Option_Ooption(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__map__insert_0) ).

fof(f4426,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f6,f4424]) ).

fof(f4424,plain,
    ( spl0_380
  <=> ! [X2,X6,X4,X0,X3,X1] :
        ( hBOOL(c_in(X4,X1,X3))
        | c_Map_Orestrict__map(X2,X1,X3,X0) = c_Map_Orestrict__map(c_Fun_Ofun__upd(X2,X4,X6,X3,tc_Option_Ooption(X0)),X1,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f6,axiom,
    ! [X2,X3,X0,X1,X6,X4] :
      ( hBOOL(c_in(X4,X1,X3))
      | c_Map_Orestrict__map(X2,X1,X3,X0) = c_Map_Orestrict__map(c_Fun_Ofun__upd(X2,X4,X6,X3,tc_Option_Ooption(X0)),X1,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__fun__upd_1) ).

fof(f4327,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f425,f4325]) ).

fof(f4325,plain,
    ( spl0_379
  <=> ! [X4,X0,X5,X3,X7] :
        ( ~ hBOOL(c_in(X4,X5,X3))
        | c_Set_Oimage(X7,X5,X3,X0) = c_Set_Oinsert(hAPP(X7,X4),c_Set_Oimage(X7,X5,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f425,axiom,
    ! [X3,X0,X7,X4,X5] :
      ( ~ hBOOL(c_in(X4,X5,X3))
      | c_Set_Oimage(X7,X5,X3,X0) = c_Set_Oinsert(hAPP(X7,X4),c_Set_Oimage(X7,X5,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

fof(f4323,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f376,f4321]) ).

fof(f4321,plain,
    ( spl0_378
  <=> ! [X20,X41,X40] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X20)),X41),X40))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X20))),X41),X40)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f376,axiom,
    ! [X40,X41,X20] :
      ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X20)),X41),X40))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X20))),X41),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).

fof(f4319,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f375,f4317]) ).

fof(f4317,plain,
    ( spl0_377
  <=> ! [X38,X73,X40] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X73)),X38),X40))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X73))),X38),X40)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f375,axiom,
    ! [X40,X38,X73] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X73)),X38),X40))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X73))),X38),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).

fof(f4315,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f312,f4313]) ).

fof(f4313,plain,
    ( spl0_376
  <=> ! [X6,X4,X0,X5,X3,X7] :
        ( hBOOL(c_in(X4,X5,X0))
        | c_Set_Oimage(X7,X5,X0,X3) = c_Set_Oimage(c_Fun_Ofun__upd(X7,X4,X6,X0,X3),X5,X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f312,axiom,
    ! [X3,X0,X6,X7,X4,X5] :
      ( hBOOL(c_in(X4,X5,X0))
      | c_Set_Oimage(X7,X5,X0,X3) = c_Set_Oimage(c_Fun_Ofun__upd(X7,X4,X6,X0,X3),X5,X0,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).

fof(f4311,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f293,f4309]) ).

fof(f4309,plain,
    ( spl0_375
  <=> ! [X41,X40,X36,X12,X37] :
        ( hBOOL(hAPP(X12,X41))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X37),X41),X40))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X12,X36,X37)),X41),X40)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f293,axiom,
    ! [X40,X41,X36,X37,X12] :
      ( hBOOL(hAPP(X12,X41))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X37),X41),X40))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X12,X36,X37)),X41),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).

fof(f4307,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f292,f4305]) ).

fof(f4305,plain,
    ( spl0_374
  <=> ! [X41,X42,X12,X43,X37] :
        ( hBOOL(hAPP(X12,X41))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X43),X41),X42))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X12,X37,X43)),X41),X42)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f292,axiom,
    ! [X41,X37,X12,X42,X43] :
      ( hBOOL(hAPP(X12,X41))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X43),X41),X42))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X12,X37,X43)),X41),X42)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).

fof(f4303,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f103,f4301]) ).

fof(f4301,plain,
    ( spl0_373
  <=> ! [X4,X9,X5,X3] :
        ( ~ hBOOL(c_in(X4,X9,X3))
        | c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X4,X5,X3),X9,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f103,axiom,
    ! [X3,X9,X4,X5] :
      ( ~ hBOOL(c_in(X4,X9,X3))
      | c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X4,X5,X3),X9,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

fof(f4299,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f78,f4297]) ).

fof(f4297,plain,
    ( spl0_372
  <=> ! [X41,X40,X12,X36,X37] :
        ( ~ hBOOL(hAPP(X12,X41))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X36),X41),X40))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X12,X36,X37)),X41),X40)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f78,axiom,
    ! [X40,X41,X36,X37,X12] :
      ( ~ hBOOL(hAPP(X12,X41))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X36),X41),X40))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X12,X36,X37)),X41),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).

fof(f4295,plain,
    ( ~ spl0_371
    | spl0_226
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4130,f4127,f1803,f4292]) ).

fof(f1803,plain,
    ( spl0_226
  <=> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),tc_Com_Ostate) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f4127,plain,
    ( spl0_368
  <=> ! [X21] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X21)),tc_Com_Ostate)
        | ~ c_Com_OWT(X21) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f4130,plain,
    ( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
    | spl0_226
    | ~ spl0_368 ),
    inference(resolution,[],[f4128,f1805]) ).

fof(f1805,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),tc_Com_Ostate)
    | spl0_226 ),
    inference(avatar_component_clause,[],[f1803]) ).

fof(f4128,plain,
    ( ! [X21] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X21)),tc_Com_Ostate)
        | ~ c_Com_OWT(X21) )
    | ~ spl0_368 ),
    inference(avatar_component_clause,[],[f4127]) ).

fof(f4290,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f77,f4288]) ).

fof(f4288,plain,
    ( spl0_370
  <=> ! [X41,X42,X12,X43,X37] :
        ( ~ hBOOL(hAPP(X12,X41))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X37),X41),X42))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X12,X37,X43)),X41),X42)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f77,axiom,
    ! [X41,X37,X12,X42,X43] :
      ( ~ hBOOL(hAPP(X12,X41))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X37),X41),X42))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X12,X37,X43)),X41),X42)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).

fof(f4286,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f62,f4284]) ).

fof(f4284,plain,
    ( spl0_369
  <=> ! [X4,X9,X0,X12,X5,X3] :
        ( ~ hBOOL(c_in(X4,X5,X3))
        | ~ hBOOL(hAPP(hAPP(X9,X4),X12))
        | hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X0,tc_bool)),X12)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f62,axiom,
    ! [X3,X0,X9,X4,X5,X12] :
      ( ~ hBOOL(c_in(X4,X5,X3))
      | ~ hBOOL(hAPP(hAPP(X9,X4),X12))
      | hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X0,tc_bool)),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).

fof(f4129,plain,
    ( spl0_368
    | ~ spl0_225
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f4121,f4118,f1791,f4127]) ).

fof(f4118,plain,
    ( spl0_366
  <=> ! [X21] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,X21),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
        | ~ c_Com_OWT(X21) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f4121,plain,
    ( ! [X21] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X21)),tc_Com_Ostate)
        | ~ c_Com_OWT(X21) )
    | ~ spl0_225
    | ~ spl0_366 ),
    inference(forward_demodulation,[],[f4119,f1792]) ).

fof(f4119,plain,
    ( ! [X21] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,X21),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
        | ~ c_Com_OWT(X21) )
    | ~ spl0_366 ),
    inference(avatar_component_clause,[],[f4118]) ).

fof(f4125,plain,
    ( spl0_367
    | ~ spl0_127
    | ~ spl0_342 ),
    inference(avatar_split_clause,[],[f4040,f3656,f1142,f4123]) ).

fof(f4123,plain,
    ( spl0_367
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f1142,plain,
    ( spl0_127
  <=> ! [X5,X8,X3] : c_Set_Oinsert(X8,X5,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f3656,plain,
    ( spl0_342
  <=> ! [X0] : c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom) = c_Set_Oinsert(v_pn,c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f4040,plain,
    ( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom)
    | ~ spl0_127
    | ~ spl0_342 ),
    inference(superposition,[],[f1143,f3657]) ).

fof(f3657,plain,
    ( ! [X0] : c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom) = c_Set_Oinsert(v_pn,c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom),X0)
    | ~ spl0_342 ),
    inference(avatar_component_clause,[],[f3656]) ).

fof(f1143,plain,
    ( ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f1142]) ).

fof(f4120,plain,
    ( ~ spl0_1
    | ~ spl0_2
    | spl0_366 ),
    inference(avatar_split_clause,[],[f589,f4118,f602,f597]) ).

fof(f597,plain,
    ( spl0_1
  <=> c_Hoare__Mirabelle_Ostate__not__singleton ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f602,plain,
    ( spl0_2
  <=> c_Com_OWT__bodies ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f589,plain,
    ! [X21] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,X21),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
      | ~ c_Com_OWT__bodies
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton
      | ~ c_Com_OWT(X21) ),
    inference(forward_demodulation,[],[f451,f435]) ).

fof(f451,axiom,
    ! [X21] :
      ( ~ c_Com_OWT__bodies
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton
      | ~ c_Com_OWT(X21)
      | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X21),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGF_0) ).

fof(f4103,plain,
    ( spl0_365
    | ~ spl0_225
    | ~ spl0_364 ),
    inference(avatar_split_clause,[],[f4099,f4096,f1791,f4101]) ).

fof(f4101,plain,
    ( spl0_365
  <=> ! [X3,X0,X5,X21] :
        ( c_Set_Oimage(c_COMBK(X21,X3,X0),X5,X0,X3) = hAPP(c_fequal(X3),X21)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f4096,plain,
    ( spl0_364
  <=> ! [X3,X0,X5,X21] :
        ( c_Set_Oimage(c_COMBK(X21,X3,X0),X5,X0,X3) = c_Option_Oset(c_Option_Ooption_OSome(X21,X3),X3)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f4099,plain,
    ( ! [X21,X3,X0,X5] :
        ( c_Set_Oimage(c_COMBK(X21,X3,X0),X5,X0,X3) = hAPP(c_fequal(X3),X21)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5 )
    | ~ spl0_225
    | ~ spl0_364 ),
    inference(forward_demodulation,[],[f4097,f1792]) ).

fof(f4097,plain,
    ( ! [X21,X3,X0,X5] :
        ( c_Set_Oimage(c_COMBK(X21,X3,X0),X5,X0,X3) = c_Option_Oset(c_Option_Ooption_OSome(X21,X3),X3)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5 )
    | ~ spl0_364 ),
    inference(avatar_component_clause,[],[f4096]) ).

fof(f4098,plain,
    spl0_364,
    inference(avatar_split_clause,[],[f553,f4096]) ).

fof(f553,plain,
    ! [X21,X3,X0,X5] :
      ( c_Set_Oimage(c_COMBK(X21,X3,X0),X5,X0,X3) = c_Option_Oset(c_Option_Ooption_OSome(X21,X3),X3)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5 ),
    inference(forward_demodulation,[],[f434,f435]) ).

fof(f434,axiom,
    ! [X21,X3,X0,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
      | c_Set_Oimage(c_COMBK(X21,X3,X0),X5,X0,X3) = c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

fof(f4079,plain,
    ( spl0_363
    | ~ spl0_225
    | ~ spl0_362 ),
    inference(avatar_split_clause,[],[f4075,f4072,f1791,f4077]) ).

fof(f4077,plain,
    ( spl0_363
  <=> ! [X4,X5,X3] :
        ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X4,X5,X3),hAPP(c_fequal(X3),X4),tc_fun(X3,tc_bool)) = X5
        | hBOOL(c_in(X4,X5,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f4072,plain,
    ( spl0_362
  <=> ! [X4,X5,X3] :
        ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X4,X5,X3),c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),tc_fun(X3,tc_bool)) = X5
        | hBOOL(c_in(X4,X5,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f4075,plain,
    ( ! [X3,X4,X5] :
        ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X4,X5,X3),hAPP(c_fequal(X3),X4),tc_fun(X3,tc_bool)) = X5
        | hBOOL(c_in(X4,X5,X3)) )
    | ~ spl0_225
    | ~ spl0_362 ),
    inference(forward_demodulation,[],[f4073,f1792]) ).

fof(f4073,plain,
    ( ! [X3,X4,X5] :
        ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X4,X5,X3),c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),tc_fun(X3,tc_bool)) = X5
        | hBOOL(c_in(X4,X5,X3)) )
    | ~ spl0_362 ),
    inference(avatar_component_clause,[],[f4072]) ).

fof(f4074,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f551,f4072]) ).

fof(f551,plain,
    ! [X3,X4,X5] :
      ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X4,X5,X3),c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),tc_fun(X3,tc_bool)) = X5
      | hBOOL(c_in(X4,X5,X3)) ),
    inference(forward_demodulation,[],[f210,f435]) ).

fof(f210,axiom,
    ! [X3,X4,X5] :
      ( hBOOL(c_in(X4,X5,X3))
      | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X4,X5,X3),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

fof(f4070,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f446,f4068]) ).

fof(f4068,plain,
    ( spl0_361
  <=> ! [X51,X60,X0,X5,X3,X7] : c_Set_Oimage(X7,c_Set_Oimage(X51,X5,X60,X0),X0,X3) = c_Set_Oimage(c_COMBB(X7,X51,X0,X3,X60),X5,X60,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f446,axiom,
    ! [X51,X3,X0,X7,X5,X60] : c_Set_Oimage(X7,c_Set_Oimage(X51,X5,X60,X0),X0,X3) = c_Set_Oimage(c_COMBB(X7,X51,X0,X3,X60),X5,X60,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).

fof(f4066,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f317,f4064]) ).

fof(f4064,plain,
    ( spl0_360
  <=> ! [X4,X9,X5,X3] :
        ( ~ hBOOL(c_in(X4,X9,X3))
        | ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
        | c_lessequals(c_Set_Oinsert(X4,X5,X3),X9,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f317,axiom,
    ! [X3,X9,X4,X5] :
      ( ~ hBOOL(c_in(X4,X9,X3))
      | ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
      | c_lessequals(c_Set_Oinsert(X4,X5,X3),X9,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

fof(f4062,plain,
    spl0_359,
    inference(avatar_split_clause,[],[f232,f4060]) ).

fof(f4060,plain,
    ( spl0_359
  <=> ! [X5,X0,X9,X3,X7] :
        ( ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
        | c_lessequals(c_Set_Oimage(X7,X5,X3,X0),c_Set_Oimage(X7,X9,X3,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f232,axiom,
    ! [X3,X0,X9,X7,X5] :
      ( ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
      | c_lessequals(c_Set_Oimage(X7,X5,X3,X0),c_Set_Oimage(X7,X9,X3,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

fof(f4034,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f156,f4032]) ).

fof(f4032,plain,
    ( spl0_358
  <=> ! [X3,X9,X5,X21] :
        ( hBOOL(c_in(X21,X9,X3))
        | hBOOL(c_in(X21,X5,X3))
        | ~ hBOOL(c_in(X21,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f156,axiom,
    ! [X21,X3,X9,X5] :
      ( hBOOL(c_in(X21,X9,X3))
      | hBOOL(c_in(X21,X5,X3))
      | ~ hBOOL(c_in(X21,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

fof(f4030,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f43,f4028]) ).

fof(f4028,plain,
    ( spl0_357
  <=> ! [X4,X9,X5,X3] :
        ( hBOOL(c_in(X4,X5,X3))
        | c_lessequals(X5,X9,tc_fun(X3,tc_bool))
        | ~ c_lessequals(X5,c_Set_Oinsert(X4,X9,X3),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f43,axiom,
    ! [X3,X9,X4,X5] :
      ( hBOOL(c_in(X4,X5,X3))
      | c_lessequals(X5,X9,tc_fun(X3,tc_bool))
      | ~ c_lessequals(X5,c_Set_Oinsert(X4,X9,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

fof(f4026,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f35,f4024]) ).

fof(f4024,plain,
    ( spl0_356
  <=> ! [X5,X3,X9,X21] :
        ( ~ hBOOL(c_in(X21,X5,X3))
        | hBOOL(c_in(X21,X9,X3))
        | hBOOL(c_in(X21,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f35,axiom,
    ! [X21,X3,X9,X5] :
      ( ~ hBOOL(c_in(X21,X5,X3))
      | hBOOL(c_in(X21,X9,X3))
      | hBOOL(c_in(X21,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

fof(f3769,plain,
    ( spl0_355
    | ~ spl0_225
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f3765,f3762,f1791,f3767]) ).

fof(f3767,plain,
    ( spl0_355
  <=> ! [X3,X4,X0,X5,X21] :
        ( c_Set_Oimage(c_COMBK(X21,X0,X3),X5,X3,X0) = hAPP(c_fequal(X0),X21)
        | ~ hBOOL(c_in(X4,X5,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f3762,plain,
    ( spl0_354
  <=> ! [X3,X4,X0,X5,X21] :
        ( c_Set_Oimage(c_COMBK(X21,X0,X3),X5,X3,X0) = c_Option_Oset(c_Option_Ooption_OSome(X21,X0),X0)
        | ~ hBOOL(c_in(X4,X5,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f3765,plain,
    ( ! [X21,X3,X0,X4,X5] :
        ( c_Set_Oimage(c_COMBK(X21,X0,X3),X5,X3,X0) = hAPP(c_fequal(X0),X21)
        | ~ hBOOL(c_in(X4,X5,X3)) )
    | ~ spl0_225
    | ~ spl0_354 ),
    inference(forward_demodulation,[],[f3763,f1792]) ).

fof(f3763,plain,
    ( ! [X21,X3,X0,X4,X5] :
        ( c_Set_Oimage(c_COMBK(X21,X0,X3),X5,X3,X0) = c_Option_Oset(c_Option_Ooption_OSome(X21,X0),X0)
        | ~ hBOOL(c_in(X4,X5,X3)) )
    | ~ spl0_354 ),
    inference(avatar_component_clause,[],[f3762]) ).

fof(f3764,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f543,f3762]) ).

fof(f543,plain,
    ! [X21,X3,X0,X4,X5] :
      ( c_Set_Oimage(c_COMBK(X21,X0,X3),X5,X3,X0) = c_Option_Oset(c_Option_Ooption_OSome(X21,X0),X0)
      | ~ hBOOL(c_in(X4,X5,X3)) ),
    inference(forward_demodulation,[],[f392,f435]) ).

fof(f392,axiom,
    ! [X21,X3,X0,X4,X5] :
      ( ~ hBOOL(c_in(X4,X5,X3))
      | c_Set_Oimage(c_COMBK(X21,X0,X3),X5,X3,X0) = c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

fof(f3758,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f525,f3756]) ).

fof(f3756,plain,
    ( spl0_353
  <=> ! [X3,X0,X9,X8] : c_Set_Oinsert(X8,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,X0,tc_fun(X3,tc_bool)),X3) = c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f525,plain,
    ! [X3,X0,X8,X9] : c_Set_Oinsert(X8,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,X0,tc_fun(X3,tc_bool)),X3) = c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),
    inference(forward_demodulation,[],[f405,f435]) ).

fof(f405,axiom,
    ! [X3,X0,X8,X9] : c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X8,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,X0,tc_fun(X3,tc_bool)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).

fof(f3754,plain,
    spl0_352,
    inference(avatar_split_clause,[],[f523,f3752]) ).

fof(f3752,plain,
    ( spl0_352
  <=> ! [X3,X10,X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X8,X9,X3),X10,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Set_Oinsert(X8,X10,X3),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f523,plain,
    ! [X3,X10,X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X8,X9,X3),X10,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Set_Oinsert(X8,X10,X3),tc_fun(X3,tc_bool)),
    inference(forward_demodulation,[],[f221,f220]) ).

fof(f220,axiom,
    ! [X3,X8,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X8,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

fof(f221,axiom,
    ! [X3,X10,X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X8,X9,X3),X10,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X3,tc_bool)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

fof(f3750,plain,
    spl0_351,
    inference(avatar_split_clause,[],[f468,f3748]) ).

fof(f3748,plain,
    ( spl0_351
  <=> ! [X4,X7,X0,X6,X3] :
        ( hAPP(X7,X4) != c_Option_Ooption_OSome(X6,X3)
        | c_Map_Odom(X7,X0,X3) = c_Set_Oinsert(X4,c_Map_Odom(X7,X0,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f468,axiom,
    ! [X3,X0,X6,X7,X4] :
      ( hAPP(X7,X4) != c_Option_Ooption_OSome(X6,X3)
      | c_Map_Odom(X7,X0,X3) = c_Set_Oinsert(X4,c_Map_Odom(X7,X0,X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__dom_0) ).

fof(f3746,plain,
    spl0_350,
    inference(avatar_split_clause,[],[f448,f3744]) ).

fof(f3744,plain,
    ( spl0_350
  <=> ! [X0,X8,X9,X3,X7] : c_Set_Oimage(X7,c_Set_Oinsert(X8,X9,X0),X0,X3) = c_Set_Oinsert(hAPP(X7,X8),c_Set_Oimage(X7,X9,X0,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f448,axiom,
    ! [X3,X0,X8,X9,X7] : c_Set_Oimage(X7,c_Set_Oinsert(X8,X9,X0),X0,X3) = c_Set_Oinsert(hAPP(X7,X8),c_Set_Oimage(X7,X9,X0,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

fof(f3742,plain,
    spl0_349,
    inference(avatar_split_clause,[],[f323,f3740]) ).

fof(f3740,plain,
    ( spl0_349
  <=> ! [X5,X3,X9,X8] :
        ( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
        | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f323,axiom,
    ! [X3,X8,X9,X5] :
      ( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
      | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

fof(f3738,plain,
    ( spl0_348
    | ~ spl0_173
    | ~ spl0_333 ),
    inference(avatar_split_clause,[],[f3659,f3374,f1386,f3736]) ).

fof(f3736,plain,
    ( spl0_348
  <=> ! [X1] :
        ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(X1,tc_Com_Ocom)
        | v_y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f1386,plain,
    ( spl0_173
  <=> ! [X0,X1] : c_Com_Obody = c_Fun_Ofun__upd(c_Com_Obody,v_pn,c_Option_Ooption_OSome(v_y,tc_Com_Ocom),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f3374,plain,
    ( spl0_333
  <=> ! [X2,X62,X4,X12,X6,X3] :
        ( X6 = X12
        | hAPP(c_Fun_Ofun__upd(X2,X4,c_Option_Ooption_OSome(X12,X62),X3,tc_Option_Ooption(X62)),X4) != c_Option_Ooption_OSome(X6,X62) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f3659,plain,
    ( ! [X1] :
        ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(X1,tc_Com_Ocom)
        | v_y = X1 )
    | ~ spl0_173
    | ~ spl0_333 ),
    inference(superposition,[],[f3375,f1387]) ).

fof(f1387,plain,
    ( ! [X0,X1] : c_Com_Obody = c_Fun_Ofun__upd(c_Com_Obody,v_pn,c_Option_Ooption_OSome(v_y,tc_Com_Ocom),X0,X1)
    | ~ spl0_173 ),
    inference(avatar_component_clause,[],[f1386]) ).

fof(f3375,plain,
    ( ! [X2,X3,X6,X62,X4,X12] :
        ( hAPP(c_Fun_Ofun__upd(X2,X4,c_Option_Ooption_OSome(X12,X62),X3,tc_Option_Ooption(X62)),X4) != c_Option_Ooption_OSome(X6,X62)
        | X6 = X12 )
    | ~ spl0_333 ),
    inference(avatar_component_clause,[],[f3374]) ).

fof(f3734,plain,
    spl0_347,
    inference(avatar_split_clause,[],[f322,f3732]) ).

fof(f3732,plain,
    ( spl0_347
  <=> ! [X5,X3,X9,X8] :
        ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
        | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f322,axiom,
    ! [X3,X8,X9,X5] :
      ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
      | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

fof(f3730,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f220,f3728]) ).

fof(f3728,plain,
    ( spl0_346
  <=> ! [X5,X3,X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X8,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f3726,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f102,f3724]) ).

fof(f3724,plain,
    ( spl0_345
  <=> ! [X3,X9,X0,X5,X8] :
        ( ~ hBOOL(c_in(X8,X5,X3))
        | c_lessequals(hAPP(X9,X8),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f102,axiom,
    ! [X3,X0,X8,X9,X5] :
      ( ~ hBOOL(c_in(X8,X5,X3))
      | c_lessequals(hAPP(X9,X8),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).

fof(f3722,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f93,f3720]) ).

fof(f3720,plain,
    ( spl0_344
  <=> ! [X0,X7,X51] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X51,tc_fun(t_a,X0)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,v_x),hAPP(X51,v_x),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f93,axiom,
    ! [X51,X0,X7] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X51,tc_fun(t_a,X0)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,v_x),hAPP(X51,v_x),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

fof(f3718,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f48,f3716]) ).

fof(f3716,plain,
    ( spl0_343
  <=> ! [X5,X9,X0] :
        ( ~ class_HOL_Ominus(X0)
        | hAPP(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(t_a,X0)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X5,v_x),hAPP(X9,v_x),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f48,axiom,
    ! [X0,X9,X5] :
      ( ~ class_HOL_Ominus(X0)
      | hAPP(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(t_a,X0)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X5,v_x),hAPP(X9,v_x),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

fof(f3658,plain,
    ( spl0_342
    | ~ spl0_167
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f3295,f3095,f1361,f3656]) ).

fof(f1361,plain,
    ( spl0_167
  <=> ! [X5,X8,X3] :
        ( ~ hBOOL(c_in(X8,X5,X3))
        | c_Set_Oinsert(X8,X5,X3) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f3095,plain,
    ( spl0_322
  <=> ! [X0] : hBOOL(c_in(v_pn,c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f3295,plain,
    ( ! [X0] : c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom) = c_Set_Oinsert(v_pn,c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom),X0)
    | ~ spl0_167
    | ~ spl0_322 ),
    inference(resolution,[],[f3096,f1362]) ).

fof(f1362,plain,
    ( ! [X3,X8,X5] :
        ( ~ hBOOL(c_in(X8,X5,X3))
        | c_Set_Oinsert(X8,X5,X3) = X5 )
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1361]) ).

fof(f3096,plain,
    ( ! [X0] : hBOOL(c_in(v_pn,c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom),X0))
    | ~ spl0_322 ),
    inference(avatar_component_clause,[],[f3095]) ).

fof(f3429,plain,
    ( spl0_341
    | ~ spl0_225
    | ~ spl0_340 ),
    inference(avatar_split_clause,[],[f3425,f3422,f1791,f3427]) ).

fof(f3427,plain,
    ( spl0_341
  <=> ! [X42,X58,X3,X65] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(X58,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X3)),X42),X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f3422,plain,
    ( spl0_340
  <=> ! [X42,X58,X3,X65] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Option_Oset(c_Option_Ooption_OSome(X42,tc_Hoare__Mirabelle_Otriple(X3)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f3425,plain,
    ( ! [X65,X58,X3,X42] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(X58,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X3)),X42),X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) )
    | ~ spl0_225
    | ~ spl0_340 ),
    inference(forward_demodulation,[],[f3423,f1792]) ).

fof(f3423,plain,
    ( ! [X65,X58,X3,X42] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Option_Oset(c_Option_Ooption_OSome(X42,tc_Hoare__Mirabelle_Otriple(X3)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) )
    | ~ spl0_340 ),
    inference(avatar_component_clause,[],[f3422]) ).

fof(f3424,plain,
    spl0_340,
    inference(avatar_split_clause,[],[f554,f3422]) ).

fof(f554,plain,
    ! [X65,X58,X3,X42] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Option_Oset(c_Option_Ooption_OSome(X42,tc_Hoare__Mirabelle_Otriple(X3)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    inference(forward_demodulation,[],[f470,f435]) ).

fof(f470,axiom,
    ! [X65,X58,X3,X42] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3)
      | c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).

fof(f3401,plain,
    ( spl0_339
    | ~ spl0_225
    | ~ spl0_338 ),
    inference(avatar_split_clause,[],[f3397,f3394,f1791,f3399]) ).

fof(f3399,plain,
    ( spl0_339
  <=> ! [X5,X8,X3] : c_Set_Oinsert(X8,X5,X3) = c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,hAPP(c_fequal(X3),X8),tc_fun(X3,tc_bool)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f3394,plain,
    ( spl0_338
  <=> ! [X5,X8,X3] : c_Set_Oinsert(X8,X5,X3) = c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),tc_fun(X3,tc_bool)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f3397,plain,
    ( ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) = c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,hAPP(c_fequal(X3),X8),tc_fun(X3,tc_bool)),X3)
    | ~ spl0_225
    | ~ spl0_338 ),
    inference(forward_demodulation,[],[f3395,f1792]) ).

fof(f3395,plain,
    ( ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) = c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),tc_fun(X3,tc_bool)),X3)
    | ~ spl0_338 ),
    inference(avatar_component_clause,[],[f3394]) ).

fof(f3396,plain,
    spl0_338,
    inference(avatar_split_clause,[],[f524,f3394]) ).

fof(f524,plain,
    ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) = c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),tc_fun(X3,tc_bool)),X3),
    inference(forward_demodulation,[],[f419,f435]) ).

fof(f419,axiom,
    ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) = c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

fof(f3392,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f469,f3390]) ).

fof(f3390,plain,
    ( spl0_337
  <=> ! [X12,X8,X3] :
        ( X8 = X12
        | c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f469,axiom,
    ! [X3,X8,X12] :
      ( X8 = X12
      | c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

fof(f3388,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f358,f3386]) ).

fof(f3386,plain,
    ( spl0_336
  <=> ! [X5,X3] :
        ( ~ class_Orderings_Olinorder(X3)
        | ~ c_Finite__Set_Ofinite(X5,X3)
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
        | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X5,X3),X5,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f358,axiom,
    ! [X3,X5] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_Finite__Set_Ofinite(X5,X3)
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
      | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X5,X3),X5,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).

fof(f3384,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f348,f3382]) ).

fof(f3382,plain,
    ( spl0_335
  <=> ! [X5,X10,X9,X3] :
        ( ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
        | ~ c_lessequals(X9,X10,tc_fun(X3,tc_bool))
        | c_lessequals(X5,X10,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f348,axiom,
    ! [X3,X10,X9,X5] :
      ( ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
      | ~ c_lessequals(X9,X10,tc_fun(X3,tc_bool))
      | c_lessequals(X5,X10,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

fof(f3380,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f339,f3378]) ).

fof(f3378,plain,
    ( spl0_334
  <=> ! [X5,X3] :
        ( ~ class_Orderings_Olinorder(X3)
        | ~ c_Finite__Set_Ofinite(X5,X3)
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
        | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X5,X3),X5,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f339,axiom,
    ! [X3,X5] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_Finite__Set_Ofinite(X5,X3)
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
      | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X5,X3),X5,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).

fof(f3376,plain,
    spl0_333,
    inference(avatar_split_clause,[],[f252,f3374]) ).

fof(f252,axiom,
    ! [X2,X3,X6,X62,X4,X12] :
      ( X6 = X12
      | hAPP(c_Fun_Ofun__upd(X2,X4,c_Option_Ooption_OSome(X12,X62),X3,tc_Option_Ooption(X62)),X4) != c_Option_Ooption_OSome(X6,X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).

fof(f3372,plain,
    ( spl0_332
    | ~ spl0_109
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f3296,f3095,f1070,f3370]) ).

fof(f3370,plain,
    ( spl0_332
  <=> ! [X0] : hBOOL(hAPP(c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom),v_pn)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f1070,plain,
    ( spl0_109
  <=> ! [X4,X3,X49] :
        ( hBOOL(hAPP(X49,X4))
        | ~ hBOOL(c_in(X4,X49,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f3296,plain,
    ( ! [X0] : hBOOL(hAPP(c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom),v_pn))
    | ~ spl0_109
    | ~ spl0_322 ),
    inference(resolution,[],[f3096,f1071]) ).

fof(f1071,plain,
    ( ! [X3,X49,X4] :
        ( ~ hBOOL(c_in(X4,X49,X3))
        | hBOOL(hAPP(X49,X4)) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f1070]) ).

fof(f3368,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f245,f3366]) ).

fof(f3366,plain,
    ( spl0_331
  <=> ! [X42,X4,X54,X0,X3] :
        ( c_Option_Ooption_OSome(X4,X3) != hAPP(X42,X54)
        | c_Fun_Ofun__upd(X42,X54,c_Option_Ooption_OSome(X4,X3),X0,tc_Option_Ooption(X3)) = X42 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f245,axiom,
    ! [X3,X0,X54,X4,X42] :
      ( c_Option_Ooption_OSome(X4,X3) != hAPP(X42,X54)
      | c_Fun_Ofun__upd(X42,X54,c_Option_Ooption_OSome(X4,X3),X0,tc_Option_Ooption(X3)) = X42 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).

fof(f3364,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f211,f3362]) ).

fof(f3362,plain,
    ( spl0_330
  <=> ! [X10,X8,X3,X1] :
        ( ~ c_lessequals(X10,X1,tc_fun(X3,tc_bool))
        | c_lessequals(c_Set_Oinsert(X8,X10,X3),c_Set_Oinsert(X8,X1,X3),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f211,axiom,
    ! [X3,X10,X1,X8] :
      ( ~ c_lessequals(X10,X1,tc_fun(X3,tc_bool))
      | c_lessequals(c_Set_Oinsert(X8,X10,X3),c_Set_Oinsert(X8,X1,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

fof(f3360,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f168,f3358]) ).

fof(f3358,plain,
    ( spl0_329
  <=> ! [X6,X4,X11,X0,X3,X7] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X7,X4,X6,X3,X0),X4,X11,X3,X0) = c_Fun_Ofun__upd(X7,X4,X11,X3,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f168,axiom,
    ! [X3,X0,X11,X6,X7,X4] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X7,X4,X6,X3,X0),X4,X11,X3,X0) = c_Fun_Ofun__upd(X7,X4,X11,X3,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

fof(f3356,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f150,f3354]) ).

fof(f3354,plain,
    ( spl0_328
  <=> ! [X3,X59,X21,X12,X8] :
        ( ~ class_Orderings_Oorder(X3)
        | c_lessequals(X8,X12,X3)
        | c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3),c_SetInterval_Oord__class_OatLeastAtMost(X21,X59,X3),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f150,axiom,
    ! [X21,X3,X59,X8,X12] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X8,X12,X3)
      | c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3),c_SetInterval_Oord__class_OatLeastAtMost(X21,X59,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

fof(f3352,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f84,f3350]) ).

fof(f3350,plain,
    ( spl0_327
  <=> ! [X9,X5,X3] : c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f84,axiom,
    ! [X3,X9,X5] : c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

fof(f3348,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f58,f3346]) ).

fof(f3346,plain,
    ( spl0_326
  <=> ! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f58,axiom,
    ! [X3,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

fof(f3344,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f47,f3342]) ).

fof(f3342,plain,
    ( spl0_325
  <=> ! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f47,axiom,
    ! [X3,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

fof(f3340,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f46,f3338]) ).

fof(f3338,plain,
    ( spl0_324
  <=> ! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f46,axiom,
    ! [X3,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

fof(f3336,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f38,f3334]) ).

fof(f3334,plain,
    ( spl0_323
  <=> ! [X24,X0,X5,X3] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
        | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X24,X0,X3),X3,X0) = X24 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f38,axiom,
    ! [X3,X0,X24,X5] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
      | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X24,X0,X3),X3,X0) = X24 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).

fof(f3097,plain,
    ( spl0_322
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f3023,f2806,f3095]) ).

fof(f2806,plain,
    ( spl0_297
  <=> ! [X2,X0,X1] :
        ( c_Option_Ooption_OSome(v_y,tc_Com_Ocom) != c_Option_Ooption_OSome(X0,X1)
        | hBOOL(c_in(v_pn,c_Map_Odom(c_Com_Obody,X2,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f3023,plain,
    ( ! [X0] : hBOOL(c_in(v_pn,c_Map_Odom(c_Com_Obody,X0,tc_Com_Ocom),X0))
    | ~ spl0_297 ),
    inference(equality_resolution,[],[f2807]) ).

fof(f2807,plain,
    ( ! [X2,X0,X1] :
        ( c_Option_Ooption_OSome(v_y,tc_Com_Ocom) != c_Option_Ooption_OSome(X0,X1)
        | hBOOL(c_in(v_pn,c_Map_Odom(c_Com_Obody,X2,X1),X2)) )
    | ~ spl0_297 ),
    inference(avatar_component_clause,[],[f2806]) ).

fof(f3042,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f556,f3040]) ).

fof(f3040,plain,
    ( spl0_321
  <=> ! [X6,X4,X3] :
        ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3) = X6
        | ~ hBOOL(hAPP(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f556,plain,
    ! [X3,X6,X4] :
      ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3) = X6
      | ~ hBOOL(hAPP(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X6)) ),
    inference(forward_demodulation,[],[f555,f435]) ).

fof(f555,plain,
    ! [X3,X6,X4] :
      ( ~ hBOOL(hAPP(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X6))
      | c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
    inference(forward_demodulation,[],[f415,f435]) ).

fof(f415,axiom,
    ! [X3,X6,X4] :
      ( ~ hBOOL(hAPP(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X6))
      | c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).

fof(f3036,plain,
    ( spl0_320
    | ~ spl0_225
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3032,f3029,f1791,f3034]) ).

fof(f3034,plain,
    ( spl0_320
  <=> ! [X12,X8,X3] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,hAPP(c_fequal(X3),X12),X3),X3)
        | ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f3029,plain,
    ( spl0_319
  <=> ! [X12,X8,X3] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,c_Option_Oset(c_Option_Ooption_OSome(X12,X3),X3),X3),X3)
        | ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f3032,plain,
    ( ! [X3,X8,X12] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,hAPP(c_fequal(X3),X12),X3),X3)
        | ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
    | ~ spl0_225
    | ~ spl0_319 ),
    inference(forward_demodulation,[],[f3030,f1792]) ).

fof(f3030,plain,
    ( ! [X3,X8,X12] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,c_Option_Oset(c_Option_Ooption_OSome(X12,X3),X3),X3),X3)
        | ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
    | ~ spl0_319 ),
    inference(avatar_component_clause,[],[f3029]) ).

fof(f3031,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f535,f3029]) ).

fof(f535,plain,
    ! [X3,X8,X12] :
      ( c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,c_Option_Oset(c_Option_Ooption_OSome(X12,X3),X3),X3),X3)
      | ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
    inference(forward_demodulation,[],[f208,f435]) ).

fof(f208,axiom,
    ! [X3,X8,X12] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

fof(f3027,plain,
    spl0_318,
    inference(avatar_split_clause,[],[f338,f3025]) ).

fof(f3025,plain,
    ( spl0_318
  <=> ! [X9,X5,X3,X10] :
        ( c_lessequals(X9,X10,tc_fun(X3,tc_bool))
        | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f338,axiom,
    ! [X3,X10,X9,X5] :
      ( c_lessequals(X9,X10,tc_fun(X3,tc_bool))
      | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

fof(f3022,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f337,f3020]) ).

fof(f3020,plain,
    ( spl0_317
  <=> ! [X5,X10,X9,X3] :
        ( c_lessequals(X5,X10,tc_fun(X3,tc_bool))
        | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f337,axiom,
    ! [X3,X10,X9,X5] :
      ( c_lessequals(X5,X10,tc_fun(X3,tc_bool))
      | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X10,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

fof(f3018,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f278,f3016]) ).

fof(f3016,plain,
    ( spl0_316
  <=> ! [X41,X42,X21,X68] :
        ( X42 = X68
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X21),X41),X42))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X21),X41),X68)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f278,axiom,
    ! [X21,X41,X68,X42] :
      ( X42 = X68
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X21),X41),X42))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X21),X41),X68)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com__det_0) ).

fof(f3014,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f239,f3012]) ).

fof(f3012,plain,
    ( spl0_315
  <=> ! [X0,X7,X3] :
        ( c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3) = X7
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Map_Odom(X7,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f239,axiom,
    ! [X3,X0,X7] :
      ( c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3) = X7
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Map_Odom(X7,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__eq__empty__conv_0) ).

fof(f3010,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f205,f3008]) ).

fof(f3008,plain,
    ( spl0_314
  <=> ! [X9,X5,X3] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f205,axiom,
    ! [X3,X9,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

fof(f3006,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f204,f3004]) ).

fof(f3004,plain,
    ( spl0_313
  <=> ! [X9,X5,X3] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X9
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f204,axiom,
    ! [X3,X9,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X9
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

fof(f3002,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f164,f3000]) ).

fof(f3000,plain,
    ( spl0_312
  <=> ! [X5,X0,X9,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,X0,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f164,axiom,
    ! [X3,X0,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,X0,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).

fof(f2998,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f163,f2996]) ).

fof(f2996,plain,
    ( spl0_311
  <=> ! [X9,X0,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,X0,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = X9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f163,axiom,
    ! [X3,X0,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X5,X0,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = X9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).

fof(f2994,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f153,f2992]) ).

fof(f2992,plain,
    ( spl0_310
  <=> ! [X4,X9,X5,X3] :
        ( hBOOL(hAPP(X9,X4))
        | hBOOL(hAPP(X5,X4))
        | ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f153,axiom,
    ! [X3,X9,X4,X5] :
      ( hBOOL(hAPP(X9,X4))
      | hBOOL(hAPP(X5,X4))
      | ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

fof(f2990,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f101,f2988]) ).

fof(f2988,plain,
    ( spl0_309
  <=> ! [X3,X0,X5,X52,X24] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | ~ hBOOL(c_in(X52,X5,X3))
        | c_lessequals(hAPP(X24,X52),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X24,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f101,axiom,
    ! [X3,X0,X52,X24,X5] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ hBOOL(c_in(X52,X5,X3))
      | c_lessequals(hAPP(X24,X52),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X24,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).

fof(f2986,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f88,f2984]) ).

fof(f2984,plain,
    ( spl0_308
  <=> ! [X5,X0,X9,X3] : c_HOL_Ominus__class_Ominus(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,X0,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f88,axiom,
    ! [X3,X0,X9,X5] : c_HOL_Ominus__class_Ominus(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,X0,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).

fof(f2982,plain,
    spl0_307,
    inference(avatar_split_clause,[],[f20,f2980]) ).

fof(f2980,plain,
    ( spl0_307
  <=> ! [X3,X4,X12,X8] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | ~ c_lessequals(X8,X4,X3)
        | ~ c_lessequals(X12,X4,X3)
        | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f20,axiom,
    ! [X3,X8,X4,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | ~ c_lessequals(X8,X4,X3)
      | ~ c_lessequals(X12,X4,X3)
      | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

fof(f2978,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f15,f2976]) ).

fof(f2976,plain,
    ( spl0_306
  <=> ! [X4,X11,X6,X3] :
        ( ~ class_Lattices_Olattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X11,X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f15,axiom,
    ! [X3,X11,X6,X4] :
      ( ~ class_Lattices_Olattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X11,X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

fof(f2974,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f14,f2972]) ).

fof(f2972,plain,
    ( spl0_305
  <=> ! [X4,X11,X6,X3] :
        ( ~ class_Lattices_Olattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X4,X11,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f14,axiom,
    ! [X3,X11,X6,X4] :
      ( ~ class_Lattices_Olattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X4,X11,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

fof(f2970,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f13,f2968]) ).

fof(f2968,plain,
    ( spl0_304
  <=> ! [X4,X11,X6,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X4,X11,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f13,axiom,
    ! [X3,X11,X6,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X4,X11,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

fof(f2966,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f12,f2964]) ).

fof(f2964,plain,
    ( spl0_303
  <=> ! [X4,X11,X6,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X11,X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f12,axiom,
    ! [X3,X11,X6,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X11,X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

fof(f2899,plain,
    ( spl0_302
    | ~ spl0_173
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2851,f2786,f1386,f2897]) ).

fof(f2897,plain,
    ( spl0_302
  <=> ! [X0] : c_Com_Obody != c_COMBK(c_Option_Ooption_ONone(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f2786,plain,
    ( spl0_292
  <=> ! [X42,X4,X54,X0,X3] : c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3) != c_Fun_Ofun__upd(X42,X54,c_Option_Ooption_OSome(X4,X0),X3,tc_Option_Ooption(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f2851,plain,
    ( ! [X0] : c_Com_Obody != c_COMBK(c_Option_Ooption_ONone(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),X0)
    | ~ spl0_173
    | ~ spl0_292 ),
    inference(superposition,[],[f2787,f1387]) ).

fof(f2787,plain,
    ( ! [X3,X0,X54,X4,X42] : c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3) != c_Fun_Ofun__upd(X42,X54,c_Option_Ooption_OSome(X4,X0),X3,tc_Option_Ooption(X0))
    | ~ spl0_292 ),
    inference(avatar_component_clause,[],[f2786]) ).

fof(f2824,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f463,f2822]) ).

fof(f2822,plain,
    ( spl0_301
  <=> ! [X0,X5,X3,X7] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X7,X5,X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f463,axiom,
    ! [X3,X0,X7,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X7,X5,X0,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

fof(f2820,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f368,f2818]) ).

fof(f2818,plain,
    ( spl0_300
  <=> ! [X4,X5,X3] :
        ( ~ class_Orderings_Olinorder(X3)
        | ~ c_Finite__Set_Ofinite(X5,X3)
        | ~ hBOOL(c_in(X4,X5,X3))
        | c_lessequals(X4,c_Finite__Set_Olinorder__class_OMax(X5,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f368,axiom,
    ! [X3,X4,X5] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_Finite__Set_Ofinite(X5,X3)
      | ~ hBOOL(c_in(X4,X5,X3))
      | c_lessequals(X4,c_Finite__Set_Olinorder__class_OMax(X5,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).

fof(f2816,plain,
    spl0_299,
    inference(avatar_split_clause,[],[f361,f2814]) ).

fof(f2814,plain,
    ( spl0_299
  <=> ! [X4,X5,X3] :
        ( ~ class_Orderings_Olinorder(X3)
        | ~ c_Finite__Set_Ofinite(X5,X3)
        | ~ hBOOL(c_in(X4,X5,X3))
        | c_lessequals(c_Finite__Set_Olinorder__class_OMin(X5,X3),X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f361,axiom,
    ! [X3,X4,X5] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_Finite__Set_Ofinite(X5,X3)
      | ~ hBOOL(c_in(X4,X5,X3))
      | c_lessequals(c_Finite__Set_Olinorder__class_OMin(X5,X3),X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).

fof(f2812,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f342,f2810]) ).

fof(f2810,plain,
    ( spl0_298
  <=> ! [X4,X9,X5,X3] :
        ( ~ hBOOL(c_in(X4,X5,X3))
        | hBOOL(c_in(X4,X9,X3))
        | ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f342,axiom,
    ! [X3,X9,X4,X5] :
      ( ~ hBOOL(c_in(X4,X5,X3))
      | hBOOL(c_in(X4,X9,X3))
      | ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

fof(f2808,plain,
    ( spl0_297
    | ~ spl0_4
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f2738,f2488,f612,f2806]) ).

fof(f2488,plain,
    ( spl0_285
  <=> ! [X3,X0,X8,X12,X2] :
        ( hAPP(X2,X8) != c_Option_Ooption_OSome(X12,X3)
        | hBOOL(c_in(X8,c_Map_Odom(X2,X0,X3),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f2738,plain,
    ( ! [X2,X0,X1] :
        ( c_Option_Ooption_OSome(v_y,tc_Com_Ocom) != c_Option_Ooption_OSome(X0,X1)
        | hBOOL(c_in(v_pn,c_Map_Odom(c_Com_Obody,X2,X1),X2)) )
    | ~ spl0_4
    | ~ spl0_285 ),
    inference(superposition,[],[f2489,f614]) ).

fof(f2489,plain,
    ( ! [X2,X3,X0,X8,X12] :
        ( hAPP(X2,X8) != c_Option_Ooption_OSome(X12,X3)
        | hBOOL(c_in(X8,c_Map_Odom(X2,X0,X3),X0)) )
    | ~ spl0_285 ),
    inference(avatar_component_clause,[],[f2488]) ).

fof(f2804,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f330,f2802]) ).

fof(f2802,plain,
    ( spl0_296
  <=> ! [X41,X42,X12,X21] :
        ( X41 = X42
        | hBOOL(hAPP(X12,X41))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X12,X21)),X41),X42)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f330,axiom,
    ! [X21,X41,X42,X12] :
      ( X41 = X42
      | hBOOL(hAPP(X12,X41))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X12,X21)),X41),X42)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).

fof(f2800,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f236,f2798]) ).

fof(f2798,plain,
    ( spl0_295
  <=> ! [X4,X0,X5,X3,X7] :
        ( ~ hBOOL(c_in(X4,X5,X0))
        | hBOOL(c_in(hAPP(X7,X4),c_Set_Oimage(X7,X5,X0,X3),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f236,axiom,
    ! [X3,X0,X7,X4,X5] :
      ( ~ hBOOL(c_in(X4,X5,X0))
      | hBOOL(c_in(hAPP(X7,X4),c_Set_Oimage(X7,X5,X0,X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

fof(f2796,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f216,f2794]) ).

fof(f2794,plain,
    ( spl0_294
  <=> ! [X3,X12,X5,X8] :
        ( X8 = X12
        | hBOOL(c_in(X8,X5,X3))
        | ~ hBOOL(c_in(X8,c_Set_Oinsert(X12,X5,X3),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f216,axiom,
    ! [X3,X8,X5,X12] :
      ( X8 = X12
      | hBOOL(c_in(X8,X5,X3))
      | ~ hBOOL(c_in(X8,c_Set_Oinsert(X12,X5,X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

fof(f2792,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f177,f2790]) ).

fof(f2790,plain,
    ( spl0_293
  <=> ! [X4,X51,X0,X3,X7] :
        ( ~ class_HOL_Oord(X0)
        | ~ c_lessequals(X7,X51,tc_fun(X3,X0))
        | c_lessequals(hAPP(X7,X4),hAPP(X51,X4),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f177,axiom,
    ! [X51,X3,X0,X7,X4] :
      ( ~ class_HOL_Oord(X0)
      | ~ c_lessequals(X7,X51,tc_fun(X3,X0))
      | c_lessequals(hAPP(X7,X4),hAPP(X51,X4),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

fof(f2788,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f128,f2786]) ).

fof(f128,axiom,
    ! [X3,X0,X54,X4,X42] : c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3) != c_Fun_Ofun__upd(X42,X54,c_Option_Ooption_OSome(X4,X0),X3,tc_Option_Ooption(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__nonempty_0) ).

fof(f2784,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f95,f2782]) ).

fof(f2782,plain,
    ( spl0_291
  <=> ! [X5,X0,X9,X3,X7] :
        ( ~ c_Finite__Set_Ofinite(X5,X3)
        | c_Finite__Set_Ofinite(X9,X0)
        | ~ c_lessequals(X9,c_Set_Oimage(X7,X5,X3,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f95,axiom,
    ! [X3,X0,X9,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X3)
      | c_Finite__Set_Ofinite(X9,X0)
      | ~ c_lessequals(X9,c_Set_Oimage(X7,X5,X3,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).

fof(f2780,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f4,f2778]) ).

fof(f2778,plain,
    ( spl0_290
  <=> ! [X3,X4,X0,X5,X2] :
        ( ~ hBOOL(c_in(X4,X5,X3))
        | hAPP(c_Map_Orestrict__map(X2,X5,X3,X0),X4) = hAPP(X2,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f4,axiom,
    ! [X2,X3,X0,X4,X5] :
      ( ~ hBOOL(c_in(X4,X5,X3))
      | hAPP(c_Map_Orestrict__map(X2,X5,X3,X0),X4) = hAPP(X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__in_0) ).

fof(f2507,plain,
    ( spl0_289
    | ~ spl0_225
    | ~ spl0_288 ),
    inference(avatar_split_clause,[],[f2503,f2500,f1791,f2505]) ).

fof(f2505,plain,
    ( spl0_289
  <=> ! [X5,X8,X3] : c_Set_Oinsert(X8,X5,X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X3),X8),X5,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f2500,plain,
    ( spl0_288
  <=> ! [X5,X8,X3] : c_Set_Oinsert(X8,X5,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X5,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f2503,plain,
    ( ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X3),X8),X5,tc_fun(X3,tc_bool))
    | ~ spl0_225
    | ~ spl0_288 ),
    inference(forward_demodulation,[],[f2501,f1792]) ).

fof(f2501,plain,
    ( ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X5,tc_fun(X3,tc_bool))
    | ~ spl0_288 ),
    inference(avatar_component_clause,[],[f2500]) ).

fof(f2502,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f521,f2500]) ).

fof(f521,plain,
    ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X5,tc_fun(X3,tc_bool)),
    inference(forward_demodulation,[],[f422,f435]) ).

fof(f422,axiom,
    ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X5,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

fof(f2498,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f464,f2496]) ).

fof(f2496,plain,
    ( spl0_287
  <=> ! [X5,X4,X6,X3] : c_Set_Oinsert(X4,c_Set_Oinsert(X6,X5,X3),X3) = c_Set_Oinsert(X6,c_Set_Oinsert(X4,X5,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f464,axiom,
    ! [X3,X6,X4,X5] : c_Set_Oinsert(X4,c_Set_Oinsert(X6,X5,X3),X3) = c_Set_Oinsert(X6,c_Set_Oinsert(X4,X5,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

fof(f2494,plain,
    ( spl0_286
    | ~ spl0_109
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f2450,f2267,f1070,f2492]) ).

fof(f2492,plain,
    ( spl0_286
  <=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oimage(c_Com_Obody,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X1),c_Option_Ooption_OSome(v_y,tc_Com_Ocom))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f2267,plain,
    ( spl0_266
  <=> ! [X0,X1] : hBOOL(c_in(c_Option_Ooption_OSome(v_y,tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f2450,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Set_Oimage(c_Com_Obody,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X1),c_Option_Ooption_OSome(v_y,tc_Com_Ocom)))
    | ~ spl0_109
    | ~ spl0_266 ),
    inference(resolution,[],[f2268,f1071]) ).

fof(f2268,plain,
    ( ! [X0,X1] : hBOOL(c_in(c_Option_Ooption_OSome(v_y,tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X1),X1))
    | ~ spl0_266 ),
    inference(avatar_component_clause,[],[f2267]) ).

fof(f2490,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f427,f2488]) ).

fof(f427,axiom,
    ! [X2,X3,X0,X8,X12] :
      ( hAPP(X2,X8) != c_Option_Ooption_OSome(X12,X3)
      | hBOOL(c_in(X8,c_Map_Odom(X2,X0,X3),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domI_0) ).

fof(f2486,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f363,f2484]) ).

fof(f2484,plain,
    ( spl0_284
  <=> ! [X6,X4,X11,X0,X3,X7] :
        ( X4 = X11
        | hAPP(X7,X11) = hAPP(c_Fun_Ofun__upd(X7,X4,X6,X3,X0),X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f363,axiom,
    ! [X3,X0,X11,X6,X7,X4] :
      ( X4 = X11
      | hAPP(X7,X11) = hAPP(c_Fun_Ofun__upd(X7,X4,X6,X3,X0),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

fof(f2482,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f356,f2480]) ).

fof(f2480,plain,
    ( spl0_283
  <=> ! [X12,X8,X3] :
        ( ~ class_Orderings_Oorder(X3)
        | c_lessequals(X8,X12,X3)
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f356,axiom,
    ! [X3,X8,X12] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X8,X12,X3)
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

fof(f2478,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f329,f2476]) ).

fof(f2476,plain,
    ( spl0_282
  <=> ! [X5,X3,X9,X21] :
        ( ~ hBOOL(c_in(X21,X5,X3))
        | hBOOL(c_in(X21,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f329,axiom,
    ! [X21,X3,X9,X5] :
      ( ~ hBOOL(c_in(X21,X5,X3))
      | hBOOL(c_in(X21,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

fof(f2474,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f328,f2472]) ).

fof(f2472,plain,
    ( spl0_281
  <=> ! [X3,X9,X5,X21] :
        ( ~ hBOOL(c_in(X21,X9,X3))
        | hBOOL(c_in(X21,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f328,axiom,
    ! [X21,X3,X9,X5] :
      ( ~ hBOOL(c_in(X21,X9,X3))
      | hBOOL(c_in(X21,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

fof(f2470,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f307,f2468]) ).

fof(f2468,plain,
    ( spl0_280
  <=> ! [X12,X8,X3] :
        ( ~ class_Orderings_Oorder(X3)
        | ~ c_lessequals(X8,X12,X3)
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f307,axiom,
    ! [X3,X8,X12] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(X8,X12,X3)
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X8,X12,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).

fof(f2466,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f277,f2464]) ).

fof(f2464,plain,
    ( spl0_279
  <=> ! [X9,X5,X3] :
        ( X5 = X9
        | ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
        | ~ c_lessequals(X9,X5,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f277,axiom,
    ! [X3,X9,X5] :
      ( X5 = X9
      | ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
      | ~ c_lessequals(X9,X5,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

fof(f2462,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f273,f2460]) ).

fof(f2460,plain,
    ( spl0_278
  <=> ! [X6,X0,X3] : c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) = c_Map_Odom(c_COMBK(c_Option_Ooption_OSome(X6,X0),tc_Option_Ooption(X0),X3),X3,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f273,axiom,
    ! [X3,X0,X6] : c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) = c_Map_Odom(c_COMBK(c_Option_Ooption_OSome(X6,X0),tc_Option_Ooption(X0),X3),X3,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__const_0) ).

fof(f2458,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f270,f2456]) ).

fof(f2456,plain,
    ( spl0_277
  <=> ! [X58,X3,X67,X65] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X67,X65,X3)
        | c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | ~ c_lessequals(X67,X58,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f270,axiom,
    ! [X65,X3,X58,X67] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X67,X65,X3)
      | c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
      | ~ c_lessequals(X67,X58,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_thin_0) ).

fof(f2454,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f269,f2452]) ).

fof(f2452,plain,
    ( spl0_276
  <=> ! [X65,X58,X3,X66] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X66,X3)
        | c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | ~ c_lessequals(X65,X66,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f269,axiom,
    ! [X65,X58,X3,X66] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X66,X3)
      | c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
      | ~ c_lessequals(X65,X66,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weaken_0) ).

fof(f2448,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f223,f2446]) ).

fof(f2446,plain,
    ( spl0_275
  <=> ! [X9,X5,X3,X4] :
        ( c_lessequals(X5,X9,tc_fun(X3,tc_bool))
        | ~ c_lessequals(c_Set_Oinsert(X4,X5,X3),X9,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f223,axiom,
    ! [X3,X9,X4,X5] :
      ( c_lessequals(X5,X9,tc_fun(X3,tc_bool))
      | ~ c_lessequals(c_Set_Oinsert(X4,X5,X3),X9,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

fof(f2444,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f222,f2442]) ).

fof(f2442,plain,
    ( spl0_274
  <=> ! [X5,X12,X9,X3] :
        ( ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
        | c_lessequals(X5,c_Set_Oinsert(X12,X9,X3),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f222,axiom,
    ! [X3,X9,X5,X12] :
      ( ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
      | c_lessequals(X5,c_Set_Oinsert(X12,X9,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

fof(f2440,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f192,f2438]) ).

fof(f2438,plain,
    ( spl0_273
  <=> ! [X5,X3] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
        | ~ c_lessequals(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f192,axiom,
    ! [X3,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X5
      | ~ c_lessequals(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

fof(f2436,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f135,f2434]) ).

fof(f2434,plain,
    ( spl0_272
  <=> ! [X3,X9,X5,X21] :
        ( ~ hBOOL(c_in(X21,X9,X3))
        | ~ hBOOL(c_in(X21,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f135,axiom,
    ! [X21,X3,X9,X5] :
      ( ~ hBOOL(c_in(X21,X9,X3))
      | ~ hBOOL(c_in(X21,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

fof(f2432,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f133,f2430]) ).

fof(f2430,plain,
    ( spl0_271
  <=> ! [X5,X3,X9,X21] :
        ( hBOOL(c_in(X21,X5,X3))
        | ~ hBOOL(c_in(X21,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f133,axiom,
    ! [X21,X3,X9,X5] :
      ( hBOOL(c_in(X21,X5,X3))
      | ~ hBOOL(c_in(X21,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

fof(f2428,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f119,f2426]) ).

fof(f2426,plain,
    ( spl0_270
  <=> ! [X5,X8,X3] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
        | c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,X5,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Complete__Lattice_OSup__class_OSup(X5,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f119,axiom,
    ! [X3,X8,X5] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,X5,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Complete__Lattice_OSup__class_OSup(X5,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).

fof(f2424,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f5,f2422]) ).

fof(f2422,plain,
    ( spl0_269
  <=> ! [X2,X4,X0,X5,X3] :
        ( hBOOL(c_in(X4,X5,X3))
        | c_Option_Ooption_ONone(X0) = hAPP(c_Map_Orestrict__map(X2,X5,X3,X0),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f5,axiom,
    ! [X2,X3,X0,X4,X5] :
      ( hBOOL(c_in(X4,X5,X3))
      | c_Option_Ooption_ONone(X0) = hAPP(c_Map_Orestrict__map(X2,X5,X3,X0),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__out_0) ).

fof(f2420,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f1,f2418]) ).

fof(f2418,plain,
    ( spl0_268
  <=> ! [X0,X1] : c_Option_Ooption_ONone(X0) = hAPP(c_Map_Orestrict__map(c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),t_a),X1,t_a,X0),v_x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f1,axiom,
    ! [X0,X1] : c_Option_Ooption_ONone(X0) = hAPP(c_Map_Orestrict__map(c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),t_a),X1,t_a,X0),v_x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__map__empty_0) ).

fof(f2409,plain,
    ( spl0_267
    | ~ spl0_4
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f2258,f2029,f612,f2407]) ).

fof(f2407,plain,
    ( spl0_267
  <=> ! [X0,X1] :
        ( c_Option_Ooption_ONone(X0) != c_Option_Ooption_OSome(v_y,tc_Com_Ocom)
        | ~ hBOOL(c_in(v_pn,c_Map_Odom(c_Com_Obody,X1,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f2029,plain,
    ( spl0_238
  <=> ! [X0,X8,X3,X2] :
        ( c_Option_Ooption_ONone(X0) != hAPP(X2,X8)
        | ~ hBOOL(c_in(X8,c_Map_Odom(X2,X3,X0),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f2258,plain,
    ( ! [X0,X1] :
        ( c_Option_Ooption_ONone(X0) != c_Option_Ooption_OSome(v_y,tc_Com_Ocom)
        | ~ hBOOL(c_in(v_pn,c_Map_Odom(c_Com_Obody,X1,X0),X1)) )
    | ~ spl0_4
    | ~ spl0_238 ),
    inference(superposition,[],[f2030,f614]) ).

fof(f2030,plain,
    ( ! [X2,X3,X0,X8] :
        ( c_Option_Ooption_ONone(X0) != hAPP(X2,X8)
        | ~ hBOOL(c_in(X8,c_Map_Odom(X2,X3,X0),X3)) )
    | ~ spl0_238 ),
    inference(avatar_component_clause,[],[f2029]) ).

fof(f2269,plain,
    ( spl0_266
    | ~ spl0_4
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f2196,f2009,f612,f2267]) ).

fof(f2009,plain,
    ( spl0_233
  <=> ! [X4,X0,X3,X7] : hBOOL(c_in(hAPP(X7,X4),c_Set_Oimage(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X3),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f2196,plain,
    ( ! [X0,X1] : hBOOL(c_in(c_Option_Ooption_OSome(v_y,tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X1),X1))
    | ~ spl0_4
    | ~ spl0_233 ),
    inference(superposition,[],[f2010,f614]) ).

fof(f2010,plain,
    ( ! [X3,X0,X7,X4] : hBOOL(c_in(hAPP(X7,X4),c_Set_Oimage(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X3),X3))
    | ~ spl0_233 ),
    inference(avatar_component_clause,[],[f2009]) ).

fof(f2186,plain,
    ( ~ spl0_19
    | spl0_265
    | ~ spl0_107
    | ~ spl0_122 ),
    inference(avatar_split_clause,[],[f1169,f1122,f1062,f2184,f687]) ).

fof(f687,plain,
    ( spl0_19
  <=> class_Lattices_Olattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f2184,plain,
    ( spl0_265
  <=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f1062,plain,
    ( spl0_107
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Olattice(X3)
        | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f1122,plain,
    ( spl0_122
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f1169,plain,
    ( ! [X0] :
        ( c_lessequals(X0,X0,tc_bool)
        | ~ class_Lattices_Olattice(tc_bool) )
    | ~ spl0_107
    | ~ spl0_122 ),
    inference(superposition,[],[f1063,f1123]) ).

fof(f1123,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f1122]) ).

fof(f1063,plain,
    ( ! [X3,X6,X4] :
        ( c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3)
        | ~ class_Lattices_Olattice(X3) )
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f1062]) ).

fof(f2156,plain,
    ( spl0_264
    | ~ spl0_225
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2152,f2149,f1791,f2154]) ).

fof(f2154,plain,
    ( spl0_264
  <=> ! [X3,X7,X12,X8] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X3),X8),X3),X12))
        | X8 = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f2149,plain,
    ( spl0_263
  <=> ! [X3,X7,X12,X8] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3),X12))
        | X8 = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f2152,plain,
    ( ! [X3,X8,X7,X12] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X3),X8),X3),X12))
        | X8 = X12 )
    | ~ spl0_225
    | ~ spl0_263 ),
    inference(forward_demodulation,[],[f2150,f1792]) ).

fof(f2150,plain,
    ( ! [X3,X8,X7,X12] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3),X12))
        | X8 = X12 )
    | ~ spl0_263 ),
    inference(avatar_component_clause,[],[f2149]) ).

fof(f2151,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f538,f2149]) ).

fof(f538,plain,
    ! [X3,X8,X7,X12] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3),X12))
      | X8 = X12 ),
    inference(forward_demodulation,[],[f413,f435]) ).

fof(f413,axiom,
    ! [X3,X8,X7,X12] :
      ( X8 = X12
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).

fof(f2146,plain,
    ( spl0_262
    | ~ spl0_225
    | ~ spl0_261 ),
    inference(avatar_split_clause,[],[f2142,f2139,f1791,f2144]) ).

fof(f2144,plain,
    ( spl0_262
  <=> ! [X4,X3] : hBOOL(hAPP(hAPP(c_fequal(X3),X4),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X3),X4),X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f2139,plain,
    ( spl0_261
  <=> ! [X4,X3] : hBOOL(hAPP(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f2142,plain,
    ( ! [X3,X4] : hBOOL(hAPP(hAPP(c_fequal(X3),X4),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X3),X4),X3)))
    | ~ spl0_225
    | ~ spl0_261 ),
    inference(forward_demodulation,[],[f2140,f1792]) ).

fof(f2140,plain,
    ( ! [X3,X4] : hBOOL(hAPP(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3)))
    | ~ spl0_261 ),
    inference(avatar_component_clause,[],[f2139]) ).

fof(f2141,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f522,f2139]) ).

fof(f522,plain,
    ! [X3,X4] : hBOOL(hAPP(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3))),
    inference(forward_demodulation,[],[f404,f435]) ).

fof(f404,axiom,
    ! [X3,X4] : hBOOL(hAPP(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).

fof(f2135,plain,
    ( spl0_260
    | ~ spl0_225
    | ~ spl0_259 ),
    inference(avatar_split_clause,[],[f2126,f2123,f1791,f2133]) ).

fof(f2133,plain,
    ( spl0_260
  <=> ! [X20,X3,X58] : c_Hoare__Mirabelle_Ohoare__derivs(X58,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X20,c_Com_Ocom_OSKIP,X20,X3)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f2123,plain,
    ( spl0_259
  <=> ! [X20,X3,X58] : c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Option_Oset(c_Option_Ooption_OSome(c_Hoare__Mirabelle_Otriple_Otriple(X20,c_Com_Ocom_OSKIP,X20,X3),tc_Hoare__Mirabelle_Otriple(X3)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f2126,plain,
    ( ! [X58,X3,X20] : c_Hoare__Mirabelle_Ohoare__derivs(X58,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X20,c_Com_Ocom_OSKIP,X20,X3)),X3)
    | ~ spl0_225
    | ~ spl0_259 ),
    inference(forward_demodulation,[],[f2124,f1792]) ).

fof(f2124,plain,
    ( ! [X58,X3,X20] : c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Option_Oset(c_Option_Ooption_OSome(c_Hoare__Mirabelle_Otriple_Otriple(X20,c_Com_Ocom_OSKIP,X20,X3),tc_Hoare__Mirabelle_Otriple(X3)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
    | ~ spl0_259 ),
    inference(avatar_component_clause,[],[f2123]) ).

fof(f2125,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f520,f2123]) ).

fof(f520,plain,
    ! [X58,X3,X20] : c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Option_Oset(c_Option_Ooption_OSome(c_Hoare__Mirabelle_Otriple_Otriple(X20,c_Com_Ocom_OSKIP,X20,X3),tc_Hoare__Mirabelle_Otriple(X3)),tc_Hoare__Mirabelle_Otriple(X3)),X3),
    inference(forward_demodulation,[],[f393,f435]) ).

fof(f393,axiom,
    ! [X58,X3,X20] : c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X20,c_Com_Ocom_OSKIP,X20,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).

fof(f2115,plain,
    ( spl0_258
    | ~ spl0_22
    | ~ spl0_108
    | ~ spl0_170
    | ~ spl0_257 ),
    inference(avatar_split_clause,[],[f2110,f2106,f1373,f1066,f702,f2112]) ).

fof(f2112,plain,
    ( spl0_258
  <=> c_in(v_x,c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),t_a) = c_Orderings_Obot__class_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f702,plain,
    ( spl0_22
  <=> class_Orderings_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f1066,plain,
    ( spl0_108
  <=> ! [X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_Option_Oset(c_Option_Ooption_ONone(X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f1373,plain,
    ( spl0_170
  <=> ! [X0] :
        ( ~ class_Orderings_Obot(X0)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X0)),v_x) = c_Orderings_Obot__class_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f2106,plain,
    ( spl0_257
  <=> hAPP(c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),v_x) = c_in(v_x,c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f2110,plain,
    ( c_in(v_x,c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),t_a) = c_Orderings_Obot__class_Obot(tc_bool)
    | ~ spl0_22
    | ~ spl0_108
    | ~ spl0_170
    | ~ spl0_257 ),
    inference(forward_demodulation,[],[f2108,f1503]) ).

fof(f1503,plain,
    ( hAPP(c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
    | ~ spl0_22
    | ~ spl0_108
    | ~ spl0_170 ),
    inference(forward_demodulation,[],[f1501,f1067]) ).

fof(f1067,plain,
    ( ! [X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_Option_Oset(c_Option_Ooption_ONone(X3),X3)
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f1066]) ).

fof(f1501,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
    | ~ spl0_22
    | ~ spl0_170 ),
    inference(resolution,[],[f1374,f704]) ).

fof(f704,plain,
    ( class_Orderings_Obot(tc_bool)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f702]) ).

fof(f1374,plain,
    ( ! [X0] :
        ( ~ class_Orderings_Obot(X0)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X0)),v_x) = c_Orderings_Obot__class_Obot(X0) )
    | ~ spl0_170 ),
    inference(avatar_component_clause,[],[f1373]) ).

fof(f2108,plain,
    ( hAPP(c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),v_x) = c_in(v_x,c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),t_a)
    | ~ spl0_257 ),
    inference(avatar_component_clause,[],[f2106]) ).

fof(f2109,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f518,f2106]) ).

fof(f518,plain,
    hAPP(c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),v_x) = c_in(v_x,c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),t_a),
    inference(forward_demodulation,[],[f290,f31]) ).

fof(f31,axiom,
    ! [X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_Option_Oset(c_Option_Ooption_ONone(X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__empty__eq_1) ).

fof(f290,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(f2104,plain,
    ( spl0_256
    | ~ spl0_205
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f2100,f2097,f1595,f2102]) ).

fof(f2102,plain,
    ( spl0_256
  <=> ! [X8,X3,X7] : c_The(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X3),X8),X3),X3) = X8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f1595,plain,
    ( spl0_205
  <=> ! [X8,X3] : c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = hAPP(c_fequal(X3),X8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f2097,plain,
    ( spl0_255
  <=> ! [X8,X3,X7] : c_The(c_Finite__Set_Ofold1Set(X7,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = X8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f2100,plain,
    ( ! [X3,X8,X7] : c_The(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X3),X8),X3),X3) = X8
    | ~ spl0_205
    | ~ spl0_255 ),
    inference(forward_demodulation,[],[f2098,f1596]) ).

fof(f1596,plain,
    ( ! [X3,X8] : c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = hAPP(c_fequal(X3),X8)
    | ~ spl0_205 ),
    inference(avatar_component_clause,[],[f1595]) ).

fof(f2098,plain,
    ( ! [X3,X8,X7] : c_The(c_Finite__Set_Ofold1Set(X7,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = X8
    | ~ spl0_255 ),
    inference(avatar_component_clause,[],[f2097]) ).

fof(f2099,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f515,f2097]) ).

fof(f515,plain,
    ! [X3,X8,X7] : c_The(c_Finite__Set_Ofold1Set(X7,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = X8,
    inference(definition_unfolding,[],[f417,f99]) ).

fof(f99,axiom,
    ! [X3,X7,X5] : c_Finite__Set_Ofold1(X7,X5,X3) = c_The(c_Finite__Set_Ofold1Set(X7,X5,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__def_0) ).

fof(f417,axiom,
    ! [X3,X8,X7] : c_Finite__Set_Ofold1(X7,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).

fof(f2095,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f512,f2093]) ).

fof(f2093,plain,
    ( spl0_254
  <=> ! [X48,X60,X20,X0,X3,X76] : hAPP(c_COMBB(X20,X48,X0,X3,X60),X76) = hAPP(X20,hAPP(X48,X76)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f512,axiom,
    ! [X3,X48,X0,X76,X60,X20] : hAPP(c_COMBB(X20,X48,X0,X3,X60),X76) = hAPP(X20,hAPP(X48,X76)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).

fof(f2091,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f460,f2089]) ).

fof(f2089,plain,
    ( spl0_253
  <=> ! [X5,X4,X6,X3] :
        ( X4 = X6
        | hBOOL(hAPP(X5,X4))
        | ~ hBOOL(hAPP(c_Set_Oinsert(X6,X5,X3),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f460,axiom,
    ! [X3,X6,X4,X5] :
      ( X4 = X6
      | hBOOL(hAPP(X5,X4))
      | ~ hBOOL(hAPP(c_Set_Oinsert(X6,X5,X3),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

fof(f2087,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f349,f2085]) ).

fof(f2085,plain,
    ( spl0_252
  <=> ! [X48,X4,X20,X3] :
        ( ~ hBOOL(hAPP(X20,X4))
        | hBOOL(hAPP(X48,X4))
        | ~ c_lessequals(X20,X48,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f349,axiom,
    ! [X3,X48,X4,X20] :
      ( ~ hBOOL(hAPP(X20,X4))
      | hBOOL(hAPP(X48,X4))
      | ~ c_lessequals(X20,X48,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

fof(f2083,plain,
    ( ~ spl0_9
    | spl0_251
    | ~ spl0_102
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f1153,f1062,f1037,f2081,f637]) ).

fof(f637,plain,
    ( spl0_9
  <=> class_Lattices_Olattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f2081,plain,
    ( spl0_251
  <=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f1037,plain,
    ( spl0_102
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f1153,plain,
    ( ! [X0] :
        ( c_lessequals(X0,X0,tc_nat)
        | ~ class_Lattices_Olattice(tc_nat) )
    | ~ spl0_102
    | ~ spl0_107 ),
    inference(superposition,[],[f1063,f1038]) ).

fof(f1038,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f1037]) ).

fof(f2079,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f341,f2077]) ).

fof(f2077,plain,
    ( spl0_250
  <=> ! [X4,X11,X6,X3] :
        ( ~ class_Orderings_Opreorder(X3)
        | ~ c_lessequals(X4,X6,X3)
        | ~ c_lessequals(X6,X11,X3)
        | c_lessequals(X4,X11,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f341,axiom,
    ! [X3,X11,X6,X4] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_lessequals(X4,X6,X3)
      | ~ c_lessequals(X6,X11,X3)
      | c_lessequals(X4,X11,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

fof(f2075,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f340,f2073]) ).

fof(f2073,plain,
    ( spl0_249
  <=> ! [X4,X11,X6,X3] :
        ( ~ class_Orderings_Oorder(X3)
        | ~ c_lessequals(X6,X4,X3)
        | ~ c_lessequals(X11,X6,X3)
        | c_lessequals(X11,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f340,axiom,
    ! [X3,X11,X6,X4] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(X6,X4,X3)
      | ~ c_lessequals(X11,X6,X3)
      | c_lessequals(X11,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

fof(f2071,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f308,f2069]) ).

fof(f2069,plain,
    ( spl0_248
  <=> ! [X5,X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f308,axiom,
    ! [X3,X5] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

fof(f2067,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f303,f2065]) ).

fof(f2065,plain,
    ( spl0_247
  <=> ! [X69,X33,X23,X71,X3,X70,X72] :
        ( X70 = X72
        | c_Hoare__Mirabelle_Otriple_Otriple(X69,X23,X70,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X71,X33,X72,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f303,axiom,
    ! [X72,X70,X3,X71,X69,X23,X33] :
      ( X70 = X72
      | c_Hoare__Mirabelle_Otriple_Otriple(X69,X23,X70,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X71,X33,X72,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).

fof(f2063,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f302,f2061]) ).

fof(f2061,plain,
    ( spl0_246
  <=> ! [X69,X33,X71,X23,X70,X3,X72] :
        ( X23 = X33
        | c_Hoare__Mirabelle_Otriple_Otriple(X69,X23,X70,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X71,X33,X72,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f302,axiom,
    ! [X3,X70,X72,X71,X69,X23,X33] :
      ( X23 = X33
      | c_Hoare__Mirabelle_Otriple_Otriple(X69,X23,X70,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X71,X33,X72,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).

fof(f2059,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f301,f2057]) ).

fof(f2057,plain,
    ( spl0_245
  <=> ! [X70,X33,X23,X71,X3,X69,X72] :
        ( X69 = X71
        | c_Hoare__Mirabelle_Otriple_Otriple(X69,X23,X70,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X71,X33,X72,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f301,axiom,
    ! [X3,X70,X72,X71,X69,X23,X33] :
      ( X69 = X71
      | c_Hoare__Mirabelle_Otriple_Otriple(X69,X23,X70,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X71,X33,X72,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).

fof(f2055,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f289,f2053]) ).

fof(f2053,plain,
    ( spl0_244
  <=> ! [X9,X5,X3] :
        ( c_lessequals(X5,X9,tc_fun(X3,tc_bool))
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) != X9 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f289,axiom,
    ! [X3,X9,X5] :
      ( c_lessequals(X5,X9,tc_fun(X3,tc_bool))
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) != X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

fof(f2051,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f288,f2049]) ).

fof(f2049,plain,
    ( spl0_243
  <=> ! [X9,X5,X3] :
        ( ~ c_lessequals(X9,X5,tc_fun(X3,tc_bool))
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f288,axiom,
    ! [X3,X9,X5] :
      ( ~ c_lessequals(X9,X5,tc_fun(X3,tc_bool))
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

fof(f2047,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f287,f2045]) ).

fof(f2045,plain,
    ( spl0_242
  <=> ! [X9,X5,X3] :
        ( ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = X9 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f287,axiom,
    ! [X3,X9,X5] :
      ( ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool))
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

fof(f2043,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f240,f2041]) ).

fof(f2041,plain,
    ( spl0_241
  <=> ! [X0,X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3),X3,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f240,axiom,
    ! [X3,X0] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(X0),tc_Option_Ooption(X0),X3),X3,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__empty_0) ).

fof(f2039,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f196,f2037]) ).

fof(f2037,plain,
    ( spl0_240
  <=> ! [X5,X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f196,axiom,
    ! [X3,X5] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

fof(f2035,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f160,f2033]) ).

fof(f2033,plain,
    ( spl0_239
  <=> ! [X0,X8,X3,X2] :
        ( c_Option_Ooption_ONone(X0) = hAPP(X2,X8)
        | hBOOL(c_in(X8,c_Map_Odom(X2,X3,X0),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f160,axiom,
    ! [X2,X3,X0,X8] :
      ( c_Option_Ooption_ONone(X0) = hAPP(X2,X8)
      | hBOOL(c_in(X8,c_Map_Odom(X2,X3,X0),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domIff_1) ).

fof(f2031,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f159,f2029]) ).

fof(f159,axiom,
    ! [X2,X3,X0,X8] :
      ( c_Option_Ooption_ONone(X0) != hAPP(X2,X8)
      | ~ hBOOL(c_in(X8,c_Map_Odom(X2,X3,X0),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domIff_0) ).

fof(f2027,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f143,f2025]) ).

fof(f2025,plain,
    ( spl0_237
  <=> ! [X57,X3,X58] :
        ( ~ c_Finite__Set_Ofinite(X57,X3)
        | ~ c_Finite__Set_Ofinite(X58,X3)
        | c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X57,X58,tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f143,axiom,
    ! [X3,X58,X57] :
      ( ~ c_Finite__Set_Ofinite(X57,X3)
      | ~ c_Finite__Set_Ofinite(X58,X3)
      | c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X57,X58,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

fof(f2023,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f125,f2021]) ).

fof(f2021,plain,
    ( spl0_236
  <=> ! [X9,X5,X3] :
        ( ~ c_Finite__Set_Ofinite(X9,X3)
        | c_Finite__Set_Ofinite(X5,X3)
        | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f125,axiom,
    ! [X3,X9,X5] :
      ( ~ c_Finite__Set_Ofinite(X9,X3)
      | c_Finite__Set_Ofinite(X5,X3)
      | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

fof(f2019,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f123,f2017]) ).

fof(f2017,plain,
    ( spl0_235
  <=> ! [X5,X3] : c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f123,axiom,
    ! [X3,X5] : c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).

fof(f2015,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f122,f2013]) ).

fof(f2013,plain,
    ( spl0_234
  <=> ! [X9,X3] : c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f122,axiom,
    ! [X3,X9] : c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

fof(f2011,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f83,f2009]) ).

fof(f83,axiom,
    ! [X3,X0,X7,X4] : hBOOL(c_in(hAPP(X7,X4),c_Set_Oimage(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

fof(f2007,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f60,f2005]) ).

fof(f2005,plain,
    ( spl0_232
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Olattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f60,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Olattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

fof(f2003,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f59,f2001]) ).

fof(f2001,plain,
    ( spl0_231
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f59,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

fof(f1999,plain,
    ( spl0_230
    | ~ spl0_96
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1756,f1715,f1010,f1997]) ).

fof(f1997,plain,
    ( spl0_230
  <=> ! [X0] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Com_Ostate)
        | c_Hoare__Mirabelle_Ohoare__valids(X0,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f1010,plain,
    ( spl0_96
  <=> ! [X65,X3,X58] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | c_Hoare__Mirabelle_Ohoare__valids(X58,X65,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1715,plain,
    ( spl0_208
  <=> ! [X0] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Com_Ostate)
        | c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f1756,plain,
    ( ! [X0] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Com_Ostate)
        | c_Hoare__Mirabelle_Ohoare__valids(X0,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
    | ~ spl0_96
    | ~ spl0_208 ),
    inference(resolution,[],[f1716,f1011]) ).

fof(f1011,plain,
    ( ! [X65,X58,X3] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | c_Hoare__Mirabelle_Ohoare__valids(X58,X65,X3) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f1010]) ).

fof(f1716,plain,
    ( ! [X0] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Com_Ostate) )
    | ~ spl0_208 ),
    inference(avatar_component_clause,[],[f1715]) ).

fof(f1995,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f37,f1993]) ).

fof(f1993,plain,
    ( spl0_229
  <=> ! [X4,X9,X5,X3] :
        ( hBOOL(c_in(X4,X9,X3))
        | ~ c_lessequals(c_Set_Oinsert(X4,X5,X3),X9,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f37,axiom,
    ! [X3,X9,X4,X5] :
      ( hBOOL(c_in(X4,X9,X3))
      | ~ c_lessequals(c_Set_Oinsert(X4,X5,X3),X9,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

fof(f1814,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f516,f1812]) ).

fof(f1812,plain,
    ( spl0_228
  <=> ! [X2,X0] : c_Option_Ooption_ONone(X0) = hAPP(c_Map_Orestrict__map(X2,c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),t_a,X0),v_x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f516,plain,
    ! [X2,X0] : c_Option_Ooption_ONone(X0) = hAPP(c_Map_Orestrict__map(X2,c_Option_Oset(c_Option_Ooption_ONone(t_a),t_a),t_a,X0),v_x),
    inference(forward_demodulation,[],[f3,f31]) ).

fof(f3,axiom,
    ! [X2,X0] : c_Option_Ooption_ONone(X0) = hAPP(c_Map_Orestrict__map(X2,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a,X0),v_x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__map__to__empty_0) ).

fof(f1810,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f467,f1808]) ).

fof(f1808,plain,
    ( spl0_227
  <=> ! [X0,X7,X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_Set_Oimage(X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f467,axiom,
    ! [X3,X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_Set_Oimage(X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

fof(f1806,plain,
    ( ~ spl0_226
    | spl0_27
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f1794,f1791,f727,f1803]) ).

fof(f727,plain,
    ( spl0_27
  <=> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f1794,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),tc_Com_Ostate)
    | spl0_27
    | ~ spl0_225 ),
    inference(superposition,[],[f729,f1792]) ).

fof(f729,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | spl0_27 ),
    inference(avatar_component_clause,[],[f727]) ).

fof(f1793,plain,
    ( spl0_225
    | ~ spl0_205
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f1789,f1786,f1595,f1791]) ).

fof(f1786,plain,
    ( spl0_224
  <=> ! [X4,X3] : c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f1789,plain,
    ( ! [X3,X4] : c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3) = hAPP(c_fequal(X3),X4)
    | ~ spl0_205
    | ~ spl0_224 ),
    inference(forward_demodulation,[],[f1787,f1596]) ).

fof(f1787,plain,
    ( ! [X3,X4] : c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3)
    | ~ spl0_224 ),
    inference(avatar_component_clause,[],[f1786]) ).

fof(f1788,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f435,f1786]) ).

fof(f1784,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f371,f1782]) ).

fof(f1782,plain,
    ( spl0_223
  <=> ! [X4,X5,X3] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
        | ~ hBOOL(c_in(X4,X5,X3))
        | c_lessequals(X4,c_Complete__Lattice_OSup__class_OSup(X5,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f371,axiom,
    ! [X3,X4,X5] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | ~ hBOOL(c_in(X4,X5,X3))
      | c_lessequals(X4,c_Complete__Lattice_OSup__class_OSup(X5,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).

fof(f1780,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f336,f1778]) ).

fof(f1778,plain,
    ( spl0_222
  <=> ! [X3,X4,X12,X8] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_lessequals(X8,X4,X3)
        | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f336,axiom,
    ! [X3,X8,X4,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_lessequals(X8,X4,X3)
      | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

fof(f1776,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f335,f1774]) ).

fof(f1774,plain,
    ( spl0_221
  <=> ! [X4,X12,X8,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_lessequals(X12,X4,X3)
        | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f335,axiom,
    ! [X3,X8,X4,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_lessequals(X12,X4,X3)
      | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

fof(f1772,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f334,f1770]) ).

fof(f1770,plain,
    ( spl0_220
  <=> ! [X3,X4,X12,X8] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | ~ c_lessequals(X4,X8,X3)
        | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f334,axiom,
    ! [X3,X8,X4,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | ~ c_lessequals(X4,X8,X3)
      | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

fof(f1768,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f333,f1766]) ).

fof(f1766,plain,
    ( spl0_219
  <=> ! [X3,X4,X12,X8] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | ~ c_lessequals(X4,X12,X3)
        | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f333,axiom,
    ! [X3,X8,X4,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | ~ c_lessequals(X4,X12,X3)
      | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X8,X12,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

fof(f1764,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f305,f1762]) ).

fof(f1762,plain,
    ( spl0_218
  <=> ! [X4,X5,X3] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
        | ~ hBOOL(c_in(X4,X5,X3))
        | c_lessequals(c_Complete__Lattice_OInf__class_OInf(X5,X3),X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f305,axiom,
    ! [X3,X4,X5] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | ~ hBOOL(c_in(X4,X5,X3))
      | c_lessequals(c_Complete__Lattice_OInf__class_OInf(X5,X3),X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).

fof(f1760,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f281,f1758]) ).

fof(f1758,plain,
    ( spl0_217
  <=> ! [X6,X4,X3] :
        ( ~ class_Orderings_Oorder(X3)
        | X4 = X6
        | ~ c_lessequals(X4,X6,X3)
        | ~ c_lessequals(X6,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f281,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Orderings_Oorder(X3)
      | X4 = X6
      | ~ c_lessequals(X4,X6,X3)
      | ~ c_lessequals(X6,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

fof(f1754,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f212,f1752]) ).

fof(f1752,plain,
    ( spl0_216
  <=> ! [X3,X12,X5,X8] :
        ( ~ hBOOL(c_in(X8,X5,X3))
        | hBOOL(c_in(X8,c_Set_Oinsert(X12,X5,X3),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f212,axiom,
    ! [X3,X8,X5,X12] :
      ( ~ hBOOL(c_in(X8,X5,X3))
      | hBOOL(c_in(X8,c_Set_Oinsert(X12,X5,X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

fof(f1750,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f182,f1748]) ).

fof(f1748,plain,
    ( spl0_215
  <=> ! [X9,X5,X3] :
        ( ~ class_Lattices_Obounded__lattice(X3)
        | c_Orderings_Obot__class_Obot(X3) = X9
        | c_Orderings_Obot__class_Obot(X3) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f182,axiom,
    ! [X3,X9,X5] :
      ( ~ class_Lattices_Obounded__lattice(X3)
      | c_Orderings_Obot__class_Obot(X3) = X9
      | c_Orderings_Obot__class_Obot(X3) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

fof(f1746,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f181,f1744]) ).

fof(f1744,plain,
    ( spl0_214
  <=> ! [X9,X5,X3] :
        ( ~ class_Lattices_Obounded__lattice(X3)
        | c_Orderings_Obot__class_Obot(X3) = X5
        | c_Orderings_Obot__class_Obot(X3) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f181,axiom,
    ! [X3,X9,X5] :
      ( ~ class_Lattices_Obounded__lattice(X3)
      | c_Orderings_Obot__class_Obot(X3) = X5
      | c_Orderings_Obot__class_Obot(X3) != c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

fof(f1742,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f155,f1740]) ).

fof(f1740,plain,
    ( spl0_213
  <=> ! [X4,X9,X5,X3] :
        ( ~ hBOOL(hAPP(X5,X4))
        | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f155,axiom,
    ! [X3,X9,X4,X5] :
      ( ~ hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

fof(f1738,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f154,f1736]) ).

fof(f1736,plain,
    ( spl0_212
  <=> ! [X4,X5,X9,X3] :
        ( ~ hBOOL(hAPP(X9,X4))
        | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f154,axiom,
    ! [X3,X9,X4,X5] :
      ( ~ hBOOL(hAPP(X9,X4))
      | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

fof(f1734,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f114,f1732]) ).

fof(f1732,plain,
    ( spl0_211
  <=> ! [X41,X21,X12] :
        ( hBOOL(hAPP(X12,X41))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X12,X21)),X41),X41)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f114,axiom,
    ! [X21,X41,X12] :
      ( hBOOL(hAPP(X12,X41))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X12,X21)),X41),X41)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).

fof(f1730,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f70,f1728]) ).

fof(f1728,plain,
    ( spl0_210
  <=> ! [X4,X0,X6,X3,X7] :
        ( hAPP(X7,X4) = X6
        | c_Fun_Ofun__upd(X7,X4,X6,X3,X0) != X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f70,axiom,
    ! [X3,X0,X6,X7,X4] :
      ( hAPP(X7,X4) = X6
      | c_Fun_Ofun__upd(X7,X4,X6,X3,X0) != X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

fof(f1726,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f53,f1724]) ).

fof(f1724,plain,
    ( spl0_209
  <=> ! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f53,axiom,
    ! [X3,X9,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

fof(f1717,plain,
    ( spl0_208
    | ~ spl0_37
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1692,f1587,f770,f1715]) ).

fof(f770,plain,
    ( spl0_37
  <=> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f1587,plain,
    ( spl0_203
  <=> ! [X58,X3,X67,X65] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X67,X65,X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X67,X3)
        | c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f1692,plain,
    ( ! [X0] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Com_Ostate)
        | c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
    | ~ spl0_37
    | ~ spl0_203 ),
    inference(resolution,[],[f1588,f772]) ).

fof(f772,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f770]) ).

fof(f1588,plain,
    ( ! [X65,X3,X58,X67] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X67,X65,X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X67,X3)
        | c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3) )
    | ~ spl0_203 ),
    inference(avatar_component_clause,[],[f1587]) ).

fof(f1605,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f537,f1603]) ).

fof(f1603,plain,
    ( spl0_207
  <=> ! [X12,X8,X3] :
        ( ~ hBOOL(c_in(X12,c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3))
        | X8 = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f537,plain,
    ! [X3,X8,X12] :
      ( ~ hBOOL(c_in(X12,c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3))
      | X8 = X12 ),
    inference(forward_demodulation,[],[f416,f435]) ).

fof(f416,axiom,
    ! [X3,X8,X12] :
      ( X8 = X12
      | ~ hBOOL(c_in(X12,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

fof(f1601,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f536,f1599]) ).

fof(f1599,plain,
    ( spl0_206
  <=> ! [X8,X3] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(X8,X8,X3) = c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3)
        | ~ class_Orderings_Oorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f536,plain,
    ! [X3,X8] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(X8,X8,X3) = c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3)
      | ~ class_Orderings_Oorder(X3) ),
    inference(forward_demodulation,[],[f420,f435]) ).

fof(f420,axiom,
    ! [X3,X8] :
      ( ~ class_Orderings_Oorder(X3)
      | c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_SetInterval_Oord__class_OatLeastAtMost(X8,X8,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

fof(f1597,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f519,f1595]) ).

fof(f519,plain,
    ! [X3,X8] : c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = hAPP(c_fequal(X3),X8),
    inference(forward_demodulation,[],[f398,f115]) ).

fof(f115,axiom,
    ! [X3,X20] : c_Collect(X20,X3) = X20,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).

fof(f398,axiom,
    ! [X3,X8] : c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_Collect(hAPP(c_fequal(X3),X8),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).

fof(f1593,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f461,f1591]) ).

fof(f1591,plain,
    ( spl0_204
  <=> ! [X4,X5,X3] : c_Set_Oinsert(X4,X5,X3) = c_Set_Oinsert(X4,c_Set_Oinsert(X4,X5,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f461,axiom,
    ! [X3,X4,X5] : c_Set_Oinsert(X4,X5,X3) = c_Set_Oinsert(X4,c_Set_Oinsert(X4,X5,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

fof(f1589,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f449,f1587]) ).

fof(f449,axiom,
    ! [X65,X3,X58,X67] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X67,X65,X3)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X67,X3)
      | c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).

fof(f1585,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f443,f1583]) ).

fof(f1583,plain,
    ( spl0_202
  <=> ! [X42,X58,X3,X65] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f443,axiom,
    ! [X65,X58,X3,X42] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(X42,X65,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).

fof(f1581,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f439,f1579]) ).

fof(f1579,plain,
    ( spl0_201
  <=> ! [X20] :
        ( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X20))
        | hAPP(c_Com_Obody,X20) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(X20),tc_Com_Ocom) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f439,axiom,
    ! [X20] :
      ( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X20))
      | hAPP(c_Com_Obody,X20) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(X20),tc_Com_Ocom) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I7_J_0) ).

fof(f1577,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f354,f1575]) ).

fof(f1575,plain,
    ( spl0_200
  <=> ! [X9,X5,X3] :
        ( ~ c_Finite__Set_Ofinite(X9,X3)
        | c_Finite__Set_Ofinite(X5,X3)
        | ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f354,axiom,
    ! [X3,X9,X5] :
      ( ~ c_Finite__Set_Ofinite(X9,X3)
      | c_Finite__Set_Ofinite(X5,X3)
      | ~ c_lessequals(X5,X9,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

fof(f1573,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f320,f1571]) ).

fof(f1571,plain,
    ( spl0_199
  <=> ! [X55,X23,X13,X33,X17,X22] :
        ( X22 = X55
        | c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OLocal(X55,X13,X33) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f320,axiom,
    ! [X55,X17,X22,X23,X13,X33] :
      ( X22 = X55
      | c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OLocal(X55,X13,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).

fof(f1569,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f319,f1567]) ).

fof(f1567,plain,
    ( spl0_198
  <=> ! [X17,X23,X55,X13,X33,X22] :
        ( X13 = X17
        | c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OLocal(X55,X13,X33) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f319,axiom,
    ! [X55,X17,X22,X23,X13,X33] :
      ( X13 = X17
      | c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OLocal(X55,X13,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).

fof(f1565,plain,
    ( spl0_197
    | ~ spl0_96
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f1521,f1497,f1010,f1563]) ).

fof(f1563,plain,
    ( spl0_197
  <=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f1497,plain,
    ( spl0_184
  <=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f1521,plain,
    ( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__valids(X0,X0,X1)
    | ~ spl0_96
    | ~ spl0_184 ),
    inference(resolution,[],[f1498,f1011]) ).

fof(f1498,plain,
    ( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X0,X1)
    | ~ spl0_184 ),
    inference(avatar_component_clause,[],[f1497]) ).

fof(f1561,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f318,f1559]) ).

fof(f1559,plain,
    ( spl0_196
  <=> ! [X55,X33,X13,X23,X17,X22] :
        ( X23 = X33
        | c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OLocal(X55,X13,X33) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f318,axiom,
    ! [X55,X17,X22,X23,X13,X33] :
      ( X23 = X33
      | c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OLocal(X55,X13,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).

fof(f1557,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f286,f1555]) ).

fof(f1555,plain,
    ( spl0_195
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | ~ c_lessequals(X4,X6,X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f286,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | ~ c_lessequals(X4,X6,X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

fof(f1553,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f285,f1551]) ).

fof(f1551,plain,
    ( spl0_194
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_lessequals(X4,X6,X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) != X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f285,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_lessequals(X4,X6,X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) != X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

fof(f1549,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f284,f1547]) ).

fof(f1547,plain,
    ( spl0_193
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | ~ c_lessequals(X6,X4,X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f284,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | ~ c_lessequals(X6,X4,X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

fof(f1545,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f173,f1543]) ).

fof(f1543,plain,
    ( spl0_192
  <=> ! [X50,X3] :
        ( c_Option_Ooption_ONone(X3) = X50
        | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Option_Oset(X50,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f173,axiom,
    ! [X50,X3] :
      ( c_Option_Ooption_ONone(X3) = X50
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Option_Oset(X50,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__empty__eq_0) ).

fof(f1541,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f141,f1539]) ).

fof(f1539,plain,
    ( spl0_191
  <=> ! [X17,X34,X13,X14,X35,X15] :
        ( X13 = X17
        | c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OCond(X17,X34,X35) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f141,axiom,
    ! [X14,X17,X15,X34,X35,X13] :
      ( X13 = X17
      | c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OCond(X17,X34,X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).

fof(f1537,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f140,f1535]) ).

fof(f1535,plain,
    ( spl0_190
  <=> ! [X17,X34,X14,X13,X35,X15] :
        ( X14 = X34
        | c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OCond(X17,X34,X35) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f140,axiom,
    ! [X14,X34,X15,X17,X35,X13] :
      ( X14 = X34
      | c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OCond(X17,X34,X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).

fof(f1533,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f139,f1531]) ).

fof(f1531,plain,
    ( spl0_189
  <=> ! [X17,X34,X14,X13,X35,X15] :
        ( X15 = X35
        | c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OCond(X17,X34,X35) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f139,axiom,
    ! [X14,X17,X15,X35,X34,X13] :
      ( X15 = X35
      | c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OCond(X17,X34,X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).

fof(f1529,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f108,f1527]) ).

fof(f1527,plain,
    ( spl0_188
  <=> ! [X18,X53,X17,X13,X16,X19] :
        ( X16 = X18
        | c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OCall(X16,X53,X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f108,axiom,
    ! [X18,X19,X16,X17,X53,X13] :
      ( X16 = X18
      | c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OCall(X16,X53,X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).

fof(f1525,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f107,f1523]) ).

fof(f1523,plain,
    ( spl0_187
  <=> ! [X17,X53,X13,X18,X16,X19] :
        ( X19 = X53
        | c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OCall(X16,X53,X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f107,axiom,
    ! [X18,X19,X16,X17,X53,X13] :
      ( X19 = X53
      | c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OCall(X16,X53,X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).

fof(f1520,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f106,f1518]) ).

fof(f1518,plain,
    ( spl0_186
  <=> ! [X17,X53,X13,X18,X16,X19] :
        ( X13 = X17
        | c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OCall(X16,X53,X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f106,axiom,
    ! [X18,X19,X16,X17,X53,X13] :
      ( X13 = X17
      | c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OCall(X16,X53,X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).

fof(f1516,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f90,f1514]) ).

fof(f1514,plain,
    ( spl0_185
  <=> ! [X50,X4,X3] :
        ( c_Option_Ooption_OSome(X4,X3) = X50
        | ~ hBOOL(c_in(X4,c_Option_Oset(X50,X3),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f90,axiom,
    ! [X50,X3,X4] :
      ( c_Option_Ooption_OSome(X4,X3) = X50
      | ~ hBOOL(c_in(X4,c_Option_Oset(X50,X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_elem__set_0) ).

fof(f1499,plain,
    ( spl0_184
    | ~ spl0_42
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1476,f1365,f791,f1497]) ).

fof(f791,plain,
    ( spl0_42
  <=> ! [X5,X3] : c_lessequals(X5,X5,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f1365,plain,
    ( spl0_168
  <=> ! [X65,X3,X58] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
        | ~ c_lessequals(X65,X58,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f1476,plain,
    ( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X0,X1)
    | ~ spl0_42
    | ~ spl0_168 ),
    inference(resolution,[],[f1366,f792]) ).

fof(f792,plain,
    ( ! [X3,X5] : c_lessequals(X5,X5,tc_fun(X3,tc_bool))
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f791]) ).

fof(f1366,plain,
    ( ! [X65,X58,X3] :
        ( ~ c_lessequals(X65,X58,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
        | c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3) )
    | ~ spl0_168 ),
    inference(avatar_component_clause,[],[f1365]) ).

fof(f1442,plain,
    ( spl0_183
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1285,f1236,f1440]) ).

fof(f1440,plain,
    ( spl0_183
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f1236,plain,
    ( spl0_142
  <=> ! [X6,X4,X3] :
        ( ~ class_Orderings_Olinorder(X3)
        | c_lessequals(X4,X6,X3)
        | c_lessequals(X6,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1285,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_142 ),
    inference(factoring,[],[f1237]) ).

fof(f1237,plain,
    ( ! [X3,X6,X4] :
        ( c_lessequals(X6,X4,X3)
        | c_lessequals(X4,X6,X3)
        | ~ class_Orderings_Olinorder(X3) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1236]) ).

fof(f1426,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f534,f1424]) ).

fof(f1424,plain,
    ( spl0_182
  <=> ! [X8,X3] :
        ( c_Complete__Lattice_OSup__class_OSup(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3) = X8
        | ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f534,plain,
    ! [X3,X8] :
      ( c_Complete__Lattice_OSup__class_OSup(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3) = X8
      | ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
    inference(forward_demodulation,[],[f403,f435]) ).

fof(f403,axiom,
    ! [X3,X8] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).

fof(f1421,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f533,f1419]) ).

fof(f1419,plain,
    ( spl0_181
  <=> ! [X8,X3] :
        ( c_Complete__Lattice_OInf__class_OInf(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3) = X8
        | ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f533,plain,
    ! [X3,X8] :
      ( c_Complete__Lattice_OInf__class_OInf(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3) = X8
      | ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
    inference(forward_demodulation,[],[f423,f435]) ).

fof(f423,axiom,
    ! [X3,X8] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).

fof(f1417,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f532,f1415]) ).

fof(f1415,plain,
    ( spl0_180
  <=> ! [X8,X3] :
        ( c_Finite__Set_Olinorder__class_OMax(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3) = X8
        | ~ class_Orderings_Olinorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f532,plain,
    ! [X3,X8] :
      ( c_Finite__Set_Olinorder__class_OMax(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3) = X8
      | ~ class_Orderings_Olinorder(X3) ),
    inference(forward_demodulation,[],[f418,f435]) ).

fof(f418,axiom,
    ! [X3,X8] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

fof(f1413,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f531,f1411]) ).

fof(f1411,plain,
    ( spl0_179
  <=> ! [X8,X3] :
        ( c_Finite__Set_Olinorder__class_OMin(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3) = X8
        | ~ class_Orderings_Olinorder(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f531,plain,
    ! [X3,X8] :
      ( c_Finite__Set_Olinorder__class_OMin(c_Option_Oset(c_Option_Ooption_OSome(X8,X3),X3),X3) = X8
      | ~ class_Orderings_Olinorder(X3) ),
    inference(forward_demodulation,[],[f407,f435]) ).

fof(f407,axiom,
    ! [X3,X8] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

fof(f1409,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f517,f1407]) ).

fof(f1407,plain,
    ( spl0_178
  <=> ! [X4,X7,X3] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f517,plain,
    ! [X3,X7,X4] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3),X4)),
    inference(forward_demodulation,[],[f406,f435]) ).

fof(f406,axiom,
    ! [X3,X7,X4] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).

fof(f1405,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f471,f1403]) ).

fof(f1403,plain,
    ( spl0_177
  <=> ! [X6,X4,X5,X3] :
        ( ~ hBOOL(hAPP(X5,X4))
        | hBOOL(hAPP(c_Set_Oinsert(X6,X5,X3),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f471,axiom,
    ! [X3,X6,X4,X5] :
      ( ~ hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(c_Set_Oinsert(X6,X5,X3),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

fof(f1401,plain,
    ( spl0_176
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1397,f1394,f1399]) ).

fof(f1399,plain,
    ( spl0_176
  <=> ! [X4,X3] : c_Set_Ocontents(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f1394,plain,
    ( spl0_175
  <=> ! [X4,X3] : c_Set_Ocontents(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f1397,plain,
    ( ! [X3,X4] : c_Set_Ocontents(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3) = X4
    | ~ spl0_175 ),
    inference(forward_demodulation,[],[f1395,f435]) ).

fof(f1395,plain,
    ( ! [X3,X4] : c_Set_Ocontents(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X4
    | ~ spl0_175 ),
    inference(avatar_component_clause,[],[f1394]) ).

fof(f1396,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f414,f1394]) ).

fof(f414,axiom,
    ! [X3,X4] : c_Set_Ocontents(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__eq_0) ).

fof(f1392,plain,
    ( spl0_174
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1384,f1381,f1390]) ).

fof(f1390,plain,
    ( spl0_174
  <=> ! [X4,X3] : c_The(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f1381,plain,
    ( spl0_172
  <=> ! [X4,X3] : c_The(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f1384,plain,
    ( ! [X3,X4] : c_The(c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3) = X4
    | ~ spl0_172 ),
    inference(forward_demodulation,[],[f1382,f435]) ).

fof(f1382,plain,
    ( ! [X3,X4] : c_The(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X4
    | ~ spl0_172 ),
    inference(avatar_component_clause,[],[f1381]) ).

fof(f1388,plain,
    ( spl0_173
    | ~ spl0_4
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1281,f1223,f612,f1386]) ).

fof(f1223,plain,
    ( spl0_139
  <=> ! [X62,X4,X7,X3] : c_Fun_Ofun__upd(X7,X4,hAPP(X7,X4),X62,X3) = X7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f1281,plain,
    ( ! [X0,X1] : c_Com_Obody = c_Fun_Ofun__upd(c_Com_Obody,v_pn,c_Option_Ooption_OSome(v_y,tc_Com_Ocom),X0,X1)
    | ~ spl0_4
    | ~ spl0_139 ),
    inference(superposition,[],[f1224,f614]) ).

fof(f1224,plain,
    ( ! [X3,X7,X62,X4] : c_Fun_Ofun__upd(X7,X4,hAPP(X7,X4),X62,X3) = X7
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1223]) ).

fof(f1383,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f408,f1381]) ).

fof(f408,axiom,
    ! [X3,X4] : c_The(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).

fof(f1379,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f396,f1377]) ).

fof(f1377,plain,
    ( spl0_171
  <=> ! [X3] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
        | c_Orderings_Obot__class_Obot(X3) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f396,axiom,
    ! [X3] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | c_Orderings_Obot__class_Obot(X3) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

fof(f1375,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f395,f1373]) ).

fof(f395,axiom,
    ! [X0] :
      ( ~ class_Orderings_Obot(X0)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X0)),v_x) = c_Orderings_Obot__class_Obot(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

fof(f1371,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f324,f1369]) ).

fof(f1369,plain,
    ( spl0_169
  <=> ! [X3] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
        | c_Orderings_Otop__class_Otop(X3) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f324,axiom,
    ! [X3] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | c_Orderings_Otop__class_Otop(X3) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).

fof(f1367,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f272,f1365]) ).

fof(f272,axiom,
    ! [X65,X58,X3] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
      | ~ c_lessequals(X65,X58,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).

fof(f1363,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f228,f1361]) ).

fof(f228,axiom,
    ! [X3,X8,X5] :
      ( ~ hBOOL(c_in(X8,X5,X3))
      | c_Set_Oinsert(X8,X5,X3) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

fof(f1359,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f200,f1357]) ).

fof(f1357,plain,
    ( spl0_166
  <=> ! [X5,X3] : c_HOL_Ominus__class_Ominus(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f200,axiom,
    ! [X3,X5] : c_HOL_Ominus__class_Ominus(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

fof(f1355,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f199,f1353]) ).

fof(f1353,plain,
    ( spl0_165
  <=> ! [X5,X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X5,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f199,axiom,
    ! [X3,X5] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X5,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

fof(f1351,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f198,f1349]) ).

fof(f1349,plain,
    ( spl0_164
  <=> ! [X9,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = X9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f198,axiom,
    ! [X3,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = X9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

fof(f1347,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f197,f1345]) ).

fof(f1345,plain,
    ( spl0_163
  <=> ! [X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f197,axiom,
    ! [X3,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

fof(f1343,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f172,f1341]) ).

fof(f1341,plain,
    ( spl0_162
  <=> ! [X0] :
        ( ~ class_Orderings_Otop(X0)
        | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X0)),v_x) = c_Orderings_Otop__class_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f172,axiom,
    ! [X0] :
      ( ~ class_Orderings_Otop(X0)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X0)),v_x) = c_Orderings_Otop__class_Otop(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

fof(f1339,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f170,f1337]) ).

fof(f1337,plain,
    ( spl0_161
  <=> ! [X3] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
        | c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3) = c_Orderings_Obot__class_Obot(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f170,axiom,
    ! [X3] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3) = c_Orderings_Obot__class_Obot(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).

fof(f1335,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f162,f1333]) ).

fof(f1333,plain,
    ( spl0_160
  <=> ! [X57,X3,X58] :
        ( c_Finite__Set_Ofinite(X58,X3)
        | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X57,X58,tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f162,axiom,
    ! [X58,X3,X57] :
      ( c_Finite__Set_Ofinite(X58,X3)
      | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X57,X58,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).

fof(f1331,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f161,f1329]) ).

fof(f1329,plain,
    ( spl0_159
  <=> ! [X57,X3,X58] :
        ( c_Finite__Set_Ofinite(X57,X3)
        | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X57,X58,tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f161,axiom,
    ! [X3,X58,X57] :
      ( c_Finite__Set_Ofinite(X57,X3)
      | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X57,X58,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).

fof(f1327,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f112,f1325]) ).

fof(f1325,plain,
    ( spl0_158
  <=> ! [X9,X5,X3] :
        ( ~ c_Finite__Set_Ofinite(X5,X3)
        | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f112,axiom,
    ! [X3,X9,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X3)
      | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

fof(f1323,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f71,f1321]) ).

fof(f1321,plain,
    ( spl0_157
  <=> ! [X3] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
        | c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3) = c_Orderings_Otop__class_Otop(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f71,axiom,
    ! [X3] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
      | c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3) = c_Orderings_Otop__class_Otop(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).

fof(f1319,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f66,f1317]) ).

fof(f1317,plain,
    ( spl0_156
  <=> ! [X21] : hAPP(c_Hoare__Mirabelle_OMGT,X21) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),X21,c_Natural_Oevalc(X21),tc_Com_Ostate) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f66,axiom,
    ! [X21] : hAPP(c_Hoare__Mirabelle_OMGT,X21) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),X21,c_Natural_Oevalc(X21),tc_Com_Ostate),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGT__def_0) ).

fof(f1315,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f55,f1313]) ).

fof(f1313,plain,
    ( spl0_155
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Olattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f55,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Olattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

fof(f1311,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f54,f1309]) ).

fof(f1309,plain,
    ( spl0_154
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f54,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

fof(f1307,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f30,f1305]) ).

fof(f1305,plain,
    ( spl0_153
  <=> ! [X9,X5,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f30,axiom,
    ! [X3,X9,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

fof(f1303,plain,
    ( spl0_152
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1282,f1266,f1300]) ).

fof(f1300,plain,
    ( spl0_152
  <=> c_Com_OWT(v_y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f1266,plain,
    ( spl0_149
  <=> ! [X0] :
        ( c_Option_Ooption_OSome(v_y,tc_Com_Ocom) != c_Option_Ooption_OSome(X0,tc_Com_Ocom)
        | c_Com_OWT(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1282,plain,
    ( c_Com_OWT(v_y)
    | ~ spl0_149 ),
    inference(equality_resolution,[],[f1267]) ).

fof(f1267,plain,
    ( ! [X0] :
        ( c_Option_Ooption_OSome(v_y,tc_Com_Ocom) != c_Option_Ooption_OSome(X0,tc_Com_Ocom)
        | c_Com_OWT(X0) )
    | ~ spl0_149 ),
    inference(avatar_component_clause,[],[f1266]) ).

fof(f1298,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f18,f1296]) ).

fof(f1296,plain,
    ( spl0_151
  <=> ! [X9,X5,X3] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f18,axiom,
    ! [X3,X9,X5] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

fof(f1294,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f17,f1292]) ).

fof(f1292,plain,
    ( spl0_150
  <=> ! [X9,X5,X3] : c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f17,axiom,
    ! [X3,X9,X5] : c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

fof(f1268,plain,
    ( spl0_149
    | ~ spl0_4
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1247,f1244,f612,f1266]) ).

fof(f1244,plain,
    ( spl0_144
  <=> ! [X73,X12] :
        ( c_Com_OWT(X12)
        | hAPP(c_Com_Obody,X73) != c_Option_Ooption_OSome(X12,tc_Com_Ocom) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f1247,plain,
    ( ! [X0] :
        ( c_Option_Ooption_OSome(v_y,tc_Com_Ocom) != c_Option_Ooption_OSome(X0,tc_Com_Ocom)
        | c_Com_OWT(X0) )
    | ~ spl0_4
    | ~ spl0_144 ),
    inference(superposition,[],[f1245,f614]) ).

fof(f1245,plain,
    ( ! [X73,X12] :
        ( hAPP(c_Com_Obody,X73) != c_Option_Ooption_OSome(X12,tc_Com_Ocom)
        | c_Com_OWT(X12) )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1244]) ).

fof(f1263,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f540,f1261]) ).

fof(f1261,plain,
    ( spl0_148
  <=> ! [X20,X4,X3] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != X20
        | ~ hBOOL(hAPP(X20,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f540,plain,
    ! [X3,X4,X20] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != X20
      | ~ hBOOL(hAPP(X20,X4)) ),
    inference(forward_demodulation,[],[f186,f115]) ).

fof(f186,axiom,
    ! [X3,X4,X20] :
      ( ~ hBOOL(hAPP(X20,X4))
      | c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X20,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).

fof(f1259,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f514,f1257]) ).

fof(f1257,plain,
    ( spl0_147
  <=> ! [X75,X3,X74] :
        ( X74 = X75
        | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X74),X75)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f514,axiom,
    ! [X3,X74,X75] :
      ( X74 = X75
      | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X74),X75)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f1255,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f472,f1253]) ).

fof(f1253,plain,
    ( spl0_146
  <=> ! [X53,X19] :
        ( X19 = X53
        | hAPP(c_Com_Ocom_OBODY,X19) != hAPP(c_Com_Ocom_OBODY,X53) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f472,axiom,
    ! [X19,X53] :
      ( X19 = X53
      | hAPP(c_Com_Ocom_OBODY,X19) != hAPP(c_Com_Ocom_OBODY,X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).

fof(f1251,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f458,f1249]) ).

fof(f1249,plain,
    ( spl0_145
  <=> ! [X64,X8,X3] :
        ( X8 = X64
        | c_Option_Ooption_OSome(X64,X3) != c_Option_Ooption_OSome(X8,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f458,axiom,
    ! [X3,X8,X64] :
      ( X8 = X64
      | c_Option_Ooption_OSome(X64,X3) != c_Option_Ooption_OSome(X8,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oinject_0) ).

fof(f1246,plain,
    ( spl0_144
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f445,f602,f1244]) ).

fof(f445,axiom,
    ! [X73,X12] :
      ( ~ c_Com_OWT__bodies
      | c_Com_OWT(X12)
      | hAPP(c_Com_Obody,X73) != c_Option_Ooption_OSome(X12,tc_Com_Ocom) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).

fof(f1242,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f436,f1240]) ).

fof(f436,axiom,
    ! [X73] :
      ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X73))
      | hAPP(c_Com_Obody,X73) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OBody_0) ).

fof(f1238,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f373,f1236]) ).

fof(f373,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X4,X6,X3)
      | c_lessequals(X6,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

fof(f1234,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f314,f1232]) ).

fof(f1232,plain,
    ( spl0_141
  <=> ! [X18,X13,X16,X17] :
        ( X16 = X18
        | c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OAss(X18,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f314,axiom,
    ! [X18,X16,X17,X13] :
      ( X16 = X18
      | c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OAss(X18,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_0) ).

fof(f1229,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f313,f1227]) ).

fof(f1227,plain,
    ( spl0_140
  <=> ! [X13,X18,X16,X17] :
        ( X13 = X17
        | c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OAss(X18,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f313,axiom,
    ! [X18,X16,X17,X13] :
      ( X13 = X17
      | c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OAss(X18,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_1) ).

fof(f1225,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f300,f1223]) ).

fof(f300,axiom,
    ! [X3,X7,X62,X4] : c_Fun_Ofun__upd(X7,X4,hAPP(X7,X4),X62,X3) = X7,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

fof(f1221,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f299,f1219]) ).

fof(f1219,plain,
    ( spl0_138
  <=> ! [X62,X4,X7,X6,X3] : hAPP(c_Fun_Ofun__upd(X7,X4,X6,X3,X62),X4) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f299,axiom,
    ! [X3,X6,X7,X62,X4] : hAPP(c_Fun_Ofun__upd(X7,X4,X6,X3,X62),X4) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

fof(f1217,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f233,f1215]) ).

fof(f1215,plain,
    ( spl0_137
  <=> ! [X61,X57,X0,X3] :
        ( ~ c_Finite__Set_Ofinite(X57,X3)
        | c_Finite__Set_Ofinite(c_Set_Oimage(X61,X57,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f233,axiom,
    ! [X3,X0,X57,X61] :
      ( ~ c_Finite__Set_Ofinite(X57,X3)
      | c_Finite__Set_Ofinite(c_Set_Oimage(X61,X57,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

fof(f1213,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f194,f1211]) ).

fof(f1211,plain,
    ( spl0_136
  <=> ! [X4,X7,X3] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f194,axiom,
    ! [X3,X7,X4] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).

fof(f1209,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f176,f1207]) ).

fof(f1207,plain,
    ( spl0_135
  <=> ! [X41,X42] :
        ( X41 = X42
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X41),X42)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f176,axiom,
    ! [X41,X42] :
      ( X41 = X42
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X41),X42)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).

fof(f1205,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f121,f1203]) ).

fof(f1203,plain,
    ( spl0_134
  <=> ! [X4,X3] :
        ( ~ class_Lattices_Obounded__lattice(X3)
        | c_Orderings_Otop__class_Otop(X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X3),X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f121,axiom,
    ! [X3,X4] :
      ( ~ class_Lattices_Obounded__lattice(X3)
      | c_Orderings_Otop__class_Otop(X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X3),X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

fof(f1201,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f120,f1199]) ).

fof(f1199,plain,
    ( spl0_133
  <=> ! [X4,X3] :
        ( ~ class_Lattices_Obounded__lattice(X3)
        | c_Orderings_Otop__class_Otop(X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Otop__class_Otop(X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f120,axiom,
    ! [X3,X4] :
      ( ~ class_Lattices_Obounded__lattice(X3)
      | c_Orderings_Otop__class_Otop(X3) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Otop__class_Otop(X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

fof(f1197,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f117,f1195]) ).

fof(f1195,plain,
    ( spl0_132
  <=> ! [X35,X34,X14,X15] :
        ( X14 = X34
        | c_Com_Ocom_OSemi(X14,X15) != c_Com_Ocom_OSemi(X34,X35) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f117,axiom,
    ! [X14,X34,X15,X35] :
      ( X14 = X34
      | c_Com_Ocom_OSemi(X14,X15) != c_Com_Ocom_OSemi(X34,X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).

fof(f1193,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f116,f1191]) ).

fof(f1191,plain,
    ( spl0_131
  <=> ! [X14,X34,X35,X15] :
        ( X15 = X35
        | c_Com_Ocom_OSemi(X14,X15) != c_Com_Ocom_OSemi(X34,X35) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f116,axiom,
    ! [X14,X34,X15,X35] :
      ( X15 = X35
      | c_Com_Ocom_OSemi(X14,X15) != c_Com_Ocom_OSemi(X34,X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).

fof(f1189,plain,
    ( spl0_130
    | ~ spl0_39
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1151,f1066,f779,f1187]) ).

fof(f1187,plain,
    ( spl0_130
  <=> ! [X0] : c_Finite__Set_Ofinite(c_Option_Oset(c_Option_Ooption_ONone(X0),X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f779,plain,
    ( spl0_39
  <=> ! [X3] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f1151,plain,
    ( ! [X0] : c_Finite__Set_Ofinite(c_Option_Oset(c_Option_Ooption_ONone(X0),X0),X0)
    | ~ spl0_39
    | ~ spl0_108 ),
    inference(superposition,[],[f780,f1067]) ).

fof(f780,plain,
    ( ! [X3] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f779]) ).

fof(f1185,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f57,f1183]) ).

fof(f1183,plain,
    ( spl0_129
  <=> ! [X13,X17,X23,X33] :
        ( X23 = X33
        | c_Com_Ocom_OWhile(X17,X23) != c_Com_Ocom_OWhile(X13,X33) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f57,axiom,
    ! [X17,X23,X13,X33] :
      ( X23 = X33
      | c_Com_Ocom_OWhile(X17,X23) != c_Com_Ocom_OWhile(X13,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).

fof(f1181,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f56,f1179]) ).

fof(f1179,plain,
    ( spl0_128
  <=> ! [X17,X33,X13,X23] :
        ( X13 = X17
        | c_Com_Ocom_OWhile(X17,X23) != c_Com_Ocom_OWhile(X13,X33) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f56,axiom,
    ! [X17,X23,X13,X33] :
      ( X13 = X17
      | c_Com_Ocom_OWhile(X17,X23) != c_Com_Ocom_OWhile(X13,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).

fof(f1144,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f462,f1142]) ).

fof(f462,axiom,
    ! [X3,X8,X5] : c_Set_Oinsert(X8,X5,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

fof(f1140,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f429,f1138]) ).

fof(f1138,plain,
    ( spl0_126
  <=> ! [X20,X8,X74] :
        ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X20))
        | ~ c_Com_OWT(c_Com_Ocom_OCall(X74,X20,X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f429,axiom,
    ! [X8,X74,X20] :
      ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X20))
      | ~ c_Com_OWT(c_Com_Ocom_OCall(X74,X20,X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).

fof(f1136,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f428,f1134]) ).

fof(f1134,plain,
    ( spl0_125
  <=> ! [X73,X8,X74] :
        ( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X73))
        | c_Com_OWT(c_Com_Ocom_OCall(X74,X73,X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f428,axiom,
    ! [X73,X8,X74] :
      ( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X73))
      | c_Com_OWT(c_Com_Ocom_OCall(X74,X73,X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OCall_0) ).

fof(f1132,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f382,f1130]) ).

fof(f1130,plain,
    ( spl0_124
  <=> ! [X36,X37,X12] :
        ( ~ c_Com_OWT(X36)
        | ~ c_Com_OWT(X37)
        | c_Com_OWT(c_Com_Ocom_OCond(X12,X36,X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f382,axiom,
    ! [X36,X37,X12] :
      ( ~ c_Com_OWT(X36)
      | ~ c_Com_OWT(X37)
      | c_Com_OWT(c_Com_Ocom_OCond(X12,X36,X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OIf_0) ).

fof(f1128,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f369,f1126]) ).

fof(f1126,plain,
    ( spl0_123
  <=> ! [X17,X19,X13,X18,X23,X22] : c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OLocal(X22,X17,X23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f369,axiom,
    ! [X18,X19,X17,X22,X23,X13] : c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OLocal(X22,X17,X23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).

fof(f1124,plain,
    ( spl0_122
    | ~ spl0_15
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f1034,f954,f667,f1122]) ).

fof(f667,plain,
    ( spl0_15
  <=> class_Lattices_Oupper__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f954,plain,
    ( spl0_82
  <=> ! [X4,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X3) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f1034,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
    | ~ spl0_15
    | ~ spl0_82 ),
    inference(resolution,[],[f955,f669]) ).

fof(f669,plain,
    ( class_Lattices_Oupper__semilattice(tc_bool)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f667]) ).

fof(f955,plain,
    ( ! [X3,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X3) = X4 )
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f954]) ).

fof(f1120,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f321,f1118]) ).

fof(f1118,plain,
    ( spl0_121
  <=> ! [X4,X3] : hBOOL(c_in(X4,c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f321,axiom,
    ! [X3,X4] : hBOOL(c_in(X4,c_Option_Oset(c_Option_Ooption_OSome(X4,X3),X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_elem__set_1) ).

fof(f1116,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f310,f1114]) ).

fof(f1114,plain,
    ( spl0_120
  <=> ! [X5,X3] : c_lessequals(X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f310,axiom,
    ! [X3,X5] : c_lessequals(X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

fof(f1112,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f219,f1110]) ).

fof(f1110,plain,
    ( spl0_119
  <=> ! [X9,X8,X3] : c_lessequals(X9,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f219,axiom,
    ! [X3,X8,X9] : c_lessequals(X9,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

fof(f1108,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f218,f1106]) ).

fof(f1106,plain,
    ( spl0_118
  <=> ! [X5,X8,X3] :
        ( c_Finite__Set_Ofinite(X5,X3)
        | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X5,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f218,axiom,
    ! [X3,X8,X5] :
      ( c_Finite__Set_Ofinite(X5,X3)
      | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X5,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

fof(f1104,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f217,f1102]) ).

fof(f1102,plain,
    ( spl0_117
  <=> ! [X5,X8,X3] :
        ( ~ c_Finite__Set_Ofinite(X5,X3)
        | c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X5,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f217,axiom,
    ! [X3,X8,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X3)
      | c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X5,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

fof(f1100,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f202,f1098]) ).

fof(f1098,plain,
    ( spl0_116
  <=> ! [X5,X3] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f202,axiom,
    ! [X3,X5] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

fof(f1096,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f195,f1094]) ).

fof(f1094,plain,
    ( spl0_115
  <=> ! [X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f195,axiom,
    ! [X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

fof(f1092,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f179,f1090]) ).

fof(f1090,plain,
    ( spl0_114
  <=> ! [X4,X3] :
        ( ~ class_Lattices_Obounded__lattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Obot__class_Obot(X3),X3) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f179,axiom,
    ! [X3,X4] :
      ( ~ class_Lattices_Obounded__lattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Obot__class_Obot(X3),X3) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

fof(f1088,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f178,f1086]) ).

fof(f1086,plain,
    ( spl0_113
  <=> ! [X4,X3] :
        ( ~ class_Lattices_Obounded__lattice(X3)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X4,X3) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f178,axiom,
    ! [X3,X4] :
      ( ~ class_Lattices_Obounded__lattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X4,X3) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

fof(f1084,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f148,f1082]) ).

fof(f1082,plain,
    ( spl0_112
  <=> ! [X17,X34,X13,X18,X35,X19] : c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OCond(X17,X34,X35) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f148,axiom,
    ! [X18,X19,X17,X34,X35,X13] : c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OCond(X17,X34,X35),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I57_J_0) ).

fof(f1080,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f134,f1078]) ).

fof(f1078,plain,
    ( spl0_111
  <=> ! [X15,X17,X14,X13,X23,X22] : c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OLocal(X22,X17,X23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f134,axiom,
    ! [X14,X17,X15,X22,X23,X13] : c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OLocal(X22,X17,X23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).

fof(f1076,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f87,f1074]) ).

fof(f1074,plain,
    ( spl0_110
  <=> ! [X4,X3,X49] :
        ( ~ hBOOL(hAPP(X49,X4))
        | hBOOL(c_in(X4,X49,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f87,axiom,
    ! [X3,X49,X4] :
      ( ~ hBOOL(hAPP(X49,X4))
      | hBOOL(c_in(X4,X49,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

fof(f1072,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f86,f1070]) ).

fof(f86,axiom,
    ! [X3,X49,X4] :
      ( hBOOL(hAPP(X49,X4))
      | ~ hBOOL(c_in(X4,X49,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

fof(f1068,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f31,f1066]) ).

fof(f1064,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f26,f1062]) ).

fof(f26,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Olattice(X3)
      | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

fof(f1060,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f25,f1058]) ).

fof(f1058,plain,
    ( spl0_106
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Olattice(X3)
        | c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f25,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Olattice(X3)
      | c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

fof(f1056,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f22,f1054]) ).

fof(f1054,plain,
    ( spl0_105
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f22,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

fof(f1052,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f21,f1050]) ).

fof(f1050,plain,
    ( spl0_104
  <=> ! [X6,X4,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X3)
        | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f21,axiom,
    ! [X3,X6,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

fof(f1047,plain,
    ( spl0_103
    | ~ spl0_37
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f1040,f1010,f770,f1044]) ).

fof(f1044,plain,
    ( spl0_103
  <=> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f1040,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ spl0_37
    | ~ spl0_96 ),
    inference(resolution,[],[f1011,f772]) ).

fof(f1039,plain,
    ( spl0_102
    | ~ spl0_6
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f1033,f954,f622,f1037]) ).

fof(f622,plain,
    ( spl0_6
  <=> class_Lattices_Oupper__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f1033,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
    | ~ spl0_6
    | ~ spl0_82 ),
    inference(resolution,[],[f955,f624]) ).

fof(f624,plain,
    ( class_Lattices_Oupper__semilattice(tc_nat)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f622]) ).

fof(f1032,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f483,f1030]) ).

fof(f1030,plain,
    ( spl0_101
  <=> ! [X78,X79] :
        ( ~ class_Finite__Set_Ofinite_Ofinite(X78)
        | ~ class_Finite__Set_Ofinite_Ofinite(X79)
        | class_Finite__Set_Ofinite_Ofinite(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f483,axiom,
    ! [X78,X79] :
      ( ~ class_Finite__Set_Ofinite_Ofinite(X78)
      | ~ class_Finite__Set_Ofinite_Ofinite(X79)
      | class_Finite__Set_Ofinite_Ofinite(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

fof(f1028,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f457,f1026]) ).

fof(f1026,plain,
    ( spl0_100
  <=> ! [X3,X58] : c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f457,axiom,
    ! [X58,X3] : c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).

fof(f1024,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f379,f1022]) ).

fof(f1022,plain,
    ( spl0_99
  <=> ! [X36,X37] :
        ( ~ c_Com_OWT(X36)
        | ~ c_Com_OWT(X37)
        | c_Com_OWT(c_Com_Ocom_OSemi(X36,X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f379,axiom,
    ! [X36,X37] :
      ( ~ c_Com_OWT(X36)
      | ~ c_Com_OWT(X37)
      | c_Com_OWT(c_Com_Ocom_OSemi(X36,X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).

fof(f1020,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f360,f1018]) ).

fof(f1018,plain,
    ( spl0_98
  <=> ! [X4,X3] : c_The(hAPP(c_fequal(X3),X4),X3) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f360,axiom,
    ! [X3,X4] : c_The(hAPP(c_fequal(X3),X4),X3) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).

fof(f1016,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f274,f1014]) ).

fof(f1014,plain,
    ( spl0_97
  <=> ! [X17,X13,X18,X23,X19] : c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OWhile(X17,X23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f274,axiom,
    ! [X18,X19,X17,X23,X13] : c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OWhile(X17,X23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I60_J_0) ).

fof(f1012,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f271,f1010]) ).

fof(f271,axiom,
    ! [X65,X58,X3] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X65,X3)
      | c_Hoare__Mirabelle_Ohoare__valids(X58,X65,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__sound_0) ).

fof(f1008,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f266,f1006]) ).

fof(f1006,plain,
    ( spl0_95
  <=> ! [X22,X17,X23,X19] : c_Com_Ocom_OLocal(X22,X17,X23) != hAPP(c_Com_Ocom_OBODY,X19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f266,axiom,
    ! [X19,X17,X22,X23] : c_Com_Ocom_OLocal(X22,X17,X23) != hAPP(c_Com_Ocom_OBODY,X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).

fof(f1004,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f263,f1002]) ).

fof(f1002,plain,
    ( spl0_94
  <=> ! [X13,X18,X53,X19] : c_Com_Ocom_OCall(X18,X19,X13) != hAPP(c_Com_Ocom_OBODY,X53) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f263,axiom,
    ! [X18,X19,X53,X13] : c_Com_Ocom_OCall(X18,X19,X13) != hAPP(c_Com_Ocom_OBODY,X53),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).

fof(f1000,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f258,f998]) ).

fof(f998,plain,
    ( spl0_93
  <=> ! [X34,X17,X19,X35] : c_Com_Ocom_OCond(X17,X34,X35) != hAPP(c_Com_Ocom_OBODY,X19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f258,axiom,
    ! [X19,X17,X34,X35] : c_Com_Ocom_OCond(X17,X34,X35) != hAPP(c_Com_Ocom_OBODY,X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).

fof(f996,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f244,f994]) ).

fof(f994,plain,
    ( spl0_92
  <=> ! [X4,X3] : hAPP(c_Option_Othe(X3),c_Option_Ooption_OSome(X4,X3)) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f244,axiom,
    ! [X3,X4] : hAPP(c_Option_Othe(X3),c_Option_Ooption_OSome(X4,X3)) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the_Osimps_0) ).

fof(f992,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f224,f990]) ).

fof(f990,plain,
    ( spl0_91
  <=> ! [X4,X5,X3] : hBOOL(c_in(X4,c_Set_Oinsert(X4,X5,X3),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f224,axiom,
    ! [X3,X4,X5] : hBOOL(c_in(X4,c_Set_Oinsert(X4,X5,X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

fof(f988,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f190,f986]) ).

fof(f986,plain,
    ( spl0_90
  <=> ! [X8,X3] : ~ hBOOL(c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f190,axiom,
    ! [X3,X8] : ~ hBOOL(c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

fof(f984,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f165,f982]) ).

fof(f982,plain,
    ( spl0_89
  <=> ! [X17,X14,X13,X16,X15] : c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OAss(X16,X17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f165,axiom,
    ! [X16,X14,X17,X15,X13] : c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OAss(X16,X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I26_J_0) ).

fof(f980,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f157,f978]) ).

fof(f978,plain,
    ( spl0_88
  <=> ! [X17,X33,X13,X23,X22] : c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OWhile(X13,X33) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f157,axiom,
    ! [X17,X22,X23,X13,X33] : c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OWhile(X13,X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).

fof(f976,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f147,f974]) ).

fof(f974,plain,
    ( spl0_87
  <=> ! [X4,X3] : hBOOL(c_in(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f147,axiom,
    ! [X3,X4] : hBOOL(c_in(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

fof(f972,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f130,f970]) ).

fof(f970,plain,
    ( spl0_86
  <=> ! [X17,X55,X13,X33,X16] : c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OLocal(X55,X13,X33) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f130,axiom,
    ! [X55,X16,X17,X13,X33] : c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OLocal(X55,X13,X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I23_J_0) ).

fof(f968,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f127,f966]) ).

fof(f966,plain,
    ( spl0_85
  <=> ! [X17,X14,X22,X23,X15] : c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OSemi(X14,X15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f127,axiom,
    ! [X14,X17,X15,X22,X23] : c_Com_Ocom_OLocal(X22,X17,X23) != c_Com_Ocom_OSemi(X14,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I35_J_0) ).

fof(f964,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f124,f962]) ).

fof(f962,plain,
    ( spl0_84
  <=> ! [X35,X34,X14,X13,X15] : c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OSemi(X34,X35) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f124,axiom,
    ! [X14,X34,X15,X35,X13] : c_Com_Ocom_OCond(X13,X14,X15) != c_Com_Ocom_OSemi(X34,X35),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).

fof(f960,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f92,f958]) ).

fof(f958,plain,
    ( spl0_83
  <=> ! [X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_fun(X3,tc_bool)) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f92,axiom,
    ! [X3,X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_fun(X3,tc_bool)) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

fof(f956,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f91,f954]) ).

fof(f91,axiom,
    ! [X3,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X3)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X3) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

fof(f952,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f89,f950]) ).

fof(f950,plain,
    ( spl0_81
  <=> ! [X35,X34,X13,X18,X19] : c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OSemi(X34,X35) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f89,axiom,
    ! [X18,X19,X34,X35,X13] : c_Com_Ocom_OCall(X18,X19,X13) != c_Com_Ocom_OSemi(X34,X35),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I51_J_0) ).

fof(f948,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f85,f946]) ).

fof(f946,plain,
    ( spl0_80
  <=> ! [X48,X20,X0,X3] : hAPP(c_COMBK(X20,X3,X0),X48) = X20 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f85,axiom,
    ! [X3,X48,X0,X20] : hAPP(c_COMBK(X20,X3,X0),X48) = X20,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

fof(f944,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f64,f942]) ).

fof(f942,plain,
    ( spl0_79
  <=> ! [X17,X34,X13,X33,X35] : c_Com_Ocom_OWhile(X13,X33) != c_Com_Ocom_OCond(X17,X34,X35) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f64,axiom,
    ! [X17,X34,X35,X13,X33] : c_Com_Ocom_OWhile(X13,X33) != c_Com_Ocom_OCond(X17,X34,X35),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).

fof(f940,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f29,f938]) ).

fof(f938,plain,
    ( spl0_78
  <=> ! [X18,X13,X16,X17,X19] : c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OCall(X18,X19,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f29,axiom,
    ! [X18,X19,X16,X17,X13] : c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OCall(X18,X19,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I32_J_0) ).

fof(f935,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f513,f933]) ).

fof(f933,plain,
    ( spl0_77
  <=> ! [X4,X3] : hBOOL(hAPP(hAPP(c_fequal(X3),X4),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f513,axiom,
    ! [X3,X4] : hBOOL(hAPP(hAPP(c_fequal(X3),X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f931,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f456,f929]) ).

fof(f929,plain,
    ( spl0_76
  <=> ! [X4,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f456,axiom,
    ! [X3,X4] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

fof(f927,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f447,f925]) ).

fof(f925,plain,
    ( spl0_75
  <=> ! [X4,X5,X3] : hBOOL(hAPP(c_Set_Oinsert(X4,X5,X3),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f447,axiom,
    ! [X3,X4,X5] : hBOOL(hAPP(c_Set_Oinsert(X4,X5,X3),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

fof(f923,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f388,f921]) ).

fof(f921,plain,
    ( spl0_74
  <=> ! [X21,X75,X8] :
        ( c_Com_OWT(X21)
        | ~ c_Com_OWT(c_Com_Ocom_OLocal(X75,X8,X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f388,axiom,
    ! [X21,X8,X75] :
      ( c_Com_OWT(X21)
      | ~ c_Com_OWT(c_Com_Ocom_OLocal(X75,X8,X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).

fof(f919,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f387,f917]) ).

fof(f917,plain,
    ( spl0_73
  <=> ! [X21,X75,X8] :
        ( ~ c_Com_OWT(X21)
        | c_Com_OWT(c_Com_Ocom_OLocal(X75,X8,X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f387,axiom,
    ! [X21,X8,X75] :
      ( ~ c_Com_OWT(X21)
      | c_Com_OWT(c_Com_Ocom_OLocal(X75,X8,X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).

fof(f915,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f378,f913]) ).

fof(f913,plain,
    ( spl0_72
  <=> ! [X12,X37,X43] :
        ( c_Com_OWT(X43)
        | ~ c_Com_OWT(c_Com_Ocom_OCond(X12,X37,X43)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f378,axiom,
    ! [X37,X12,X43] :
      ( c_Com_OWT(X43)
      | ~ c_Com_OWT(c_Com_Ocom_OCond(X12,X37,X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).

fof(f911,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f377,f909]) ).

fof(f909,plain,
    ( spl0_71
  <=> ! [X12,X37,X43] :
        ( c_Com_OWT(X37)
        | ~ c_Com_OWT(c_Com_Ocom_OCond(X12,X37,X43)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f377,axiom,
    ! [X37,X12,X43] :
      ( c_Com_OWT(X37)
      | ~ c_Com_OWT(c_Com_Ocom_OCond(X12,X37,X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).

fof(f907,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f326,f905]) ).

fof(f905,plain,
    ( spl0_70
  <=> ! [X13,X34,X35,X33] : c_Com_Ocom_OWhile(X13,X33) != c_Com_Ocom_OSemi(X34,X35) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f326,axiom,
    ! [X34,X35,X13,X33] : c_Com_Ocom_OWhile(X13,X33) != c_Com_Ocom_OSemi(X34,X35),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).

fof(f903,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f311,f901]) ).

fof(f901,plain,
    ( spl0_69
  <=> ! [X4,X3] :
        ( ~ class_Orderings_Otop(X3)
        | c_lessequals(X4,c_Orderings_Otop__class_Otop(X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f311,axiom,
    ! [X3,X4] :
      ( ~ class_Orderings_Otop(X3)
      | c_lessequals(X4,c_Orderings_Otop__class_Otop(X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).

fof(f899,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f304,f897]) ).

fof(f897,plain,
    ( spl0_68
  <=> ! [X13,X16,X17,X33] : c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OWhile(X13,X33) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f304,axiom,
    ! [X16,X17,X13,X33] : c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OWhile(X13,X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I29_J_0) ).

fof(f895,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f276,f893]) ).

fof(f893,plain,
    ( spl0_67
  <=> ! [X16,X17,X14,X15] : c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OSemi(X14,X15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f276,axiom,
    ! [X16,X14,X17,X15] : c_Com_Ocom_OAss(X16,X17) != c_Com_Ocom_OSemi(X14,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I25_J_0) ).

fof(f891,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f275,f889]) ).

fof(f889,plain,
    ( spl0_66
  <=> ! [X41] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X41),X41)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f275,axiom,
    ! [X41] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X41),X41)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).

fof(f887,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f265,f885]) ).

fof(f885,plain,
    ( spl0_65
  <=> ! [X34,X19,X35] : c_Com_Ocom_OSemi(X34,X35) != hAPP(c_Com_Ocom_OBODY,X19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f265,axiom,
    ! [X19,X34,X35] : c_Com_Ocom_OSemi(X34,X35) != hAPP(c_Com_Ocom_OBODY,X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).

fof(f883,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f262,f881]) ).

fof(f881,plain,
    ( spl0_64
  <=> ! [X17,X23,X19] : c_Com_Ocom_OWhile(X17,X23) != hAPP(c_Com_Ocom_OBODY,X19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f262,axiom,
    ! [X19,X17,X23] : c_Com_Ocom_OWhile(X17,X23) != hAPP(c_Com_Ocom_OBODY,X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).

fof(f879,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f259,f877]) ).

fof(f877,plain,
    ( spl0_63
  <=> ! [X16,X17,X19] : c_Com_Ocom_OAss(X16,X17) != hAPP(c_Com_Ocom_OBODY,X19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f259,axiom,
    ! [X19,X16,X17] : c_Com_Ocom_OAss(X16,X17) != hAPP(c_Com_Ocom_OBODY,X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I31_J_0) ).

fof(f875,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f180,f873]) ).

fof(f873,plain,
    ( spl0_62
  <=> ! [X4,X3] :
        ( ~ class_Orderings_Obot(X3)
        | c_lessequals(c_Orderings_Obot__class_Obot(X3),X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f180,axiom,
    ! [X3,X4] :
      ( ~ class_Orderings_Obot(X3)
      | c_lessequals(c_Orderings_Obot__class_Obot(X3),X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

fof(f871,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f171,f869]) ).

fof(f869,plain,
    ( spl0_61
  <=> ! [X4,X3] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f171,axiom,
    ! [X3,X4] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

fof(f866,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f490,f864]) ).

fof(f864,plain,
    ( spl0_60
  <=> ! [X78,X79] :
        ( ~ class_HOL_Oord(X79)
        | class_HOL_Oord(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f490,axiom,
    ! [X78,X79] :
      ( ~ class_HOL_Oord(X79)
      | class_HOL_Oord(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

fof(f862,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f489,f860]) ).

fof(f860,plain,
    ( spl0_59
  <=> ! [X78,X79] :
        ( ~ class_HOL_Ominus(X79)
        | class_HOL_Ominus(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f489,axiom,
    ! [X78,X79] :
      ( ~ class_HOL_Ominus(X79)
      | class_HOL_Ominus(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

fof(f858,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f488,f856]) ).

fof(f856,plain,
    ( spl0_58
  <=> ! [X78,X79] :
        ( ~ class_Orderings_Obot(X79)
        | class_Orderings_Obot(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f488,axiom,
    ! [X78,X79] :
      ( ~ class_Orderings_Obot(X79)
      | class_Orderings_Obot(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

fof(f854,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f487,f852]) ).

fof(f852,plain,
    ( spl0_57
  <=> ! [X78,X79] :
        ( ~ class_Orderings_Otop(X79)
        | class_Orderings_Otop(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f487,axiom,
    ! [X78,X79] :
      ( ~ class_Orderings_Otop(X79)
      | class_Orderings_Otop(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

fof(f850,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f486,f848]) ).

fof(f848,plain,
    ( spl0_56
  <=> ! [X78,X79] :
        ( ~ class_Orderings_Oorder(X79)
        | class_Orderings_Oorder(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f486,axiom,
    ! [X78,X79] :
      ( ~ class_Orderings_Oorder(X79)
      | class_Orderings_Oorder(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f846,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f485,f844]) ).

fof(f844,plain,
    ( spl0_55
  <=> ! [X78,X79] :
        ( ~ class_Lattices_Olattice(X79)
        | class_Lattices_Olattice(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f485,axiom,
    ! [X78,X79] :
      ( ~ class_Lattices_Olattice(X79)
      | class_Lattices_Olattice(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

fof(f842,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f484,f840]) ).

fof(f840,plain,
    ( spl0_54
  <=> ! [X78,X79] :
        ( ~ class_Orderings_Opreorder(X79)
        | class_Orderings_Opreorder(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f484,axiom,
    ! [X78,X79] :
      ( ~ class_Orderings_Opreorder(X79)
      | class_Orderings_Opreorder(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f838,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f482,f836]) ).

fof(f836,plain,
    ( spl0_53
  <=> ! [X78,X79] :
        ( ~ class_Lattices_Obounded__lattice(X79)
        | class_Lattices_Obounded__lattice(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f482,axiom,
    ! [X78,X79] :
      ( ~ class_Lattices_Obounded__lattice(X79)
      | class_Lattices_Obounded__lattice(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

fof(f834,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f481,f832]) ).

fof(f832,plain,
    ( spl0_52
  <=> ! [X78,X79] :
        ( ~ class_Lattices_Olattice(X79)
        | class_Lattices_Oupper__semilattice(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f481,axiom,
    ! [X78,X79] :
      ( ~ class_Lattices_Olattice(X79)
      | class_Lattices_Oupper__semilattice(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

fof(f830,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f480,f828]) ).

fof(f828,plain,
    ( spl0_51
  <=> ! [X78,X79] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X79)
        | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X78,X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f480,axiom,
    ! [X78,X79] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X79)
      | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X78,X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(f826,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f433,f823]) ).

fof(f823,plain,
    ( spl0_50
  <=> c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f433,axiom,
    c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).

fof(f821,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f386,f819]) ).

fof(f819,plain,
    ( spl0_49
  <=> ! [X21,X12] :
        ( c_Com_OWT(X21)
        | ~ c_Com_OWT(c_Com_Ocom_OWhile(X12,X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f386,axiom,
    ! [X21,X12] :
      ( c_Com_OWT(X21)
      | ~ c_Com_OWT(c_Com_Ocom_OWhile(X12,X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).

fof(f817,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f385,f815]) ).

fof(f815,plain,
    ( spl0_48
  <=> ! [X21,X12] :
        ( ~ c_Com_OWT(X21)
        | c_Com_OWT(c_Com_Ocom_OWhile(X12,X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f385,axiom,
    ! [X21,X12] :
      ( ~ c_Com_OWT(X21)
      | c_Com_OWT(c_Com_Ocom_OWhile(X12,X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_While_0) ).

fof(f813,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f381,f811]) ).

fof(f811,plain,
    ( spl0_47
  <=> ! [X37,X43] :
        ( c_Com_OWT(X43)
        | ~ c_Com_OWT(c_Com_Ocom_OSemi(X37,X43)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f381,axiom,
    ! [X37,X43] :
      ( c_Com_OWT(X43)
      | ~ c_Com_OWT(c_Com_Ocom_OSemi(X37,X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).

fof(f809,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f380,f807]) ).

fof(f807,plain,
    ( spl0_46
  <=> ! [X37,X43] :
        ( c_Com_OWT(X37)
        | ~ c_Com_OWT(c_Com_Ocom_OSemi(X37,X43)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f380,axiom,
    ! [X37,X43] :
      ( c_Com_OWT(X37)
      | ~ c_Com_OWT(c_Com_Ocom_OSemi(X37,X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).

fof(f805,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f355,f803]) ).

fof(f803,plain,
    ( spl0_45
  <=> ! [X13,X18,X19] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X18,X19,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f355,axiom,
    ! [X18,X19,X13] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X18,X19,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I21_J_0) ).

fof(f801,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f351,f799]) ).

fof(f799,plain,
    ( spl0_44
  <=> ! [X4,X3] :
        ( ~ class_Orderings_Opreorder(X3)
        | c_lessequals(X4,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f351,axiom,
    ! [X3,X4] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X4,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

fof(f797,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f350,f795]) ).

fof(f795,plain,
    ( spl0_43
  <=> ! [X4,X3] :
        ( ~ class_Orderings_Oorder(X3)
        | c_lessequals(X4,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f350,axiom,
    ! [X3,X4] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X4,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

fof(f793,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f347,f791]) ).

fof(f347,axiom,
    ! [X3,X5] : c_lessequals(X5,X5,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

fof(f789,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f283,f787]) ).

fof(f787,plain,
    ( spl0_41
  <=> ! [X13,X55,X33] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X55,X13,X33) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f283,axiom,
    ! [X55,X13,X33] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X55,X13,X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I11_J_0) ).

fof(f785,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f253,f783]) ).

fof(f253,axiom,
    ! [X3,X6] : c_Option_Ooption_ONone(X3) != c_Option_Ooption_OSome(X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).

fof(f781,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f201,f779]) ).

fof(f201,axiom,
    ! [X3] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

fof(f777,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f61,f775]) ).

fof(f775,plain,
    ( spl0_38
  <=> ! [X13,X14,X15] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X13,X14,X15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f61,axiom,
    ! [X14,X15,X13] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X13,X14,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).

fof(f773,plain,
    ( spl0_37
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f768,f764,f770]) ).

fof(f764,plain,
    ( spl0_36
  <=> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f768,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ spl0_36 ),
    inference(forward_demodulation,[],[f766,f446]) ).

fof(f766,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f764]) ).

fof(f767,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f478,f764]) ).

fof(f478,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f762,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f510,f760]) ).

fof(f760,plain,
    ( spl0_35
  <=> ! [X79] :
        ( ~ class_Finite__Set_Ofinite_Ofinite(X79)
        | class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X79)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f510,axiom,
    ! [X79] :
      ( ~ class_Finite__Set_Ofinite_Ofinite(X79)
      | class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X79)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).

fof(f758,plain,
    ( spl0_34
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f391,f597,f756]) ).

fof(f756,plain,
    ( spl0_34
  <=> ! [X42] : v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X42) != X42 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f391,axiom,
    ! [X42] :
      ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
      | v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X42) != X42 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__stateE_0) ).

fof(f754,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f316,f752]) ).

fof(f752,plain,
    ( spl0_33
  <=> ! [X14,X15] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X14,X15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f316,axiom,
    ! [X14,X15] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X14,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).

fof(f750,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f294,f748]) ).

fof(f748,plain,
    ( spl0_32
  <=> ! [X13,X18] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X18,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f294,axiom,
    ! [X18,X13] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X18,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I8_J_0) ).

fof(f746,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f268,f744]) ).

fof(f744,plain,
    ( spl0_31
  <=> ! [X19] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f268,axiom,
    ! [X19] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).

fof(f742,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f115,f740]) ).

fof(f740,plain,
    ( spl0_30
  <=> ! [X20,X3] : c_Collect(X20,X3) = X20 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f738,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f111,f736]) ).

fof(f736,plain,
    ( spl0_29
  <=> ! [X13,X33] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X13,X33) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f111,axiom,
    ! [X13,X33] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X13,X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).

fof(f734,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f65,f732]) ).

fof(f732,plain,
    ( spl0_28
  <=> ! [X5,X3] :
        ( ~ class_Finite__Set_Ofinite_Ofinite(X3)
        | c_Finite__Set_Ofinite(X5,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f65,axiom,
    ! [X3,X5] :
      ( ~ class_Finite__Set_Ofinite_Ofinite(X3)
      | c_Finite__Set_Ofinite(X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

fof(f730,plain,
    ( ~ spl0_27
    | spl0_26 ),
    inference(avatar_split_clause,[],[f725,f721,f727]) ).

fof(f721,plain,
    ( spl0_26
  <=> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f725,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | spl0_26 ),
    inference(forward_demodulation,[],[f723,f435]) ).

fof(f723,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | spl0_26 ),
    inference(avatar_component_clause,[],[f721]) ).

fof(f724,plain,
    ~ spl0_26,
    inference(avatar_split_clause,[],[f479,f721]) ).

fof(f479,axiom,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

fof(f719,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f384,f717]) ).

fof(f717,plain,
    ( spl0_25
  <=> ! [X8,X74] : c_Com_OWT(c_Com_Ocom_OAss(X74,X8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f384,axiom,
    ! [X8,X74] : c_Com_OWT(c_Com_Ocom_OAss(X74,X8)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OAssign_0) ).

fof(f715,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f509,f712]) ).

fof(f712,plain,
    ( spl0_24
  <=> class_HOL_Oord(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f509,axiom,
    class_HOL_Oord(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

fof(f710,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f508,f707]) ).

fof(f707,plain,
    ( spl0_23
  <=> class_HOL_Ominus(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f508,axiom,
    class_HOL_Ominus(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

fof(f705,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f507,f702]) ).

fof(f507,axiom,
    class_Orderings_Obot(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

fof(f700,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f506,f697]) ).

fof(f697,plain,
    ( spl0_21
  <=> class_Orderings_Otop(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f506,axiom,
    class_Orderings_Otop(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

fof(f695,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f505,f692]) ).

fof(f692,plain,
    ( spl0_20
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f505,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f690,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f504,f687]) ).

fof(f504,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

fof(f685,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f503,f682]) ).

fof(f682,plain,
    ( spl0_18
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f503,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f680,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f502,f677]) ).

fof(f677,plain,
    ( spl0_17
  <=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f502,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

fof(f675,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f501,f672]) ).

fof(f672,plain,
    ( spl0_16
  <=> class_Lattices_Obounded__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f501,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

fof(f670,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f500,f667]) ).

fof(f500,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

fof(f665,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f499,f662]) ).

fof(f662,plain,
    ( spl0_14
  <=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f499,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

fof(f660,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f498,f657]) ).

fof(f657,plain,
    ( spl0_13
  <=> class_HOL_Oord(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f498,axiom,
    class_HOL_Oord(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

fof(f655,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f497,f652]) ).

fof(f652,plain,
    ( spl0_12
  <=> class_HOL_Ominus(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f497,axiom,
    class_HOL_Ominus(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).

fof(f650,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f496,f647]) ).

fof(f647,plain,
    ( spl0_11
  <=> class_Orderings_Obot(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f496,axiom,
    class_Orderings_Obot(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

fof(f645,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f495,f642]) ).

fof(f642,plain,
    ( spl0_10
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f495,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f640,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f494,f637]) ).

fof(f494,axiom,
    class_Lattices_Olattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

fof(f635,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f493,f632]) ).

fof(f632,plain,
    ( spl0_8
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f493,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f630,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f492,f627]) ).

fof(f627,plain,
    ( spl0_7
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f492,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f625,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f491,f622]) ).

fof(f491,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

fof(f620,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f383,f617]) ).

fof(f617,plain,
    ( spl0_5
  <=> c_Com_OWT(c_Com_Ocom_OSKIP) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f383,axiom,
    c_Com_OWT(c_Com_Ocom_OSKIP),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).

fof(f615,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f477,f612]) ).

fof(f477,axiom,
    hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f610,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f476,f607]) ).

fof(f607,plain,
    ( spl0_3
  <=> c_Com_OWT(v_c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f476,axiom,
    c_Com_OWT(v_c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f605,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f475,f602]) ).

fof(f475,axiom,
    c_Com_OWT__bodies,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f600,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f474,f597]) ).

fof(f474,axiom,
    c_Hoare__Mirabelle_Ostate__not__singleton,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SWV906-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37  % Computer : n027.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Tue Apr 30 05:21:47 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  % (21568)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.41  % (21572)WARNING: value z3 for option sas not known
% 0.23/0.41  % (21573)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.41  % (21569)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.41  % (21574)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)
% 0.23/0.41  % (21575)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)
% 0.23/0.41  % (21572)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)
% 0.23/0.41  % (21576)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)
% 0.23/0.41  % (21571)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.50  TRYING [1]
% 0.23/0.51  TRYING [2]
% 0.23/0.55  % (21574)First to succeed.
% 0.23/0.56  % (21574)Refutation found. Thanks to Tanya!
% 0.23/0.56  % SZS status Unsatisfiable for theBenchmark
% 0.23/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.57  % (21574)------------------------------
% 0.23/0.57  % (21574)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.23/0.57  % (21574)Termination reason: Refutation
% 0.23/0.57  
% 0.23/0.57  % (21574)Memory used [KB]: 3433
% 0.23/0.57  % (21574)Time elapsed: 0.151 s
% 0.23/0.57  % (21574)Instructions burned: 296 (million)
% 0.23/0.57  % (21574)------------------------------
% 0.23/0.57  % (21574)------------------------------
% 0.23/0.57  % (21568)Success in time 0.194 s
%------------------------------------------------------------------------------