TSTP Solution File: SWV884-1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV884-1 : 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 : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 11:12:04 EDT 2024

% Result   : Unsatisfiable 12.17s 2.22s
% Output   : Refutation 12.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      : 1634
% Syntax   : Number of formulae    : 2873 ( 969 unt;   0 def)
%            Number of atoms       : 6702 (1002 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 6659 (2830   ~;2960   |;   0   &)
%                                         ( 869 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    7 (   1 avg)
%            Number of predicates  :  920 ( 918 usr; 870 prp; 0-4 aty)
%            Number of functors    :   47 (  47 usr;   9 con; 0-5 aty)
%            Number of variables   : 5280 (5280   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f50146,plain,
    $false,
    inference(avatar_sat_refutation,[],[f1353,f1358,f1363,f1368,f1373,f1378,f1383,f1388,f1393,f1398,f1403,f1408,f1413,f1418,f1423,f1428,f1433,f1438,f1443,f1448,f1453,f1458,f1463,f1468,f1473,f1478,f1483,f1488,f1493,f1498,f1503,f1508,f1513,f1518,f1523,f1528,f1533,f1538,f1543,f1548,f1553,f1558,f1563,f1568,f1573,f1578,f1583,f1588,f1593,f1598,f1603,f1608,f1613,f1617,f1621,f1625,f1629,f1634,f1638,f1642,f1646,f1650,f1654,f1658,f1662,f1666,f1670,f1674,f1678,f1682,f1686,f1690,f1694,f1698,f1702,f1706,f1710,f1714,f1718,f1722,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1844,f1850,f1854,f1858,f1862,f1866,f1870,f1874,f1878,f1882,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f1914,f1918,f1923,f1927,f1953,f1957,f1961,f1965,f1969,f1973,f1977,f1981,f1985,f1989,f1993,f1998,f2002,f2006,f2010,f2014,f2018,f2022,f2026,f2030,f2034,f2038,f2042,f2046,f2050,f2054,f2058,f2062,f2066,f2070,f2074,f2078,f2083,f2087,f2091,f2095,f2099,f2103,f2107,f2111,f2115,f2119,f2124,f2128,f2132,f2136,f2140,f2144,f2148,f2219,f2230,f2249,f2288,f2298,f2302,f2306,f2310,f2314,f2318,f2322,f2326,f2334,f2338,f2342,f2346,f2350,f2354,f2358,f2362,f2366,f2370,f2378,f2382,f2386,f2390,f2394,f2398,f2402,f2406,f2410,f2414,f2538,f2588,f2592,f2596,f2600,f2604,f2608,f2612,f2616,f2620,f2624,f2628,f2632,f2636,f2640,f2644,f2648,f2652,f2656,f2660,f2664,f2668,f2672,f2676,f2685,f2689,f2693,f2697,f2701,f2705,f2709,f2713,f2717,f2721,f2725,f2729,f2733,f2737,f2741,f2745,f2749,f2753,f2757,f2761,f2916,f3021,f3177,f3181,f3185,f3189,f3193,f3197,f3201,f3205,f3209,f3213,f3218,f3222,f3226,f3231,f3236,f3240,f3244,f3248,f3252,f3256,f3260,f3269,f3273,f3277,f3281,f3285,f3289,f3293,f3297,f3301,f3305,f3311,f3415,f3538,f3727,f3731,f3735,f3739,f3743,f3747,f3751,f3755,f3759,f3763,f3768,f3772,f3776,f3780,f3784,f3788,f3792,f3796,f3800,f3804,f3808,f3812,f3816,f3820,f3824,f3828,f3832,f3836,f3840,f3844,f3848,f3853,f3857,f3861,f3865,f3869,f3873,f3877,f3881,f3885,f3889,f3893,f3897,f3901,f3905,f3909,f4275,f4656,f4660,f4665,f4669,f4673,f4677,f4681,f4685,f4689,f4693,f4697,f4701,f4705,f4710,f4714,f4718,f4722,f4726,f4730,f4734,f4738,f4742,f4746,f4750,f4759,f4763,f4767,f4771,f4775,f4779,f4783,f4787,f4791,f4795,f4806,f4810,f4814,f4818,f4822,f4826,f4830,f4834,f4838,f4842,f4851,f4855,f4859,f4863,f4867,f4871,f4875,f4879,f4883,f4887,f4891,f4895,f4899,f4903,f4907,f4911,f4915,f4919,f4923,f4927,f4931,f4944,f4948,f4952,f5089,f5479,f5825,f6325,f6329,f6334,f6338,f6342,f6346,f6350,f6354,f6358,f6362,f6366,f6370,f6374,f6379,f6383,f6387,f6391,f6395,f6399,f6403,f6407,f6411,f6415,f6419,f6423,f6427,f6431,f6435,f6439,f6443,f6447,f6451,f6455,f6459,f6463,f6467,f6471,f7491,f7495,f7499,f7503,f7507,f7511,f7517,f7521,f7525,f7529,f7533,f7537,f7541,f7545,f7549,f7553,f7558,f7562,f7566,f7570,f7574,f7578,f7582,f7586,f7590,f7594,f7598,f7602,f7606,f7610,f7614,f7618,f7622,f7626,f7630,f7634,f7638,f7642,f7646,f7650,f7654,f7658,f7662,f7666,f7670,f8958,f9171,f9175,f9181,f9185,f9189,f9193,f9197,f9201,f9205,f9209,f9213,f9217,f9221,f9225,f9229,f9233,f9237,f9241,f9245,f9249,f9253,f9257,f9261,f9287,f9291,f9295,f9299,f9303,f9307,f9311,f9315,f9319,f9323,f9327,f9331,f9335,f9339,f9343,f9347,f9351,f9355,f9359,f9363,f9367,f9372,f9376,f9380,f9384,f9396,f9511,f9948,f9952,f9956,f9960,f9964,f9968,f9972,f9976,f9980,f9984,f9988,f9992,f9996,f10000,f10004,f10008,f10012,f10016,f10020,f10024,f10028,f10032,f10039,f10043,f10047,f10051,f10055,f10059,f10063,f10067,f10071,f10075,f10082,f10086,f10090,f10094,f10098,f10102,f10106,f10110,f10114,f10118,f10304,f10775,f11094,f11336,f11340,f11344,f11351,f11355,f11359,f11363,f11367,f11371,f11375,f11379,f11383,f11387,f11394,f11398,f11402,f11406,f11410,f11414,f11418,f11422,f11426,f11430,f11436,f11440,f11444,f11448,f11452,f11457,f11732,f12369,f12373,f12377,f12381,f12385,f12389,f12393,f12397,f12401,f12405,f12409,f12413,f12417,f12421,f12425,f12429,f12433,f12437,f12441,f12445,f12449,f12453,f12457,f12461,f12465,f12469,f12473,f12477,f12481,f12485,f12489,f12493,f12497,f12501,f12505,f12509,f12513,f12517,f12521,f12525,f12529,f12533,f12537,f12541,f12545,f12549,f12553,f12557,f12561,f12565,f12569,f12573,f12577,f12581,f12585,f12589,f12593,f12597,f12601,f12605,f13137,f15714,f22106,f22291,f22533,f22639,f22643,f22647,f22651,f22655,f22659,f22673,f22677,f22681,f22685,f22689,f22693,f22697,f22701,f22705,f22709,f22718,f22722,f22726,f22730,f23410,f23680,f23684,f23688,f23692,f23696,f23700,f23732,f23736,f23740,f23744,f23748,f23752,f23756,f23760,f23813,f24134,f24138,f24142,f24146,f24150,f24154,f24158,f24162,f24167,f24171,f24175,f24179,f24183,f24187,f24191,f24195,f24199,f24203,f24207,f24211,f24215,f24219,f24223,f24227,f24262,f25185,f25189,f25193,f25197,f25201,f25491,f25495,f25500,f25521,f25525,f25529,f25533,f25537,f25541,f25545,f25549,f25553,f25557,f25585,f26075,f26081,f26085,f26089,f26093,f26097,f26101,f26302,f26306,f26310,f26314,f26318,f26322,f26326,f26343,f26347,f27011,f27015,f27019,f27023,f27027,f27031,f27035,f27116,f35052,f35474,f35528,f35533,f35537,f35541,f35545,f35549,f35553,f35558,f44816,f45955,f46314,f46318,f46322,f46326,f46556,f46560,f46638,f46642,f46646,f46650,f46654,f46707,f47150,f47233,f47237,f47241,f47245,f47249,f47253,f47257,f47261,f47265,f47269,f47273,f47277,f48217,f48221,f48225,f48229,f48233,f48237,f48241,f48245,f48671,f48675,f48679,f48683,f48789,f48808,f48812,f48965,f48995,f49034,f49078,f49097,f49101,f49106,f49110,f49114,f49118,f49191,f49195,f49204,f49220,f49268,f49273,f49278,f49282,f49323,f49327,f49336,f49679,f49869,f49899,f49905,f49911,f49912,f49942,f50122,f50145]) ).

fof(f50145,plain,
    ( ~ spl0_2
    | ~ spl0_404
    | spl0_867 ),
    inference(avatar_split_clause,[],[f49943,f49939,f4950,f1355]) ).

fof(f1355,plain,
    ( spl0_2
  <=> c_in(v_pn,v_U,tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f4950,plain,
    ( spl0_404
  <=> ! [X19,X13,X5,X2,X7] :
        ( ~ c_in(X7,X5,X13)
        | c_in(hAPP(X19,X7),c_Set_Oimage(X19,X5,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f49939,plain,
    ( spl0_867
  <=> c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).

fof(f49943,plain,
    ( ~ c_in(v_pn,v_U,tc_Com_Opname)
    | ~ spl0_404
    | spl0_867 ),
    inference(resolution,[],[f49941,f4951]) ).

fof(f4951,plain,
    ( ! [X2,X19,X7,X5,X13] :
        ( c_in(hAPP(X19,X7),c_Set_Oimage(X19,X5,X13,X2),X2)
        | ~ c_in(X7,X5,X13) )
    | ~ spl0_404 ),
    inference(avatar_component_clause,[],[f4950]) ).

fof(f49941,plain,
    ( ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
    | spl0_867 ),
    inference(avatar_component_clause,[],[f49939]) ).

fof(f50122,plain,
    ( spl0_868
    | ~ spl0_869
    | ~ spl0_58
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f3486,f3242,f1631,f50119,f50115]) ).

fof(f50115,plain,
    ( spl0_868
  <=> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f50119,plain,
    ( spl0_869
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f1631,plain,
    ( spl0_58
  <=> c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f3242,plain,
    ( spl0_272
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f3486,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_58
    | ~ spl0_272 ),
    inference(superposition,[],[f3243,f1633]) ).

fof(f1633,plain,
    ( c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f1631]) ).

fof(f3243,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_272 ),
    inference(avatar_component_clause,[],[f3242]) ).

fof(f49942,plain,
    ( ~ spl0_867
    | ~ spl0_51
    | spl0_53
    | ~ spl0_608 ),
    inference(avatar_split_clause,[],[f12166,f11428,f1610,f1600,f49939]) ).

fof(f1600,plain,
    ( spl0_51
  <=> c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f1610,plain,
    ( spl0_53
  <=> c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f11428,plain,
    ( spl0_608
  <=> ! [X5,X7,X6,X2] :
        ( ~ c_in(X7,X6,X2)
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_lessequals(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f12166,plain,
    ( ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
    | ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
    | spl0_53
    | ~ spl0_608 ),
    inference(resolution,[],[f11429,f1612]) ).

fof(f1612,plain,
    ( ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
    | spl0_53 ),
    inference(avatar_component_clause,[],[f1610]) ).

fof(f11429,plain,
    ( ! [X2,X6,X7,X5] :
        ( c_lessequals(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_in(X7,X6,X2) )
    | ~ spl0_608 ),
    inference(avatar_component_clause,[],[f11428]) ).

fof(f49912,plain,
    ( ~ spl0_47
    | ~ spl0_77
    | spl0_863 ),
    inference(avatar_split_clause,[],[f49900,f49893,f1708,f1580]) ).

fof(f1580,plain,
    ( spl0_47
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f1708,plain,
    ( spl0_77
  <=> ! [X52,X51] :
        ( ~ class_Orderings_Oorder(X52)
        | class_Orderings_Oorder(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f49893,plain,
    ( spl0_863
  <=> class_Orderings_Oorder(tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).

fof(f49900,plain,
    ( ~ class_Orderings_Oorder(tc_bool)
    | ~ spl0_77
    | spl0_863 ),
    inference(resolution,[],[f49895,f1709]) ).

fof(f1709,plain,
    ( ! [X51,X52] :
        ( class_Orderings_Oorder(tc_fun(X51,X52))
        | ~ class_Orderings_Oorder(X52) )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f1708]) ).

fof(f49895,plain,
    ( ~ class_Orderings_Oorder(tc_fun(t_a,tc_bool))
    | spl0_863 ),
    inference(avatar_component_clause,[],[f49893]) ).

fof(f49911,plain,
    ( spl0_866
    | ~ spl0_851
    | ~ spl0_865 ),
    inference(avatar_split_clause,[],[f49906,f49902,f49201,f49908]) ).

fof(f49908,plain,
    ( spl0_866
  <=> c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(c_Finite__Set_Ocard(v_G,t_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).

fof(f49201,plain,
    ( spl0_851
  <=> v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f49902,plain,
    ( spl0_865
  <=> c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).

fof(f49906,plain,
    ( c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(c_Finite__Set_Ocard(v_G,t_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_851
    | ~ spl0_865 ),
    inference(forward_demodulation,[],[f49904,f49203]) ).

fof(f49203,plain,
    ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)
    | ~ spl0_851 ),
    inference(avatar_component_clause,[],[f49201]) ).

fof(f49904,plain,
    ( c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_865 ),
    inference(avatar_component_clause,[],[f49902]) ).

fof(f49905,plain,
    ( spl0_865
    | ~ spl0_52
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f9055,f7652,f1605,f49902]) ).

fof(f1605,plain,
    ( spl0_52
  <=> c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f7652,plain,
    ( spl0_485
  <=> ! [X1,X47] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X47,tc_nat)
        | c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X47),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X47 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f9055,plain,
    ( c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_52
    | ~ spl0_485 ),
    inference(resolution,[],[f7653,f1607]) ).

fof(f1607,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f1605]) ).

fof(f7653,plain,
    ( ! [X1,X47] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X47,tc_nat)
        | c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X47),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X47 )
    | ~ spl0_485 ),
    inference(avatar_component_clause,[],[f7652]) ).

fof(f49899,plain,
    ( ~ spl0_863
    | spl0_864
    | ~ spl0_51
    | ~ spl0_398 ),
    inference(avatar_split_clause,[],[f6202,f4917,f1600,f49897,f49893]) ).

fof(f49897,plain,
    ( spl0_864
  <=> ! [X0] :
        ( ~ c_lessequals(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0,tc_fun(t_a,tc_bool))
        | c_lessequals(v_G,X0,tc_fun(t_a,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f4917,plain,
    ( spl0_398
  <=> ! [X7,X8,X14,X2] :
        ( ~ class_Orderings_Oorder(X2)
        | ~ c_lessequals(X8,X7,X2)
        | ~ c_lessequals(X14,X8,X2)
        | c_lessequals(X14,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f6202,plain,
    ( ! [X0] :
        ( ~ c_lessequals(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0,tc_fun(t_a,tc_bool))
        | ~ class_Orderings_Oorder(tc_fun(t_a,tc_bool))
        | c_lessequals(v_G,X0,tc_fun(t_a,tc_bool)) )
    | ~ spl0_51
    | ~ spl0_398 ),
    inference(resolution,[],[f4918,f1602]) ).

fof(f1602,plain,
    ( c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f1600]) ).

fof(f4918,plain,
    ( ! [X2,X8,X7,X14] :
        ( ~ c_lessequals(X14,X8,X2)
        | ~ c_lessequals(X8,X7,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(X14,X7,X2) )
    | ~ spl0_398 ),
    inference(avatar_component_clause,[],[f4917]) ).

fof(f49869,plain,
    ( spl0_862
    | ~ spl0_290
    | spl0_3
    | ~ spl0_701 ),
    inference(avatar_split_clause,[],[f23670,f22728,f1360,f3535,f49866]) ).

fof(f49866,plain,
    ( spl0_862
  <=> c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat) = c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).

fof(f3535,plain,
    ( spl0_290
  <=> c_Finite__Set_Ofinite(v_G,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f1360,plain,
    ( spl0_3
  <=> c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f22728,plain,
    ( spl0_701
  <=> ! [X2,X5,X7] :
        ( c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(X5,X2),tc_nat)
        | ~ c_Finite__Set_Ofinite(X5,X2)
        | c_in(X7,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f23670,plain,
    ( ~ c_Finite__Set_Ofinite(v_G,t_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat) = c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a)
    | spl0_3
    | ~ spl0_701 ),
    inference(resolution,[],[f22729,f1362]) ).

fof(f1362,plain,
    ( ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
    | spl0_3 ),
    inference(avatar_component_clause,[],[f1360]) ).

fof(f22729,plain,
    ( ! [X2,X7,X5] :
        ( c_in(X7,X5,X2)
        | ~ c_Finite__Set_Ofinite(X5,X2)
        | c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(X5,X2),tc_nat) )
    | ~ spl0_701 ),
    inference(avatar_component_clause,[],[f22728]) ).

fof(f49679,plain,
    ( spl0_861
    | ~ spl0_606
    | spl0_852 ),
    inference(avatar_split_clause,[],[f49221,f49217,f11420,f49676]) ).

fof(f49676,plain,
    ( spl0_861
  <=> c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f11420,plain,
    ( spl0_606
  <=> ! [X6,X19,X13,X5,X2] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X5,X6,X19,X13,X2),X5,X13)
        | c_lessequals(c_Set_Oimage(X19,X5,X13,X2),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f49217,plain,
    ( spl0_852
  <=> c_lessequals(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).

fof(f49221,plain,
    ( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
    | ~ spl0_606
    | spl0_852 ),
    inference(resolution,[],[f49219,f11421]) ).

fof(f11421,plain,
    ( ! [X2,X6,X19,X5,X13] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X5,X6,X19,X13,X2),X5,X13)
        | c_lessequals(c_Set_Oimage(X19,X5,X13,X2),X6,tc_fun(X2,tc_bool)) )
    | ~ spl0_606 ),
    inference(avatar_component_clause,[],[f11420]) ).

fof(f49219,plain,
    ( ~ c_lessequals(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))
    | spl0_852 ),
    inference(avatar_component_clause,[],[f49217]) ).

fof(f49336,plain,
    ( spl0_859
    | ~ spl0_860
    | ~ spl0_51
    | ~ spl0_779 ),
    inference(avatar_split_clause,[],[f27059,f27013,f1600,f49333,f49329]) ).

fof(f49329,plain,
    ( spl0_859
  <=> c_lessequals(c_Set_Ovimage(v_mgt__call,v_G,tc_Com_Opname,t_a),v_U,tc_fun(tc_Com_Opname,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f49333,plain,
    ( spl0_860
  <=> c_Fun_Oinj__on(v_mgt__call,c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f27013,plain,
    ( spl0_779
  <=> ! [X6,X19,X13,X5,X2] :
        ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
        | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X2,X13),tc_fun(X13,tc_bool))
        | c_lessequals(c_Set_Ovimage(X19,X6,X2,X13),X5,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).

fof(f27059,plain,
    ( ~ c_Fun_Oinj__on(v_mgt__call,c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a)
    | c_lessequals(c_Set_Ovimage(v_mgt__call,v_G,tc_Com_Opname,t_a),v_U,tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_51
    | ~ spl0_779 ),
    inference(resolution,[],[f27014,f1602]) ).

fof(f27014,plain,
    ( ! [X2,X6,X19,X5,X13] :
        ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X2,X13),tc_fun(X13,tc_bool))
        | ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
        | c_lessequals(c_Set_Ovimage(X19,X6,X2,X13),X5,tc_fun(X2,tc_bool)) )
    | ~ spl0_779 ),
    inference(avatar_component_clause,[],[f27013]) ).

fof(f49327,plain,
    ( spl0_858
    | spl0_3
    | ~ spl0_665 ),
    inference(avatar_split_clause,[],[f22403,f12563,f1360,f49325]) ).

fof(f49325,plain,
    ( spl0_858
  <=> ! [X2,X0,X1] : c_Set_Oimage(c_Fun_Ofun__upd(X0,hAPP(v_mgt__call,v_pn),X1,t_a,X2),v_G,t_a,X2) = c_Set_Oimage(X0,v_G,t_a,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).

fof(f12563,plain,
    ( spl0_665
  <=> ! [X19,X13,X8,X5,X2,X7] :
        ( c_in(X7,X5,X13)
        | c_Set_Oimage(c_Fun_Ofun__upd(X19,X7,X8,X13,X2),X5,X13,X2) = c_Set_Oimage(X19,X5,X13,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f22403,plain,
    ( ! [X2,X0,X1] : c_Set_Oimage(c_Fun_Ofun__upd(X0,hAPP(v_mgt__call,v_pn),X1,t_a,X2),v_G,t_a,X2) = c_Set_Oimage(X0,v_G,t_a,X2)
    | spl0_3
    | ~ spl0_665 ),
    inference(resolution,[],[f12564,f1362]) ).

fof(f12564,plain,
    ( ! [X2,X8,X19,X7,X5,X13] :
        ( c_in(X7,X5,X13)
        | c_Set_Oimage(c_Fun_Ofun__upd(X19,X7,X8,X13,X2),X5,X13,X2) = c_Set_Oimage(X19,X5,X13,X2) )
    | ~ spl0_665 ),
    inference(avatar_component_clause,[],[f12563]) ).

fof(f49323,plain,
    ( spl0_857
    | spl0_3
    | ~ spl0_660 ),
    inference(avatar_split_clause,[],[f22278,f12543,f1360,f49321]) ).

fof(f49321,plain,
    ( spl0_857
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(v_G,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),X0,t_a),tc_fun(t_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(v_G,X0,tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f12543,plain,
    ( spl0_660
  <=> ! [X5,X3,X6,X2] :
        ( c_in(X3,X5,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f22278,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(v_G,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),X0,t_a),tc_fun(t_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(v_G,X0,tc_fun(t_a,tc_bool))
    | spl0_3
    | ~ spl0_660 ),
    inference(resolution,[],[f12544,f1362]) ).

fof(f12544,plain,
    ( ! [X2,X3,X6,X5] :
        ( c_in(X3,X5,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) )
    | ~ spl0_660 ),
    inference(avatar_component_clause,[],[f12543]) ).

fof(f49282,plain,
    ( spl0_856
    | spl0_3
    | ~ spl0_659 ),
    inference(avatar_split_clause,[],[f22257,f12539,f1360,f49280]) ).

fof(f49280,plain,
    ( spl0_856
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,v_G,tc_fun(t_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),X0,t_a),v_G,tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).

fof(f12539,plain,
    ( spl0_659
  <=> ! [X15,X3,X6,X2] :
        ( c_in(X3,X15,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X6,X2),X15,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f22257,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,v_G,tc_fun(t_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),X0,t_a),v_G,tc_fun(t_a,tc_bool))
    | spl0_3
    | ~ spl0_659 ),
    inference(resolution,[],[f12540,f1362]) ).

fof(f12540,plain,
    ( ! [X2,X3,X6,X15] :
        ( c_in(X3,X15,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X6,X2),X15,tc_fun(X2,tc_bool)) )
    | ~ spl0_659 ),
    inference(avatar_component_clause,[],[f12539]) ).

fof(f49278,plain,
    ( spl0_855
    | ~ spl0_52
    | ~ spl0_58
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f4625,f3899,f1631,f1605,f49275]) ).

fof(f49275,plain,
    ( spl0_855
  <=> c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).

fof(f3899,plain,
    ( spl0_334
  <=> ! [X20,X1] :
        ( ~ c_lessequals(X20,X1,tc_nat)
        | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X20,tc_nat),tc_nat) = X20 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f4625,plain,
    ( c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
    | ~ spl0_52
    | ~ spl0_58
    | ~ spl0_334 ),
    inference(forward_demodulation,[],[f4602,f1633]) ).

fof(f4602,plain,
    ( c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_52
    | ~ spl0_334 ),
    inference(resolution,[],[f3900,f1607]) ).

fof(f3900,plain,
    ( ! [X1,X20] :
        ( ~ c_lessequals(X20,X1,tc_nat)
        | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X20,tc_nat),tc_nat) = X20 )
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f3899]) ).

fof(f49273,plain,
    ( spl0_854
    | ~ spl0_52
    | ~ spl0_58
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f4526,f3887,f1631,f1605,f49270]) ).

fof(f49270,plain,
    ( spl0_854
  <=> c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).

fof(f3887,plain,
    ( spl0_331
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X1,X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f4526,plain,
    ( c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
    | ~ spl0_52
    | ~ spl0_58
    | ~ spl0_331 ),
    inference(forward_demodulation,[],[f4504,f1633]) ).

fof(f4504,plain,
    ( c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_52
    | ~ spl0_331 ),
    inference(resolution,[],[f3888,f1607]) ).

fof(f3888,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X1,X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X0 )
    | ~ spl0_331 ),
    inference(avatar_component_clause,[],[f3887]) ).

fof(f49268,plain,
    ( spl0_853
    | ~ spl0_52
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f3558,f3271,f1605,f49266]) ).

fof(f49266,plain,
    ( spl0_853
  <=> ! [X0] :
        ( ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_lessequals(X0,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f3271,plain,
    ( spl0_278
  <=> ! [X20,X21,X4] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | ~ c_lessequals(X21,X4,tc_nat)
        | c_lessequals(X20,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f3558,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_lessequals(X0,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) )
    | ~ spl0_52
    | ~ spl0_278 ),
    inference(resolution,[],[f3272,f1607]) ).

fof(f3272,plain,
    ( ! [X21,X4,X20] :
        ( ~ c_lessequals(X21,X4,tc_nat)
        | ~ c_lessequals(X20,X21,tc_nat)
        | c_lessequals(X20,X4,tc_nat) )
    | ~ spl0_278 ),
    inference(avatar_component_clause,[],[f3271]) ).

fof(f49220,plain,
    ( spl0_851
    | ~ spl0_852
    | ~ spl0_51
    | ~ spl0_431 ),
    inference(avatar_split_clause,[],[f7249,f6417,f1600,f49217,f49201]) ).

fof(f6417,plain,
    ( spl0_431
  <=> ! [X6,X2,X5] :
        ( X5 = X6
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X6,X5,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f7249,plain,
    ( ~ c_lessequals(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))
    | v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)
    | ~ spl0_51
    | ~ spl0_431 ),
    inference(resolution,[],[f6418,f1602]) ).

fof(f6418,plain,
    ( ! [X2,X6,X5] :
        ( ~ c_lessequals(X6,X5,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | X5 = X6 )
    | ~ spl0_431 ),
    inference(avatar_component_clause,[],[f6417]) ).

fof(f49204,plain,
    ( spl0_850
    | spl0_851
    | ~ spl0_51
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f6961,f6372,f1600,f49201,f49197]) ).

fof(f49197,plain,
    ( spl0_850
  <=> c_HOL_Oord__class_Oless(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).

fof(f6372,plain,
    ( spl0_420
  <=> ! [X6,X2,X5] :
        ( X5 = X6
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f6961,plain,
    ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)
    | c_HOL_Oord__class_Oless(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
    | ~ spl0_51
    | ~ spl0_420 ),
    inference(resolution,[],[f6373,f1602]) ).

fof(f6373,plain,
    ( ! [X2,X6,X5] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | X5 = X6
        | c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool)) )
    | ~ spl0_420 ),
    inference(avatar_component_clause,[],[f6372]) ).

fof(f49195,plain,
    ( spl0_849
    | ~ spl0_85
    | ~ spl0_847 ),
    inference(avatar_split_clause,[],[f49177,f49116,f1740,f49193]) ).

fof(f49193,plain,
    ( spl0_849
  <=> ! [X0] : c_lessequals(v_na,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),v_na),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).

fof(f1740,plain,
    ( spl0_85
  <=> ! [X2,X7] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f49116,plain,
    ( spl0_847
  <=> ! [X0] :
        ( hBOOL(hAPP(X0,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)))
        | c_lessequals(v_na,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X0,v_na),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).

fof(f49177,plain,
    ( ! [X0] : c_lessequals(v_na,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),v_na),tc_nat)
    | ~ spl0_85
    | ~ spl0_847 ),
    inference(resolution,[],[f49117,f1741]) ).

fof(f1741,plain,
    ( ! [X2,X7] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X7))
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f1740]) ).

fof(f49117,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(X0,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)))
        | c_lessequals(v_na,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X0,v_na),tc_nat) )
    | ~ spl0_847 ),
    inference(avatar_component_clause,[],[f49116]) ).

fof(f49191,plain,
    ( spl0_848
    | ~ spl0_52
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3081,f2735,f1605,f49188]) ).

fof(f49188,plain,
    ( spl0_848
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f2735,plain,
    ( spl0_247
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f3081,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_52
    | ~ spl0_247 ),
    inference(resolution,[],[f2736,f1607]) ).

fof(f2736,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) )
    | ~ spl0_247 ),
    inference(avatar_component_clause,[],[f2735]) ).

fof(f49118,plain,
    ( spl0_847
    | ~ spl0_52
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f11281,f10104,f1605,f49116]) ).

fof(f10104,plain,
    ( spl0_579
  <=> ! [X25,X1,X47] :
        ( hBOOL(hAPP(X25,X47))
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X47,tc_nat)
        | c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X25,X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f11281,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(X0,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)))
        | c_lessequals(v_na,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X0,v_na),tc_nat) )
    | ~ spl0_52
    | ~ spl0_579 ),
    inference(resolution,[],[f10105,f1607]) ).

fof(f10105,plain,
    ( ! [X1,X47,X25] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X47,tc_nat)
        | hBOOL(hAPP(X25,X47))
        | c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X25,X1),tc_nat) )
    | ~ spl0_579 ),
    inference(avatar_component_clause,[],[f10104]) ).

fof(f49114,plain,
    ( spl0_846
    | ~ spl0_51
    | ~ spl0_564 ),
    inference(avatar_split_clause,[],[f10809,f10041,f1600,f49112]) ).

fof(f49112,plain,
    ( spl0_846
  <=> ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(X0,v_G,tc_fun(t_a,tc_bool))
        | c_HOL_Oord__class_Oless(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).

fof(f10041,plain,
    ( spl0_564
  <=> ! [X5,X15,X6,X2] :
        ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(X5,X15,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f10809,plain,
    ( ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(X0,v_G,tc_fun(t_a,tc_bool))
        | c_HOL_Oord__class_Oless(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) )
    | ~ spl0_51
    | ~ spl0_564 ),
    inference(resolution,[],[f10042,f1602]) ).

fof(f10042,plain,
    ( ! [X2,X6,X15,X5] :
        ( ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
        | ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(X5,X15,tc_fun(X2,tc_bool)) )
    | ~ spl0_564 ),
    inference(avatar_component_clause,[],[f10041]) ).

fof(f49110,plain,
    ( spl0_845
    | ~ spl0_51
    | ~ spl0_563 ),
    inference(avatar_split_clause,[],[f10771,f10037,f1600,f49108]) ).

fof(f49108,plain,
    ( spl0_845
  <=> ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0,tc_fun(t_a,tc_bool))
        | c_HOL_Oord__class_Oless(v_G,X0,tc_fun(t_a,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f10037,plain,
    ( spl0_563
  <=> ! [X5,X15,X6,X2] :
        ( ~ c_HOL_Oord__class_Oless(X6,X15,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(X5,X15,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f10771,plain,
    ( ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0,tc_fun(t_a,tc_bool))
        | c_HOL_Oord__class_Oless(v_G,X0,tc_fun(t_a,tc_bool)) )
    | ~ spl0_51
    | ~ spl0_563 ),
    inference(resolution,[],[f10038,f1602]) ).

fof(f10038,plain,
    ( ! [X2,X6,X15,X5] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_HOL_Oord__class_Oless(X6,X15,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(X5,X15,tc_fun(X2,tc_bool)) )
    | ~ spl0_563 ),
    inference(avatar_component_clause,[],[f10037]) ).

fof(f49106,plain,
    ( spl0_844
    | ~ spl0_58
    | ~ spl0_141
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f3142,f2751,f2004,f1631,f49103]) ).

fof(f49103,plain,
    ( spl0_844
  <=> c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_G,t_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f2004,plain,
    ( spl0_141
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f2751,plain,
    ( spl0_251
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f3142,plain,
    ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_G,t_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),tc_nat)
    | ~ spl0_58
    | ~ spl0_141
    | ~ spl0_251 ),
    inference(forward_demodulation,[],[f3136,f2005]) ).

fof(f2005,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f2004]) ).

fof(f3136,plain,
    ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_G,t_a),c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_58
    | ~ spl0_251 ),
    inference(superposition,[],[f2752,f1633]) ).

fof(f2752,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_251 ),
    inference(avatar_component_clause,[],[f2751]) ).

fof(f49101,plain,
    ( spl0_843
    | ~ spl0_395
    | ~ spl0_839 ),
    inference(avatar_split_clause,[],[f48999,f48992,f4905,f49099]) ).

fof(f49099,plain,
    ( spl0_843
  <=> ! [X0] :
        ( hBOOL(hAPP(v_U,X0))
        | ~ hBOOL(hAPP(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f4905,plain,
    ( spl0_395
  <=> ! [X2,X7,X49,X25] :
        ( ~ hBOOL(hAPP(X25,X7))
        | hBOOL(hAPP(X49,X7))
        | ~ c_lessequals(X25,X49,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f48992,plain,
    ( spl0_839
  <=> c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_fun(tc_Com_Opname,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f48999,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(v_U,X0))
        | ~ hBOOL(hAPP(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),X0)) )
    | ~ spl0_395
    | ~ spl0_839 ),
    inference(resolution,[],[f48994,f4906]) ).

fof(f4906,plain,
    ( ! [X2,X49,X7,X25] :
        ( ~ c_lessequals(X25,X49,tc_fun(X2,tc_bool))
        | hBOOL(hAPP(X49,X7))
        | ~ hBOOL(hAPP(X25,X7)) )
    | ~ spl0_395 ),
    inference(avatar_component_clause,[],[f4905]) ).

fof(f48994,plain,
    ( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_839 ),
    inference(avatar_component_clause,[],[f48992]) ).

fof(f49097,plain,
    ( spl0_842
    | ~ spl0_58
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3052,f2727,f1631,f49095]) ).

fof(f49095,plain,
    ( spl0_842
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_G,t_a),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f2727,plain,
    ( spl0_245
  <=> ! [X4,X21,X1] :
        ( ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X1,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f3052,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_G,t_a),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),X0,tc_nat) )
    | ~ spl0_58
    | ~ spl0_245 ),
    inference(superposition,[],[f2728,f1633]) ).

fof(f2728,plain,
    ( ! [X21,X1,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X1,tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat) )
    | ~ spl0_245 ),
    inference(avatar_component_clause,[],[f2727]) ).

fof(f49078,plain,
    ( ~ spl0_36
    | ~ spl0_841
    | ~ spl0_52
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f2483,f2368,f1605,f49075,f1525]) ).

fof(f1525,plain,
    ( spl0_36
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f49075,plain,
    ( spl0_841
  <=> c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f2368,plain,
    ( spl0_198
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
        | ~ c_lessequals(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f2483,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ class_Orderings_Olinorder(tc_nat)
    | ~ spl0_52
    | ~ spl0_198 ),
    inference(resolution,[],[f2369,f1607]) ).

fof(f2369,plain,
    ( ! [X2,X8,X7] :
        ( ~ c_lessequals(X8,X7,X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_198 ),
    inference(avatar_component_clause,[],[f2368]) ).

fof(f49034,plain,
    ( spl0_840
    | ~ spl0_290
    | ~ spl0_51
    | ~ spl0_758 ),
    inference(avatar_split_clause,[],[f25901,f25547,f1600,f3535,f49031]) ).

fof(f49031,plain,
    ( spl0_840
  <=> v_G = c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f25547,plain,
    ( spl0_758
  <=> ! [X5,X19,X13,X6,X2] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | c_Set_Oimage(X19,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X5,X6,X19,X13,X2),X13,X2) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).

fof(f25901,plain,
    ( ~ c_Finite__Set_Ofinite(v_G,t_a)
    | v_G = c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a)
    | ~ spl0_51
    | ~ spl0_758 ),
    inference(resolution,[],[f25548,f1602]) ).

fof(f25548,plain,
    ( ! [X2,X6,X19,X5,X13] :
        ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | ~ c_Finite__Set_Ofinite(X6,X2)
        | c_Set_Oimage(X19,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X5,X6,X19,X13,X2),X13,X2) = X6 )
    | ~ spl0_758 ),
    inference(avatar_component_clause,[],[f25547]) ).

fof(f48995,plain,
    ( spl0_839
    | ~ spl0_290
    | ~ spl0_51
    | ~ spl0_746 ),
    inference(avatar_split_clause,[],[f25454,f25195,f1600,f3535,f48992]) ).

fof(f25195,plain,
    ( spl0_746
  <=> ! [X5,X19,X13,X6,X2] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X5,X6,X19,X13,X2),X5,tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f25454,plain,
    ( ~ c_Finite__Set_Ofinite(v_G,t_a)
    | c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_51
    | ~ spl0_746 ),
    inference(resolution,[],[f25196,f1602]) ).

fof(f25196,plain,
    ( ! [X2,X6,X19,X5,X13] :
        ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | ~ c_Finite__Set_Ofinite(X6,X2)
        | c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X5,X6,X19,X13,X2),X5,tc_fun(X13,tc_bool)) )
    | ~ spl0_746 ),
    inference(avatar_component_clause,[],[f25195]) ).

fof(f48965,plain,
    spl0_838,
    inference(avatar_split_clause,[],[f952,f48963]) ).

fof(f48963,plain,
    ( spl0_838
  <=> ! [X6,X41,X19,X13,X5,X2] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_Finite__Set_Ofinite(X6,X13)
        | ~ c_Fun_Oinj__on(X19,X5,X2,X13)
        | ~ c_Fun_Oinj__on(X41,X6,X13,X2)
        | c_Finite__Set_Ocard(X5,X2) = c_Finite__Set_Ocard(X6,X13)
        | ~ c_lessequals(c_Set_Oimage(X19,X5,X2,X13),X6,tc_fun(X13,tc_bool))
        | ~ c_lessequals(c_Set_Oimage(X41,X6,X13,X2),X5,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).

fof(f952,axiom,
    ! [X2,X41,X6,X19,X5,X13] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_Finite__Set_Ofinite(X6,X13)
      | ~ c_Fun_Oinj__on(X19,X5,X2,X13)
      | ~ c_Fun_Oinj__on(X41,X6,X13,X2)
      | c_Finite__Set_Ocard(X5,X2) = c_Finite__Set_Ocard(X6,X13)
      | ~ c_lessequals(c_Set_Oimage(X19,X5,X2,X13),X6,tc_fun(X13,tc_bool))
      | ~ c_lessequals(c_Set_Oimage(X41,X6,X13,X2),X5,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).

fof(f48812,plain,
    spl0_837,
    inference(avatar_split_clause,[],[f785,f48810]) ).

fof(f48810,plain,
    ( spl0_837
  <=> ! [X15,X6,X19,X13,X5,X2] :
        ( ~ c_Fun_Oinj__on(X19,X15,X2,X13)
        | ~ c_lessequals(X5,X15,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
        | c_Set_Oimage(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2,X13) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).

fof(f785,axiom,
    ! [X2,X19,X6,X15,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,X15,X2,X13)
      | ~ c_lessequals(X5,X15,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
      | c_Set_Oimage(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2,X13) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

fof(f48808,plain,
    spl0_836,
    inference(avatar_split_clause,[],[f781,f48806]) ).

fof(f48806,plain,
    ( spl0_836
  <=> ! [X15,X6,X19,X13,X5,X2] :
        ( ~ c_Fun_Oinj__on(X19,X15,X2,X13)
        | ~ c_lessequals(X5,X15,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
        | c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2,X13) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f781,axiom,
    ! [X2,X19,X6,X15,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,X15,X2,X13)
      | ~ c_lessequals(X5,X15,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
      | c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2,X13) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

fof(f48789,plain,
    spl0_835,
    inference(avatar_split_clause,[],[f612,f48787]) ).

fof(f48787,plain,
    ( spl0_835
  <=> ! [X5,X7,X6,X2] :
        ( c_in(X7,X6,X2)
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f612,axiom,
    ! [X2,X6,X7,X5] :
      ( c_in(X7,X6,X2)
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).

fof(f48683,plain,
    spl0_834,
    inference(avatar_split_clause,[],[f928,f48681]) ).

fof(f48681,plain,
    ( spl0_834
  <=> ! [X5,X3,X6,X2] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_in(X3,X5,X2)
        | c_in(X3,X6,X2)
        | c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).

fof(f928,axiom,
    ! [X2,X3,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X3,X5,X2)
      | c_in(X3,X6,X2)
      | c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__insert_0) ).

fof(f48679,plain,
    ( spl0_833
    | ~ spl0_50
    | ~ spl0_51
    | ~ spl0_478 ),
    inference(avatar_split_clause,[],[f8640,f7624,f1600,f1595,f48677]) ).

fof(f48677,plain,
    ( spl0_833
  <=> ! [X0] : c_lessequals(hAPP(v_G,X0),hAPP(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).

fof(f1595,plain,
    ( spl0_50
  <=> class_HOL_Oord(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f7624,plain,
    ( spl0_478
  <=> ! [X41,X19,X13,X2,X7] :
        ( ~ class_HOL_Oord(X13)
        | ~ c_lessequals(X19,X41,tc_fun(X2,X13))
        | c_lessequals(hAPP(X19,X7),hAPP(X41,X7),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f8640,plain,
    ( ! [X0] :
        ( ~ class_HOL_Oord(tc_bool)
        | c_lessequals(hAPP(v_G,X0),hAPP(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0),tc_bool) )
    | ~ spl0_51
    | ~ spl0_478 ),
    inference(resolution,[],[f7625,f1602]) ).

fof(f7625,plain,
    ( ! [X2,X41,X19,X7,X13] :
        ( ~ c_lessequals(X19,X41,tc_fun(X2,X13))
        | ~ class_HOL_Oord(X13)
        | c_lessequals(hAPP(X19,X7),hAPP(X41,X7),X13) )
    | ~ spl0_478 ),
    inference(avatar_component_clause,[],[f7624]) ).

fof(f48675,plain,
    spl0_832,
    inference(avatar_split_clause,[],[f308,f48673]) ).

fof(f48673,plain,
    ( spl0_832
  <=> ! [X3,X9,X10,X27,X2,X26] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(X3,X10,X2) != c_Divides_Odiv__class_Omod(X27,X10,X2)
        | c_Divides_Odiv__class_Omod(X9,X10,X2) != c_Divides_Odiv__class_Omod(X26,X10,X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X27,X26,X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).

fof(f308,axiom,
    ! [X2,X3,X10,X9,X26,X27] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(X3,X10,X2) != c_Divides_Odiv__class_Omod(X27,X10,X2)
      | c_Divides_Odiv__class_Omod(X9,X10,X2) != c_Divides_Odiv__class_Omod(X26,X10,X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X27,X26,X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).

fof(f48671,plain,
    spl0_831,
    inference(avatar_split_clause,[],[f266,f48669]) ).

fof(f48669,plain,
    ( spl0_831
  <=> ! [X3,X9,X10,X27,X2,X26] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(X3,X10,X2) != c_Divides_Odiv__class_Omod(X27,X10,X2)
        | c_Divides_Odiv__class_Omod(X9,X10,X2) != c_Divides_Odiv__class_Omod(X26,X10,X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X27,X26,X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f266,axiom,
    ! [X2,X3,X10,X9,X26,X27] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(X3,X10,X2) != c_Divides_Odiv__class_Omod(X27,X10,X2)
      | c_Divides_Odiv__class_Omod(X9,X10,X2) != c_Divides_Odiv__class_Omod(X26,X10,X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X27,X26,X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).

fof(f48245,plain,
    spl0_830,
    inference(avatar_split_clause,[],[f859,f48243]) ).

fof(f48243,plain,
    ( spl0_830
  <=> ! [X19,X13,X8,X5,X2,X7] :
        ( X7 = X8
        | ~ c_in(X7,c_Set_Oimage(X19,X5,X2,X13),X13)
        | ~ c_in(X8,c_Set_Oimage(X19,X5,X2,X13),X13)
        | hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X2,X13),X7) != hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X2,X13),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).

fof(f859,axiom,
    ! [X2,X8,X19,X7,X5,X13] :
      ( X7 = X8
      | ~ c_in(X7,c_Set_Oimage(X19,X5,X2,X13),X13)
      | ~ c_in(X8,c_Set_Oimage(X19,X5,X2,X13),X13)
      | hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X2,X13),X7) != hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X2,X13),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).

fof(f48241,plain,
    ( spl0_829
    | ~ spl0_51
    | ~ spl0_470 ),
    inference(avatar_split_clause,[],[f8459,f7592,f1600,f48239]) ).

fof(f48239,plain,
    ( spl0_829
  <=> ! [X0,X1] :
        ( c_Fun_Oinj__on(X0,v_G,t_a,X1)
        | ~ c_Fun_Oinj__on(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).

fof(f7592,plain,
    ( spl0_470
  <=> ! [X5,X19,X13,X6,X2] :
        ( ~ c_Fun_Oinj__on(X19,X6,X2,X13)
        | c_Fun_Oinj__on(X19,X5,X2,X13)
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f8459,plain,
    ( ! [X0,X1] :
        ( c_Fun_Oinj__on(X0,v_G,t_a,X1)
        | ~ c_Fun_Oinj__on(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a,X1) )
    | ~ spl0_51
    | ~ spl0_470 ),
    inference(resolution,[],[f7593,f1602]) ).

fof(f7593,plain,
    ( ! [X2,X6,X19,X5,X13] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_Fun_Oinj__on(X19,X5,X2,X13)
        | ~ c_Fun_Oinj__on(X19,X6,X2,X13) )
    | ~ spl0_470 ),
    inference(avatar_component_clause,[],[f7592]) ).

fof(f48237,plain,
    spl0_828,
    inference(avatar_split_clause,[],[f836,f48235]) ).

fof(f48235,plain,
    ( spl0_828
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X21,X20,tc_nat)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f836,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X21,X20,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).

fof(f48233,plain,
    spl0_827,
    inference(avatar_split_clause,[],[f835,f48231]) ).

fof(f48231,plain,
    ( spl0_827
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f835,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).

fof(f48229,plain,
    spl0_826,
    inference(avatar_split_clause,[],[f614,f48227]) ).

fof(f48227,plain,
    ( spl0_826
  <=> ! [X3,X19,X13,X5,X2] :
        ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
        | c_Fun_Oinj__on(X19,c_Set_Oinsert(X3,X5,X2),X2,X13)
        | c_in(hAPP(X19,X3),c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X13),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f614,axiom,
    ! [X2,X3,X19,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
      | c_Fun_Oinj__on(X19,c_Set_Oinsert(X3,X5,X2),X2,X13)
      | c_in(hAPP(X19,X3),c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X13),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

fof(f48225,plain,
    spl0_825,
    inference(avatar_split_clause,[],[f613,f48223]) ).

fof(f48223,plain,
    ( spl0_825
  <=> ! [X19,X13,X8,X5,X2,X7] :
        ( ~ c_in(X7,X5,X13)
        | c_Set_Oimage(c_Fun_Ofun__upd(X19,X7,X8,X13,X2),X5,X13,X2) = c_Set_Oinsert(X8,c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).

fof(f613,axiom,
    ! [X2,X8,X19,X7,X5,X13] :
      ( ~ c_in(X7,X5,X13)
      | c_Set_Oimage(c_Fun_Ofun__upd(X19,X7,X8,X13,X2),X5,X13,X2) = c_Set_Oinsert(X8,c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).

fof(f48221,plain,
    spl0_824,
    inference(avatar_split_clause,[],[f78,f48219]) ).

fof(f48219,plain,
    ( spl0_824
  <=> ! [X5,X7,X6,X2] :
        ( ~ c_in(X7,X5,X2)
        | c_in(X7,X6,X2)
        | c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f78,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ c_in(X7,X5,X2)
      | c_in(X7,X6,X2)
      | c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).

fof(f48217,plain,
    spl0_823,
    inference(avatar_split_clause,[],[f77,f48215]) ).

fof(f48215,plain,
    ( spl0_823
  <=> ! [X5,X7,X6,X2] :
        ( ~ c_in(X7,X5,X2)
        | c_in(X7,X6,X2)
        | ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).

fof(f77,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ c_in(X7,X5,X2)
      | c_in(X7,X6,X2)
      | ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).

fof(f47277,plain,
    spl0_822,
    inference(avatar_split_clause,[],[f1347,f47275]) ).

fof(f47275,plain,
    ( spl0_822
  <=> ! [X7,X8,X5,X2] :
        ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X5,X2),tc_nat)
        | ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_in(X7,X5,X2)
        | ~ c_in(X8,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).

fof(f1347,plain,
    ! [X2,X8,X7,X5] :
      ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X5,X2),tc_nat)
      | ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2)
      | ~ c_in(X8,X5,X2) ),
    inference(forward_demodulation,[],[f855,f100]) ).

fof(f100,axiom,
    ! [X2,X3,X6,X5] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

fof(f855,axiom,
    ! [X2,X8,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2)
      | ~ c_in(X8,X5,X2)
      | c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X5,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff2__less_0) ).

fof(f47273,plain,
    spl0_821,
    inference(avatar_split_clause,[],[f830,f47271]) ).

fof(f47271,plain,
    ( spl0_821
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X21,X20,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f830,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X21,X20,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).

fof(f47269,plain,
    spl0_820,
    inference(avatar_split_clause,[],[f829,f47267]) ).

fof(f47267,plain,
    ( spl0_820
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X21,X20,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f829,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X21,X20,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).

fof(f47265,plain,
    ( spl0_819
    | ~ spl0_120
    | ~ spl0_809 ),
    inference(avatar_split_clause,[],[f47140,f46705,f1896,f47263]) ).

fof(f47263,plain,
    ( spl0_819
  <=> ! [X4,X0,X3,X2,X1] : c_in(v_pn,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_U,X2),X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f1896,plain,
    ( spl0_120
  <=> ! [X2,X7,X46] :
        ( ~ hBOOL(hAPP(X46,X7))
        | c_in(X7,X46,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f46705,plain,
    ( spl0_809
  <=> ! [X2,X0,X1,X3] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_U,X2),X3),v_pn)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).

fof(f47140,plain,
    ( ! [X2,X3,X0,X1,X4] : c_in(v_pn,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_U,X2),X3),X4)
    | ~ spl0_120
    | ~ spl0_809 ),
    inference(resolution,[],[f46706,f1897]) ).

fof(f1897,plain,
    ( ! [X2,X46,X7] :
        ( ~ hBOOL(hAPP(X46,X7))
        | c_in(X7,X46,X2) )
    | ~ spl0_120 ),
    inference(avatar_component_clause,[],[f1896]) ).

fof(f46706,plain,
    ( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_U,X2),X3),v_pn))
    | ~ spl0_809 ),
    inference(avatar_component_clause,[],[f46705]) ).

fof(f47261,plain,
    spl0_818,
    inference(avatar_split_clause,[],[f828,f47259]) ).

fof(f47259,plain,
    ( spl0_818
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f828,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).

fof(f47257,plain,
    spl0_817,
    inference(avatar_split_clause,[],[f827,f47255]) ).

fof(f47255,plain,
    ( spl0_817
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f827,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).

fof(f47253,plain,
    spl0_816,
    inference(avatar_split_clause,[],[f200,f47251]) ).

fof(f47251,plain,
    ( spl0_816
  <=> ! [X5,X19,X13,X6,X2] :
        ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
        | c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2,X13) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f200,axiom,
    ! [X2,X19,X6,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
      | c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2,X13) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).

fof(f47249,plain,
    spl0_815,
    inference(avatar_split_clause,[],[f137,f47247]) ).

fof(f47247,plain,
    ( spl0_815
  <=> ! [X5,X19,X13,X6,X2] :
        ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
        | c_Set_Oimage(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2,X13) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).

fof(f137,axiom,
    ! [X2,X19,X6,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
      | c_Set_Oimage(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2,X13) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).

fof(f47245,plain,
    spl0_814,
    inference(avatar_split_clause,[],[f92,f47243]) ).

fof(f47243,plain,
    ( spl0_814
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f92,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).

fof(f47241,plain,
    spl0_813,
    inference(avatar_split_clause,[],[f91,f47239]) ).

fof(f47239,plain,
    ( spl0_813
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).

fof(f91,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).

fof(f47237,plain,
    spl0_812,
    inference(avatar_split_clause,[],[f90,f47235]) ).

fof(f47235,plain,
    ( spl0_812
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X21,X20,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).

fof(f90,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X21,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).

fof(f47233,plain,
    spl0_811,
    inference(avatar_split_clause,[],[f89,f47231]) ).

fof(f47231,plain,
    ( spl0_811
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X21,X20,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f89,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X21,X20,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).

fof(f47150,plain,
    spl0_810,
    inference(avatar_split_clause,[],[f832,f47148]) ).

fof(f47148,plain,
    ( spl0_810
  <=> ! [X17,X20,X0,X21,X1] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat) = X0
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).

fof(f832,axiom,
    ! [X21,X0,X1,X17,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X17,tc_nat),X1,tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).

fof(f46707,plain,
    ( spl0_809
    | ~ spl0_121
    | ~ spl0_797 ),
    inference(avatar_split_clause,[],[f46541,f45953,f1900,f46705]) ).

fof(f1900,plain,
    ( spl0_121
  <=> ! [X2,X7,X46] :
        ( ~ c_in(X7,X46,X2)
        | hBOOL(hAPP(X46,X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f45953,plain,
    ( spl0_797
  <=> ! [X2,X0,X1,X3] : c_in(v_pn,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_U,X2),X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).

fof(f46541,plain,
    ( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_U,X2),X3),v_pn))
    | ~ spl0_121
    | ~ spl0_797 ),
    inference(resolution,[],[f45954,f1901]) ).

fof(f1901,plain,
    ( ! [X2,X46,X7] :
        ( ~ c_in(X7,X46,X2)
        | hBOOL(hAPP(X46,X7)) )
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f1900]) ).

fof(f45954,plain,
    ( ! [X2,X3,X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_U,X2),X3),X3)
    | ~ spl0_797 ),
    inference(avatar_component_clause,[],[f45953]) ).

fof(f46654,plain,
    spl0_808,
    inference(avatar_split_clause,[],[f1346,f46652]) ).

fof(f46652,plain,
    ( spl0_808
  <=> ! [X48,X19,X2,X1] :
        ( ~ c_lessequals(hAPP(X19,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X19,X2)),hAPP(X19,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X19,X2),tc_nat)),X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_lessequals(X1,X48,tc_nat)
        | c_lessequals(hAPP(X19,X1),hAPP(X19,X48),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).

fof(f1346,plain,
    ! [X2,X48,X1,X19] :
      ( ~ c_lessequals(hAPP(X19,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X19,X2)),hAPP(X19,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X19,X2),tc_nat)),X2)
      | ~ class_Orderings_Oorder(X2)
      | ~ c_lessequals(X1,X48,tc_nat)
      | c_lessequals(hAPP(X19,X1),hAPP(X19,X48),X2) ),
    inference(forward_demodulation,[],[f1241,f126]) ).

fof(f126,axiom,
    ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

fof(f1241,plain,
    ! [X2,X48,X1,X19] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_lessequals(X1,X48,tc_nat)
      | c_lessequals(hAPP(X19,X1),hAPP(X19,X48),X2)
      | ~ c_lessequals(hAPP(X19,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X19,X2)),hAPP(X19,c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X19,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2) ),
    inference(definition_unfolding,[],[f934,f61]) ).

fof(f61,axiom,
    ! [X1] : c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

fof(f934,axiom,
    ! [X2,X48,X1,X19] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_lessequals(X1,X48,tc_nat)
      | c_lessequals(hAPP(X19,X1),hAPP(X19,X48),X2)
      | ~ c_lessequals(hAPP(X19,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X19,X2)),hAPP(X19,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X19,X2))),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__Suc__mono__le_0) ).

fof(f46650,plain,
    spl0_807,
    inference(avatar_split_clause,[],[f938,f46648]) ).

fof(f46648,plain,
    ( spl0_807
  <=> ! [X24,X41,X19,X13,X3,X2] :
        ( ~ c_in(X3,X24,X2)
        | c_in(hAPP(X41,X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X19,tc_fun(X13,tc_bool)),X13)
        | ~ c_lessequals(c_Set_Oimage(X41,X24,X2,X13),hAPP(X19,c_Set_Oimage(X41,X24,X2,X13)),tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f938,axiom,
    ! [X2,X3,X41,X19,X24,X13] :
      ( ~ c_in(X3,X24,X2)
      | c_in(hAPP(X41,X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X19,tc_fun(X13,tc_bool)),X13)
      | ~ c_lessequals(c_Set_Oimage(X41,X24,X2,X13),hAPP(X19,c_Set_Oimage(X41,X24,X2,X13)),tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct__image_0) ).

fof(f46646,plain,
    spl0_806,
    inference(avatar_split_clause,[],[f737,f46644]) ).

fof(f46644,plain,
    ( spl0_806
  <=> ! [X6,X2,X5] :
        ( ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2)
        | c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).

fof(f737,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2)
      | c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset__Int_0) ).

fof(f46642,plain,
    spl0_805,
    inference(avatar_split_clause,[],[f735,f46640]) ).

fof(f46640,plain,
    ( spl0_805
  <=> ! [X5,X7,X6,X2] :
        ( ~ c_in(X7,X5,X2)
        | c_lessequals(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f735,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ c_in(X7,X5,X2)
      | c_lessequals(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

fof(f46638,plain,
    spl0_804,
    inference(avatar_split_clause,[],[f733,f46636]) ).

fof(f46636,plain,
    ( spl0_804
  <=> ! [X5,X7,X6,X2] :
        ( ~ c_in(X7,X5,X2)
        | ~ c_lessequals(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
        | c_lessequals(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).

fof(f733,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ c_in(X7,X5,X2)
      | ~ c_lessequals(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool))
      | c_lessequals(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

fof(f46560,plain,
    spl0_803,
    inference(avatar_split_clause,[],[f1305,f46558]) ).

fof(f46558,plain,
    ( spl0_803
  <=> ! [X2,X5,X7] :
        ( c_Finite__Set_Ocard(X5,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),tc_nat)
        | ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_in(X7,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f1305,plain,
    ! [X2,X7,X5] :
      ( c_Finite__Set_Ocard(X5,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),tc_nat)
      | ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2) ),
    inference(forward_demodulation,[],[f1215,f126]) ).

fof(f1215,plain,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2)
      | c_Finite__Set_Ocard(X5,X2) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f927,f61]) ).

fof(f927,axiom,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2)
      | c_Finite__Set_Ocard(X5,X2) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__Diff1_0) ).

fof(f46556,plain,
    spl0_802,
    inference(avatar_split_clause,[],[f738,f46554]) ).

fof(f46554,plain,
    ( spl0_802
  <=> ! [X2,X5,X7] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_in(X7,X5,X2)
        | c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X5,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f738,axiom,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2)
      | c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X5,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton_0) ).

fof(f46326,plain,
    spl0_801,
    inference(avatar_split_clause,[],[f1263,f46324]) ).

fof(f46324,plain,
    ( spl0_801
  <=> ! [X2,X5,X7] :
        ( c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),tc_nat)
        | ~ c_Finite__Set_Ofinite(X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f1263,plain,
    ! [X2,X7,X5] :
      ( c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),tc_nat)
      | ~ c_Finite__Set_Ofinite(X5,X2) ),
    inference(forward_demodulation,[],[f1163,f126]) ).

fof(f1163,plain,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f889,f61]) ).

fof(f889,axiom,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert_0) ).

fof(f46322,plain,
    spl0_800,
    inference(avatar_split_clause,[],[f1262,f46320]) ).

fof(f46320,plain,
    ( spl0_800
  <=> ! [X5,X15,X6,X2] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X15,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f1262,plain,
    ! [X2,X6,X15,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X15,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    inference(forward_demodulation,[],[f343,f670]) ).

fof(f670,axiom,
    ! [X2,X6,X15,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

fof(f343,axiom,
    ! [X2,X6,X15,X5] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

fof(f46318,plain,
    spl0_799,
    inference(avatar_split_clause,[],[f822,f46316]) ).

fof(f46316,plain,
    ( spl0_799
  <=> ! [X41,X19,X13,X2,X7] :
        ( c_Set_Oimage(X19,X7,X2,X13) = c_Set_Oimage(X41,X7,X2,X13)
        | hAPP(X19,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X7,X19,X41,X2,X13)) != hAPP(X41,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X7,X19,X41,X2,X13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f822,axiom,
    ! [X2,X41,X19,X7,X13] :
      ( c_Set_Oimage(X19,X7,X2,X13) = c_Set_Oimage(X41,X7,X2,X13)
      | hAPP(X19,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X7,X19,X41,X2,X13)) != hAPP(X41,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X7,X19,X41,X2,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_1) ).

fof(f46314,plain,
    spl0_798,
    inference(avatar_split_clause,[],[f327,f46312]) ).

fof(f46312,plain,
    ( spl0_798
  <=> ! [X5,X15,X6,X2] : c_Lattices_Olower__semilattice__class_Oinf(X15,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X15,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X15,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f327,axiom,
    ! [X2,X6,X15,X5] : c_Lattices_Olower__semilattice__class_Oinf(X15,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X15,X5,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X15,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

fof(f45955,plain,
    ( spl0_797
    | ~ spl0_174
    | ~ spl0_796 ),
    inference(avatar_split_clause,[],[f45290,f44814,f2138,f45953]) ).

fof(f2138,plain,
    ( spl0_174
  <=> ! [X6,X2,X3] : c_lessequals(X6,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f44814,plain,
    ( spl0_796
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(c_Set_Oinsert(X0,v_U,X1),X3,tc_fun(X2,tc_bool))
        | c_in(v_pn,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f45290,plain,
    ( ! [X2,X3,X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_U,X2),X3),X3)
    | ~ spl0_174
    | ~ spl0_796 ),
    inference(resolution,[],[f44815,f2139]) ).

fof(f2139,plain,
    ( ! [X2,X3,X6] : c_lessequals(X6,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool))
    | ~ spl0_174 ),
    inference(avatar_component_clause,[],[f2138]) ).

fof(f44815,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_Set_Oinsert(X0,v_U,X1),X3,tc_fun(X2,tc_bool))
        | c_in(v_pn,X3,X2) )
    | ~ spl0_796 ),
    inference(avatar_component_clause,[],[f44814]) ).

fof(f44816,plain,
    ( spl0_796
    | ~ spl0_333
    | ~ spl0_503 ),
    inference(avatar_split_clause,[],[f9274,f9219,f3895,f44814]) ).

fof(f3895,plain,
    ( spl0_333
  <=> ! [X5,X7,X6,X2] :
        ( c_in(X7,X6,X2)
        | ~ c_lessequals(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f9219,plain,
    ( spl0_503
  <=> ! [X2,X0,X1] : c_Set_Oinsert(X0,v_U,X1) = c_Set_Oinsert(v_pn,c_Set_Oinsert(X0,v_U,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f9274,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_Set_Oinsert(X0,v_U,X1),X3,tc_fun(X2,tc_bool))
        | c_in(v_pn,X3,X2) )
    | ~ spl0_333
    | ~ spl0_503 ),
    inference(superposition,[],[f3896,f9220]) ).

fof(f9220,plain,
    ( ! [X2,X0,X1] : c_Set_Oinsert(X0,v_U,X1) = c_Set_Oinsert(v_pn,c_Set_Oinsert(X0,v_U,X1),X2)
    | ~ spl0_503 ),
    inference(avatar_component_clause,[],[f9219]) ).

fof(f3896,plain,
    ( ! [X2,X6,X7,X5] :
        ( ~ c_lessequals(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool))
        | c_in(X7,X6,X2) )
    | ~ spl0_333 ),
    inference(avatar_component_clause,[],[f3895]) ).

fof(f35558,plain,
    ( spl0_795
    | ~ spl0_6
    | ~ spl0_676 ),
    inference(avatar_split_clause,[],[f14178,f13132,f1375,f35555]) ).

fof(f35555,plain,
    ( spl0_795
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(v_pn) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).

fof(f1375,plain,
    ( spl0_6
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f13132,plain,
    ( spl0_676
  <=> ! [X1] : v_pn = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f14178,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(v_pn)
    | ~ spl0_6
    | ~ spl0_676 ),
    inference(superposition,[],[f1377,f13133]) ).

fof(f13133,plain,
    ( ! [X1] : v_pn = X1
    | ~ spl0_676 ),
    inference(avatar_component_clause,[],[f13132]) ).

fof(f1377,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f1375]) ).

fof(f35553,plain,
    spl0_794,
    inference(avatar_split_clause,[],[f677,f35551]) ).

fof(f35551,plain,
    ( spl0_794
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).

fof(f677,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

fof(f35549,plain,
    spl0_793,
    inference(avatar_split_clause,[],[f507,f35547]) ).

fof(f35547,plain,
    ( spl0_793
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
        | ~ c_lessequals(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).

fof(f507,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
      | ~ c_lessequals(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

fof(f35545,plain,
    spl0_792,
    inference(avatar_split_clause,[],[f506,f35543]) ).

fof(f35543,plain,
    ( spl0_792
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_lessequals(X10,X16,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f506,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_lessequals(X10,X16,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

fof(f35541,plain,
    spl0_791,
    inference(avatar_split_clause,[],[f359,f35539]) ).

fof(f35539,plain,
    ( spl0_791
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X2)
        | ~ c_lessequals(X3,X9,X2)
        | ~ c_lessequals(X10,X16,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).

fof(f359,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X2)
      | ~ c_lessequals(X3,X9,X2)
      | ~ c_lessequals(X10,X16,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

fof(f35537,plain,
    spl0_790,
    inference(avatar_split_clause,[],[f358,f35535]) ).

fof(f35535,plain,
    ( spl0_790
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X2)
        | ~ c_lessequals(X3,X9,X2)
        | ~ c_lessequals(X10,X16,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).

fof(f358,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X2)
      | ~ c_lessequals(X3,X9,X2)
      | ~ c_lessequals(X10,X16,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).

fof(f35533,plain,
    spl0_789,
    inference(avatar_split_clause,[],[f85,f35531]) ).

fof(f35531,plain,
    ( spl0_789
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f85,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

fof(f35528,plain,
    spl0_788,
    inference(avatar_split_clause,[],[f615,f35526]) ).

fof(f35526,plain,
    ( spl0_788
  <=> ! [X3,X19,X13,X5,X2] :
        ( ~ c_Fun_Oinj__on(X19,c_Set_Oinsert(X3,X5,X2),X2,X13)
        | ~ c_in(hAPP(X19,X3),c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X13),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f615,axiom,
    ! [X2,X3,X19,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,c_Set_Oinsert(X3,X5,X2),X2,X13)
      | ~ c_in(hAPP(X19,X3),c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X13),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

fof(f35474,plain,
    ( spl0_676
    | spl0_787
    | ~ spl0_401
    | ~ spl0_679 ),
    inference(avatar_split_clause,[],[f22662,f22104,f4929,f35472,f13132]) ).

fof(f35472,plain,
    ( spl0_787
  <=> ! [X0,X1] :
        ( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
        | hBOOL(hAPP(X0,v_pn)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f4929,plain,
    ( spl0_401
  <=> ! [X7,X8,X5,X2] :
        ( X7 = X8
        | hBOOL(hAPP(X5,X7))
        | ~ hBOOL(hAPP(c_Set_Oinsert(X8,X5,X2),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f22104,plain,
    ( spl0_679
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
        | hBOOL(hAPP(c_Set_Oinsert(X2,X0,X1),v_pn)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f22662,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
        | hBOOL(hAPP(X0,v_pn))
        | v_pn = X2 )
    | ~ spl0_401
    | ~ spl0_679 ),
    inference(resolution,[],[f22105,f4930]) ).

fof(f4930,plain,
    ( ! [X2,X8,X7,X5] :
        ( ~ hBOOL(hAPP(c_Set_Oinsert(X8,X5,X2),X7))
        | hBOOL(hAPP(X5,X7))
        | X7 = X8 )
    | ~ spl0_401 ),
    inference(avatar_component_clause,[],[f4929]) ).

fof(f22105,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(hAPP(c_Set_Oinsert(X2,X0,X1),v_pn))
        | ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool)) )
    | ~ spl0_679 ),
    inference(avatar_component_clause,[],[f22104]) ).

fof(f35052,plain,
    ( spl0_786
    | ~ spl0_120
    | ~ spl0_679 ),
    inference(avatar_split_clause,[],[f22661,f22104,f1896,f35050]) ).

fof(f35050,plain,
    ( spl0_786
  <=> ! [X2,X0,X1,X3] :
        ( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
        | c_in(v_pn,c_Set_Oinsert(X2,X0,X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).

fof(f22661,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
        | c_in(v_pn,c_Set_Oinsert(X2,X0,X1),X3) )
    | ~ spl0_120
    | ~ spl0_679 ),
    inference(resolution,[],[f22105,f1897]) ).

fof(f27116,plain,
    ( spl0_785
    | ~ spl0_5
    | ~ spl0_676 ),
    inference(avatar_split_clause,[],[f14177,f13132,f1370,f27113]) ).

fof(f27113,plain,
    ( spl0_785
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(v_pn) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f1370,plain,
    ( spl0_5
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f14177,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(v_pn)
    | ~ spl0_5
    | ~ spl0_676 ),
    inference(superposition,[],[f1372,f13133]) ).

fof(f1372,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f1370]) ).

fof(f27035,plain,
    spl0_784,
    inference(avatar_split_clause,[],[f895,f27033]) ).

fof(f27033,plain,
    ( spl0_784
  <=> ! [X5,X19,X13,X6,X2] : c_lessequals(c_Set_Oimage(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X13,tc_bool)),X13,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X19,X5,X13,X2),c_Set_Oimage(X19,X6,X13,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f895,axiom,
    ! [X2,X19,X6,X5,X13] : c_lessequals(c_Set_Oimage(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X13,tc_bool)),X13,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X19,X5,X13,X2),c_Set_Oimage(X19,X6,X13,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

fof(f27031,plain,
    spl0_783,
    inference(avatar_split_clause,[],[f892,f27029]) ).

fof(f27029,plain,
    ( spl0_783
  <=> ! [X6,X19,X13,X5,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X19,X5,X13,X2),c_Set_Oimage(X19,X6,X13,X2),tc_fun(X2,tc_bool)),c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X13,tc_bool)),X13,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f892,axiom,
    ! [X2,X19,X6,X5,X13] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X19,X5,X13,X2),c_Set_Oimage(X19,X6,X13,X2),tc_fun(X2,tc_bool)),c_Set_Oimage(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X13,tc_bool)),X13,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

fof(f27027,plain,
    spl0_782,
    inference(avatar_split_clause,[],[f784,f27025]) ).

fof(f27025,plain,
    ( spl0_782
  <=> ! [X5,X19,X13,X6,X2] :
        ( c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
        | ~ c_lessequals(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f784,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
      | ~ c_lessequals(c_Set_Oimage(X19,X5,X2,X13),c_Set_Oimage(X19,X6,X2,X13),tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).

fof(f27023,plain,
    spl0_781,
    inference(avatar_split_clause,[],[f770,f27021]) ).

fof(f27021,plain,
    ( spl0_781
  <=> ! [X5,X15,X43,X6,X2] :
        ( ~ c_lessequals(X5,X15,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X43,X6,tc_fun(X2,tc_bool))
        | c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X15,X43,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f770,axiom,
    ! [X2,X6,X15,X5,X43] :
      ( ~ c_lessequals(X5,X15,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X43,X6,tc_fun(X2,tc_bool))
      | c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X15,X43,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

fof(f27019,plain,
    spl0_780,
    inference(avatar_split_clause,[],[f758,f27017]) ).

fof(f27017,plain,
    ( spl0_780
  <=> ! [X15,X6,X43,X5,X2] :
        ( ~ c_lessequals(X5,X15,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X6,X43,tc_fun(X2,tc_bool))
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X15,X43,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).

fof(f758,axiom,
    ! [X2,X6,X15,X5,X43] :
      ( ~ c_lessequals(X5,X15,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X43,tc_fun(X2,tc_bool))
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X15,X43,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

fof(f27015,plain,
    spl0_779,
    inference(avatar_split_clause,[],[f373,f27013]) ).

fof(f373,axiom,
    ! [X2,X19,X6,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
      | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X2,X13),tc_fun(X13,tc_bool))
      | c_lessequals(c_Set_Ovimage(X19,X6,X2,X13),X5,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).

fof(f27011,plain,
    ( spl0_778
    | ~ spl0_197
    | ~ spl0_677 ),
    inference(avatar_split_clause,[],[f17113,f13135,f2364,f27009]) ).

fof(f27009,plain,
    ( spl0_778
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),v_U,tc_fun(X0,tc_bool))
        | ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f2364,plain,
    ( spl0_197
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_HOL_Oord__class_Oless(X7,X8,X2)
        | c_lessequals(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f13135,plain,
    ( spl0_677
  <=> ! [X0] : ~ c_lessequals(v_U,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f17113,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),v_U,tc_fun(X0,tc_bool))
        | ~ class_Orderings_Olinorder(tc_fun(X0,tc_bool)) )
    | ~ spl0_197
    | ~ spl0_677 ),
    inference(resolution,[],[f13136,f2365]) ).

fof(f2365,plain,
    ( ! [X2,X8,X7] :
        ( c_lessequals(X8,X7,X2)
        | c_HOL_Oord__class_Oless(X7,X8,X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f2364]) ).

fof(f13136,plain,
    ( ! [X0] : ~ c_lessequals(v_U,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
    | ~ spl0_677 ),
    inference(avatar_component_clause,[],[f13135]) ).

fof(f26347,plain,
    spl0_777,
    inference(avatar_split_clause,[],[f1268,f26345]) ).

fof(f26345,plain,
    ( spl0_777
  <=> ! [X4,X0,X21] :
        ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat),X0,tc_nat)
        | ~ c_lessequals(X4,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).

fof(f1268,plain,
    ! [X21,X0,X4] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat),X0,tc_nat)
      | ~ c_lessequals(X4,X21,tc_nat) ),
    inference(forward_demodulation,[],[f1182,f126]) ).

fof(f1182,plain,
    ! [X21,X0,X4] :
      ( ~ c_lessequals(X4,X21,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f948,f61,f61]) ).

fof(f948,axiom,
    ! [X21,X0,X4] :
      ( ~ c_lessequals(X4,X21,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat)),X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X21),c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).

fof(f26343,plain,
    spl0_776,
    inference(avatar_split_clause,[],[f1267,f26341]) ).

fof(f26341,plain,
    ( spl0_776
  <=> ! [X4,X21,X0] :
        ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X4,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).

fof(f1267,plain,
    ! [X21,X0,X4] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat),tc_nat)
      | ~ c_lessequals(X4,X21,tc_nat) ),
    inference(forward_demodulation,[],[f1181,f126]) ).

fof(f1181,plain,
    ! [X21,X0,X4] :
      ( ~ c_lessequals(X4,X21,tc_nat)
      | c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f949,f61,f61]) ).

fof(f949,axiom,
    ! [X21,X0,X4] :
      ( ~ c_lessequals(X4,X21,tc_nat)
      | c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),c_Suc(X21),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).

fof(f26326,plain,
    spl0_775,
    inference(avatar_split_clause,[],[f1213,f26324]) ).

fof(f26324,plain,
    ( spl0_775
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).

fof(f1213,plain,
    ! [X0,X1] :
      ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f632,f61,f61,f61]) ).

fof(f632,axiom,
    ! [X0,X1] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) = X1
      | c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) = c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).

fof(f26322,plain,
    spl0_774,
    inference(avatar_split_clause,[],[f873,f26320]) ).

fof(f26320,plain,
    ( spl0_774
  <=> ! [X2,X5,X7] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
        | c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = X5
        | ~ c_lessequals(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f873,axiom,
    ! [X2,X7,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
      | c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = X5
      | ~ c_lessequals(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

fof(f26318,plain,
    spl0_773,
    inference(avatar_split_clause,[],[f644,f26316]) ).

fof(f26316,plain,
    ( spl0_773
  <=> ! [X3,X16,X10,X9,X2] :
        ( X3 = X10
        | X9 = X10
        | c_Set_Oinsert(X3,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X10,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).

fof(f644,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( X3 = X10
      | X9 = X10
      | c_Set_Oinsert(X3,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X10,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

fof(f26314,plain,
    spl0_772,
    inference(avatar_split_clause,[],[f643,f26312]) ).

fof(f26312,plain,
    ( spl0_772
  <=> ! [X2,X3,X10,X9,X16] :
        ( X9 = X16
        | X3 = X16
        | c_Set_Oinsert(X3,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X10,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).

fof(f643,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( X9 = X16
      | X3 = X16
      | c_Set_Oinsert(X3,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X10,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

fof(f26310,plain,
    spl0_771,
    inference(avatar_split_clause,[],[f297,f26308]) ).

fof(f26308,plain,
    ( spl0_771
  <=> ! [X3,X10,X9,X16] :
        ( X3 = X9
        | X10 = X16
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X10,tc_nat),c_HOL_Otimes__class_Otimes(X9,X16,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,tc_nat),c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).

fof(f297,axiom,
    ! [X3,X10,X9,X16] :
      ( X3 = X9
      | X10 = X16
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X10,tc_nat),c_HOL_Otimes__class_Otimes(X9,X16,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,tc_nat),c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).

fof(f26306,plain,
    spl0_770,
    inference(avatar_split_clause,[],[f101,f26304]) ).

fof(f26304,plain,
    ( spl0_770
  <=> ! [X5,X3,X6,X2] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f101,axiom,
    ! [X2,X3,X6,X5] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

fof(f26302,plain,
    spl0_769,
    inference(avatar_split_clause,[],[f100,f26300]) ).

fof(f26300,plain,
    ( spl0_769
  <=> ! [X5,X3,X6,X2] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f26101,plain,
    spl0_768,
    inference(avatar_split_clause,[],[f954,f26099]) ).

fof(f26099,plain,
    ( spl0_768
  <=> ! [X6,X19,X13,X5,X2] :
        ( ~ c_Finite__Set_Ofinite(X6,X13)
        | ~ c_Fun_Oinj__on(X19,X5,X2,X13)
        | c_lessequals(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X13),tc_nat)
        | ~ c_lessequals(c_Set_Oimage(X19,X5,X2,X13),X6,tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).

fof(f954,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( ~ c_Finite__Set_Ofinite(X6,X13)
      | ~ c_Fun_Oinj__on(X19,X5,X2,X13)
      | c_lessequals(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X13),tc_nat)
      | ~ c_lessequals(c_Set_Oimage(X19,X5,X2,X13),X6,tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).

fof(f26097,plain,
    spl0_767,
    inference(avatar_split_clause,[],[f953,f26095]) ).

fof(f26095,plain,
    ( spl0_767
  <=> ! [X6,X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | ~ c_lessequals(X6,X5,tc_fun(X2,tc_bool))
        | c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).

fof(f953,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | ~ c_lessequals(X6,X5,tc_fun(X2,tc_bool))
      | c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset_0) ).

fof(f26093,plain,
    spl0_766,
    inference(avatar_split_clause,[],[f854,f26091]) ).

fof(f26091,plain,
    ( spl0_766
  <=> ! [X2,X5,X7] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_in(X7,X5,X2)
        | c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X5,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).

fof(f854,axiom,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2)
      | c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X5,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).

fof(f26089,plain,
    spl0_765,
    inference(avatar_split_clause,[],[f786,f26087]) ).

fof(f26087,plain,
    ( spl0_765
  <=> ! [X19,X13,X5,X2,X46] :
        ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
        | ~ c_lessequals(X46,X5,tc_fun(X2,tc_bool))
        | c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X5,X19,X2,X13),c_Set_Oimage(X19,X46,X2,X13),X13,X2) = X46 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).

fof(f786,axiom,
    ! [X2,X46,X19,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
      | ~ c_lessequals(X46,X5,tc_fun(X2,tc_bool))
      | c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X5,X19,X2,X13),c_Set_Oimage(X19,X46,X2,X13),X13,X2) = X46 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).

fof(f26085,plain,
    spl0_764,
    inference(avatar_split_clause,[],[f264,f26083]) ).

fof(f26083,plain,
    ( spl0_764
  <=> ! [X16,X10,X9,X13,X0,X3,X2] :
        ( X3 = X10
        | c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X3,X9,X2,X13),X10,X16,X2,X13) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X10,X16,X2,X13),X3,X9,X2,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).

fof(f264,axiom,
    ! [X2,X3,X10,X0,X9,X16,X13] :
      ( X3 = X10
      | c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X3,X9,X2,X13),X10,X16,X2,X13) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X0,X10,X16,X2,X13),X3,X9,X2,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

fof(f26081,plain,
    spl0_763,
    inference(avatar_split_clause,[],[f225,f26079]) ).

fof(f26079,plain,
    ( spl0_763
  <=> ! [X19,X13,X5,X2] :
        ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
        | c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X19,X2,X13),c_Set_Oimage(X19,X5,X2,X13),X13,X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).

fof(f225,axiom,
    ! [X2,X19,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
      | c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X19,X2,X13),c_Set_Oimage(X19,X5,X2,X13),X13,X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).

fof(f26075,plain,
    spl0_762,
    inference(avatar_split_clause,[],[f179,f26073]) ).

fof(f26073,plain,
    ( spl0_762
  <=> ! [X18,X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Osemiring(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X18,X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X18,X2),X10,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X9,X2),X18,X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f179,axiom,
    ! [X2,X3,X10,X18,X9] :
      ( ~ class_Ring__and__Field_Osemiring(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X18,X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X18,X2),X10,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X9,X2),X18,X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

fof(f25585,plain,
    ( ~ spl0_50
    | ~ spl0_761
    | ~ spl0_375
    | ~ spl0_702 ),
    inference(avatar_split_clause,[],[f23714,f23407,f4820,f25582,f1595]) ).

fof(f25582,plain,
    ( spl0_761
  <=> c_HOL_Oord__class_Oless(v_U,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_fun(tc_Com_Opname,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f4820,plain,
    ( spl0_375
  <=> ! [X41,X19,X13,X2] :
        ( ~ class_HOL_Oord(X13)
        | ~ c_HOL_Oord__class_Oless(X19,X41,tc_fun(X2,X13))
        | ~ c_lessequals(X41,X19,tc_fun(X2,X13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f23407,plain,
    ( spl0_702
  <=> c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_fun(tc_Com_Opname,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f23714,plain,
    ( ~ c_HOL_Oord__class_Oless(v_U,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_fun(tc_Com_Opname,tc_bool))
    | ~ class_HOL_Oord(tc_bool)
    | ~ spl0_375
    | ~ spl0_702 ),
    inference(resolution,[],[f23409,f4821]) ).

fof(f4821,plain,
    ( ! [X2,X41,X19,X13] :
        ( ~ c_lessequals(X41,X19,tc_fun(X2,X13))
        | ~ c_HOL_Oord__class_Oless(X19,X41,tc_fun(X2,X13))
        | ~ class_HOL_Oord(X13) )
    | ~ spl0_375 ),
    inference(avatar_component_clause,[],[f4820]) ).

fof(f23409,plain,
    ( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_702 ),
    inference(avatar_component_clause,[],[f23407]) ).

fof(f25557,plain,
    spl0_760,
    inference(avatar_split_clause,[],[f1269,f25555]) ).

fof(f25555,plain,
    ( spl0_760
  <=> ! [X17,X20,X0,X21] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X21,c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),tc_nat),X17,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X21,X20,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).

fof(f1269,plain,
    ! [X21,X0,X17,X20] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X21,c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),tc_nat),X17,tc_nat),X0,tc_nat)
      | ~ c_lessequals(X21,X20,tc_nat) ),
    inference(forward_demodulation,[],[f834,f178]) ).

fof(f178,axiom,
    ! [X21,X4,X17,X20] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X20,X21,tc_nat),X17,tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).

fof(f834,axiom,
    ! [X21,X0,X17,X20] :
      ( ~ c_lessequals(X21,X20,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),X0,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X17,tc_nat),X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_1) ).

fof(f25553,plain,
    spl0_759,
    inference(avatar_split_clause,[],[f943,f25551]) ).

fof(f25551,plain,
    ( spl0_759
  <=> ! [X2,X5,X19] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_Fun_Oinj__on(X19,X5,X2,X2)
        | c_Set_Oimage(X19,X5,X2,X2) = X5
        | ~ c_lessequals(c_Set_Oimage(X19,X5,X2,X2),X5,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).

fof(f943,axiom,
    ! [X2,X19,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_Fun_Oinj__on(X19,X5,X2,X2)
      | c_Set_Oimage(X19,X5,X2,X2) = X5
      | ~ c_lessequals(c_Set_Oimage(X19,X5,X2,X2),X5,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).

fof(f25549,plain,
    spl0_758,
    inference(avatar_split_clause,[],[f941,f25547]) ).

fof(f941,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
      | c_Set_Oimage(X19,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X5,X6,X19,X13,X2),X13,X2) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_2) ).

fof(f25545,plain,
    spl0_757,
    inference(avatar_split_clause,[],[f871,f25543]) ).

fof(f25543,plain,
    ( spl0_757
  <=> ! [X2,X5,X7] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_in(X7,X5,X2)
        | c_Finite__Set_Ocard(X5,X2) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f871,axiom,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_in(X7,X5,X2)
      | c_Finite__Set_Ocard(X5,X2) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).

fof(f25541,plain,
    spl0_756,
    inference(avatar_split_clause,[],[f757,f25539]) ).

fof(f25539,plain,
    ( spl0_756
  <=> ! [X5,X15,X6,X2] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
        | c_HOL_Ominus__class_Ominus(X6,c_HOL_Ominus__class_Ominus(X15,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).

fof(f757,axiom,
    ! [X2,X6,X15,X5] :
      ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
      | c_HOL_Ominus__class_Ominus(X6,c_HOL_Ominus__class_Ominus(X15,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

fof(f25537,plain,
    spl0_755,
    inference(avatar_split_clause,[],[f732,f25535]) ).

fof(f25535,plain,
    ( spl0_755
  <=> ! [X45,X2,X44] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_Finite__Set_Ofinite(X45,X2)
        | ~ c_lessequals(X44,X45,tc_fun(X2,tc_bool))
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X44
        | c_lessequals(c_Finite__Set_Olinorder__class_OMin(X45,X2),c_Finite__Set_Olinorder__class_OMin(X44,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f732,axiom,
    ! [X2,X44,X45] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_Finite__Set_Ofinite(X45,X2)
      | ~ c_lessequals(X44,X45,tc_fun(X2,tc_bool))
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X44
      | c_lessequals(c_Finite__Set_Olinorder__class_OMin(X45,X2),c_Finite__Set_Olinorder__class_OMin(X44,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

fof(f25533,plain,
    spl0_754,
    inference(avatar_split_clause,[],[f731,f25531]) ).

fof(f25531,plain,
    ( spl0_754
  <=> ! [X45,X2,X44] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_Finite__Set_Ofinite(X45,X2)
        | ~ c_lessequals(X44,X45,tc_fun(X2,tc_bool))
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X44
        | c_lessequals(c_Finite__Set_Olinorder__class_OMax(X44,X2),c_Finite__Set_Olinorder__class_OMax(X45,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).

fof(f731,axiom,
    ! [X2,X44,X45] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_Finite__Set_Ofinite(X45,X2)
      | ~ c_lessequals(X44,X45,tc_fun(X2,tc_bool))
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X44
      | c_lessequals(c_Finite__Set_Olinorder__class_OMax(X44,X2),c_Finite__Set_Olinorder__class_OMax(X45,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).

fof(f25529,plain,
    spl0_753,
    inference(avatar_split_clause,[],[f539,f25527]) ).

fof(f25527,plain,
    ( spl0_753
  <=> ! [X35,X10,X36,X9] :
        ( ~ c_HOL_Oord__class_Oless(X36,X9,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,c_Divides_Odiv__class_Omod(X35,X10,tc_nat),tc_nat),X36,tc_nat),c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f539,axiom,
    ! [X10,X36,X9,X35] :
      ( ~ c_HOL_Oord__class_Oless(X36,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,c_Divides_Odiv__class_Omod(X35,X10,tc_nat),tc_nat),X36,tc_nat),c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__lemma_0) ).

fof(f25525,plain,
    spl0_752,
    inference(avatar_split_clause,[],[f394,f25523]) ).

fof(f25523,plain,
    ( spl0_752
  <=> ! [X5,X19,X13,X6,X2] : c_Set_Ovimage(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X13,tc_bool)),X2,X13) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X19,X5,X2,X13),c_Set_Ovimage(X19,X6,X2,X13),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f394,axiom,
    ! [X2,X19,X6,X5,X13] : c_Set_Ovimage(X19,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X13,tc_bool)),X2,X13) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X19,X5,X2,X13),c_Set_Ovimage(X19,X6,X2,X13),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

fof(f25521,plain,
    ( spl0_751
    | ~ spl0_396
    | ~ spl0_702 ),
    inference(avatar_split_clause,[],[f23705,f23407,f4909,f25519]) ).

fof(f25519,plain,
    ( spl0_751
  <=> ! [X0] :
        ( c_in(X0,v_U,tc_Com_Opname)
        | ~ c_in(X0,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f4909,plain,
    ( spl0_396
  <=> ! [X5,X7,X6,X2] :
        ( ~ c_in(X7,X5,X2)
        | c_in(X7,X6,X2)
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f23705,plain,
    ( ! [X0] :
        ( c_in(X0,v_U,tc_Com_Opname)
        | ~ c_in(X0,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname) )
    | ~ spl0_396
    | ~ spl0_702 ),
    inference(resolution,[],[f23409,f4910]) ).

fof(f4910,plain,
    ( ! [X2,X6,X7,X5] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_in(X7,X6,X2)
        | ~ c_in(X7,X5,X2) )
    | ~ spl0_396 ),
    inference(avatar_component_clause,[],[f4909]) ).

fof(f25500,plain,
    ( spl0_750
    | ~ spl0_129
    | ~ spl0_417
    | ~ spl0_749 ),
    inference(avatar_split_clause,[],[f25496,f25493,f6360,f1955,f25498]) ).

fof(f25498,plain,
    ( spl0_750
  <=> ! [X4,X21,X25] :
        ( ~ hBOOL(hAPP(X25,c_Divides_Odiv__class_Omod(X21,X4,tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | hBOOL(hAPP(X25,X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f1955,plain,
    ( spl0_129
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f6360,plain,
    ( spl0_417
  <=> ! [X4,X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),X0,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f25493,plain,
    ( spl0_749
  <=> ! [X4,X20,X25,X21] :
        ( ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | hBOOL(hAPP(X25,X21))
        | ~ hBOOL(hAPP(X25,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,tc_nat),X21,tc_nat),X4,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f25496,plain,
    ( ! [X21,X4,X25] :
        ( ~ hBOOL(hAPP(X25,c_Divides_Odiv__class_Omod(X21,X4,tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | hBOOL(hAPP(X25,X21)) )
    | ~ spl0_129
    | ~ spl0_417
    | ~ spl0_749 ),
    inference(forward_demodulation,[],[f25494,f6814]) ).

fof(f6814,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X2,tc_nat),X1,tc_nat)
    | ~ spl0_129
    | ~ spl0_417 ),
    inference(superposition,[],[f6361,f1956]) ).

fof(f1956,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat)
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1955]) ).

fof(f6361,plain,
    ( ! [X0,X1,X4] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),X0,tc_nat),X1,tc_nat)
    | ~ spl0_417 ),
    inference(avatar_component_clause,[],[f6360]) ).

fof(f25494,plain,
    ( ! [X21,X4,X25,X20] :
        ( ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | hBOOL(hAPP(X25,X21))
        | ~ hBOOL(hAPP(X25,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,tc_nat),X21,tc_nat),X4,tc_nat))) )
    | ~ spl0_749 ),
    inference(avatar_component_clause,[],[f25493]) ).

fof(f25495,plain,
    spl0_749,
    inference(avatar_split_clause,[],[f391,f25493]) ).

fof(f391,axiom,
    ! [X21,X4,X25,X20] :
      ( ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | hBOOL(hAPP(X25,X21))
      | ~ hBOOL(hAPP(X25,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,tc_nat),X21,tc_nat),X4,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_1) ).

fof(f25491,plain,
    spl0_748,
    inference(avatar_split_clause,[],[f86,f25489]) ).

fof(f25489,plain,
    ( spl0_748
  <=> ! [X5,X19,X13,X6,X2] : c_Set_Ovimage(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X13,tc_bool)),X2,X13) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X19,X5,X2,X13),c_Set_Ovimage(X19,X6,X2,X13),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f86,axiom,
    ! [X2,X19,X6,X5,X13] : c_Set_Ovimage(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X13,tc_bool)),X2,X13) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X19,X5,X2,X13),c_Set_Ovimage(X19,X6,X2,X13),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

fof(f25201,plain,
    spl0_747,
    inference(avatar_split_clause,[],[f1319,f25199]) ).

fof(f25199,plain,
    ( spl0_747
  <=> ! [X2,X7,X33] :
        ( c_Finite__Set_Ocard(c_Set_Oinsert(X7,X33,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(X33,X2),tc_nat)
        | c_in(X7,X33,X2)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(X33,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f1319,plain,
    ! [X2,X7,X33] :
      ( c_Finite__Set_Ocard(c_Set_Oinsert(X7,X33,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(X33,X2),tc_nat)
      | c_in(X7,X33,X2)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(X33,X2) ),
    inference(forward_demodulation,[],[f1234,f126]) ).

fof(f1234,plain,
    ! [X2,X7,X33] :
      ( c_in(X7,X33,X2)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(X33,X2)
      | c_Finite__Set_Ocard(c_Set_Oinsert(X7,X33,X2),X2) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(X33,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f951,f61]) ).

fof(f951,axiom,
    ! [X2,X7,X33] :
      ( c_in(X7,X33,X2)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(X33,X2)
      | c_Finite__Set_Ocard(c_Set_Oinsert(X7,X33,X2),X2) = c_Suc(c_Finite__Set_Ocard(X33,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_4) ).

fof(f25197,plain,
    spl0_746,
    inference(avatar_split_clause,[],[f944,f25195]) ).

fof(f944,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
      | c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X5,X6,X19,X13,X2),X5,tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_0) ).

fof(f25193,plain,
    ( spl0_745
    | ~ spl0_395
    | ~ spl0_702 ),
    inference(avatar_split_clause,[],[f23704,f23407,f4905,f25191]) ).

fof(f25191,plain,
    ( spl0_745
  <=> ! [X0] :
        ( hBOOL(hAPP(v_U,X0))
        | ~ hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f23704,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(v_U,X0))
        | ~ hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),X0)) )
    | ~ spl0_395
    | ~ spl0_702 ),
    inference(resolution,[],[f23409,f4906]) ).

fof(f25189,plain,
    spl0_744,
    inference(avatar_split_clause,[],[f503,f25187]) ).

fof(f25187,plain,
    ( spl0_744
  <=> ! [X34,X7,X8,X33,X1] :
        ( c_Divides_Odiv__class_Omod(X7,X1,tc_nat) = c_Divides_Odiv__class_Omod(X8,X1,tc_nat)
        | c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X1,X33,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X1,X34,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f503,axiom,
    ! [X1,X8,X7,X34,X33] :
      ( c_Divides_Odiv__class_Omod(X7,X1,tc_nat) = c_Divides_Odiv__class_Omod(X8,X1,tc_nat)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X1,X33,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X1,X34,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).

fof(f25185,plain,
    spl0_743,
    inference(avatar_split_clause,[],[f178,f25183]) ).

fof(f25183,plain,
    ( spl0_743
  <=> ! [X17,X4,X20,X21] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X17,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X20,X21,tc_nat),X17,tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f24262,plain,
    ( spl0_742
    | ~ spl0_51
    | ~ spl0_709 ),
    inference(avatar_split_clause,[],[f23939,f23730,f1600,f24259]) ).

fof(f24259,plain,
    ( spl0_742
  <=> v_G = c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f23730,plain,
    ( spl0_709
  <=> ! [X6,X19,X13,X5,X2] :
        ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | c_Set_Oimage(X19,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X5,X6,X19,X13,X2),X13,X2) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f23939,plain,
    ( v_G = c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a)
    | ~ spl0_51
    | ~ spl0_709 ),
    inference(resolution,[],[f23731,f1602]) ).

fof(f23731,plain,
    ( ! [X2,X6,X19,X5,X13] :
        ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | c_Set_Oimage(X19,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X5,X6,X19,X13,X2),X13,X2) = X6 )
    | ~ spl0_709 ),
    inference(avatar_component_clause,[],[f23730]) ).

fof(f24227,plain,
    spl0_741,
    inference(avatar_split_clause,[],[f15715,f24225]) ).

fof(f24225,plain,
    ( spl0_741
  <=> ! [X5,X15,X6,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X15,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f15715,plain,
    ! [X2,X6,X15,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X15,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    inference(forward_demodulation,[],[f328,f1262]) ).

fof(f328,axiom,
    ! [X2,X6,X15,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

fof(f24223,plain,
    spl0_740,
    inference(avatar_split_clause,[],[f1307,f24221]) ).

fof(f24221,plain,
    ( spl0_740
  <=> ! [X4,X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X4,X0,tc_nat)
        | ~ c_lessequals(X4,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f1307,plain,
    ! [X0,X1,X4] :
      ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),tc_nat),tc_nat)
      | ~ c_lessequals(X4,X0,tc_nat)
      | ~ c_lessequals(X4,X1,tc_nat) ),
    inference(forward_demodulation,[],[f1031,f846]) ).

fof(f846,axiom,
    ! [X21,X4,X20] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X4,tc_nat) = c_HOL_Ominus__class_Ominus(X20,c_HOL_Oplus__class_Oplus(X21,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

fof(f1031,axiom,
    ! [X0,X1,X4] :
      ( ~ c_lessequals(X4,X0,tc_nat)
      | ~ c_lessequals(X4,X1,tc_nat)
      | c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X4,tc_nat),c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).

fof(f24219,plain,
    spl0_739,
    inference(avatar_split_clause,[],[f1261,f24217]) ).

fof(f24217,plain,
    ( spl0_739
  <=> ! [X4,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f1261,plain,
    ! [X0,X1,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f1161,f846]) ).

fof(f1161,plain,
    ! [X0,X1,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1043,f61,f61]) ).

fof(f1043,axiom,
    ! [X0,X1,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X0),X1,tc_nat),c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

fof(f24215,plain,
    spl0_738,
    inference(avatar_split_clause,[],[f1260,f24213]) ).

fof(f24213,plain,
    ( spl0_738
  <=> ! [X4,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),X0,tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f1260,plain,
    ! [X0,X1,X4] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),X0,tc_nat),tc_nat),X1,tc_nat),
    inference(forward_demodulation,[],[f1160,f126]) ).

fof(f1160,plain,
    ! [X0,X1,X4] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),X0,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(definition_unfolding,[],[f294,f61,f61]) ).

fof(f294,axiom,
    ! [X0,X1,X4] : c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),X0,tc_nat)),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).

fof(f24211,plain,
    spl0_737,
    inference(avatar_split_clause,[],[f932,f24209]) ).

fof(f24209,plain,
    ( spl0_737
  <=> ! [X5,X7,X6,X2] :
        ( c_in(X7,X6,X2)
        | c_in(X7,X5,X2)
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f932,axiom,
    ! [X2,X6,X7,X5] :
      ( c_in(X7,X6,X2)
      | c_in(X7,X5,X2)
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

fof(f24207,plain,
    spl0_736,
    inference(avatar_split_clause,[],[f931,f24205]) ).

fof(f24205,plain,
    ( spl0_736
  <=> ! [X5,X7,X6,X2] :
        ( c_in(X7,X5,X2)
        | c_in(X7,X6,X2)
        | c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f931,axiom,
    ! [X2,X6,X7,X5] :
      ( c_in(X7,X5,X2)
      | c_in(X7,X6,X2)
      | c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

fof(f24203,plain,
    spl0_735,
    inference(avatar_split_clause,[],[f763,f24201]) ).

fof(f24201,plain,
    ( spl0_735
  <=> ! [X5,X15,X6,X2] :
        ( ~ c_lessequals(X15,X5,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X15,X6,tc_fun(X2,tc_bool))
        | c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f763,axiom,
    ! [X2,X6,X15,X5] :
      ( ~ c_lessequals(X15,X5,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X15,X6,tc_fun(X2,tc_bool))
      | c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

fof(f24199,plain,
    spl0_734,
    inference(avatar_split_clause,[],[f752,f24197]) ).

fof(f24197,plain,
    ( spl0_734
  <=> ! [X5,X3,X6,X2] :
        ( ~ c_in(X3,X5,X2)
        | c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f752,axiom,
    ! [X2,X3,X6,X5] :
      ( ~ c_in(X3,X5,X2)
      | c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

fof(f24195,plain,
    spl0_733,
    inference(avatar_split_clause,[],[f751,f24193]) ).

fof(f24193,plain,
    ( spl0_733
  <=> ! [X15,X3,X6,X2] :
        ( ~ c_in(X3,X15,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X6,X2),X15,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f751,axiom,
    ! [X2,X3,X6,X15] :
      ( ~ c_in(X3,X15,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X6,X2),X15,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

fof(f24191,plain,
    spl0_732,
    inference(avatar_split_clause,[],[f743,f24189]) ).

fof(f24189,plain,
    ( spl0_732
  <=> ! [X5,X7,X6,X2] :
        ( c_in(X7,X6,X2)
        | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X7,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f743,axiom,
    ! [X2,X6,X7,X5] :
      ( c_in(X7,X6,X2)
      | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X7,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

fof(f24187,plain,
    spl0_731,
    inference(avatar_split_clause,[],[f736,f24185]) ).

fof(f24185,plain,
    ( spl0_731
  <=> ! [X6,X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f736,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__psubset_0) ).

fof(f24183,plain,
    spl0_730,
    inference(avatar_split_clause,[],[f670,f24181]) ).

fof(f24181,plain,
    ( spl0_730
  <=> ! [X5,X15,X6,X2] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f24179,plain,
    spl0_729,
    inference(avatar_split_clause,[],[f609,f24177]) ).

fof(f24177,plain,
    ( spl0_729
  <=> ! [X19,X13,X8,X5,X2,X7] :
        ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
        | c_in(X8,c_Set_Oimage(X19,X5,X2,X13),X13)
        | c_Fun_Oinj__on(c_Fun_Ofun__upd(X19,X7,X8,X2,X13),X5,X2,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f609,axiom,
    ! [X2,X8,X19,X7,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
      | c_in(X8,c_Set_Oimage(X19,X5,X2,X13),X13)
      | c_Fun_Oinj__on(c_Fun_Ofun__upd(X19,X7,X8,X2,X13),X5,X2,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).

fof(f24175,plain,
    spl0_728,
    inference(avatar_split_clause,[],[f416,f24173]) ).

fof(f24173,plain,
    ( spl0_728
  <=> ! [X19,X7,X8,X13,X5,X2] :
        ( X7 = X8
        | ~ c_in(X8,X5,X2)
        | ~ c_in(X7,X5,X2)
        | ~ c_Fun_Oinj__on(X19,X5,X2,X13)
        | hAPP(X19,X7) != hAPP(X19,X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f416,axiom,
    ! [X2,X8,X19,X7,X5,X13] :
      ( X7 = X8
      | ~ c_in(X8,X5,X2)
      | ~ c_in(X7,X5,X2)
      | ~ c_Fun_Oinj__on(X19,X5,X2,X13)
      | hAPP(X19,X7) != hAPP(X19,X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

fof(f24171,plain,
    spl0_727,
    inference(avatar_split_clause,[],[f340,f24169]) ).

fof(f24169,plain,
    ( spl0_727
  <=> ! [X19,X13,X5,X2] : c_Set_Oimage(X19,c_Set_Ovimage(X19,X5,X13,X2),X13,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oimage(X19,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_bool)),X13,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f340,axiom,
    ! [X2,X19,X5,X13] : c_Set_Oimage(X19,c_Set_Ovimage(X19,X5,X13,X2),X13,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oimage(X19,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_bool)),X13,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).

fof(f24167,plain,
    ( ~ spl0_1
    | spl0_726
    | ~ spl0_277
    | ~ spl0_702 ),
    inference(avatar_split_clause,[],[f23701,f23407,f3267,f24164,f1350]) ).

fof(f1350,plain,
    ( spl0_1
  <=> c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f24164,plain,
    ( spl0_726
  <=> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f3267,plain,
    ( spl0_277
  <=> ! [X6,X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | c_Finite__Set_Ofinite(X5,X2)
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f23701,plain,
    ( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname)
    | ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
    | ~ spl0_277
    | ~ spl0_702 ),
    inference(resolution,[],[f23409,f3268]) ).

fof(f3268,plain,
    ( ! [X2,X6,X5] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_Finite__Set_Ofinite(X5,X2)
        | ~ c_Finite__Set_Ofinite(X6,X2) )
    | ~ spl0_277 ),
    inference(avatar_component_clause,[],[f3267]) ).

fof(f24162,plain,
    spl0_725,
    inference(avatar_split_clause,[],[f311,f24160]) ).

fof(f24160,plain,
    ( spl0_725
  <=> ! [X31,X32,X29,X30,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X30,X2),c_HOL_Otimes__class_Otimes(X31,X32,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X31,X2),c_HOL_Otimes__class_Otimes(X30,X32,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f311,axiom,
    ! [X2,X31,X29,X32,X30] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X30,X2),c_HOL_Otimes__class_Otimes(X31,X32,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X31,X2),c_HOL_Otimes__class_Otimes(X30,X32,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(f24158,plain,
    spl0_724,
    inference(avatar_split_clause,[],[f288,f24156]) ).

fof(f24156,plain,
    ( spl0_724
  <=> ! [X5,X15,X6,X2] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f288,axiom,
    ! [X2,X6,X15,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

fof(f24154,plain,
    spl0_723,
    inference(avatar_split_clause,[],[f287,f24152]) ).

fof(f24152,plain,
    ( spl0_723
  <=> ! [X5,X15,X6,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f287,axiom,
    ! [X2,X6,X15,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

fof(f24150,plain,
    spl0_722,
    inference(avatar_split_clause,[],[f220,f24148]) ).

fof(f24148,plain,
    ( spl0_722
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Oplus__class_Oplus(X10,X16,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f220,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Oplus__class_Oplus(X10,X16,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(f24146,plain,
    spl0_721,
    inference(avatar_split_clause,[],[f150,f24144]) ).

fof(f24144,plain,
    ( spl0_721
  <=> ! [X2,X7,X8] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | c_HOL_Ozero__class_Ozero(X2) = X7
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X7,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
        | c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oplus__class_Oplus(X7,X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f150,axiom,
    ! [X2,X8,X7] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | c_HOL_Ozero__class_Ozero(X2) = X7
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X7,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
      | c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oplus__class_Oplus(X7,X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

fof(f24142,plain,
    spl0_720,
    inference(avatar_split_clause,[],[f149,f24140]) ).

fof(f24140,plain,
    ( spl0_720
  <=> ! [X2,X8,X7] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | c_HOL_Ozero__class_Ozero(X2) = X8
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X7,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
        | c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oplus__class_Oplus(X7,X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f149,axiom,
    ! [X2,X8,X7] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | c_HOL_Ozero__class_Ozero(X2) = X8
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X7,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
      | c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oplus__class_Oplus(X7,X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

fof(f24138,plain,
    spl0_719,
    inference(avatar_split_clause,[],[f142,f24136]) ).

fof(f24136,plain,
    ( spl0_719
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X10,X2),c_Divides_Odiv__class_Omod(X9,X10,X2),X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f142,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X10,X2),c_Divides_Odiv__class_Omod(X9,X10,X2),X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).

fof(f24134,plain,
    spl0_718,
    inference(avatar_split_clause,[],[f15,f24132]) ).

fof(f24132,plain,
    ( spl0_718
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X10,X2),c_Divides_Odiv__class_Omod(X9,X10,X2),X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f15,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X10,X2),c_Divides_Odiv__class_Omod(X9,X10,X2),X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).

fof(f23813,plain,
    ( ~ spl0_290
    | spl0_717
    | ~ spl0_51
    | ~ spl0_698 ),
    inference(avatar_split_clause,[],[f23434,f22716,f1600,f23810,f3535]) ).

fof(f23810,plain,
    ( spl0_717
  <=> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f22716,plain,
    ( spl0_698
  <=> ! [X5,X19,X13,X6,X2] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X5,X6,X19,X13,X2),X13)
        | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f23434,plain,
    ( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname)
    | ~ c_Finite__Set_Ofinite(v_G,t_a)
    | ~ spl0_51
    | ~ spl0_698 ),
    inference(resolution,[],[f22717,f1602]) ).

fof(f22717,plain,
    ( ! [X2,X6,X19,X5,X13] :
        ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X5,X6,X19,X13,X2),X13)
        | ~ c_Finite__Set_Ofinite(X6,X2) )
    | ~ spl0_698 ),
    inference(avatar_component_clause,[],[f22716]) ).

fof(f23760,plain,
    spl0_716,
    inference(avatar_split_clause,[],[f1348,f23758]) ).

fof(f23758,plain,
    ( spl0_716
  <=> ! [X20,X25,X21] :
        ( hBOOL(hAPP(X25,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X25,X21),tc_nat)))
        | ~ hBOOL(hAPP(X25,X21))
        | ~ c_lessequals(X20,X21,tc_nat)
        | hBOOL(hAPP(X25,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f1348,plain,
    ! [X21,X25,X20] :
      ( hBOOL(hAPP(X25,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X25,X21),tc_nat)))
      | ~ hBOOL(hAPP(X25,X21))
      | ~ c_lessequals(X20,X21,tc_nat)
      | hBOOL(hAPP(X25,X20)) ),
    inference(forward_demodulation,[],[f1242,f126]) ).

fof(f1242,plain,
    ! [X21,X25,X20] :
      ( ~ hBOOL(hAPP(X25,X21))
      | ~ c_lessequals(X20,X21,tc_nat)
      | hBOOL(hAPP(X25,X20))
      | hBOOL(hAPP(X25,c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X25,X21),c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    inference(definition_unfolding,[],[f884,f61]) ).

fof(f884,axiom,
    ! [X21,X25,X20] :
      ( ~ hBOOL(hAPP(X25,X21))
      | ~ c_lessequals(X20,X21,tc_nat)
      | hBOOL(hAPP(X25,X20))
      | hBOOL(hAPP(X25,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X25,X21)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inc__induct_1) ).

fof(f23756,plain,
    spl0_715,
    inference(avatar_split_clause,[],[f1318,f23754]) ).

fof(f23754,plain,
    ( spl0_715
  <=> ! [X25,X1,X47] :
        ( ~ hBOOL(hAPP(X25,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X25,X1),tc_nat)))
        | hBOOL(hAPP(X25,X47))
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X47,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f1318,plain,
    ! [X1,X47,X25] :
      ( ~ hBOOL(hAPP(X25,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X25,X1),tc_nat)))
      | hBOOL(hAPP(X25,X47))
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X47,tc_nat) ),
    inference(forward_demodulation,[],[f1233,f126]) ).

fof(f1233,plain,
    ! [X47,X1,X25] :
      ( hBOOL(hAPP(X25,X47))
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X47,tc_nat)
      | ~ hBOOL(hAPP(X25,c_HOL_Oplus__class_Oplus(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X25,X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    inference(definition_unfolding,[],[f887,f61,f61]) ).

fof(f887,axiom,
    ! [X47,X1,X25] :
      ( hBOOL(hAPP(X25,X47))
      | ~ c_lessequals(c_Suc(X1),X47,tc_nat)
      | ~ hBOOL(hAPP(X25,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X25,X1)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__D__lemma_1) ).

fof(f23752,plain,
    spl0_714,
    inference(avatar_split_clause,[],[f1196,f23750]) ).

fof(f23750,plain,
    ( spl0_714
  <=> ! [X4,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f1196,plain,
    ! [X0,X1,X4] :
      ( c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f875,f61,f61]) ).

fof(f875,axiom,
    ! [X0,X1,X4] :
      ( c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X4),X0,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X4),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).

fof(f23748,plain,
    spl0_713,
    inference(avatar_split_clause,[],[f1173,f23746]) ).

fof(f23746,plain,
    ( spl0_713
  <=> ! [X4,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f1173,plain,
    ! [X0,X1,X4] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f201,f61,f61]) ).

fof(f201,axiom,
    ! [X0,X1,X4] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X4),X0,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X4),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

fof(f23744,plain,
    spl0_712,
    inference(avatar_split_clause,[],[f1026,f23742]) ).

fof(f23742,plain,
    ( spl0_712
  <=> ! [X4,X0,X1] :
        ( ~ c_lessequals(X4,X0,tc_nat)
        | ~ c_lessequals(X4,X1,tc_nat)
        | c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_nat),c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f1026,axiom,
    ! [X0,X1,X4] :
      ( ~ c_lessequals(X4,X0,tc_nat)
      | ~ c_lessequals(X4,X1,tc_nat)
      | c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_nat),c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).

fof(f23740,plain,
    spl0_711,
    inference(avatar_split_clause,[],[f924,f23738]) ).

fof(f23738,plain,
    ( spl0_711
  <=> ! [X4,X0,X1] :
        ( ~ c_lessequals(X4,X0,tc_nat)
        | ~ c_lessequals(X4,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X4,tc_nat),c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f924,axiom,
    ! [X0,X1,X4] :
      ( ~ c_lessequals(X4,X0,tc_nat)
      | ~ c_lessequals(X4,X1,tc_nat)
      | c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X4,tc_nat),c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

fof(f23736,plain,
    spl0_710,
    inference(avatar_split_clause,[],[f896,f23734]) ).

fof(f23734,plain,
    ( spl0_710
  <=> ! [X2,X5] :
        ( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
        | c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)) = X5
        | c_Finite__Set_Ocard(X5,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f896,axiom,
    ! [X2,X5] :
      ( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
      | c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)) = X5
      | c_Finite__Set_Ocard(X5,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).

fof(f23732,plain,
    spl0_709,
    inference(avatar_split_clause,[],[f891,f23730]) ).

fof(f891,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
      | c_Set_Oimage(X19,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X5,X6,X19,X13,X2),X13,X2) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_1) ).

fof(f23700,plain,
    spl0_708,
    inference(avatar_split_clause,[],[f890,f23698]) ).

fof(f23698,plain,
    ( spl0_708
  <=> ! [X2,X5,X7] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X5,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f890,axiom,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X5,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).

fof(f23696,plain,
    spl0_707,
    inference(avatar_split_clause,[],[f667,f23694]) ).

fof(f23694,plain,
    ( spl0_707
  <=> ! [X2,X19,X7,X22] :
        ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X22,tc_bool)),X22,X2)
        | hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X22,tc_bool)),X19,X22,X2),hAPP(X19,X7)) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f667,axiom,
    ! [X2,X19,X7,X22] :
      ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X22,tc_bool)),X22,X2)
      | hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X22,tc_bool)),X19,X22,X2),hAPP(X19,X7)) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).

fof(f23692,plain,
    spl0_706,
    inference(avatar_split_clause,[],[f646,f23690]) ).

fof(f23690,plain,
    ( spl0_706
  <=> ! [X5,X3,X6,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X5,X2),c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f646,axiom,
    ! [X2,X3,X6,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X5,X2),c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

fof(f23688,plain,
    spl0_705,
    inference(avatar_split_clause,[],[f611,f23686]) ).

fof(f23686,plain,
    ( spl0_705
  <=> ! [X3,X19,X13,X5,X2] :
        ( c_in(X3,X5,X2)
        | ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
        | ~ c_in(hAPP(X19,X3),c_Set_Oimage(X19,X5,X2,X13),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f611,axiom,
    ! [X2,X3,X19,X5,X13] :
      ( c_in(X3,X5,X2)
      | ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
      | ~ c_in(hAPP(X19,X3),c_Set_Oimage(X19,X5,X2,X13),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

fof(f23684,plain,
    spl0_704,
    inference(avatar_split_clause,[],[f547,f23682]) ).

fof(f23682,plain,
    ( spl0_704
  <=> ! [X10,X7,X36,X16] :
        ( X10 = X16
        | c_HOL_Ozero__class_Ozero(tc_nat) = X36
        | c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X36,X10,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X36,X16,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f547,axiom,
    ! [X10,X36,X16,X7] :
      ( X10 = X16
      | c_HOL_Ozero__class_Ozero(tc_nat) = X36
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X36,X10,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X36,X16,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

fof(f23680,plain,
    spl0_703,
    inference(avatar_split_clause,[],[f301,f23678]) ).

fof(f23678,plain,
    ( spl0_703
  <=> ! [X5,X19,X13,X6,X2] :
        ( X5 = X6
        | ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
        | c_Set_Oimage(X19,X5,X2,X13) != c_Set_Oimage(X19,X6,X2,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f301,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( X5 = X6
      | ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
      | c_Set_Oimage(X19,X5,X2,X13) != c_Set_Oimage(X19,X6,X2,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

fof(f23410,plain,
    ( spl0_702
    | ~ spl0_51
    | ~ spl0_695 ),
    inference(avatar_split_clause,[],[f23373,f22699,f1600,f23407]) ).

fof(f22699,plain,
    ( spl0_695
  <=> ! [X6,X19,X13,X5,X2] :
        ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X5,X6,X19,X13,X2),X5,tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f23373,plain,
    ( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_51
    | ~ spl0_695 ),
    inference(resolution,[],[f22700,f1602]) ).

fof(f22700,plain,
    ( ! [X2,X6,X19,X5,X13] :
        ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X5,X6,X19,X13,X2),X5,tc_fun(X13,tc_bool)) )
    | ~ spl0_695 ),
    inference(avatar_component_clause,[],[f22699]) ).

fof(f22730,plain,
    spl0_701,
    inference(avatar_split_clause,[],[f1306,f22728]) ).

fof(f1306,plain,
    ! [X2,X7,X5] :
      ( c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(X5,X2),tc_nat)
      | ~ c_Finite__Set_Ofinite(X5,X2)
      | c_in(X7,X5,X2) ),
    inference(forward_demodulation,[],[f1216,f126]) ).

fof(f1216,plain,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_in(X7,X5,X2)
      | c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(X5,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1022,f61]) ).

fof(f1022,axiom,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_in(X7,X5,X2)
      | c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) = c_Suc(c_Finite__Set_Ocard(X5,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).

fof(f22726,plain,
    spl0_700,
    inference(avatar_split_clause,[],[f1212,f22724]) ).

fof(f22724,plain,
    ( spl0_700
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f1212,plain,
    ! [X0,X1] :
      ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(definition_unfolding,[],[f213,f61,f61]) ).

fof(f213,axiom,
    ! [X0,X1] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) != X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).

fof(f22722,plain,
    spl0_699,
    inference(avatar_split_clause,[],[f1184,f22720]) ).

fof(f22720,plain,
    ( spl0_699
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f1184,plain,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f331,f61]) ).

fof(f331,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

fof(f22718,plain,
    spl0_698,
    inference(avatar_split_clause,[],[f942,f22716]) ).

fof(f942,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X5,X6,X19,X13,X2),X13)
      | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_1) ).

fof(f22709,plain,
    spl0_697,
    inference(avatar_split_clause,[],[f939,f22707]) ).

fof(f22707,plain,
    ( spl0_697
  <=> ! [X6,X19,X13,X5,X2] :
        ( c_lessequals(c_Set_Oimage(X19,X5,X2,X13),X6,tc_fun(X13,tc_bool))
        | ~ c_in(hAPP(X19,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X5,X6,X19,X2,X13)),X6,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f939,axiom,
    ! [X2,X19,X6,X5,X13] :
      ( c_lessequals(c_Set_Oimage(X19,X5,X2,X13),X6,tc_fun(X13,tc_bool))
      | ~ c_in(hAPP(X19,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X5,X6,X19,X2,X13)),X6,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_1) ).

fof(f22705,plain,
    spl0_696,
    inference(avatar_split_clause,[],[f936,f22703]) ).

fof(f22703,plain,
    ( spl0_696
  <=> ! [X5,X19,X13,X6,X2] :
        ( c_lessequals(c_Set_Oimage(X19,X5,X13,X2),X6,tc_fun(X2,tc_bool))
        | ~ c_in(hAPP(X19,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X5,X6,X19,X13,X2)),X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f936,axiom,
    ! [X2,X19,X6,X5,X13] :
      ( c_lessequals(c_Set_Oimage(X19,X5,X13,X2),X6,tc_fun(X2,tc_bool))
      | ~ c_in(hAPP(X19,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X5,X6,X19,X13,X2)),X6,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_2) ).

fof(f22701,plain,
    spl0_695,
    inference(avatar_split_clause,[],[f893,f22699]) ).

fof(f893,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
      | c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X5,X6,X19,X13,X2),X5,tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_0) ).

fof(f22697,plain,
    spl0_694,
    inference(avatar_split_clause,[],[f601,f22695]) ).

fof(f22695,plain,
    ( spl0_694
  <=> ! [X2,X5,X7] :
        ( c_in(X7,X5,X2)
        | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X7,X5,X2),c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f601,axiom,
    ! [X2,X7,X5] :
      ( c_in(X7,X5,X2)
      | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X7,X5,X2),c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

fof(f22693,plain,
    spl0_693,
    inference(avatar_split_clause,[],[f544,f22691]) ).

fof(f22691,plain,
    ( spl0_693
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Omult__mono1(X2)
        | ~ c_lessequals(X3,X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f544,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Omult__mono1(X2)
      | ~ c_lessequals(X3,X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

fof(f22689,plain,
    spl0_692,
    inference(avatar_split_clause,[],[f543,f22687]) ).

fof(f22687,plain,
    ( spl0_692
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Omult__mono(X2)
        | ~ c_lessequals(X3,X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f543,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Omult__mono(X2)
      | ~ c_lessequals(X3,X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

fof(f22685,plain,
    spl0_691,
    inference(avatar_split_clause,[],[f542,f22683]) ).

fof(f22683,plain,
    ( spl0_691
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Omult__mono(X2)
        | ~ c_lessequals(X3,X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f542,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Omult__mono(X2)
      | ~ c_lessequals(X3,X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

fof(f22681,plain,
    spl0_690,
    inference(avatar_split_clause,[],[f255,f22679]) ).

fof(f22679,plain,
    ( spl0_690
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f255,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

fof(f22677,plain,
    spl0_689,
    inference(avatar_split_clause,[],[f252,f22675]) ).

fof(f22675,plain,
    ( spl0_689
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f252,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

fof(f22673,plain,
    spl0_688,
    inference(avatar_split_clause,[],[f248,f22671]) ).

fof(f22671,plain,
    ( spl0_688
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f248,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

fof(f22659,plain,
    spl0_687,
    inference(avatar_split_clause,[],[f170,f22657]) ).

fof(f22657,plain,
    ( spl0_687
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | c_lessequals(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f170,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | c_lessequals(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

fof(f22655,plain,
    spl0_686,
    inference(avatar_split_clause,[],[f169,f22653]) ).

fof(f22653,plain,
    ( spl0_686
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | c_lessequals(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f169,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | c_lessequals(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

fof(f22651,plain,
    spl0_685,
    inference(avatar_split_clause,[],[f141,f22649]) ).

fof(f22649,plain,
    ( spl0_685
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring(X2)
        | c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f141,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X2)
      | c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).

fof(f22647,plain,
    spl0_684,
    inference(avatar_split_clause,[],[f140,f22645]) ).

fof(f22645,plain,
    ( spl0_684
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring(X2)
        | c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f140,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X2)
      | c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

fof(f22643,plain,
    spl0_683,
    inference(avatar_split_clause,[],[f139,f22641]) ).

fof(f22641,plain,
    ( spl0_683
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f139,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

fof(f22639,plain,
    spl0_682,
    inference(avatar_split_clause,[],[f138,f22637]) ).

fof(f22637,plain,
    ( spl0_682
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f138,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

fof(f22533,plain,
    ( spl0_681
    | ~ spl0_120
    | ~ spl0_644 ),
    inference(avatar_split_clause,[],[f20917,f12479,f1896,f22531]) ).

fof(f22531,plain,
    ( spl0_681
  <=> ! [X0,X1] :
        ( ~ c_in(X0,v_G,t_a)
        | c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f12479,plain,
    ( spl0_644
  <=> ! [X0] :
        ( ~ c_in(X0,v_G,t_a)
        | hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f20917,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,v_G,t_a)
        | c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,X1) )
    | ~ spl0_120
    | ~ spl0_644 ),
    inference(resolution,[],[f12480,f1897]) ).

fof(f12480,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a)))
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_644 ),
    inference(avatar_component_clause,[],[f12479]) ).

fof(f22291,plain,
    ( spl0_680
    | ~ spl0_120
    | ~ spl0_633 ),
    inference(avatar_split_clause,[],[f20757,f12435,f1896,f22289]) ).

fof(f22289,plain,
    ( spl0_680
  <=> ! [X0,X1] :
        ( ~ c_in(X0,v_G,t_a)
        | c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f12435,plain,
    ( spl0_633
  <=> ! [X0] :
        ( ~ c_in(X0,v_G,t_a)
        | hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f20757,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,v_G,t_a)
        | c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,X1) )
    | ~ spl0_120
    | ~ spl0_633 ),
    inference(resolution,[],[f12436,f1897]) ).

fof(f12436,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a)))
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_633 ),
    inference(avatar_component_clause,[],[f12435]) ).

fof(f22106,plain,
    ( spl0_679
    | ~ spl0_121
    | ~ spl0_622 ),
    inference(avatar_split_clause,[],[f12662,f12391,f1900,f22104]) ).

fof(f12391,plain,
    ( spl0_622
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
        | c_in(v_pn,c_Set_Oinsert(X2,X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f12662,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
        | hBOOL(hAPP(c_Set_Oinsert(X2,X0,X1),v_pn)) )
    | ~ spl0_121
    | ~ spl0_622 ),
    inference(resolution,[],[f12392,f1901]) ).

fof(f12392,plain,
    ( ! [X2,X0,X1] :
        ( c_in(v_pn,c_Set_Oinsert(X2,X0,X1),X1)
        | ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool)) )
    | ~ spl0_622 ),
    inference(avatar_component_clause,[],[f12391]) ).

fof(f15714,plain,
    ( spl0_678
    | ~ spl0_4
    | ~ spl0_676 ),
    inference(avatar_split_clause,[],[f14176,f13132,f1365,f15711]) ).

fof(f15711,plain,
    ( spl0_678
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(v_pn) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f1365,plain,
    ( spl0_4
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f14176,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(v_pn)
    | ~ spl0_4
    | ~ spl0_676 ),
    inference(superposition,[],[f1367,f13133]) ).

fof(f1367,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f1365]) ).

fof(f13137,plain,
    ( spl0_676
    | spl0_677
    | ~ spl0_328
    | ~ spl0_622 ),
    inference(avatar_split_clause,[],[f12658,f12391,f3875,f13135,f13132]) ).

fof(f3875,plain,
    ( spl0_328
  <=> ! [X9,X2,X3] :
        ( X3 = X9
        | ~ c_in(X9,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f12658,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(v_U,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
        | v_pn = X1 )
    | ~ spl0_328
    | ~ spl0_622 ),
    inference(resolution,[],[f12392,f3876]) ).

fof(f3876,plain,
    ( ! [X2,X3,X9] :
        ( ~ c_in(X9,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
        | X3 = X9 )
    | ~ spl0_328 ),
    inference(avatar_component_clause,[],[f3875]) ).

fof(f12605,plain,
    spl0_675,
    inference(avatar_split_clause,[],[f1258,f12603]) ).

fof(f12603,plain,
    ( spl0_675
  <=> ! [X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f1258,plain,
    ! [X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),X1,tc_nat),
    inference(forward_demodulation,[],[f1158,f126]) ).

fof(f1158,plain,
    ! [X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(definition_unfolding,[],[f619,f61,f61]) ).

fof(f619,axiom,
    ! [X0,X1] : c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).

fof(f12601,plain,
    spl0_674,
    inference(avatar_split_clause,[],[f1221,f12599]) ).

fof(f12599,plain,
    ( spl0_674
  <=> ! [X20,X4,X25] :
        ( ~ hBOOL(hAPP(X25,X4))
        | hBOOL(hAPP(X25,c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X25),c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
        | hBOOL(hAPP(X25,c_HOL_Ominus__class_Ominus(X4,X20,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f1221,plain,
    ! [X4,X25,X20] :
      ( ~ hBOOL(hAPP(X25,X4))
      | hBOOL(hAPP(X25,c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X25),c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
      | hBOOL(hAPP(X25,c_HOL_Ominus__class_Ominus(X4,X20,tc_nat))) ),
    inference(definition_unfolding,[],[f899,f61]) ).

fof(f899,axiom,
    ! [X4,X25,X20] :
      ( ~ hBOOL(hAPP(X25,X4))
      | hBOOL(hAPP(X25,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X25))))
      | hBOOL(hAPP(X25,c_HOL_Ominus__class_Ominus(X4,X20,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct__lemma_0) ).

fof(f12597,plain,
    spl0_673,
    inference(avatar_split_clause,[],[f1166,f12595]) ).

fof(f12595,plain,
    ( spl0_673
  <=> ! [X4,X0,X1] :
        ( X0 = X1
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) != c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f1166,plain,
    ! [X0,X1,X4] :
      ( X0 = X1
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) != c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(definition_unfolding,[],[f616,f61,f61]) ).

fof(f616,axiom,
    ! [X0,X1,X4] :
      ( X0 = X1
      | c_HOL_Otimes__class_Otimes(c_Suc(X4),X0,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X4),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).

fof(f12593,plain,
    spl0_672,
    inference(avatar_split_clause,[],[f1042,f12591]) ).

fof(f12591,plain,
    ( spl0_672
  <=> ! [X5,X7,X6,X2] :
        ( X5 = X6
        | c_in(X7,X5,X2)
        | c_in(X7,X6,X2)
        | c_Set_Oinsert(X7,X6,X2) != c_Set_Oinsert(X7,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f1042,axiom,
    ! [X2,X6,X7,X5] :
      ( X5 = X6
      | c_in(X7,X5,X2)
      | c_in(X7,X6,X2)
      | c_Set_Oinsert(X7,X6,X2) != c_Set_Oinsert(X7,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

fof(f12589,plain,
    spl0_671,
    inference(avatar_split_clause,[],[f1037,f12587]) ).

fof(f12587,plain,
    ( spl0_671
  <=> ! [X19,X13,X5,X2,X7] :
        ( ~ c_in(X7,X5,X2)
        | c_Set_Oimage(X19,X5,X2,X13) = c_Set_Oinsert(hAPP(X19,X7),c_Set_Oimage(X19,X5,X2,X13),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f1037,axiom,
    ! [X2,X19,X7,X5,X13] :
      ( ~ c_in(X7,X5,X2)
      | c_Set_Oimage(X19,X5,X2,X13) = c_Set_Oinsert(hAPP(X19,X7),c_Set_Oimage(X19,X5,X2,X13),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

fof(f12585,plain,
    spl0_670,
    inference(avatar_split_clause,[],[f1029,f12583]) ).

fof(f12583,plain,
    ( spl0_670
  <=> ! [X4,X0,X1] :
        ( X0 = X1
        | ~ c_lessequals(X4,X0,tc_nat)
        | ~ c_lessequals(X4,X1,tc_nat)
        | c_HOL_Ominus__class_Ominus(X0,X4,tc_nat) != c_HOL_Ominus__class_Ominus(X1,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f1029,axiom,
    ! [X0,X1,X4] :
      ( X0 = X1
      | ~ c_lessequals(X4,X0,tc_nat)
      | ~ c_lessequals(X4,X1,tc_nat)
      | c_HOL_Ominus__class_Ominus(X0,X4,tc_nat) != c_HOL_Ominus__class_Ominus(X1,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).

fof(f12581,plain,
    spl0_669,
    inference(avatar_split_clause,[],[f1015,f12579]) ).

fof(f12579,plain,
    ( spl0_669
  <=> ! [X6,X19,X13,X5,X2,X7] :
        ( ~ c_in(X7,X5,X13)
        | c_in(hAPP(X19,X7),X6,X2)
        | ~ c_lessequals(c_Set_Oimage(X19,X5,X13,X2),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f1015,axiom,
    ! [X2,X19,X6,X7,X5,X13] :
      ( ~ c_in(X7,X5,X13)
      | c_in(hAPP(X19,X7),X6,X2)
      | ~ c_lessequals(c_Set_Oimage(X19,X5,X13,X2),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

fof(f12577,plain,
    spl0_668,
    inference(avatar_split_clause,[],[f1001,f12575]) ).

fof(f12575,plain,
    ( spl0_668
  <=> ! [X6,X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | X5 = X6
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_lessequals(c_Finite__Set_Ocard(X6,X2),c_Finite__Set_Ocard(X5,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f1001,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | X5 = X6
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_lessequals(c_Finite__Set_Ocard(X6,X2),c_Finite__Set_Ocard(X5,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).

fof(f12573,plain,
    spl0_667,
    inference(avatar_split_clause,[],[f960,f12571]) ).

fof(f12571,plain,
    ( spl0_667
  <=> ! [X19,X13,X5,X2,X7] :
        ( ~ c_lessequals(X7,X5,tc_fun(X13,tc_bool))
        | c_lessequals(c_Set_Oimage(X19,X7,X13,X2),c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f960,axiom,
    ! [X2,X19,X7,X5,X13] :
      ( ~ c_lessequals(X7,X5,tc_fun(X13,tc_bool))
      | c_lessequals(c_Set_Oimage(X19,X7,X13,X2),c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

fof(f12569,plain,
    ( spl0_666
    | ~ spl0_120
    | ~ spl0_585 ),
    inference(avatar_split_clause,[],[f11542,f11092,f1896,f12567]) ).

fof(f12567,plain,
    ( spl0_666
  <=> ! [X0,X1] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f11092,plain,
    ( spl0_585
  <=> ! [X0] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f11542,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,X1) )
    | ~ spl0_120
    | ~ spl0_585 ),
    inference(resolution,[],[f11093,f1897]) ).

fof(f11093,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a)))
        | ~ hBOOL(hAPP(v_G,X0)) )
    | ~ spl0_585 ),
    inference(avatar_component_clause,[],[f11092]) ).

fof(f12565,plain,
    spl0_665,
    inference(avatar_split_clause,[],[f865,f12563]) ).

fof(f865,axiom,
    ! [X2,X8,X19,X7,X5,X13] :
      ( c_in(X7,X5,X13)
      | c_Set_Oimage(c_Fun_Ofun__upd(X19,X7,X8,X13,X2),X5,X13,X2) = c_Set_Oimage(X19,X5,X13,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).

fof(f12561,plain,
    spl0_664,
    inference(avatar_split_clause,[],[f862,f12559]) ).

fof(f12559,plain,
    ( spl0_664
  <=> ! [X41,X19,X13,X2,X7] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X7,X19,X41,X2,X13),X7,X2)
        | c_Set_Oimage(X19,X7,X2,X13) = c_Set_Oimage(X41,X7,X2,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f862,axiom,
    ! [X2,X41,X19,X7,X13] :
      ( c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X7,X19,X41,X2,X13),X7,X2)
      | c_Set_Oimage(X19,X7,X2,X13) = c_Set_Oimage(X41,X7,X2,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_0) ).

fof(f12557,plain,
    spl0_663,
    inference(avatar_split_clause,[],[f775,f12555]) ).

fof(f12555,plain,
    ( spl0_663
  <=> ! [X5,X19,X13,X6,X2] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_lessequals(c_Set_Ovimage(X19,X5,X13,X2),c_Set_Ovimage(X19,X6,X13,X2),tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f775,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_lessequals(c_Set_Ovimage(X19,X5,X13,X2),c_Set_Ovimage(X19,X6,X13,X2),tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

fof(f12553,plain,
    spl0_662,
    inference(avatar_split_clause,[],[f754,f12551]) ).

fof(f12551,plain,
    ( spl0_662
  <=> ! [X24,X19,X3,X2] :
        ( ~ c_in(X3,X24,X2)
        | ~ c_lessequals(X24,hAPP(X19,X24),tc_fun(X2,tc_bool))
        | c_in(X3,c_Inductive_Ocomplete__lattice__class_Ogfp(X19,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f754,axiom,
    ! [X2,X3,X19,X24] :
      ( ~ c_in(X3,X24,X2)
      | ~ c_lessequals(X24,hAPP(X19,X24),tc_fun(X2,tc_bool))
      | c_in(X3,c_Inductive_Ocomplete__lattice__class_Ogfp(X19,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct_0) ).

fof(f12549,plain,
    spl0_661,
    inference(avatar_split_clause,[],[f748,f12547]) ).

fof(f12547,plain,
    ( spl0_661
  <=> ! [X5,X7,X6,X2] :
        ( ~ c_in(X7,X6,X2)
        | c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f748,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ c_in(X7,X6,X2)
      | c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

fof(f12545,plain,
    spl0_660,
    inference(avatar_split_clause,[],[f745,f12543]) ).

fof(f745,axiom,
    ! [X2,X3,X6,X5] :
      ( c_in(X3,X5,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

fof(f12541,plain,
    spl0_659,
    inference(avatar_split_clause,[],[f744,f12539]) ).

fof(f744,axiom,
    ! [X2,X3,X6,X15] :
      ( c_in(X3,X15,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X6,X15,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X6,X2),X15,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

fof(f12537,plain,
    spl0_658,
    inference(avatar_split_clause,[],[f724,f12535]) ).

fof(f12535,plain,
    ( spl0_658
  <=> ! [X14,X8,X2,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X8,X2),c_HOL_Otimes__class_Otimes(X7,X14,X2),X2) = c_HOL_Otimes__class_Otimes(X7,c_HOL_Oplus__class_Oplus(X8,X14,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f724,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X8,X2),c_HOL_Otimes__class_Otimes(X7,X14,X2),X2) = c_HOL_Otimes__class_Otimes(X7,c_HOL_Oplus__class_Oplus(X8,X14,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

fof(f12533,plain,
    spl0_657,
    inference(avatar_split_clause,[],[f721,f12531]) ).

fof(f12531,plain,
    ( spl0_657
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring(X2)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f721,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X2)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

fof(f12529,plain,
    spl0_656,
    inference(avatar_split_clause,[],[f720,f12527]) ).

fof(f12527,plain,
    ( spl0_656
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f720,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(f12525,plain,
    ( spl0_655
    | ~ spl0_120
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f11432,f10773,f1896,f12523]) ).

fof(f12523,plain,
    ( spl0_655
  <=> ! [X0,X1] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f10773,plain,
    ( spl0_584
  <=> ! [X0] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f11432,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,X1) )
    | ~ spl0_120
    | ~ spl0_584 ),
    inference(resolution,[],[f10774,f1897]) ).

fof(f10774,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a)))
        | ~ hBOOL(hAPP(v_G,X0)) )
    | ~ spl0_584 ),
    inference(avatar_component_clause,[],[f10773]) ).

fof(f12521,plain,
    spl0_654,
    inference(avatar_split_clause,[],[f708,f12519]) ).

fof(f12519,plain,
    ( spl0_654
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) = c_HOL_Otimes__class_Otimes(X10,c_Divides_Odiv__class_Omod(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f708,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X10,X3,X2),c_HOL_Otimes__class_Otimes(X10,X9,X2),X2) = c_HOL_Otimes__class_Otimes(X10,c_Divides_Odiv__class_Omod(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).

fof(f12517,plain,
    spl0_653,
    inference(avatar_split_clause,[],[f707,f12515]) ).

fof(f12515,plain,
    ( spl0_653
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X9,X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f707,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X9,X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).

fof(f12513,plain,
    spl0_652,
    inference(avatar_split_clause,[],[f700,f12511]) ).

fof(f12511,plain,
    ( spl0_652
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f700,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

fof(f12509,plain,
    spl0_651,
    inference(avatar_split_clause,[],[f694,f12507]) ).

fof(f12507,plain,
    ( spl0_651
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X9,X10,X2),X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f694,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X9,X10,X2),X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).

fof(f12505,plain,
    spl0_650,
    inference(avatar_split_clause,[],[f665,f12503]) ).

fof(f12503,plain,
    ( spl0_650
  <=> ! [X2,X9,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
        | ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f665,axiom,
    ! [X2,X3,X9] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
      | ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

fof(f12501,plain,
    spl0_649,
    inference(avatar_split_clause,[],[f653,f12499]) ).

fof(f12499,plain,
    ( spl0_649
  <=> ! [X41,X19,X13,X2] :
        ( ~ class_HOL_Oord(X13)
        | ~ c_lessequals(X19,X41,tc_fun(X2,X13))
        | c_HOL_Oord__class_Oless(X19,X41,tc_fun(X2,X13))
        | c_lessequals(X41,X19,tc_fun(X2,X13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f653,axiom,
    ! [X2,X41,X19,X13] :
      ( ~ class_HOL_Oord(X13)
      | ~ c_lessequals(X19,X41,tc_fun(X2,X13))
      | c_HOL_Oord__class_Oless(X19,X41,tc_fun(X2,X13))
      | c_lessequals(X41,X19,tc_fun(X2,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

fof(f12497,plain,
    spl0_648,
    inference(avatar_split_clause,[],[f557,f12495]) ).

fof(f12495,plain,
    ( spl0_648
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ c_lessequals(X3,X9,X2)
        | ~ c_lessequals(X10,X16,X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f557,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
      | ~ c_lessequals(X3,X9,X2)
      | ~ c_lessequals(X10,X16,X2)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

fof(f12493,plain,
    spl0_647,
    inference(avatar_split_clause,[],[f538,f12491]) ).

fof(f12491,plain,
    ( spl0_647
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X16,X2)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f538,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X16,X2)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X10,X2),c_HOL_Otimes__class_Otimes(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).

fof(f12489,plain,
    spl0_646,
    inference(avatar_split_clause,[],[f520,f12487]) ).

fof(f12487,plain,
    ( spl0_646
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f520,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).

fof(f12485,plain,
    spl0_645,
    inference(avatar_split_clause,[],[f519,f12483]) ).

fof(f12483,plain,
    ( spl0_645
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f519,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

fof(f12481,plain,
    ( spl0_644
    | ~ spl0_121
    | ~ spl0_583 ),
    inference(avatar_split_clause,[],[f11390,f10302,f1900,f12479]) ).

fof(f10302,plain,
    ( spl0_583
  <=> ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ c_in(X0,v_G,t_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f11390,plain,
    ( ! [X0] :
        ( ~ c_in(X0,v_G,t_a)
        | hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a))) )
    | ~ spl0_121
    | ~ spl0_583 ),
    inference(resolution,[],[f10303,f1901]) ).

fof(f10303,plain,
    ( ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_583 ),
    inference(avatar_component_clause,[],[f10302]) ).

fof(f12477,plain,
    spl0_643,
    inference(avatar_split_clause,[],[f473,f12475]) ).

fof(f12475,plain,
    ( spl0_643
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f473,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

fof(f12473,plain,
    spl0_642,
    inference(avatar_split_clause,[],[f393,f12471]) ).

fof(f12471,plain,
    ( spl0_642
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_lessequals(X10,X16,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f393,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_lessequals(X10,X16,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

fof(f12469,plain,
    spl0_641,
    inference(avatar_split_clause,[],[f392,f12467]) ).

fof(f12467,plain,
    ( spl0_641
  <=> ! [X3,X9,X10,X16,X2] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
        | ~ c_lessequals(X3,X9,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f392,axiom,
    ! [X2,X3,X10,X9,X16] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
      | ~ c_HOL_Oord__class_Oless(X10,X16,X2)
      | ~ c_lessequals(X3,X9,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

fof(f12465,plain,
    spl0_640,
    inference(avatar_split_clause,[],[f390,f12463]) ).

fof(f12463,plain,
    ( spl0_640
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X0,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X1,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),c_HOL_Otimes__class_Otimes(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f390,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X0,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X1,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),c_HOL_Otimes__class_Otimes(X0,X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

fof(f12461,plain,
    spl0_639,
    inference(avatar_split_clause,[],[f353,f12459]) ).

fof(f12459,plain,
    ( spl0_639
  <=> ! [X2,X9,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f353,axiom,
    ! [X2,X3,X9] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

fof(f12457,plain,
    spl0_638,
    inference(avatar_split_clause,[],[f303,f12455]) ).

fof(f12455,plain,
    ( spl0_638
  <=> ! [X2,X9,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
        | ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f303,axiom,
    ! [X2,X3,X9] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
      | ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

fof(f12453,plain,
    spl0_637,
    inference(avatar_split_clause,[],[f302,f12451]) ).

fof(f12451,plain,
    ( spl0_637
  <=> ! [X2,X9,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f302,axiom,
    ! [X2,X3,X9] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

fof(f12449,plain,
    spl0_636,
    inference(avatar_split_clause,[],[f276,f12447]) ).

fof(f12447,plain,
    ( spl0_636
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f276,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

fof(f12445,plain,
    spl0_635,
    inference(avatar_split_clause,[],[f275,f12443]) ).

fof(f12443,plain,
    ( spl0_635
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f275,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

fof(f12441,plain,
    spl0_634,
    inference(avatar_split_clause,[],[f274,f12439]) ).

fof(f12439,plain,
    ( spl0_634
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X9,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f274,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X9,X3,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

fof(f12437,plain,
    ( spl0_633
    | ~ spl0_121
    | ~ spl0_582 ),
    inference(avatar_split_clause,[],[f11347,f10116,f1900,f12435]) ).

fof(f10116,plain,
    ( spl0_582
  <=> ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ c_in(X0,v_G,t_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f11347,plain,
    ( ! [X0] :
        ( ~ c_in(X0,v_G,t_a)
        | hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a))) )
    | ~ spl0_121
    | ~ spl0_582 ),
    inference(resolution,[],[f10117,f1901]) ).

fof(f10117,plain,
    ( ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_582 ),
    inference(avatar_component_clause,[],[f10116]) ).

fof(f12433,plain,
    spl0_632,
    inference(avatar_split_clause,[],[f215,f12431]) ).

fof(f12431,plain,
    ( spl0_632
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X9,X10,X2),X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f215,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X9,X10,X2),X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).

fof(f12429,plain,
    spl0_631,
    inference(avatar_split_clause,[],[f214,f12427]) ).

fof(f12427,plain,
    ( spl0_631
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X10,X2),X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f214,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X10,X2),X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).

fof(f12425,plain,
    spl0_630,
    inference(avatar_split_clause,[],[f195,f12423]) ).

fof(f12423,plain,
    ( spl0_630
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f195,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).

fof(f12421,plain,
    spl0_629,
    inference(avatar_split_clause,[],[f194,f12419]) ).

fof(f12419,plain,
    ( spl0_629
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
        | ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f194,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
      | ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).

fof(f12417,plain,
    spl0_628,
    inference(avatar_split_clause,[],[f191,f12415]) ).

fof(f12415,plain,
    ( spl0_628
  <=> ! [X2,X9,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f191,axiom,
    ! [X2,X3,X9] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

fof(f12413,plain,
    spl0_627,
    inference(avatar_split_clause,[],[f190,f12411]) ).

fof(f12411,plain,
    ( spl0_627
  <=> ! [X2,X9,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f190,axiom,
    ! [X2,X3,X9] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

fof(f12409,plain,
    spl0_626,
    inference(avatar_split_clause,[],[f184,f12407]) ).

fof(f12407,plain,
    ( spl0_626
  <=> ! [X2,X9,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
        | ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f184,axiom,
    ! [X2,X3,X9] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
      | ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X9,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

fof(f12405,plain,
    spl0_625,
    inference(avatar_split_clause,[],[f181,f12403]) ).

fof(f12403,plain,
    ( spl0_625
  <=> ! [X2,X5,X3] : c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Set_Oinsert(X3,X5,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f181,axiom,
    ! [X2,X3,X5] : c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Set_Oinsert(X3,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

fof(f12401,plain,
    spl0_624,
    inference(avatar_split_clause,[],[f115,f12399]) ).

fof(f12399,plain,
    ( spl0_624
  <=> ! [X19,X13,X5,X2,X7] :
        ( ~ c_in(X7,X5,X2)
        | ~ c_Fun_Oinj__on(X19,X5,X2,X13)
        | hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X2,X13),hAPP(X19,X7)) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f115,axiom,
    ! [X2,X19,X7,X5,X13] :
      ( ~ c_in(X7,X5,X2)
      | ~ c_Fun_Oinj__on(X19,X5,X2,X13)
      | hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X2,X13),hAPP(X19,X7)) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).

fof(f12397,plain,
    spl0_623,
    inference(avatar_split_clause,[],[f103,f12395]) ).

fof(f12395,plain,
    ( spl0_623
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_lessequals(X9,X3,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
        | c_lessequals(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f103,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | ~ c_lessequals(X9,X3,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X10,X2)
      | c_lessequals(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

fof(f12393,plain,
    ( spl0_622
    | ~ spl0_391
    | ~ spl0_433 ),
    inference(avatar_split_clause,[],[f7273,f6425,f4889,f12391]) ).

fof(f4889,plain,
    ( spl0_391
  <=> ! [X0,X1] :
        ( ~ c_lessequals(v_U,X1,tc_fun(X0,tc_bool))
        | c_in(v_pn,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f6425,plain,
    ( spl0_433
  <=> ! [X5,X9,X6,X2] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_lessequals(X5,c_Set_Oinsert(X9,X6,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f7273,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(v_U,X0,tc_fun(X1,tc_bool))
        | c_in(v_pn,c_Set_Oinsert(X2,X0,X1),X1) )
    | ~ spl0_391
    | ~ spl0_433 ),
    inference(resolution,[],[f6426,f4890]) ).

fof(f4890,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(v_U,X1,tc_fun(X0,tc_bool))
        | c_in(v_pn,X1,X0) )
    | ~ spl0_391 ),
    inference(avatar_component_clause,[],[f4889]) ).

fof(f6426,plain,
    ( ! [X2,X6,X9,X5] :
        ( c_lessequals(X5,c_Set_Oinsert(X9,X6,X2),tc_fun(X2,tc_bool))
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool)) )
    | ~ spl0_433 ),
    inference(avatar_component_clause,[],[f6425]) ).

fof(f12389,plain,
    spl0_621,
    inference(avatar_split_clause,[],[f102,f12387]) ).

fof(f12387,plain,
    ( spl0_621
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_lessequals(X9,X10,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_lessequals(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f102,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | ~ c_lessequals(X9,X10,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_lessequals(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).

fof(f12385,plain,
    spl0_620,
    inference(avatar_split_clause,[],[f68,f12383]) ).

fof(f12383,plain,
    ( spl0_620
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_lessequals(X9,X10,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f68,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | ~ c_lessequals(X9,X10,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

fof(f12381,plain,
    spl0_619,
    inference(avatar_split_clause,[],[f50,f12379]) ).

fof(f12379,plain,
    ( spl0_619
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_HOL_Oord__class_Oless(X9,X10,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f50,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | ~ c_HOL_Oord__class_Oless(X9,X10,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

fof(f12377,plain,
    spl0_618,
    inference(avatar_split_clause,[],[f45,f12375]) ).

fof(f12375,plain,
    ( spl0_618
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X10,X2),X9,X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f45,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X10,X2),X9,X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).

fof(f12373,plain,
    spl0_617,
    inference(avatar_split_clause,[],[f18,f12371]) ).

fof(f12371,plain,
    ( spl0_617
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__if_1) ).

fof(f12369,plain,
    spl0_616,
    inference(avatar_split_clause,[],[f16,f12367]) ).

fof(f12367,plain,
    ( spl0_616
  <=> ! [X2,X9,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f16,axiom,
    ! [X2,X3,X9] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

fof(f11732,plain,
    ( spl0_615
    | ~ spl0_51
    | ~ spl0_596 ),
    inference(avatar_split_clause,[],[f11698,f11377,f1600,f11729]) ).

fof(f11729,plain,
    ( spl0_615
  <=> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),v_G,t_a,tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f11377,plain,
    ( spl0_596
  <=> ! [X5,X19,X13,X6,X2] :
        ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X5,X19,X13,X2),X6,X2,X13)
        | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f11698,plain,
    ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),v_G,t_a,tc_Com_Opname)
    | ~ spl0_51
    | ~ spl0_596 ),
    inference(resolution,[],[f11378,f1602]) ).

fof(f11378,plain,
    ( ! [X2,X6,X19,X5,X13] :
        ( ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool))
        | c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X5,X19,X13,X2),X6,X2,X13) )
    | ~ spl0_596 ),
    inference(avatar_component_clause,[],[f11377]) ).

fof(f11457,plain,
    spl0_614,
    inference(avatar_split_clause,[],[f1304,f11455]) ).

fof(f11455,plain,
    ( spl0_614
  <=> ! [X2,X7] :
        ( c_HOL_Oone__class_Oone(tc_nat) = c_Finite__Set_Ocard(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
        | c_in(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f1304,plain,
    ! [X2,X7] :
      ( c_HOL_Oone__class_Oone(tc_nat) = c_Finite__Set_Ocard(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
      | c_in(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    inference(forward_demodulation,[],[f1303,f378]) ).

fof(f378,axiom,
    ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

fof(f1303,plain,
    ! [X2,X7] :
      ( c_Finite__Set_Ocard(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
      | c_in(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    inference(forward_demodulation,[],[f1302,f356]) ).

fof(f356,axiom,
    ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__empty_0) ).

fof(f1302,plain,
    ! [X2,X7] :
      ( c_Finite__Set_Ocard(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_nat)
      | c_in(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    inference(forward_demodulation,[],[f1214,f126]) ).

fof(f1214,plain,
    ! [X2,X7] :
      ( c_in(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Finite__Set_Ocard(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f950,f61]) ).

fof(f950,axiom,
    ! [X2,X7] :
      ( c_in(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Finite__Set_Ocard(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).

fof(f11452,plain,
    spl0_613,
    inference(avatar_split_clause,[],[f1276,f11450]) ).

fof(f11450,plain,
    ( spl0_613
  <=> ! [X4,X0] :
        ( c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f1276,plain,
    ! [X0,X4] :
      ( c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat) ),
    inference(forward_demodulation,[],[f1197,f126]) ).

fof(f1197,plain,
    ! [X0,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ),
    inference(definition_unfolding,[],[f113,f61]) ).

fof(f113,axiom,
    ! [X0,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat)),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).

fof(f11448,plain,
    spl0_612,
    inference(avatar_split_clause,[],[f1230,f11446]) ).

fof(f11446,plain,
    ( spl0_612
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
        | c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f1230,plain,
    ! [X0,X1] :
      ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
      | c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1050,f61,f61]) ).

fof(f1050,axiom,
    ! [X0,X1] :
      ( c_Suc(X1) = X0
      | c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(X0,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).

fof(f11444,plain,
    spl0_611,
    inference(avatar_split_clause,[],[f1223,f11442]) ).

fof(f11442,plain,
    ( spl0_611
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f1223,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(definition_unfolding,[],[f634,f61,f61]) ).

fof(f634,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_Suc(X0) = X1
      | c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

fof(f11440,plain,
    spl0_610,
    inference(avatar_split_clause,[],[f1039,f11438]) ).

fof(f11438,plain,
    ( spl0_610
  <=> ! [X5,X7,X6,X2] :
        ( c_in(X7,X5,X2)
        | c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f1039,axiom,
    ! [X2,X6,X7,X5] :
      ( c_in(X7,X5,X2)
      | c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

fof(f11436,plain,
    spl0_609,
    inference(avatar_split_clause,[],[f991,f11434]) ).

fof(f11434,plain,
    ( spl0_609
  <=> ! [X3,X19,X13,X6,X2] : c_Set_Oimage(X19,c_Set_Oinsert(X3,X6,X13),X13,X2) = c_Set_Oinsert(hAPP(X19,X3),c_Set_Oimage(X19,X6,X13,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f991,axiom,
    ! [X2,X3,X19,X6,X13] : c_Set_Oimage(X19,c_Set_Oinsert(X3,X6,X13),X13,X2) = c_Set_Oinsert(hAPP(X19,X3),c_Set_Oimage(X19,X6,X13,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

fof(f11430,plain,
    spl0_608,
    inference(avatar_split_clause,[],[f986,f11428]) ).

fof(f986,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ c_in(X7,X6,X2)
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_lessequals(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

fof(f11426,plain,
    spl0_607,
    inference(avatar_split_clause,[],[f946,f11424]) ).

fof(f11424,plain,
    ( spl0_607
  <=> ! [X19,X13,X5,X2] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_Fun_Oinj__on(X19,X5,X2,X13)
        | c_Finite__Set_Ocard(X5,X2) != c_Finite__Set_Ocard(c_Set_Oimage(X19,X5,X2,X13),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f946,axiom,
    ! [X2,X19,X5,X13] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Fun_Oinj__on(X19,X5,X2,X13)
      | c_Finite__Set_Ocard(X5,X2) != c_Finite__Set_Ocard(c_Set_Oimage(X19,X5,X2,X13),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).

fof(f11422,plain,
    spl0_606,
    inference(avatar_split_clause,[],[f937,f11420]) ).

fof(f937,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X5,X6,X19,X13,X2),X5,X13)
      | c_lessequals(c_Set_Oimage(X19,X5,X13,X2),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_1) ).

fof(f11418,plain,
    spl0_605,
    inference(avatar_split_clause,[],[f935,f11416]) ).

fof(f11416,plain,
    ( spl0_605
  <=> ! [X6,X19,X13,X5,X2] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X5,X6,X19,X2,X13),X5,X2)
        | c_lessequals(c_Set_Oimage(X19,X5,X2,X13),X6,tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f935,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X5,X6,X19,X2,X13),X5,X2)
      | c_lessequals(c_Set_Oimage(X19,X5,X2,X13),X6,tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_0) ).

fof(f11414,plain,
    spl0_604,
    inference(avatar_split_clause,[],[f923,f11412]) ).

fof(f11412,plain,
    ( spl0_604
  <=> ! [X20,X4,X21] :
        ( ~ c_lessequals(X4,X21,tc_nat)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X21,X20,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),X20,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f923,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(X4,X21,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X21,X20,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),X20,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).

fof(f11410,plain,
    spl0_603,
    inference(avatar_split_clause,[],[f922,f11408]) ).

fof(f11408,plain,
    ( spl0_603
  <=> ! [X20,X4,X21] :
        ( ~ c_lessequals(X4,X21,tc_nat)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X20,X21,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f922,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(X4,X21,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X20,X21,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).

fof(f11406,plain,
    spl0_602,
    inference(avatar_split_clause,[],[f917,f11404]) ).

fof(f11404,plain,
    ( spl0_602
  <=> ! [X20,X4,X21] :
        ( ~ c_lessequals(X4,X21,tc_nat)
        | c_HOL_Ominus__class_Ominus(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f917,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(X4,X21,tc_nat)
      | c_HOL_Ominus__class_Ominus(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),X21,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).

fof(f11402,plain,
    spl0_601,
    inference(avatar_split_clause,[],[f909,f11400]) ).

fof(f11400,plain,
    ( spl0_601
  <=> ! [X4,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f909,axiom,
    ! [X0,X1,X4] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,tc_nat)
      | ~ c_lessequals(X1,X0,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diffD1_0) ).

fof(f11398,plain,
    spl0_600,
    inference(avatar_split_clause,[],[f908,f11396]) ).

fof(f11396,plain,
    ( spl0_600
  <=> ! [X4,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,X0,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f908,axiom,
    ! [X0,X1,X4] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
      | ~ c_lessequals(X1,X0,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X4,X0,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diffD_0) ).

fof(f11394,plain,
    spl0_599,
    inference(avatar_split_clause,[],[f870,f11392]) ).

fof(f11392,plain,
    ( spl0_599
  <=> ! [X5,X3,X6,X2] :
        ( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2)
        | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f870,axiom,
    ! [X2,X3,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2)
      | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

fof(f11387,plain,
    spl0_598,
    inference(avatar_split_clause,[],[f869,f11385]) ).

fof(f11385,plain,
    ( spl0_598
  <=> ! [X5,X3,X6,X2] :
        ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2)
        | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f869,axiom,
    ! [X2,X3,X6,X5] :
      ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2)
      | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

fof(f11383,plain,
    spl0_597,
    inference(avatar_split_clause,[],[f863,f11381]) ).

fof(f11381,plain,
    ( spl0_597
  <=> ! [X19,X13,X8,X5,X2] :
        ( ~ c_in(X8,c_Set_Oimage(X19,X5,X13,X2),X2)
        | hAPP(X19,hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X13,X2),X8)) = X8 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f863,axiom,
    ! [X2,X8,X19,X5,X13] :
      ( ~ c_in(X8,c_Set_Oimage(X19,X5,X13,X2),X2)
      | hAPP(X19,hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X13,X2),X8)) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).

fof(f11379,plain,
    spl0_596,
    inference(avatar_split_clause,[],[f782,f11377]) ).

fof(f782,axiom,
    ! [X2,X19,X6,X5,X13] :
      ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X5,X19,X13,X2),X6,X2,X13)
      | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X13,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).

fof(f11375,plain,
    spl0_595,
    inference(avatar_split_clause,[],[f749,f11373]) ).

fof(f11373,plain,
    ( spl0_595
  <=> ! [X5,X7,X6,X2] :
        ( ~ c_in(X7,X6,X2)
        | c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f749,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ c_in(X7,X6,X2)
      | c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X7,X6,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

fof(f11371,plain,
    spl0_594,
    inference(avatar_split_clause,[],[f599,f11369]) ).

fof(f11369,plain,
    ( spl0_594
  <=> ! [X3,X19,X13,X9,X2] :
        ( hAPP(X19,X3) = X9
        | ~ c_in(X3,c_Set_Ovimage(X19,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),X2,X13),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f599,axiom,
    ! [X2,X3,X19,X9,X13] :
      ( hAPP(X19,X3) = X9
      | ~ c_in(X3,c_Set_Ovimage(X19,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),X2,X13),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

fof(f11367,plain,
    spl0_593,
    inference(avatar_split_clause,[],[f499,f11365]) ).

fof(f11365,plain,
    ( spl0_593
  <=> ! [X4,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f499,axiom,
    ! [X0,X1,X4] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).

fof(f11363,plain,
    spl0_592,
    inference(avatar_split_clause,[],[f334,f11361]) ).

fof(f11361,plain,
    ( spl0_592
  <=> ! [X5,X7,X6,X2] :
        ( ~ c_in(X7,X6,X2)
        | ~ c_in(X7,X5,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f334,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ c_in(X7,X6,X2)
      | ~ c_in(X7,X5,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

fof(f11359,plain,
    spl0_591,
    inference(avatar_split_clause,[],[f240,f11357]) ).

fof(f11357,plain,
    ( spl0_591
  <=> ! [X20,X21,X4] :
        ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X4,tc_nat),c_HOL_Otimes__class_Otimes(X21,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f240,axiom,
    ! [X21,X4,X20] :
      ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X4,tc_nat),c_HOL_Otimes__class_Otimes(X21,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).

fof(f11355,plain,
    spl0_590,
    inference(avatar_split_clause,[],[f238,f11353]) ).

fof(f11353,plain,
    ( spl0_590
  <=> ! [X4,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f238,axiom,
    ! [X0,X1,X4] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).

fof(f11351,plain,
    spl0_589,
    inference(avatar_split_clause,[],[f162,f11349]) ).

fof(f11349,plain,
    ( spl0_589
  <=> ! [X4,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f162,axiom,
    ! [X0,X1,X4] :
      ( c_lessequals(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).

fof(f11344,plain,
    spl0_588,
    inference(avatar_split_clause,[],[f161,f11342]) ).

fof(f11342,plain,
    ( spl0_588
  <=> ! [X4,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f161,axiom,
    ! [X0,X1,X4] :
      ( c_lessequals(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).

fof(f11340,plain,
    spl0_587,
    inference(avatar_split_clause,[],[f98,f11338]) ).

fof(f11338,plain,
    ( spl0_587
  <=> ! [X19,X13,X5,X2] :
        ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
        | c_Set_Ovimage(X19,c_Set_Oimage(X19,X5,X2,X13),X2,X13) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f98,axiom,
    ! [X2,X19,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13)
      | c_Set_Ovimage(X19,c_Set_Oimage(X19,X5,X2,X13),X2,X13) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).

fof(f11336,plain,
    spl0_586,
    inference(avatar_split_clause,[],[f8,f11334]) ).

fof(f11334,plain,
    ( spl0_586
  <=> ! [X6,X2,X5] :
        ( c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)) = X5
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f8,axiom,
    ! [X2,X6,X5] :
      ( c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)) = X5
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

fof(f11094,plain,
    ( spl0_585
    | ~ spl0_121
    | ~ spl0_552 ),
    inference(avatar_split_clause,[],[f10078,f9990,f1900,f11092]) ).

fof(f9990,plain,
    ( spl0_552
  <=> ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ hBOOL(hAPP(v_G,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f10078,plain,
    ( ! [X0] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a))) )
    | ~ spl0_121
    | ~ spl0_552 ),
    inference(resolution,[],[f9991,f1901]) ).

fof(f9991,plain,
    ( ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ hBOOL(hAPP(v_G,X0)) )
    | ~ spl0_552 ),
    inference(avatar_component_clause,[],[f9990]) ).

fof(f10775,plain,
    ( spl0_584
    | ~ spl0_121
    | ~ spl0_541 ),
    inference(avatar_split_clause,[],[f10035,f9946,f1900,f10773]) ).

fof(f9946,plain,
    ( spl0_541
  <=> ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ hBOOL(hAPP(v_G,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f10035,plain,
    ( ! [X0] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | hBOOL(hAPP(v_U,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a))) )
    | ~ spl0_121
    | ~ spl0_541 ),
    inference(resolution,[],[f9947,f1901]) ).

fof(f9947,plain,
    ( ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ hBOOL(hAPP(v_G,X0)) )
    | ~ spl0_541 ),
    inference(avatar_component_clause,[],[f9946]) ).

fof(f10304,plain,
    ( spl0_583
    | ~ spl0_490
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f9811,f9345,f8956,f10302]) ).

fof(f8956,plain,
    ( spl0_490
  <=> ! [X0,X1] :
        ( ~ c_in(X0,v_G,t_a)
        | c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f9345,plain,
    ( spl0_529
  <=> ! [X19,X13,X14,X5,X2] :
        ( ~ c_in(X14,c_Set_Oimage(X19,X5,X13,X2),X2)
        | c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X5,X19,X14,X13,X2),X5,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f9811,plain,
    ( ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_490
    | ~ spl0_529 ),
    inference(resolution,[],[f9346,f8957]) ).

fof(f8957,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X1)
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_490 ),
    inference(avatar_component_clause,[],[f8956]) ).

fof(f9346,plain,
    ( ! [X2,X19,X14,X5,X13] :
        ( ~ c_in(X14,c_Set_Oimage(X19,X5,X13,X2),X2)
        | c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X5,X19,X14,X13,X2),X5,X13) )
    | ~ spl0_529 ),
    inference(avatar_component_clause,[],[f9345]) ).

fof(f10118,plain,
    ( spl0_582
    | ~ spl0_490
    | ~ spl0_528 ),
    inference(avatar_split_clause,[],[f9782,f9341,f8956,f10116]) ).

fof(f9341,plain,
    ( spl0_528
  <=> ! [X9,X19,X13,X5,X2] :
        ( ~ c_in(X9,c_Set_Oimage(X19,X5,X13,X2),X2)
        | c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X5,X9,X19,X13,X2),X5,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f9782,plain,
    ( ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_490
    | ~ spl0_528 ),
    inference(resolution,[],[f9342,f8957]) ).

fof(f9342,plain,
    ( ! [X2,X19,X9,X5,X13] :
        ( ~ c_in(X9,c_Set_Oimage(X19,X5,X13,X2),X2)
        | c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X5,X9,X19,X13,X2),X5,X13) )
    | ~ spl0_528 ),
    inference(avatar_component_clause,[],[f9341]) ).

fof(f10114,plain,
    spl0_581,
    inference(avatar_split_clause,[],[f1345,f10112]) ).

fof(f10112,plain,
    ( spl0_581
  <=> ! [X0,X1] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f1345,plain,
    ! [X0,X1] :
      ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
    inference(forward_demodulation,[],[f1344,f378]) ).

fof(f1344,plain,
    ! [X0,X1] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
    inference(forward_demodulation,[],[f1343,f126]) ).

fof(f1343,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1342,f378]) ).

fof(f1342,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1341,f126]) ).

fof(f1341,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1340,f378]) ).

fof(f1340,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1240,f126]) ).

fof(f1240,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f778,f61,f61,f61]) ).

fof(f778,axiom,
    ! [X0,X1] :
      ( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
      | c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).

fof(f10110,plain,
    spl0_580,
    inference(avatar_split_clause,[],[f1339,f10108]) ).

fof(f10108,plain,
    ( spl0_580
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f1339,plain,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    inference(forward_demodulation,[],[f1338,f378]) ).

fof(f1338,plain,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    inference(forward_demodulation,[],[f1337,f126]) ).

fof(f1337,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1336,f378]) ).

fof(f1336,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1335,f126]) ).

fof(f1335,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1334,f378]) ).

fof(f1334,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1239,f126]) ).

fof(f1239,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f171,f61,f61,f61]) ).

fof(f171,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

fof(f10106,plain,
    spl0_579,
    inference(avatar_split_clause,[],[f1232,f10104]) ).

fof(f1232,plain,
    ! [X47,X1,X25] :
      ( hBOOL(hAPP(X25,X47))
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X47,tc_nat)
      | c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X25,X1),tc_nat) ),
    inference(definition_unfolding,[],[f886,f61]) ).

fof(f886,axiom,
    ! [X47,X1,X25] :
      ( hBOOL(hAPP(X25,X47))
      | ~ c_lessequals(c_Suc(X1),X47,tc_nat)
      | c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X25,X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__D__lemma_0) ).

fof(f10102,plain,
    spl0_578,
    inference(avatar_split_clause,[],[f972,f10100]) ).

fof(f10100,plain,
    ( spl0_578
  <=> ! [X5,X15,X6,X2] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
        | c_lessequals(X5,X15,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f972,axiom,
    ! [X2,X6,X15,X5] :
      ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
      | c_lessequals(X5,X15,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

fof(f10098,plain,
    spl0_577,
    inference(avatar_split_clause,[],[f959,f10096]) ).

fof(f10096,plain,
    ( spl0_577
  <=> ! [X15,X43,X3,X2] :
        ( ~ c_lessequals(X15,X43,tc_fun(X2,tc_bool))
        | c_lessequals(c_Set_Oinsert(X3,X15,X2),c_Set_Oinsert(X3,X43,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f959,axiom,
    ! [X2,X3,X15,X43] :
      ( ~ c_lessequals(X15,X43,tc_fun(X2,tc_bool))
      | c_lessequals(c_Set_Oinsert(X3,X15,X2),c_Set_Oinsert(X3,X43,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

fof(f10094,plain,
    spl0_576,
    inference(avatar_split_clause,[],[f940,f10092]) ).

fof(f10092,plain,
    ( spl0_576
  <=> ! [X2,X5,X19] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_Fun_Oinj__on(X19,X5,X2,X2)
        | ~ c_lessequals(X5,c_Set_Oimage(X19,X5,X2,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f940,axiom,
    ! [X2,X19,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Fun_Oinj__on(X19,X5,X2,X2)
      | ~ c_lessequals(X5,c_Set_Oimage(X19,X5,X2,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

fof(f10090,plain,
    spl0_575,
    inference(avatar_split_clause,[],[f910,f10088]) ).

fof(f10088,plain,
    ( spl0_575
  <=> ! [X20,X4,X21] :
        ( ~ c_lessequals(X4,X21,tc_nat)
        | ~ c_lessequals(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f910,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(X4,X21,tc_nat)
      | ~ c_lessequals(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),X21,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).

fof(f10086,plain,
    spl0_574,
    inference(avatar_split_clause,[],[f905,f10084]) ).

fof(f10084,plain,
    ( spl0_574
  <=> ! [X9,X3,X10] :
        ( ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat)
        | ~ c_lessequals(X10,X3,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X10,tc_nat),c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f905,axiom,
    ! [X3,X10,X9] :
      ( ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat)
      | ~ c_lessequals(X10,X3,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X10,tc_nat),c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).

fof(f10082,plain,
    spl0_573,
    inference(avatar_split_clause,[],[f866,f10080]) ).

fof(f10080,plain,
    ( spl0_573
  <=> ! [X9,X19,X13,X5,X2] :
        ( ~ c_in(X9,c_Set_Oimage(X19,X5,X13,X2),X2)
        | hAPP(X19,c_ATP__Linkup_Osko__Set__XimageE__1__1(X5,X9,X19,X13,X2)) = X9 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f866,axiom,
    ! [X2,X19,X9,X5,X13] :
      ( ~ c_in(X9,c_Set_Oimage(X19,X5,X13,X2),X2)
      | hAPP(X19,c_ATP__Linkup_Osko__Set__XimageE__1__1(X5,X9,X19,X13,X2)) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageE_0) ).

fof(f10075,plain,
    spl0_572,
    inference(avatar_split_clause,[],[f861,f10073]) ).

fof(f10073,plain,
    ( spl0_572
  <=> ! [X19,X13,X14,X5,X2] :
        ( ~ c_in(X14,c_Set_Oimage(X19,X5,X13,X2),X2)
        | hAPP(X19,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X5,X19,X14,X13,X2)) = X14 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f861,axiom,
    ! [X2,X19,X14,X5,X13] :
      ( ~ c_in(X14,c_Set_Oimage(X19,X5,X13,X2),X2)
      | hAPP(X19,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X5,X19,X14,X13,X2)) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_1) ).

fof(f10071,plain,
    spl0_571,
    inference(avatar_split_clause,[],[f858,f10069]) ).

fof(f10069,plain,
    ( spl0_571
  <=> ! [X19,X13,X5,X2,X7] :
        ( ~ c_in(X7,c_Set_Oimage(X19,X5,X13,X2),X2)
        | c_in(hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X13,X2),X7),X5,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f858,axiom,
    ! [X2,X19,X7,X5,X13] :
      ( ~ c_in(X7,c_Set_Oimage(X19,X5,X13,X2),X2)
      | c_in(hAPP(c_Hilbert__Choice_Oinv__into(X5,X19,X13,X2),X7),X5,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).

fof(f10067,plain,
    spl0_570,
    inference(avatar_split_clause,[],[f851,f10065]) ).

fof(f10065,plain,
    ( spl0_570
  <=> ! [X4,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f851,axiom,
    ! [X0,X1,X4] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).

fof(f10063,plain,
    spl0_569,
    inference(avatar_split_clause,[],[f850,f10061]) ).

fof(f10061,plain,
    ( spl0_569
  <=> ! [X4,X0,X1] : c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f850,axiom,
    ! [X0,X1,X4] : c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).

fof(f10059,plain,
    spl0_568,
    inference(avatar_split_clause,[],[f842,f10057]) ).

fof(f10057,plain,
    ( spl0_568
  <=> ! [X0,X1,X23] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X23,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X23,X1,tc_nat),c_HOL_Ominus__class_Ominus(X23,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f842,axiom,
    ! [X0,X1,X23] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X0,X23,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X23,X1,tc_nat),c_HOL_Ominus__class_Ominus(X23,X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

fof(f10055,plain,
    spl0_567,
    inference(avatar_split_clause,[],[f818,f10053]) ).

fof(f10053,plain,
    ( spl0_567
  <=> ! [X4,X20,X23,X21] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | ~ c_lessequals(X4,X23,tc_nat)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X4,tc_nat),c_HOL_Otimes__class_Otimes(X21,X23,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f818,axiom,
    ! [X21,X4,X23,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | ~ c_lessequals(X4,X23,tc_nat)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X4,tc_nat),c_HOL_Otimes__class_Otimes(X21,X23,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).

fof(f10051,plain,
    spl0_566,
    inference(avatar_split_clause,[],[f808,f10049]) ).

fof(f10049,plain,
    ( spl0_566
  <=> ! [X4,X20,X23,X21] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | ~ c_lessequals(X4,X23,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,X23,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f808,axiom,
    ! [X21,X4,X23,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | ~ c_lessequals(X4,X23,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,X23,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).

fof(f10047,plain,
    spl0_565,
    inference(avatar_split_clause,[],[f798,f10045]) ).

fof(f10045,plain,
    ( spl0_565
  <=> ! [X20,X25,X21] :
        ( ~ hBOOL(hAPP(X25,X21))
        | ~ c_lessequals(X20,X21,tc_nat)
        | hBOOL(hAPP(X25,X20))
        | ~ hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X25,X21))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f798,axiom,
    ! [X21,X25,X20] :
      ( ~ hBOOL(hAPP(X25,X21))
      | ~ c_lessequals(X20,X21,tc_nat)
      | hBOOL(hAPP(X25,X20))
      | ~ hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X25,X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inc__induct_2) ).

fof(f10043,plain,
    spl0_564,
    inference(avatar_split_clause,[],[f760,f10041]) ).

fof(f760,axiom,
    ! [X2,X6,X15,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X15,tc_fun(X2,tc_bool))
      | c_HOL_Oord__class_Oless(X5,X15,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

fof(f10039,plain,
    spl0_563,
    inference(avatar_split_clause,[],[f759,f10037]) ).

fof(f759,axiom,
    ! [X2,X6,X15,X5] :
      ( ~ c_HOL_Oord__class_Oless(X6,X15,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_HOL_Oord__class_Oless(X5,X15,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

fof(f10032,plain,
    spl0_562,
    inference(avatar_split_clause,[],[f723,f10030]) ).

fof(f10030,plain,
    ( spl0_562
  <=> ! [X4,X0,X1] : c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f723,axiom,
    ! [X0,X1,X4] : c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).

fof(f10028,plain,
    spl0_561,
    inference(avatar_split_clause,[],[f722,f10026]) ).

fof(f10026,plain,
    ( spl0_561
  <=> ! [X4,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f722,axiom,
    ! [X0,X1,X4] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).

fof(f10024,plain,
    spl0_560,
    inference(avatar_split_clause,[],[f650,f10022]) ).

fof(f10022,plain,
    ( spl0_560
  <=> ! [X9,X2,X3] :
        ( X3 = X9
        | c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f650,axiom,
    ! [X2,X3,X9] :
      ( X3 = X9
      | c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

fof(f10020,plain,
    spl0_559,
    inference(avatar_split_clause,[],[f531,f10018]) ).

fof(f10018,plain,
    ( spl0_559
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X2)
        | c_Divides_Odiv__class_Omod(X3,X10,X2) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X9,X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f531,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X2)
      | c_Divides_Odiv__class_Omod(X3,X10,X2) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X9,X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).

fof(f10016,plain,
    spl0_558,
    inference(avatar_split_clause,[],[f530,f10014]) ).

fof(f10014,plain,
    ( spl0_558
  <=> ! [X6,X2,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f530,axiom,
    ! [X2,X6,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

fof(f10012,plain,
    spl0_557,
    inference(avatar_split_clause,[],[f527,f10010]) ).

fof(f10010,plain,
    ( spl0_557
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_HOL_Oord__class_Oless(X9,X10,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
        | c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f527,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | ~ c_HOL_Oord__class_Oless(X9,X10,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
      | c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

fof(f10008,plain,
    spl0_556,
    inference(avatar_split_clause,[],[f474,f10006]) ).

fof(f10006,plain,
    ( spl0_556
  <=> ! [X4,X20,X23,X21] :
        ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,X23,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,X23,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f474,axiom,
    ! [X21,X4,X23,X20] :
      ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,X23,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,X23,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

fof(f10004,plain,
    spl0_555,
    inference(avatar_split_clause,[],[f368,f10002]) ).

fof(f10002,plain,
    ( spl0_555
  <=> ! [X4,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f368,axiom,
    ! [X0,X1,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).

fof(f10000,plain,
    spl0_554,
    inference(avatar_split_clause,[],[f333,f9998]) ).

fof(f9998,plain,
    ( spl0_554
  <=> ! [X8,X19,X13,X14,X2,X7] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X19,X7,X8,X2,X13),X7,X14,X2,X13) = c_Fun_Ofun__upd(X19,X7,X14,X2,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f333,axiom,
    ! [X2,X8,X19,X7,X14,X13] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X19,X7,X8,X2,X13),X7,X14,X2,X13) = c_Fun_Ofun__upd(X19,X7,X14,X2,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

fof(f9996,plain,
    spl0_553,
    inference(avatar_split_clause,[],[f332,f9994]) ).

fof(f9994,plain,
    ( spl0_553
  <=> ! [X20,X25,X21] :
        ( ~ hBOOL(hAPP(X25,X21))
        | ~ c_lessequals(X20,X21,tc_nat)
        | hBOOL(hAPP(X25,X20))
        | c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X25,X21),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f332,axiom,
    ! [X21,X25,X20] :
      ( ~ hBOOL(hAPP(X25,X21))
      | ~ c_lessequals(X20,X21,tc_nat)
      | hBOOL(hAPP(X25,X20))
      | c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X25,X21),X21,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inc__induct_0) ).

fof(f9992,plain,
    ( spl0_552
    | ~ spl0_472
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f9812,f9345,f7600,f9990]) ).

fof(f7600,plain,
    ( spl0_472
  <=> ! [X0,X1] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f9812,plain,
    ( ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ hBOOL(hAPP(v_G,X0)) )
    | ~ spl0_472
    | ~ spl0_529 ),
    inference(resolution,[],[f9346,f7601]) ).

fof(f7601,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X1)
        | ~ hBOOL(hAPP(v_G,X0)) )
    | ~ spl0_472 ),
    inference(avatar_component_clause,[],[f7600]) ).

fof(f9988,plain,
    spl0_551,
    inference(avatar_split_clause,[],[f325,f9986]) ).

fof(f9986,plain,
    ( spl0_551
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X2),X2),X0,X2) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f325,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X2),X2),X0,X2) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

fof(f9984,plain,
    spl0_550,
    inference(avatar_split_clause,[],[f324,f9982]) ).

fof(f9982,plain,
    ( spl0_550
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X0,X2),X0,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X2),X2),X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f324,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X0,X2),X0,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X2),X2),X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

fof(f9980,plain,
    spl0_549,
    inference(avatar_split_clause,[],[f279,f9978]) ).

fof(f9978,plain,
    ( spl0_549
  <=> ! [X2,X13,X8,X19,X7] :
        ( X7 = X8
        | hAPP(X19,X7) != hAPP(X19,X8)
        | ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f279,axiom,
    ! [X2,X8,X19,X7,X13] :
      ( X7 = X8
      | hAPP(X19,X7) != hAPP(X19,X8)
      | ~ c_Fun_Oinj__on(X19,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).

fof(f9976,plain,
    spl0_548,
    inference(avatar_split_clause,[],[f278,f9974]) ).

fof(f9974,plain,
    ( spl0_548
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f278,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

fof(f9972,plain,
    spl0_547,
    inference(avatar_split_clause,[],[f236,f9970]) ).

fof(f9970,plain,
    ( spl0_547
  <=> ! [X4,X0,X1] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f236,axiom,
    ! [X0,X1,X4] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).

fof(f9968,plain,
    spl0_546,
    inference(avatar_split_clause,[],[f235,f9966]) ).

fof(f9966,plain,
    ( spl0_546
  <=> ! [X4,X0,X1] : c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f235,axiom,
    ! [X0,X1,X4] : c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).

fof(f9964,plain,
    spl0_545,
    inference(avatar_split_clause,[],[f38,f9962]) ).

fof(f9962,plain,
    ( spl0_545
  <=> ! [X6,X2,X5] : c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f38,axiom,
    ! [X2,X6,X5] : c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

fof(f9960,plain,
    spl0_544,
    inference(avatar_split_clause,[],[f33,f9958]) ).

fof(f9958,plain,
    ( spl0_544
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

fof(f9956,plain,
    spl0_543,
    inference(avatar_split_clause,[],[f20,f9954]) ).

fof(f9954,plain,
    ( spl0_543
  <=> ! [X5,X15,X6,X2] :
        ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_HOL_Oord__class_Oless(X6,X15,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(X5,X15,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f20,axiom,
    ! [X2,X6,X15,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_HOL_Oord__class_Oless(X6,X15,tc_fun(X2,tc_bool))
      | c_HOL_Oord__class_Oless(X5,X15,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

fof(f9952,plain,
    spl0_542,
    inference(avatar_split_clause,[],[f17,f9950]) ).

fof(f9950,plain,
    ( spl0_542
  <=> ! [X11,X13,X12,X2] :
        ( ~ c_Finite__Set_Ofinite(X12,X2)
        | c_Finite__Set_Ofinite(c_Set_Ovimage(X11,X12,X13,X2),X13)
        | ~ c_Fun_Oinj__on(X11,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_bool)),X13,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f17,axiom,
    ! [X2,X11,X12,X13] :
      ( ~ c_Finite__Set_Ofinite(X12,X2)
      | c_Finite__Set_Ofinite(c_Set_Ovimage(X11,X12,X13,X2),X13)
      | ~ c_Fun_Oinj__on(X11,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_bool)),X13,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).

fof(f9948,plain,
    ( spl0_541
    | ~ spl0_472
    | ~ spl0_528 ),
    inference(avatar_split_clause,[],[f9783,f9341,f7600,f9946]) ).

fof(f9783,plain,
    ( ! [X0] :
        ( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)
        | ~ hBOOL(hAPP(v_G,X0)) )
    | ~ spl0_472
    | ~ spl0_528 ),
    inference(resolution,[],[f9342,f7601]) ).

fof(f9511,plain,
    ( ~ spl0_35
    | ~ spl0_540
    | ~ spl0_199
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f3264,f3215,f2376,f9508,f1520]) ).

fof(f1520,plain,
    ( spl0_35
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f9508,plain,
    ( spl0_540
  <=> c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f2376,plain,
    ( spl0_199
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
        | ~ c_lessequals(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f3215,plain,
    ( spl0_266
  <=> c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f3264,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ class_Orderings_Opreorder(tc_nat)
    | ~ spl0_199
    | ~ spl0_266 ),
    inference(resolution,[],[f3217,f2377]) ).

fof(f2377,plain,
    ( ! [X2,X8,X7] :
        ( ~ c_lessequals(X8,X7,X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl0_199 ),
    inference(avatar_component_clause,[],[f2376]) ).

fof(f3217,plain,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_266 ),
    inference(avatar_component_clause,[],[f3215]) ).

fof(f9396,plain,
    ( spl0_539
    | ~ spl0_247
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f3170,f3018,f2735,f9393]) ).

fof(f9393,plain,
    ( spl0_539
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f3018,plain,
    ( spl0_255
  <=> c_lessequals(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f3170,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_247
    | ~ spl0_255 ),
    inference(resolution,[],[f3020,f2736]) ).

fof(f3020,plain,
    ( c_lessequals(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_255 ),
    inference(avatar_component_clause,[],[f3018]) ).

fof(f9384,plain,
    spl0_538,
    inference(avatar_split_clause,[],[f1333,f9382]) ).

fof(f9382,plain,
    ( spl0_538
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f1333,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1332,f378]) ).

fof(f1332,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1331,f126]) ).

fof(f1331,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1330,f378]) ).

fof(f1330,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1238,f126]) ).

fof(f1238,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f522,f61,f61]) ).

fof(f522,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

fof(f9380,plain,
    spl0_537,
    inference(avatar_split_clause,[],[f1329,f9378]) ).

fof(f9378,plain,
    ( spl0_537
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f1329,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1328,f378]) ).

fof(f1328,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1327,f126]) ).

fof(f1327,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1326,f378]) ).

fof(f1326,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1237,f126]) ).

fof(f1237,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f521,f61,f61]) ).

fof(f521,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

fof(f9376,plain,
    spl0_536,
    inference(avatar_split_clause,[],[f1243,f9374]) ).

fof(f9374,plain,
    ( spl0_536
  <=> ! [X2] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f1243,plain,
    ! [X2] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(duplicate_literal_removal,[],[f13]) ).

fof(f13,axiom,
    ! [X2] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

fof(f9372,plain,
    spl0_535,
    inference(avatar_split_clause,[],[f1231,f9370]) ).

fof(f9370,plain,
    ( spl0_535
  <=> ! [X25,X0,X1] :
        ( hBOOL(hAPP(X25,X1))
        | hBOOL(hAPP(X25,X0))
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X25),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f1231,plain,
    ! [X0,X1,X25] :
      ( hBOOL(hAPP(X25,X1))
      | hBOOL(hAPP(X25,X0))
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X25),tc_nat) ),
    inference(definition_unfolding,[],[f874,f61]) ).

fof(f874,axiom,
    ! [X0,X1,X25] :
      ( hBOOL(hAPP(X25,X1))
      | hBOOL(hAPP(X25,X0))
      | ~ c_lessequals(c_Suc(X0),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X25),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_full__nat__induct_0) ).

fof(f9367,plain,
    spl0_534,
    inference(avatar_split_clause,[],[f1207,f9365]) ).

fof(f9365,plain,
    ( spl0_534
  <=> ! [X4,X5,X2] :
        ( c_Finite__Set_Ocard(X5,X2) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X5,X4,X2),X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f1207,plain,
    ! [X2,X4,X5] :
      ( c_Finite__Set_Ocard(X5,X2) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
      | c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X5,X4,X2),X2) = X4 ),
    inference(definition_unfolding,[],[f902,f61]) ).

fof(f902,axiom,
    ! [X2,X4,X5] :
      ( c_Finite__Set_Ocard(X5,X2) != c_Suc(X4)
      | c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X5,X4,X2),X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__SucD_2) ).

fof(f9363,plain,
    spl0_533,
    inference(avatar_split_clause,[],[f1206,f9361]) ).

fof(f9361,plain,
    ( spl0_533
  <=> ! [X4,X5,X2] :
        ( c_Finite__Set_Ocard(X5,X2) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X5,X4,X2),X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f1206,plain,
    ! [X2,X4,X5] :
      ( c_Finite__Set_Ocard(X5,X2) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
      | c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X5,X4,X2),X2) = X4 ),
    inference(definition_unfolding,[],[f903,f61]) ).

fof(f903,axiom,
    ! [X2,X4,X5] :
      ( c_Finite__Set_Ocard(X5,X2) != c_Suc(X4)
      | c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X5,X4,X2),X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_2) ).

fof(f9359,plain,
    spl0_532,
    inference(avatar_split_clause,[],[f1162,f9357]) ).

fof(f9357,plain,
    ( spl0_532
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f1162,plain,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2) ),
    inference(definition_unfolding,[],[f160,f61]) ).

fof(f160,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X2)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X0),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

fof(f9355,plain,
    spl0_531,
    inference(avatar_split_clause,[],[f1046,f9353]) ).

fof(f9353,plain,
    ( spl0_531
  <=> ! [X6,X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_lessequals(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f1046,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_lessequals(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).

fof(f9351,plain,
    spl0_530,
    inference(avatar_split_clause,[],[f992,f9349]) ).

fof(f9349,plain,
    ( spl0_530
  <=> ! [X2,X5,X7] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_in(X7,X5,X2)
        | c_Finite__Set_Ocard(X5,X2) = c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f992,axiom,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2)
      | c_Finite__Set_Ocard(X5,X2) = c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).

fof(f9347,plain,
    spl0_529,
    inference(avatar_split_clause,[],[f864,f9345]) ).

fof(f864,axiom,
    ! [X2,X19,X14,X5,X13] :
      ( ~ c_in(X14,c_Set_Oimage(X19,X5,X13,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X5,X19,X14,X13,X2),X5,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_0) ).

fof(f9343,plain,
    spl0_528,
    inference(avatar_split_clause,[],[f860,f9341]) ).

fof(f860,axiom,
    ! [X2,X19,X9,X5,X13] :
      ( ~ c_in(X9,c_Set_Oimage(X19,X5,X13,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X5,X9,X19,X13,X2),X5,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageE_1) ).

fof(f9339,plain,
    spl0_527,
    inference(avatar_split_clause,[],[f837,f9337]) ).

fof(f9337,plain,
    ( spl0_527
  <=> ! [X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f837,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

fof(f9335,plain,
    spl0_526,
    inference(avatar_split_clause,[],[f788,f9333]) ).

fof(f9333,plain,
    ( spl0_526
  <=> ! [X6,X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
        | c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f788,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
      | c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(X6,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).

fof(f9331,plain,
    spl0_525,
    inference(avatar_split_clause,[],[f777,f9329]) ).

fof(f9329,plain,
    ( spl0_525
  <=> ! [X5,X15,X6,X2] :
        ( c_lessequals(X15,X5,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f777,axiom,
    ! [X2,X6,X15,X5] :
      ( c_lessequals(X15,X5,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

fof(f9327,plain,
    ( spl0_524
    | ~ spl0_163
    | ~ spl0_503 ),
    inference(avatar_split_clause,[],[f9266,f9219,f2093,f9325]) ).

fof(f9325,plain,
    ( spl0_524
  <=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X0,v_U,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f2093,plain,
    ( spl0_163
  <=> ! [X2,X5,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X3,X5,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f9266,plain,
    ( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X0,v_U,X1)
    | ~ spl0_163
    | ~ spl0_503 ),
    inference(superposition,[],[f2094,f9220]) ).

fof(f2094,plain,
    ( ! [X2,X3,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X3,X5,X2)
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f2093]) ).

fof(f9323,plain,
    spl0_523,
    inference(avatar_split_clause,[],[f776,f9321]) ).

fof(f9321,plain,
    ( spl0_523
  <=> ! [X5,X15,X6,X2] :
        ( c_lessequals(X15,X6,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f776,axiom,
    ! [X2,X6,X15,X5] :
      ( c_lessequals(X15,X6,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

fof(f9319,plain,
    spl0_522,
    inference(avatar_split_clause,[],[f719,f9317]) ).

fof(f9317,plain,
    ( spl0_522
  <=> ! [X14,X8,X2,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X8,X14,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X7,X8,X2),X14,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f719,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X8,X14,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X7,X8,X2),X14,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

fof(f9315,plain,
    spl0_521,
    inference(avatar_split_clause,[],[f717,f9313]) ).

fof(f9313,plain,
    ( spl0_521
  <=> ! [X31,X32,X29,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(X29,c_HOL_Otimes__class_Otimes(X31,X32,X2),X2) = c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(X29,X32,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f717,axiom,
    ! [X2,X31,X29,X32] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Otimes__class_Otimes(X29,c_HOL_Otimes__class_Otimes(X31,X32,X2),X2) = c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(X29,X32,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(f9311,plain,
    spl0_520,
    inference(avatar_split_clause,[],[f714,f9309]) ).

fof(f9309,plain,
    ( spl0_520
  <=> ! [X31,X29,X2,X30] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X30,X2),X31,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X31,X2),X30,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f714,axiom,
    ! [X2,X31,X29,X30] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X30,X2),X31,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X31,X2),X30,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(f9307,plain,
    spl0_519,
    inference(avatar_split_clause,[],[f713,f9305]) ).

fof(f9305,plain,
    ( spl0_519
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X2)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f713,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X2)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(f9303,plain,
    spl0_518,
    inference(avatar_split_clause,[],[f690,f9301]) ).

fof(f9301,plain,
    ( spl0_518
  <=> ! [X5,X7,X6,X2] :
        ( ~ hBOOL(hAPP(X5,X7))
        | ~ hBOOL(hAPP(X6,X7))
        | hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f690,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ hBOOL(hAPP(X5,X7))
      | ~ hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

fof(f9299,plain,
    spl0_517,
    inference(avatar_split_clause,[],[f689,f9297]) ).

fof(f9297,plain,
    ( spl0_517
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f689,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).

fof(f9295,plain,
    spl0_516,
    inference(avatar_split_clause,[],[f688,f9293]) ).

fof(f9293,plain,
    ( spl0_516
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Osemiring__1(X2)
        | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f688,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Osemiring__1(X2)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

fof(f9291,plain,
    spl0_515,
    inference(avatar_split_clause,[],[f580,f9289]) ).

fof(f9289,plain,
    ( spl0_515
  <=> ! [X2,X5] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_Finite__Set_Ofinite(X5,X2)
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
        | c_in(c_Finite__Set_Olinorder__class_OMax(X5,X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f580,axiom,
    ! [X2,X5] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
      | c_in(c_Finite__Set_Olinorder__class_OMax(X5,X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).

fof(f9287,plain,
    spl0_514,
    inference(avatar_split_clause,[],[f579,f9285]) ).

fof(f9285,plain,
    ( spl0_514
  <=> ! [X2,X5] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_Finite__Set_Ofinite(X5,X2)
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
        | c_in(c_Finite__Set_Olinorder__class_OMin(X5,X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f579,axiom,
    ! [X2,X5] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
      | c_in(c_Finite__Set_Olinorder__class_OMin(X5,X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).

fof(f9261,plain,
    spl0_513,
    inference(avatar_split_clause,[],[f444,f9259]) ).

fof(f9259,plain,
    ( spl0_513
  <=> ! [X7,X8,X14,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X7,X8,X2)
        | ~ c_lessequals(X7,X14,X2)
        | c_lessequals(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f444,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X7,X8,X2)
      | ~ c_lessequals(X7,X14,X2)
      | c_lessequals(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

fof(f9257,plain,
    spl0_512,
    inference(avatar_split_clause,[],[f418,f9255]) ).

fof(f9255,plain,
    ( spl0_512
  <=> ! [X5,X10,X6,X2] :
        ( ~ c_in(X10,X5,X2)
        | c_in(X10,X6,X2)
        | c_in(X10,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f418,axiom,
    ! [X2,X10,X6,X5] :
      ( ~ c_in(X10,X5,X2)
      | c_in(X10,X6,X2)
      | c_in(X10,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

fof(f9253,plain,
    spl0_511,
    inference(avatar_split_clause,[],[f401,f9251]) ).

fof(f9251,plain,
    ( spl0_511
  <=> ! [X5,X10,X6,X2] :
        ( ~ c_in(X10,X5,X2)
        | ~ c_in(X10,X6,X2)
        | c_in(X10,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f401,axiom,
    ! [X2,X10,X6,X5] :
      ( ~ c_in(X10,X5,X2)
      | ~ c_in(X10,X6,X2)
      | c_in(X10,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

fof(f9249,plain,
    spl0_510,
    inference(avatar_split_clause,[],[f365,f9247]) ).

fof(f9247,plain,
    ( spl0_510
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X9,X10,X2),X2),X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f365,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X9,X10,X2),X2),X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).

fof(f9245,plain,
    spl0_509,
    inference(avatar_split_clause,[],[f364,f9243]) ).

fof(f9243,plain,
    ( spl0_509
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X10,X9,X2),X2),X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f364,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X10,X9,X2),X2),X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).

fof(f9241,plain,
    spl0_508,
    inference(avatar_split_clause,[],[f293,f9239]) ).

fof(f9239,plain,
    ( spl0_508
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Osemiring__1(X2)
        | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f293,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Osemiring__1(X2)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).

fof(f9237,plain,
    spl0_507,
    inference(avatar_split_clause,[],[f286,f9235]) ).

fof(f9235,plain,
    ( spl0_507
  <=> ! [X14,X8,X2,X7] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X14,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f286,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X14,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

fof(f9233,plain,
    spl0_506,
    inference(avatar_split_clause,[],[f285,f9231]) ).

fof(f9231,plain,
    ( spl0_506
  <=> ! [X8,X7,X14,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X7,X14,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f285,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X7,X14,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

fof(f9229,plain,
    spl0_505,
    inference(avatar_split_clause,[],[f284,f9227]) ).

fof(f9227,plain,
    ( spl0_505
  <=> ! [X8,X7,X14,X2] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X7,X14,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f284,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X7,X14,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

fof(f9225,plain,
    spl0_504,
    inference(avatar_split_clause,[],[f283,f9223]) ).

fof(f9223,plain,
    ( spl0_504
  <=> ! [X14,X8,X2,X7] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X14,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f283,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X14,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

fof(f9221,plain,
    ( spl0_503
    | ~ spl0_208
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f6102,f5823,f2412,f9219]) ).

fof(f2412,plain,
    ( spl0_208
  <=> ! [X2,X5,X3] :
        ( ~ c_in(X3,X5,X2)
        | c_Set_Oinsert(X3,X5,X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f5823,plain,
    ( spl0_407
  <=> ! [X2,X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f6102,plain,
    ( ! [X2,X0,X1] : c_Set_Oinsert(X0,v_U,X1) = c_Set_Oinsert(v_pn,c_Set_Oinsert(X0,v_U,X1),X2)
    | ~ spl0_208
    | ~ spl0_407 ),
    inference(resolution,[],[f5824,f2413]) ).

fof(f2413,plain,
    ( ! [X2,X3,X5] :
        ( ~ c_in(X3,X5,X2)
        | c_Set_Oinsert(X3,X5,X2) = X5 )
    | ~ spl0_208 ),
    inference(avatar_component_clause,[],[f2412]) ).

fof(f5824,plain,
    ( ! [X2,X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X2)
    | ~ spl0_407 ),
    inference(avatar_component_clause,[],[f5823]) ).

fof(f9217,plain,
    spl0_502,
    inference(avatar_split_clause,[],[f262,f9215]) ).

fof(f9215,plain,
    ( spl0_502
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
        | c_HOL_Ozero__class_Ozero(X2) = X9
        | c_HOL_Ozero__class_Ozero(X2) = X3
        | c_HOL_Ozero__class_Ozero(X2) != c_HOL_Otimes__class_Otimes(X3,X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f262,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
      | c_HOL_Ozero__class_Ozero(X2) = X9
      | c_HOL_Ozero__class_Ozero(X2) = X3
      | c_HOL_Ozero__class_Ozero(X2) != c_HOL_Otimes__class_Otimes(X3,X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

fof(f9213,plain,
    spl0_501,
    inference(avatar_split_clause,[],[f223,f9211]) ).

fof(f9211,plain,
    ( spl0_501
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f223,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).

fof(f9209,plain,
    spl0_500,
    inference(avatar_split_clause,[],[f127,f9207]) ).

fof(f9207,plain,
    ( spl0_500
  <=> ! [X4,X0,X23,X1] :
        ( ~ c_HOL_Oord__class_Oless(X4,X23,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X23,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f127,axiom,
    ! [X0,X1,X4,X23] :
      ( ~ c_HOL_Oord__class_Oless(X4,X23,tc_nat)
      | c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oplus__class_Oplus(X0,X23,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

fof(f9205,plain,
    spl0_499,
    inference(avatar_split_clause,[],[f112,f9203]) ).

fof(f9203,plain,
    ( spl0_499
  <=> ! [X4,X0,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,c_Divides_Odiv__class_Omod(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f112,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ class_Divides_Osemiring__div(X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X4,c_Divides_Odiv__class_Omod(X0,X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod_0) ).

fof(f9201,plain,
    spl0_498,
    inference(avatar_split_clause,[],[f111,f9199]) ).

fof(f9199,plain,
    ( spl0_498
  <=> ! [X4,X0,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,X0,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_Divides_Odiv__class_Omod(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f111,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ class_Divides_Osemiring__div(X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X4,X0,X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_Divides_Odiv__class_Omod(X0,X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).

fof(f9197,plain,
    spl0_497,
    inference(avatar_split_clause,[],[f54,f9195]) ).

fof(f9195,plain,
    ( spl0_497
  <=> ! [X4,X0,X1] :
        ( X0 = X1
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_HOL_Otimes__class_Otimes(X4,X0,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f54,axiom,
    ! [X0,X1,X4] :
      ( X0 = X1
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Otimes__class_Otimes(X4,X0,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

fof(f9193,plain,
    spl0_496,
    inference(avatar_split_clause,[],[f31,f9191]) ).

fof(f9191,plain,
    ( spl0_496
  <=> ! [X3,X10,X16,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X16,X2),X2) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X3,X16,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f31,axiom,
    ! [X2,X3,X10,X16] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X16,X2),X2) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X3,X16,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(f9189,plain,
    spl0_495,
    inference(avatar_split_clause,[],[f30,f9187]) ).

fof(f9187,plain,
    ( spl0_495
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X2),X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f30,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X2),X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(f9185,plain,
    spl0_494,
    inference(avatar_split_clause,[],[f28,f9183]) ).

fof(f9183,plain,
    ( spl0_494
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f28,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(f9181,plain,
    spl0_493,
    inference(avatar_split_clause,[],[f27,f9179]) ).

fof(f9179,plain,
    ( spl0_493
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
        | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f27,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X3,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(f9175,plain,
    spl0_492,
    inference(avatar_split_clause,[],[f26,f9173]) ).

fof(f9173,plain,
    ( spl0_492
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f26,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X2),X10,X2) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

fof(f9171,plain,
    spl0_491,
    inference(avatar_split_clause,[],[f22,f9169]) ).

fof(f9169,plain,
    ( spl0_491
  <=> ! [X14,X8,X2,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X8,X14,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X8,X2),X14,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f22,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X8,X14,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X8,X2),X14,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

fof(f8958,plain,
    ( spl0_490
    | ~ spl0_120
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f8425,f7644,f1896,f8956]) ).

fof(f7644,plain,
    ( spl0_483
  <=> ! [X0] :
        ( ~ c_in(X0,v_G,t_a)
        | hBOOL(hAPP(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f8425,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,v_G,t_a)
        | c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X1) )
    | ~ spl0_120
    | ~ spl0_483 ),
    inference(resolution,[],[f7645,f1897]) ).

fof(f7645,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0))
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_483 ),
    inference(avatar_component_clause,[],[f7644]) ).

fof(f7670,plain,
    spl0_489,
    inference(avatar_split_clause,[],[f1301,f7668]) ).

fof(f7668,plain,
    ( spl0_489
  <=> ! [X2,X5] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_Finite__Set_Ocard(X5,X2)
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f1301,plain,
    ! [X2,X5] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_Finite__Set_Ocard(X5,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
    inference(forward_demodulation,[],[f1211,f377]) ).

fof(f377,axiom,
    ! [X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

fof(f1211,plain,
    ! [X2,X5] :
      ( c_Finite__Set_Ocard(X5,X2) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
    inference(definition_unfolding,[],[f132,f61]) ).

fof(f132,axiom,
    ! [X2,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_Finite__Set_Ocard(X5,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_3) ).

fof(f7666,plain,
    spl0_488,
    inference(avatar_split_clause,[],[f1300,f7664]) ).

fof(f7664,plain,
    ( spl0_488
  <=> ! [X2,X5] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_Finite__Set_Ocard(X5,X2)
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f1300,plain,
    ! [X2,X5] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_Finite__Set_Ocard(X5,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
    inference(forward_demodulation,[],[f1210,f377]) ).

fof(f1210,plain,
    ! [X2,X5] :
      ( c_Finite__Set_Ocard(X5,X2) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
    inference(definition_unfolding,[],[f259,f61]) ).

fof(f259,axiom,
    ! [X2,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_Finite__Set_Ocard(X5,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__SucD_3) ).

fof(f7662,plain,
    spl0_487,
    inference(avatar_split_clause,[],[f1277,f7660]) ).

fof(f7660,plain,
    ( spl0_487
  <=> ! [X1] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X1
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f1277,plain,
    ! [X1] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X1
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(forward_demodulation,[],[f1198,f126]) ).

fof(f1198,plain,
    ! [X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1 ),
    inference(definition_unfolding,[],[f472,f61]) ).

fof(f472,axiom,
    ! [X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).

fof(f7658,plain,
    spl0_486,
    inference(avatar_split_clause,[],[f1222,f7656]) ).

fof(f7656,plain,
    ( spl0_486
  <=> ! [X20,X21,X4] :
        ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f1222,plain,
    ! [X21,X4,X20] :
      ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ),
    inference(definition_unfolding,[],[f620,f61]) ).

fof(f620,axiom,
    ! [X21,X4,X20] :
      ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(X20),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

fof(f7654,plain,
    spl0_485,
    inference(avatar_split_clause,[],[f1202,f7652]) ).

fof(f1202,plain,
    ! [X1,X47] :
      ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X47,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X47),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X47 ),
    inference(definition_unfolding,[],[f885,f61,f61]) ).

fof(f885,axiom,
    ! [X1,X47] :
      ( ~ c_lessequals(c_Suc(X1),X47,tc_nat)
      | c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X47)) = X47 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__D_0) ).

fof(f7650,plain,
    spl0_484,
    inference(avatar_split_clause,[],[f1200,f7648]) ).

fof(f7648,plain,
    ( spl0_484
  <=> ! [X20,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X20,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f1200,plain,
    ! [X1,X20] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X20,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X1,tc_nat) ),
    inference(definition_unfolding,[],[f820,f61]) ).

fof(f820,axiom,
    ! [X1,X20] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X20),tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

fof(f7646,plain,
    ( spl0_483
    | ~ spl0_121
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f7513,f6465,f1900,f7644]) ).

fof(f6465,plain,
    ( spl0_443
  <=> ! [X0] :
        ( c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
        | ~ c_in(X0,v_G,t_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f7513,plain,
    ( ! [X0] :
        ( ~ c_in(X0,v_G,t_a)
        | hBOOL(hAPP(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0)) )
    | ~ spl0_121
    | ~ spl0_443 ),
    inference(resolution,[],[f6466,f1901]) ).

fof(f6466,plain,
    ( ! [X0] :
        ( c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_443 ),
    inference(avatar_component_clause,[],[f6465]) ).

fof(f7642,plain,
    spl0_482,
    inference(avatar_split_clause,[],[f1195,f7640]) ).

fof(f7640,plain,
    ( spl0_482
  <=> ! [X0,X1] :
        ( c_lessequals(X1,X0,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f1195,plain,
    ! [X0,X1] :
      ( c_lessequals(X1,X0,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f958,f61,f61]) ).

fof(f958,axiom,
    ! [X0,X1] :
      ( c_lessequals(X1,X0,tc_nat)
      | ~ c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).

fof(f7638,plain,
    spl0_481,
    inference(avatar_split_clause,[],[f1190,f7636]) ).

fof(f7636,plain,
    ( spl0_481
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f1190,plain,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f639,f61,f61]) ).

fof(f639,axiom,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

fof(f7634,plain,
    spl0_480,
    inference(avatar_split_clause,[],[f1157,f7632]) ).

fof(f7632,plain,
    ( spl0_480
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f1157,plain,
    ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(definition_unfolding,[],[f281,f61]) ).

fof(f281,axiom,
    ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).

fof(f7630,plain,
    spl0_479,
    inference(avatar_split_clause,[],[f1156,f7628]) ).

fof(f7628,plain,
    ( spl0_479
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f1156,plain,
    ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f280,f61]) ).

fof(f280,axiom,
    ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).

fof(f7626,plain,
    spl0_478,
    inference(avatar_split_clause,[],[f1055,f7624]) ).

fof(f1055,axiom,
    ! [X2,X41,X19,X7,X13] :
      ( ~ class_HOL_Oord(X13)
      | ~ c_lessequals(X19,X41,tc_fun(X2,X13))
      | c_lessequals(hAPP(X19,X7),hAPP(X41,X7),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

fof(f7622,plain,
    spl0_477,
    inference(avatar_split_clause,[],[f1014,f7620]) ).

fof(f7620,plain,
    ( spl0_477
  <=> ! [X6,X19,X13,X5,X2] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_Finite__Set_Ofinite(X6,X13)
        | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X2,X13),tc_fun(X13,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f1014,axiom,
    ! [X2,X6,X19,X5,X13] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Finite__Set_Ofinite(X6,X13)
      | ~ c_lessequals(X6,c_Set_Oimage(X19,X5,X2,X13),tc_fun(X13,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).

fof(f7618,plain,
    spl0_476,
    inference(avatar_split_clause,[],[f926,f7616]) ).

fof(f7616,plain,
    ( spl0_476
  <=> ! [X19,X13,X5,X2] :
        ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
        | c_Finite__Set_Ocard(X5,X2) = c_Finite__Set_Ocard(c_Set_Oimage(X19,X5,X2,X13),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f926,axiom,
    ! [X2,X19,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
      | c_Finite__Set_Ocard(X5,X2) = c_Finite__Set_Ocard(c_Set_Oimage(X19,X5,X2,X13),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).

fof(f7614,plain,
    spl0_475,
    inference(avatar_split_clause,[],[f912,f7612]) ).

fof(f7612,plain,
    ( spl0_475
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X1,X0,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f912,axiom,
    ! [X0,X1] :
      ( ~ c_lessequals(X1,X0,tc_nat)
      | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).

fof(f7610,plain,
    spl0_474,
    inference(avatar_split_clause,[],[f856,f7608]) ).

fof(f7608,plain,
    ( spl0_474
  <=> ! [X2,X7,X8] :
        ( ~ class_Orderings_Oorder(X2)
        | ~ c_lessequals(X8,X7,X2)
        | c_lessequals(c_SetInterval_Oord__class_OatLeast(X7,X2),c_SetInterval_Oord__class_OatLeast(X8,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f856,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_lessequals(X8,X7,X2)
      | c_lessequals(c_SetInterval_Oord__class_OatLeast(X7,X2),c_SetInterval_Oord__class_OatLeast(X8,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_1) ).

fof(f7606,plain,
    spl0_473,
    inference(avatar_split_clause,[],[f845,f7604]) ).

fof(f7604,plain,
    ( spl0_473
  <=> ! [X20,X4,X25] :
        ( ~ hBOOL(hAPP(X25,X4))
        | ~ hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X25)))
        | hBOOL(hAPP(X25,c_HOL_Ominus__class_Ominus(X4,X20,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f845,axiom,
    ! [X4,X25,X20] :
      ( ~ hBOOL(hAPP(X25,X4))
      | ~ hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X25)))
      | hBOOL(hAPP(X25,c_HOL_Ominus__class_Ominus(X4,X20,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct__lemma_1) ).

fof(f7602,plain,
    ( spl0_472
    | ~ spl0_120
    | ~ spl0_432 ),
    inference(avatar_split_clause,[],[f7458,f6421,f1896,f7600]) ).

fof(f6421,plain,
    ( spl0_432
  <=> ! [X0] :
        ( hBOOL(hAPP(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0))
        | ~ hBOOL(hAPP(v_G,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f7458,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(hAPP(v_G,X0))
        | c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X1) )
    | ~ spl0_120
    | ~ spl0_432 ),
    inference(resolution,[],[f6422,f1897]) ).

fof(f6422,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0))
        | ~ hBOOL(hAPP(v_G,X0)) )
    | ~ spl0_432 ),
    inference(avatar_component_clause,[],[f6421]) ).

fof(f7598,plain,
    spl0_471,
    inference(avatar_split_clause,[],[f823,f7596]) ).

fof(f7596,plain,
    ( spl0_471
  <=> ! [X19,X13,X5,X2] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)) = X5
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X19,X5,X13,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f823,axiom,
    ! [X2,X19,X5,X13] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)) = X5
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X19,X5,X13,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

fof(f7594,plain,
    spl0_470,
    inference(avatar_split_clause,[],[f761,f7592]) ).

fof(f761,axiom,
    ! [X2,X19,X6,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,X6,X2,X13)
      | c_Fun_Oinj__on(X19,X5,X2,X13)
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

fof(f7590,plain,
    spl0_469,
    inference(avatar_split_clause,[],[f755,f7588]) ).

fof(f7588,plain,
    ( spl0_469
  <=> ! [X2,X7,X8] :
        ( ~ class_Orderings_Oorder(X2)
        | c_lessequals(X8,X7,X2)
        | ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X7,X2),c_SetInterval_Oord__class_OatLeast(X8,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f755,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Oorder(X2)
      | c_lessequals(X8,X7,X2)
      | ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X7,X2),c_SetInterval_Oord__class_OatLeast(X8,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_0) ).

fof(f7586,plain,
    spl0_468,
    inference(avatar_split_clause,[],[f672,f7584]) ).

fof(f7584,plain,
    ( spl0_468
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X1
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f672,axiom,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X1
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_0) ).

fof(f7582,plain,
    spl0_467,
    inference(avatar_split_clause,[],[f671,f7580]) ).

fof(f7580,plain,
    ( spl0_467
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X1
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f671,axiom,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X1
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_0) ).

fof(f7578,plain,
    spl0_466,
    inference(avatar_split_clause,[],[f668,f7576]) ).

fof(f7576,plain,
    ( spl0_466
  <=> ! [X9,X25,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat)
        | hBOOL(hAPP(X25,c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ hBOOL(hAPP(X25,c_HOL_Ominus__class_Ominus(X3,X9,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f668,axiom,
    ! [X3,X9,X25] :
      ( ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat)
      | hBOOL(hAPP(X25,c_HOL_Ozero__class_Ozero(tc_nat)))
      | ~ hBOOL(hAPP(X25,c_HOL_Ominus__class_Ominus(X3,X9,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).

fof(f7574,plain,
    spl0_465,
    inference(avatar_split_clause,[],[f659,f7572]) ).

fof(f7572,plain,
    ( spl0_465
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f659,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

fof(f7570,plain,
    spl0_464,
    inference(avatar_split_clause,[],[f658,f7568]) ).

fof(f7568,plain,
    ( spl0_464
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f658,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

fof(f7566,plain,
    spl0_463,
    inference(avatar_split_clause,[],[f657,f7564]) ).

fof(f7564,plain,
    ( spl0_463
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f657,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

fof(f7562,plain,
    spl0_462,
    inference(avatar_split_clause,[],[f656,f7560]) ).

fof(f7560,plain,
    ( spl0_462
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_HOL_Oord__class_Oless(X3,X9,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f656,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | c_HOL_Oord__class_Oless(X3,X9,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

fof(f7558,plain,
    ( spl0_461
    | ~ spl0_191
    | ~ spl0_350 ),
    inference(avatar_split_clause,[],[f4796,f4707,f2340,f7555]) ).

fof(f7555,plain,
    ( spl0_461
  <=> v_na = c_Divides_Odiv__class_Omod(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f2340,plain,
    ( spl0_191
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f4707,plain,
    ( spl0_350
  <=> c_HOL_Oord__class_Oless(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f4796,plain,
    ( v_na = c_Divides_Odiv__class_Omod(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_191
    | ~ spl0_350 ),
    inference(resolution,[],[f4709,f2341]) ).

fof(f2341,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 )
    | ~ spl0_191 ),
    inference(avatar_component_clause,[],[f2340]) ).

fof(f4709,plain,
    ( c_HOL_Oord__class_Oless(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_350 ),
    inference(avatar_component_clause,[],[f4707]) ).

fof(f7553,plain,
    spl0_460,
    inference(avatar_split_clause,[],[f600,f7551]) ).

fof(f7551,plain,
    ( spl0_460
  <=> ! [X2,X19,X3,X22] : c_in(X3,c_Set_Ovimage(X19,c_Set_Oinsert(hAPP(X19,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X22,X2),X22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f600,axiom,
    ! [X2,X3,X19,X22] : c_in(X3,c_Set_Ovimage(X19,c_Set_Oinsert(hAPP(X19,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X22,X2),X22),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

fof(f7549,plain,
    spl0_459,
    inference(avatar_split_clause,[],[f555,f7547]) ).

fof(f7547,plain,
    ( spl0_459
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f555,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

fof(f7545,plain,
    spl0_458,
    inference(avatar_split_clause,[],[f554,f7543]) ).

fof(f7543,plain,
    ( spl0_458
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f554,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

fof(f7541,plain,
    spl0_457,
    inference(avatar_split_clause,[],[f545,f7539]) ).

fof(f7539,plain,
    ( spl0_457
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f545,axiom,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).

fof(f7537,plain,
    spl0_456,
    inference(avatar_split_clause,[],[f452,f7535]) ).

fof(f7535,plain,
    ( spl0_456
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_lessequals(X3,X9,X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f452,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | ~ c_lessequals(X3,X9,X2)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

fof(f7533,plain,
    spl0_455,
    inference(avatar_split_clause,[],[f451,f7531]) ).

fof(f7531,plain,
    ( spl0_455
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(X3,X9,X2)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f451,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | c_lessequals(X3,X9,X2)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

fof(f7529,plain,
    spl0_454,
    inference(avatar_split_clause,[],[f450,f7527]) ).

fof(f7527,plain,
    ( spl0_454
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_lessequals(X3,X9,X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f450,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | ~ c_lessequals(X3,X9,X2)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

fof(f7525,plain,
    spl0_453,
    inference(avatar_split_clause,[],[f449,f7523]) ).

fof(f7523,plain,
    ( spl0_453
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(X3,X9,X2)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f449,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
      | c_lessequals(X3,X9,X2)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

fof(f7521,plain,
    spl0_452,
    inference(avatar_split_clause,[],[f448,f7519]) ).

fof(f7519,plain,
    ( spl0_452
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ c_lessequals(X3,X9,X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f448,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
      | ~ c_lessequals(X3,X9,X2)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X2),c_HOL_Oplus__class_Oplus(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

fof(f7517,plain,
    spl0_451,
    inference(avatar_split_clause,[],[f447,f7515]) ).

fof(f7515,plain,
    ( spl0_451
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ c_lessequals(X3,X9,X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f447,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
      | ~ c_lessequals(X3,X9,X2)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,X2),c_HOL_Oplus__class_Oplus(X10,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

fof(f7511,plain,
    spl0_450,
    inference(avatar_split_clause,[],[f357,f7509]) ).

fof(f7509,plain,
    ( spl0_450
  <=> ! [X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X5,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f357,axiom,
    ! [X2,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X5,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_2) ).

fof(f7507,plain,
    spl0_449,
    inference(avatar_split_clause,[],[f290,f7505]) ).

fof(f7505,plain,
    ( spl0_449
  <=> ! [X2] :
        ( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f290,axiom,
    ! [X2] :
      ( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV__card__ge__0_0) ).

fof(f7503,plain,
    spl0_448,
    inference(avatar_split_clause,[],[f226,f7501]) ).

fof(f7501,plain,
    ( spl0_448
  <=> ! [X6,X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X6,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f226,axiom,
    ! [X2,X6,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ominus__class_Ominus(X6,X5,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

fof(f7499,plain,
    spl0_447,
    inference(avatar_split_clause,[],[f146,f7497]) ).

fof(f7497,plain,
    ( spl0_447
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(X0,X0,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f146,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(X0,X0,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

fof(f7495,plain,
    spl0_446,
    inference(avatar_split_clause,[],[f145,f7493]) ).

fof(f7493,plain,
    ( spl0_446
  <=> ! [X4,X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Otimes__class_Otimes(X0,X4,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f145,axiom,
    ! [X0,X1,X4] :
      ( X0 = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Otimes__class_Otimes(X0,X4,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).

fof(f7491,plain,
    spl0_445,
    inference(avatar_split_clause,[],[f144,f7489]) ).

fof(f7489,plain,
    ( spl0_445
  <=> ! [X4,X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Otimes__class_Otimes(X4,X0,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f144,axiom,
    ! [X0,X1,X4] :
      ( X0 = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Otimes__class_Otimes(X4,X0,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).

fof(f6471,plain,
    spl0_444,
    inference(avatar_split_clause,[],[f1322,f6469]) ).

fof(f6469,plain,
    ( spl0_444
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X1
        | c_HOL_Oone__class_Oone(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f1322,plain,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = X1
      | c_HOL_Oone__class_Oone(tc_nat) = X0 ),
    inference(forward_demodulation,[],[f1321,f377]) ).

fof(f1321,plain,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X1
      | c_HOL_Oone__class_Oone(tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1320,f377]) ).

fof(f1320,plain,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1235,f377]) ).

fof(f1235,plain,
    ! [X0,X1] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f272,f61,f61,f61]) ).

fof(f272,axiom,
    ! [X0,X1] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X0
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

fof(f6467,plain,
    ( spl0_443
    | ~ spl0_51
    | ~ spl0_396 ),
    inference(avatar_split_clause,[],[f6101,f4909,f1600,f6465]) ).

fof(f6101,plain,
    ( ! [X0] :
        ( c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
        | ~ c_in(X0,v_G,t_a) )
    | ~ spl0_51
    | ~ spl0_396 ),
    inference(resolution,[],[f4910,f1602]) ).

fof(f6463,plain,
    spl0_442,
    inference(avatar_split_clause,[],[f1315,f6461]) ).

fof(f6461,plain,
    ( spl0_442
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f1315,plain,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
    inference(forward_demodulation,[],[f1314,f377]) ).

fof(f1314,plain,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1228,f377]) ).

fof(f1228,plain,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f55,f61,f61]) ).

fof(f55,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

fof(f6459,plain,
    spl0_441,
    inference(avatar_split_clause,[],[f1311,f6457]) ).

fof(f6457,plain,
    ( spl0_441
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f1311,plain,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = X0
      | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
    inference(forward_demodulation,[],[f1310,f377]) ).

fof(f1310,plain,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X0
      | c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1226,f377]) ).

fof(f1226,plain,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f156,f61,f61]) ).

fof(f156,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X0
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

fof(f6455,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f1308,f6453]) ).

fof(f6453,plain,
    ( spl0_440
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f1308,plain,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
    inference(forward_demodulation,[],[f1224,f377]) ).

fof(f1224,plain,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f699,f61]) ).

fof(f699,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

fof(f6451,plain,
    spl0_439,
    inference(avatar_split_clause,[],[f1259,f6449]) ).

fof(f6449,plain,
    ( spl0_439
  <=> ! [X20,X4,X21] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X4,tc_nat) = c_HOL_Ominus__class_Ominus(X20,c_HOL_Oplus__class_Oplus(X4,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f1259,plain,
    ! [X21,X4,X20] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X4,tc_nat) = c_HOL_Ominus__class_Ominus(X20,c_HOL_Oplus__class_Oplus(X4,X21,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f1032,f846]) ).

fof(f1032,axiom,
    ! [X21,X4,X20] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X20,X4,tc_nat),X21,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

fof(f6447,plain,
    spl0_438,
    inference(avatar_split_clause,[],[f1218,f6445]) ).

fof(f6445,plain,
    ( spl0_438
  <=> ! [X0,X1] :
        ( X0 = X1
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f1218,plain,
    ! [X0,X1] :
      ( X0 = X1
      | c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f627,f61]) ).

fof(f627,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

fof(f6443,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f1217,f6441]) ).

fof(f6441,plain,
    ( spl0_437
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f1217,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_lessequals(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f888,f61]) ).

fof(f888,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_lessequals(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

fof(f6439,plain,
    spl0_436,
    inference(avatar_split_clause,[],[f1047,f6437]) ).

fof(f6437,plain,
    ( spl0_436
  <=> ! [X13,X2,X5,X19] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X19,X5,X2,X13),X13),c_Finite__Set_Ocard(X5,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f1047,axiom,
    ! [X2,X19,X5,X13] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X19,X5,X2,X13),X13),c_Finite__Set_Ocard(X5,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image__le_0) ).

fof(f6435,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f1019,f6433]) ).

fof(f6433,plain,
    ( spl0_435
  <=> ! [X7,X8,X5,X2] : c_Set_Oinsert(X7,c_Set_Oinsert(X8,X5,X2),X2) = c_Set_Oinsert(X8,c_Set_Oinsert(X7,X5,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f1019,axiom,
    ! [X2,X8,X7,X5] : c_Set_Oinsert(X7,c_Set_Oinsert(X8,X5,X2),X2) = c_Set_Oinsert(X8,c_Set_Oinsert(X7,X5,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

fof(f6431,plain,
    spl0_434,
    inference(avatar_split_clause,[],[f1013,f6429]) ).

fof(f6429,plain,
    ( spl0_434
  <=> ! [X6,X2,X5,X7] :
        ( c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | ~ c_lessequals(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f1013,axiom,
    ! [X2,X6,X7,X5] :
      ( c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_lessequals(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

fof(f6427,plain,
    spl0_433,
    inference(avatar_split_clause,[],[f1012,f6425]) ).

fof(f1012,axiom,
    ! [X2,X6,X9,X5] :
      ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_lessequals(X5,c_Set_Oinsert(X9,X6,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

fof(f6423,plain,
    ( spl0_432
    | ~ spl0_51
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f6076,f4905,f1600,f6421]) ).

fof(f6076,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X0))
        | ~ hBOOL(hAPP(v_G,X0)) )
    | ~ spl0_51
    | ~ spl0_395 ),
    inference(resolution,[],[f4906,f1602]) ).

fof(f6419,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f997,f6417]) ).

fof(f997,axiom,
    ! [X2,X6,X5] :
      ( X5 = X6
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X5,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

fof(f6415,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f930,f6413]) ).

fof(f6413,plain,
    ( spl0_430
  <=> ! [X2,X5,X7] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_in(X7,X5,X2)
        | c_lessequals(X7,c_Finite__Set_Olinorder__class_OMax(X5,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f930,axiom,
    ! [X2,X7,X5] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2)
      | c_lessequals(X7,c_Finite__Set_Olinorder__class_OMax(X5,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).

fof(f6411,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f929,f6409]) ).

fof(f6409,plain,
    ( spl0_429
  <=> ! [X2,X5,X7] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_Finite__Set_Ofinite(X5,X2)
        | ~ c_in(X7,X5,X2)
        | c_lessequals(c_Finite__Set_Olinorder__class_OMin(X5,X2),X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f929,axiom,
    ! [X2,X7,X5] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_Finite__Set_Ofinite(X5,X2)
      | ~ c_in(X7,X5,X2)
      | c_lessequals(c_Finite__Set_Olinorder__class_OMin(X5,X2),X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).

fof(f6407,plain,
    spl0_428,
    inference(avatar_split_clause,[],[f872,f6405]) ).

fof(f6405,plain,
    ( spl0_428
  <=> ! [X19,X13,X5,X2] :
        ( c_Finite__Set_Ofinite(X5,X13)
        | ~ c_Fun_Oinj__on(X19,X5,X13,X2)
        | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X19,X5,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f872,axiom,
    ! [X2,X19,X5,X13] :
      ( c_Finite__Set_Ofinite(X5,X13)
      | ~ c_Fun_Oinj__on(X19,X5,X13,X2)
      | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X19,X5,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).

fof(f6403,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f849,f6401]) ).

fof(f6401,plain,
    ( spl0_427
  <=> ! [X4,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f849,axiom,
    ! [X0,X1,X4] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

fof(f6399,plain,
    spl0_426,
    inference(avatar_split_clause,[],[f848,f6397]) ).

fof(f6397,plain,
    ( spl0_426
  <=> ! [X4,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f848,axiom,
    ! [X0,X1,X4] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

fof(f6395,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f846,f6393]) ).

fof(f6393,plain,
    ( spl0_425
  <=> ! [X20,X4,X21] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X4,tc_nat) = c_HOL_Ominus__class_Ominus(X20,c_HOL_Oplus__class_Oplus(X21,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f6391,plain,
    spl0_424,
    inference(avatar_split_clause,[],[f839,f6389]) ).

fof(f6389,plain,
    ( spl0_424
  <=> ! [X4,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f839,axiom,
    ! [X0,X1,X4] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff__nat_0) ).

fof(f6387,plain,
    spl0_423,
    inference(avatar_split_clause,[],[f787,f6385]) ).

fof(f6385,plain,
    ( spl0_423
  <=> ! [X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_Finite__Set_Ocard(X5,X2)
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f787,axiom,
    ! [X2,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_Finite__Set_Ocard(X5,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).

fof(f6383,plain,
    spl0_422,
    inference(avatar_split_clause,[],[f768,f6381]) ).

fof(f6381,plain,
    ( spl0_422
  <=> ! [X2,X5] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
        | ~ c_lessequals(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f768,axiom,
    ! [X2,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X5
      | ~ c_lessequals(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

fof(f6379,plain,
    ( spl0_421
    | ~ spl0_51
    | ~ spl0_382 ),
    inference(avatar_split_clause,[],[f5709,f4853,f1600,f6376]) ).

fof(f6376,plain,
    ( spl0_421
  <=> v_G = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f4853,plain,
    ( spl0_382
  <=> ! [X6,X2,X5] :
        ( ~ c_lessequals(X6,X5,tc_fun(X2,tc_bool))
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f5709,plain,
    ( v_G = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))
    | ~ spl0_51
    | ~ spl0_382 ),
    inference(resolution,[],[f4854,f1602]) ).

fof(f4854,plain,
    ( ! [X2,X6,X5] :
        ( ~ c_lessequals(X6,X5,tc_fun(X2,tc_bool))
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = X6 )
    | ~ spl0_382 ),
    inference(avatar_component_clause,[],[f4853]) ).

fof(f6374,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f756,f6372]) ).

fof(f756,axiom,
    ! [X2,X6,X5] :
      ( X5 = X6
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

fof(f6370,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f718,f6368]) ).

fof(f6368,plain,
    ( spl0_419
  <=> ! [X4,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X4,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f718,axiom,
    ! [X0,X1,X4] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X4,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

fof(f6366,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f692,f6364]) ).

fof(f6364,plain,
    ( spl0_418
  <=> ! [X8,X19,X13,X14,X2,X7] :
        ( X7 = X14
        | hAPP(X19,X14) = hAPP(c_Fun_Ofun__upd(X19,X7,X8,X2,X13),X14) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f692,axiom,
    ! [X2,X8,X19,X7,X14,X13] :
      ( X7 = X14
      | hAPP(X19,X14) = hAPP(c_Fun_Ofun__upd(X19,X7,X8,X2,X13),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

fof(f6362,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f363,f6360]) ).

fof(f363,axiom,
    ! [X0,X1,X4] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),X0,tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).

fof(f6358,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f263,f6356]) ).

fof(f6356,plain,
    ( spl0_416
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f263,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

fof(f6354,plain,
    spl0_415,
    inference(avatar_split_clause,[],[f159,f6352]) ).

fof(f6352,plain,
    ( spl0_415
  <=> ! [X4,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f159,axiom,
    ! [X0,X1,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

fof(f6350,plain,
    spl0_414,
    inference(avatar_split_clause,[],[f158,f6348]) ).

fof(f6348,plain,
    ( spl0_414
  <=> ! [X4,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f158,axiom,
    ! [X0,X1,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

fof(f6346,plain,
    spl0_413,
    inference(avatar_split_clause,[],[f80,f6344]) ).

fof(f6344,plain,
    ( spl0_413
  <=> ! [X6,X19,X13,X5,X2] :
        ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
        | c_Fun_Oinj__on(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f80,axiom,
    ! [X2,X19,X6,X5,X13] :
      ( ~ c_Fun_Oinj__on(X19,X5,X2,X13)
      | c_Fun_Oinj__on(X19,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

fof(f6342,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f25,f6340]) ).

fof(f6340,plain,
    ( spl0_412
  <=> ! [X4,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f25,axiom,
    ! [X0,X1,X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

fof(f6338,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f24,f6336]) ).

fof(f6336,plain,
    ( spl0_411
  <=> ! [X7,X14,X8] : c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X14,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f24,axiom,
    ! [X8,X7,X14] : c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X14,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

fof(f6334,plain,
    ( spl0_410
    | ~ spl0_51
    | ~ spl0_381 ),
    inference(avatar_split_clause,[],[f5685,f4849,f1600,f6331]) ).

fof(f6331,plain,
    ( spl0_410
  <=> v_G = c_Lattices_Olower__semilattice__class_Oinf(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f4849,plain,
    ( spl0_381
  <=> ! [X6,X2,X5] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f5685,plain,
    ( v_G = c_Lattices_Olower__semilattice__class_Oinf(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
    | ~ spl0_51
    | ~ spl0_381 ),
    inference(resolution,[],[f4850,f1602]) ).

fof(f4850,plain,
    ( ! [X2,X6,X5] :
        ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = X5 )
    | ~ spl0_381 ),
    inference(avatar_component_clause,[],[f4849]) ).

fof(f6329,plain,
    spl0_409,
    inference(avatar_split_clause,[],[f7,f6327]) ).

fof(f6327,plain,
    ( spl0_409
  <=> ! [X4,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f7,axiom,
    ! [X0,X1,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).

fof(f6325,plain,
    spl0_408,
    inference(avatar_split_clause,[],[f6,f6323]) ).

fof(f6323,plain,
    ( spl0_408
  <=> ! [X4,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f6,axiom,
    ! [X0,X1,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).

fof(f5825,plain,
    ( spl0_407
    | ~ spl0_120
    | ~ spl0_406 ),
    inference(avatar_split_clause,[],[f5574,f5477,f1896,f5823]) ).

fof(f5477,plain,
    ( spl0_406
  <=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,X1),v_pn)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f5574,plain,
    ( ! [X2,X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X2)
    | ~ spl0_120
    | ~ spl0_406 ),
    inference(resolution,[],[f5478,f1897]) ).

fof(f5478,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,X1),v_pn))
    | ~ spl0_406 ),
    inference(avatar_component_clause,[],[f5477]) ).

fof(f5479,plain,
    ( spl0_406
    | ~ spl0_121
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f5262,f5087,f1900,f5477]) ).

fof(f5087,plain,
    ( spl0_405
  <=> ! [X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f5262,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,X1),v_pn))
    | ~ spl0_121
    | ~ spl0_405 ),
    inference(resolution,[],[f5088,f1901]) ).

fof(f5088,plain,
    ( ! [X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X1)
    | ~ spl0_405 ),
    inference(avatar_component_clause,[],[f5087]) ).

fof(f5089,plain,
    ( spl0_405
    | ~ spl0_174
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4940,f4889,f2138,f5087]) ).

fof(f4940,plain,
    ( ! [X0,X1] : c_in(v_pn,c_Set_Oinsert(X0,v_U,X1),X1)
    | ~ spl0_174
    | ~ spl0_391 ),
    inference(resolution,[],[f4890,f2139]) ).

fof(f4952,plain,
    spl0_404,
    inference(avatar_split_clause,[],[f1053,f4950]) ).

fof(f1053,axiom,
    ! [X2,X19,X7,X5,X13] :
      ( ~ c_in(X7,X5,X13)
      | c_in(hAPP(X19,X7),c_Set_Oimage(X19,X5,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

fof(f4948,plain,
    spl0_403,
    inference(avatar_split_clause,[],[f1024,f4946]) ).

fof(f4946,plain,
    ( spl0_403
  <=> ! [X0,X1,X23] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X23,tc_nat),c_HOL_Ominus__class_Ominus(X1,X23,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f1024,axiom,
    ! [X0,X1,X23] :
      ( ~ c_lessequals(X0,X1,tc_nat)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X23,tc_nat),c_HOL_Ominus__class_Ominus(X1,X23,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).

fof(f4944,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f1023,f4942]) ).

fof(f4942,plain,
    ( spl0_402
  <=> ! [X0,X1,X23] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X23,X1,tc_nat),c_HOL_Ominus__class_Ominus(X23,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f1023,axiom,
    ! [X0,X1,X23] :
      ( ~ c_lessequals(X0,X1,tc_nat)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X23,X1,tc_nat),c_HOL_Ominus__class_Ominus(X23,X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).

fof(f4931,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f1010,f4929]) ).

fof(f1010,axiom,
    ! [X2,X8,X7,X5] :
      ( X7 = X8
      | hBOOL(hAPP(X5,X7))
      | ~ hBOOL(hAPP(c_Set_Oinsert(X8,X5,X2),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

fof(f4927,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f1005,f4925]) ).

fof(f4925,plain,
    ( spl0_400
  <=> ! [X2,X5,X7] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_lessequals(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f1005,axiom,
    ! [X2,X7,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_lessequals(c_Finite__Set_Ocard(X5,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X7,X5,X2),X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).

fof(f4923,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f1000,f4921]) ).

fof(f4921,plain,
    ( spl0_399
  <=> ! [X5,X3,X9,X2] :
        ( X3 = X9
        | c_in(X3,X5,X2)
        | ~ c_in(X3,c_Set_Oinsert(X9,X5,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f1000,axiom,
    ! [X2,X3,X9,X5] :
      ( X3 = X9
      | c_in(X3,X5,X2)
      | ~ c_in(X3,c_Set_Oinsert(X9,X5,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

fof(f4919,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f983,f4917]) ).

fof(f983,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_lessequals(X8,X7,X2)
      | ~ c_lessequals(X14,X8,X2)
      | c_lessequals(X14,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

fof(f4915,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f982,f4913]) ).

fof(f4913,plain,
    ( spl0_397
  <=> ! [X7,X8,X14,X2] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_lessequals(X7,X8,X2)
        | ~ c_lessequals(X8,X14,X2)
        | c_lessequals(X7,X14,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f982,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_lessequals(X7,X8,X2)
      | ~ c_lessequals(X8,X14,X2)
      | c_lessequals(X7,X14,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

fof(f4911,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f981,f4909]) ).

fof(f981,axiom,
    ! [X2,X6,X7,X5] :
      ( ~ c_in(X7,X5,X2)
      | c_in(X7,X6,X2)
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

fof(f4907,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f967,f4905]) ).

fof(f967,axiom,
    ! [X2,X49,X7,X25] :
      ( ~ hBOOL(hAPP(X25,X7))
      | hBOOL(hAPP(X49,X7))
      | ~ c_lessequals(X25,X49,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

fof(f4903,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f914,f4901]) ).

fof(f4901,plain,
    ( spl0_394
  <=> ! [X20,X4,X21] :
        ( ~ c_lessequals(X21,c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),X20,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f914,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(X21,c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),tc_nat)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),X20,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).

fof(f4899,plain,
    spl0_393,
    inference(avatar_split_clause,[],[f913,f4897]) ).

fof(f4897,plain,
    ( spl0_393
  <=> ! [X20,X21,X4] :
        ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),X20,tc_nat)
        | c_lessequals(X21,c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f913,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),X20,tc_nat)
      | c_lessequals(X21,c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).

fof(f4895,plain,
    spl0_392,
    inference(avatar_split_clause,[],[f904,f4893]) ).

fof(f4893,plain,
    ( spl0_392
  <=> ! [X4,X0,X1] :
        ( ~ c_lessequals(X4,X1,tc_nat)
        | c_lessequals(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f904,axiom,
    ! [X0,X1,X4] :
      ( ~ c_lessequals(X4,X1,tc_nat)
      | c_lessequals(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).

fof(f4891,plain,
    ( spl0_391
    | ~ spl0_223
    | ~ spl0_333 ),
    inference(avatar_split_clause,[],[f4581,f3895,f2634,f4889]) ).

fof(f2634,plain,
    ( spl0_223
  <=> ! [X0] : v_U = c_Set_Oinsert(v_pn,v_U,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f4581,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(v_U,X1,tc_fun(X0,tc_bool))
        | c_in(v_pn,X1,X0) )
    | ~ spl0_223
    | ~ spl0_333 ),
    inference(superposition,[],[f3896,f2635]) ).

fof(f2635,plain,
    ( ! [X0] : v_U = c_Set_Oinsert(v_pn,v_U,X0)
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2634]) ).

fof(f4887,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f894,f4885]) ).

fof(f4885,plain,
    ( spl0_390
  <=> ! [X19,X13,X5,X2] : c_lessequals(c_Set_Oimage(X19,c_Set_Ovimage(X19,X5,X13,X2),X13,X2),X5,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f894,axiom,
    ! [X2,X19,X5,X13] : c_lessequals(c_Set_Oimage(X19,c_Set_Ovimage(X19,X5,X13,X2),X13,X2),X5,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

fof(f4883,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f868,f4881]) ).

fof(f4881,plain,
    ( spl0_389
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f868,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).

fof(f4879,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f867,f4877]) ).

fof(f4877,plain,
    ( spl0_388
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f867,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | ~ c_lessequals(X0,X1,tc_nat)
      | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).

fof(f4875,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f801,f4873]) ).

fof(f4873,plain,
    ( spl0_387
  <=> ! [X20,X21,X4] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f801,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

fof(f4871,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f800,f4869]) ).

fof(f4869,plain,
    ( spl0_386
  <=> ! [X4,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f800,axiom,
    ! [X0,X1,X4] :
      ( c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

fof(f4867,plain,
    spl0_385,
    inference(avatar_split_clause,[],[f799,f4865]) ).

fof(f4865,plain,
    ( spl0_385
  <=> ! [X4,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f799,axiom,
    ! [X0,X1,X4] :
      ( ~ c_lessequals(X0,X1,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

fof(f4863,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f796,f4861]) ).

fof(f4861,plain,
    ( spl0_384
  <=> ! [X20,X21,X4] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X4,tc_nat),c_HOL_Otimes__class_Otimes(X21,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f796,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X4,tc_nat),c_HOL_Otimes__class_Otimes(X21,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).

fof(f4859,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f795,f4857]) ).

fof(f4857,plain,
    ( spl0_383
  <=> ! [X20,X21,X4] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X20,tc_nat),c_HOL_Otimes__class_Otimes(X4,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f795,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X20,tc_nat),c_HOL_Otimes__class_Otimes(X4,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).

fof(f4855,plain,
    spl0_382,
    inference(avatar_split_clause,[],[f773,f4853]) ).

fof(f773,axiom,
    ! [X2,X6,X5] :
      ( ~ c_lessequals(X6,X5,tc_fun(X2,tc_bool))
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

fof(f4851,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f772,f4849]) ).

fof(f772,axiom,
    ! [X2,X6,X5] :
      ( ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

fof(f4842,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f687,f4840]) ).

fof(f4840,plain,
    ( spl0_380
  <=> ! [X2,X13,X5,X19,X7] :
        ( ~ hBOOL(hAPP(X5,hAPP(X19,X7)))
        | hBOOL(hAPP(c_Set_Ovimage(X19,X5,X2,X13),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f687,axiom,
    ! [X2,X19,X7,X5,X13] :
      ( ~ hBOOL(hAPP(X5,hAPP(X19,X7)))
      | hBOOL(hAPP(c_Set_Ovimage(X19,X5,X2,X13),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).

fof(f4838,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f686,f4836]) ).

fof(f4836,plain,
    ( spl0_379
  <=> ! [X2,X13,X5,X19,X7] :
        ( hBOOL(hAPP(X5,hAPP(X19,X7)))
        | ~ hBOOL(hAPP(c_Set_Ovimage(X19,X5,X2,X13),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f686,axiom,
    ! [X2,X19,X7,X5,X13] :
      ( hBOOL(hAPP(X5,hAPP(X19,X7)))
      | ~ hBOOL(hAPP(c_Set_Ovimage(X19,X5,X2,X13),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

fof(f4834,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f662,f4832]) ).

fof(f4832,plain,
    ( spl0_378
  <=> ! [X4,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f662,axiom,
    ! [X0,X1,X4] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

fof(f4830,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f661,f4828]) ).

fof(f4828,plain,
    ( spl0_377
  <=> ! [X4,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f661,axiom,
    ! [X0,X1,X4] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X0,tc_nat),c_HOL_Oplus__class_Oplus(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

fof(f4826,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f660,f4824]) ).

fof(f4824,plain,
    ( spl0_376
  <=> ! [X20,X21,X4] :
        ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f660,axiom,
    ! [X21,X4,X20] :
      ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),c_HOL_Oplus__class_Oplus(X21,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

fof(f4822,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f654,f4820]) ).

fof(f654,axiom,
    ! [X2,X41,X19,X13] :
      ( ~ class_HOL_Oord(X13)
      | ~ c_HOL_Oord__class_Oless(X19,X41,tc_fun(X2,X13))
      | ~ c_lessequals(X41,X19,tc_fun(X2,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

fof(f4818,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f652,f4816]) ).

fof(f4816,plain,
    ( spl0_374
  <=> ! [X41,X19,X13,X2] :
        ( ~ class_HOL_Oord(X13)
        | ~ c_HOL_Oord__class_Oless(X19,X41,tc_fun(X2,X13))
        | c_lessequals(X19,X41,tc_fun(X2,X13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f652,axiom,
    ! [X2,X41,X19,X13] :
      ( ~ class_HOL_Oord(X13)
      | ~ c_HOL_Oord__class_Oless(X19,X41,tc_fun(X2,X13))
      | c_lessequals(X19,X41,tc_fun(X2,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

fof(f4814,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f605,f4812]) ).

fof(f4812,plain,
    ( spl0_373
  <=> ! [X6,X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X6,X2)
        | c_Finite__Set_Ofinite(X5,X2)
        | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f605,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | c_Finite__Set_Ofinite(X5,X2)
      | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

fof(f4810,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f551,f4808]) ).

fof(f4808,plain,
    ( spl0_372
  <=> ! [X20,X4,X21] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),X21,tc_nat)
        | c_HOL_Oord__class_Oless(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f551,axiom,
    ! [X21,X4,X20] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),X21,tc_nat)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

fof(f4806,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f550,f4804]) ).

fof(f4804,plain,
    ( spl0_371
  <=> ! [X20,X4,X21] :
        ( ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f550,axiom,
    ! [X21,X4,X20] :
      ( ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ominus__class_Ominus(X21,X4,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X4,tc_nat),X21,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

fof(f4795,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f529,f4793]) ).

fof(f4793,plain,
    ( spl0_370
  <=> ! [X2,X8,X7] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f529,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

fof(f4791,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f528,f4789]) ).

fof(f4789,plain,
    ( spl0_369
  <=> ! [X2,X8,X7] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f528,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

fof(f4787,plain,
    spl0_368,
    inference(avatar_split_clause,[],[f513,f4785]) ).

fof(f4785,plain,
    ( spl0_368
  <=> ! [X2,X9,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X9,X3,X2),X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f513,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X9,X3,X2),X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).

fof(f4783,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f512,f4781]) ).

fof(f4781,plain,
    ( spl0_367
  <=> ! [X2,X9,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f512,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X9,X2),X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).

fof(f4779,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f509,f4777]) ).

fof(f4777,plain,
    ( spl0_366
  <=> ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f509,axiom,
    ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

fof(f4775,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f505,f4773]) ).

fof(f4773,plain,
    ( spl0_365
  <=> ! [X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f505,axiom,
    ! [X2,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

fof(f4771,plain,
    spl0_364,
    inference(avatar_split_clause,[],[f504,f4769]) ).

fof(f4769,plain,
    ( spl0_364
  <=> ! [X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f504,axiom,
    ! [X2,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

fof(f4767,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f492,f4765]) ).

fof(f4765,plain,
    ( spl0_363
  <=> ! [X4,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f492,axiom,
    ! [X0,X1,X4] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).

fof(f4763,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f491,f4761]) ).

fof(f4761,plain,
    ( spl0_362
  <=> ! [X4,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f491,axiom,
    ! [X0,X1,X4] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

fof(f4759,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f485,f4757]) ).

fof(f4757,plain,
    ( spl0_361
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f485,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

fof(f4750,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f484,f4748]) ).

fof(f4748,plain,
    ( spl0_360
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f484,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

fof(f4746,plain,
    spl0_359,
    inference(avatar_split_clause,[],[f477,f4744]) ).

fof(f4744,plain,
    ( spl0_359
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f477,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).

fof(f4742,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f455,f4740]) ).

fof(f4740,plain,
    ( spl0_358
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_lessequals(X7,X8,X2)
        | c_HOL_Oord__class_Oless(X7,X8,X2)
        | c_lessequals(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f455,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_lessequals(X7,X8,X2)
      | c_HOL_Oord__class_Oless(X7,X8,X2)
      | c_lessequals(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

fof(f4738,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f438,f4736]) ).

fof(f4736,plain,
    ( spl0_357
  <=> ! [X2,X24,X19] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
        | ~ c_lessequals(X24,hAPP(X19,X24),X2)
        | c_lessequals(X24,c_Inductive_Ocomplete__lattice__class_Ogfp(X19,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f438,axiom,
    ! [X2,X19,X24] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
      | ~ c_lessequals(X24,hAPP(X19,X24),X2)
      | c_lessequals(X24,c_Inductive_Ocomplete__lattice__class_Ogfp(X19,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gfp__upperbound_0) ).

fof(f4734,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f437,f4732]) ).

fof(f4732,plain,
    ( spl0_356
  <=> ! [X7,X8,X14,X2] :
        ( ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(X8,X7,X2)
        | ~ c_lessequals(X14,X8,X2)
        | c_HOL_Oord__class_Oless(X14,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f437,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_HOL_Oord__class_Oless(X8,X7,X2)
      | ~ c_lessequals(X14,X8,X2)
      | c_HOL_Oord__class_Oless(X14,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

fof(f4730,plain,
    spl0_355,
    inference(avatar_split_clause,[],[f436,f4728]) ).

fof(f4728,plain,
    ( spl0_355
  <=> ! [X14,X8,X2,X7] :
        ( ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(X14,X8,X2)
        | ~ c_lessequals(X8,X7,X2)
        | c_HOL_Oord__class_Oless(X14,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f436,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_HOL_Oord__class_Oless(X14,X8,X2)
      | ~ c_lessequals(X8,X7,X2)
      | c_HOL_Oord__class_Oless(X14,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

fof(f4726,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f435,f4724]) ).

fof(f4724,plain,
    ( spl0_354
  <=> ! [X14,X8,X2,X7] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(X8,X14,X2)
        | ~ c_lessequals(X7,X8,X2)
        | c_HOL_Oord__class_Oless(X7,X14,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f435,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_HOL_Oord__class_Oless(X8,X14,X2)
      | ~ c_lessequals(X7,X8,X2)
      | c_HOL_Oord__class_Oless(X7,X14,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

fof(f4722,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f434,f4720]) ).

fof(f4720,plain,
    ( spl0_353
  <=> ! [X7,X8,X14,X2] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
        | ~ c_lessequals(X8,X14,X2)
        | c_HOL_Oord__class_Oless(X7,X14,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f434,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
      | ~ c_lessequals(X8,X14,X2)
      | c_HOL_Oord__class_Oless(X7,X14,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

fof(f4718,plain,
    spl0_352,
    inference(avatar_split_clause,[],[f423,f4716]) ).

fof(f4716,plain,
    ( spl0_352
  <=> ! [X2,X6,X13,X3,X19] :
        ( c_in(hAPP(X19,X3),X6,X13)
        | ~ c_in(X3,c_Set_Ovimage(X19,X6,X2,X13),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f423,axiom,
    ! [X2,X3,X19,X6,X13] :
      ( c_in(hAPP(X19,X3),X6,X13)
      | ~ c_in(X3,c_Set_Ovimage(X19,X6,X2,X13),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).

fof(f4714,plain,
    spl0_351,
    inference(avatar_split_clause,[],[f420,f4712]) ).

fof(f4712,plain,
    ( spl0_351
  <=> ! [X2,X6,X13,X3,X19] :
        ( ~ c_in(hAPP(X19,X3),X6,X13)
        | c_in(X3,c_Set_Ovimage(X19,X6,X2,X13),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f420,axiom,
    ! [X2,X3,X19,X6,X13] :
      ( ~ c_in(hAPP(X19,X3),X6,X13)
      | c_in(X3,c_Set_Ovimage(X19,X6,X2,X13),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

fof(f4710,plain,
    ( spl0_350
    | ~ spl0_52
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f3648,f3295,f1605,f4707]) ).

fof(f3295,plain,
    ( spl0_284
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f3648,plain,
    ( c_HOL_Oord__class_Oless(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_52
    | ~ spl0_284 ),
    inference(resolution,[],[f3296,f1607]) ).

fof(f3296,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_284 ),
    inference(avatar_component_clause,[],[f3295]) ).

fof(f4705,plain,
    spl0_349,
    inference(avatar_split_clause,[],[f410,f4703]) ).

fof(f4703,plain,
    ( spl0_349
  <=> ! [X5,X10,X6,X2] :
        ( ~ c_in(X10,X5,X2)
        | c_in(X10,X6,X2)
        | ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f410,axiom,
    ! [X2,X10,X6,X5] :
      ( ~ c_in(X10,X5,X2)
      | c_in(X10,X6,X2)
      | ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).

fof(f4701,plain,
    spl0_348,
    inference(avatar_split_clause,[],[f304,f4699]) ).

fof(f4699,plain,
    ( spl0_348
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f304,axiom,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) != X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).

fof(f4697,plain,
    spl0_347,
    inference(avatar_split_clause,[],[f300,f4695]) ).

fof(f4695,plain,
    ( spl0_347
  <=> ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f300,axiom,
    ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

fof(f4693,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f210,f4691]) ).

fof(f4691,plain,
    ( spl0_346
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
        | X9 = X10
        | c_HOL_Oplus__class_Oplus(X10,X3,X2) != c_HOL_Oplus__class_Oplus(X9,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f210,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
      | X9 = X10
      | c_HOL_Oplus__class_Oplus(X10,X3,X2) != c_HOL_Oplus__class_Oplus(X9,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f4689,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f209,f4687]) ).

fof(f4687,plain,
    ( spl0_345
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
        | X9 = X10
        | c_HOL_Oplus__class_Oplus(X3,X9,X2) != c_HOL_Oplus__class_Oplus(X3,X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f209,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
      | X9 = X10
      | c_HOL_Oplus__class_Oplus(X3,X9,X2) != c_HOL_Oplus__class_Oplus(X3,X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f4685,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f208,f4683]) ).

fof(f4683,plain,
    ( spl0_344
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2)
        | X9 = X10
        | c_HOL_Oplus__class_Oplus(X3,X9,X2) != c_HOL_Oplus__class_Oplus(X3,X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f208,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2)
      | X9 = X10
      | c_HOL_Oplus__class_Oplus(X3,X9,X2) != c_HOL_Oplus__class_Oplus(X3,X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f4681,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f123,f4679]) ).

fof(f4679,plain,
    ( spl0_343
  <=> ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f123,axiom,
    ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

fof(f4677,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f122,f4675]) ).

fof(f4675,plain,
    ( spl0_342
  <=> ! [X6,X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f122,axiom,
    ! [X2,X6] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

fof(f4673,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f83,f4671]) ).

fof(f4671,plain,
    ( spl0_341
  <=> ! [X4,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f83,axiom,
    ! [X0,X1,X4] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).

fof(f4669,plain,
    spl0_340,
    inference(avatar_split_clause,[],[f63,f4667]) ).

fof(f4667,plain,
    ( spl0_340
  <=> ! [X2,X9,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X9,X2),X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f63,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(X3,X9,X2) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X9,X2),X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).

fof(f4665,plain,
    ( ~ spl0_339
    | ~ spl0_52
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3608,f3287,f1605,f4662]) ).

fof(f4662,plain,
    ( spl0_339
  <=> c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f3287,plain,
    ( spl0_282
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f3608,plain,
    ( ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat)
    | ~ spl0_52
    | ~ spl0_282 ),
    inference(resolution,[],[f3288,f1607]) ).

fof(f3288,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_282 ),
    inference(avatar_component_clause,[],[f3287]) ).

fof(f4660,plain,
    spl0_338,
    inference(avatar_split_clause,[],[f21,f4658]) ).

fof(f4658,plain,
    ( spl0_338
  <=> ! [X7,X8,X14,X2] :
        ( ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(X8,X7,X2)
        | ~ c_HOL_Oord__class_Oless(X14,X8,X2)
        | c_HOL_Oord__class_Oless(X14,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f21,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_HOL_Oord__class_Oless(X8,X7,X2)
      | ~ c_HOL_Oord__class_Oless(X14,X8,X2)
      | c_HOL_Oord__class_Oless(X14,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

fof(f4656,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f19,f4654]) ).

fof(f4654,plain,
    ( spl0_337
  <=> ! [X7,X8,X14,X2] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
        | ~ c_HOL_Oord__class_Oless(X8,X14,X2)
        | c_HOL_Oord__class_Oless(X7,X14,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f19,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
      | ~ c_HOL_Oord__class_Oless(X8,X14,X2)
      | c_HOL_Oord__class_Oless(X7,X14,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

fof(f4275,plain,
    ( ~ spl0_1
    | ~ spl0_207
    | spl0_289 ),
    inference(avatar_split_clause,[],[f4003,f3531,f2408,f1350]) ).

fof(f2408,plain,
    ( spl0_207
  <=> ! [X13,X2,X12,X11] :
        ( ~ c_Finite__Set_Ofinite(X12,X2)
        | c_Finite__Set_Ofinite(c_Set_Oimage(X11,X12,X2,X13),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f3531,plain,
    ( spl0_289
  <=> c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f4003,plain,
    ( ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
    | ~ spl0_207
    | spl0_289 ),
    inference(resolution,[],[f3533,f2409]) ).

fof(f2409,plain,
    ( ! [X2,X11,X12,X13] :
        ( c_Finite__Set_Ofinite(c_Set_Oimage(X11,X12,X2,X13),X13)
        | ~ c_Finite__Set_Ofinite(X12,X2) )
    | ~ spl0_207 ),
    inference(avatar_component_clause,[],[f2408]) ).

fof(f3533,plain,
    ( ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
    | spl0_289 ),
    inference(avatar_component_clause,[],[f3531]) ).

fof(f3909,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f1299,f3907]) ).

fof(f3907,plain,
    ( spl0_336
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f1299,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
      | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
    inference(forward_demodulation,[],[f1298,f378]) ).

fof(f1298,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
      | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
    inference(forward_demodulation,[],[f1297,f126]) ).

fof(f1297,plain,
    ! [X0,X1] :
      ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1296,f378]) ).

fof(f1296,plain,
    ! [X0,X1] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1209,f126]) ).

fof(f1209,plain,
    ! [X0,X1] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f780,f61,f61]) ).

fof(f780,axiom,
    ! [X0,X1] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).

fof(f3905,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f1295,f3903]) ).

fof(f3903,plain,
    ( spl0_335
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f1295,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
      | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    inference(forward_demodulation,[],[f1294,f378]) ).

fof(f1294,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
      | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    inference(forward_demodulation,[],[f1293,f126]) ).

fof(f1293,plain,
    ! [X0,X1] :
      ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1292,f378]) ).

fof(f1292,plain,
    ! [X0,X1] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1208,f126]) ).

fof(f1208,plain,
    ! [X0,X1] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f779,f61,f61]) ).

fof(f779,axiom,
    ! [X0,X1] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).

fof(f3901,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f1049,f3899]) ).

fof(f1049,axiom,
    ! [X1,X20] :
      ( ~ c_lessequals(X20,X1,tc_nat)
      | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X20,tc_nat),tc_nat) = X20 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).

fof(f3897,plain,
    spl0_333,
    inference(avatar_split_clause,[],[f1033,f3895]) ).

fof(f1033,axiom,
    ! [X2,X6,X7,X5] :
      ( c_in(X7,X6,X2)
      | ~ c_lessequals(c_Set_Oinsert(X7,X5,X2),X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

fof(f3893,plain,
    spl0_332,
    inference(avatar_split_clause,[],[f995,f3891]) ).

fof(f3891,plain,
    ( spl0_332
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Oorder(X2)
        | X7 = X8
        | ~ c_lessequals(X7,X8,X2)
        | ~ c_lessequals(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f995,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Oorder(X2)
      | X7 = X8
      | ~ c_lessequals(X7,X8,X2)
      | ~ c_lessequals(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

fof(f3889,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f920,f3887]) ).

fof(f920,axiom,
    ! [X0,X1] :
      ( ~ c_lessequals(X1,X0,tc_nat)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).

fof(f3885,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f857,f3883]) ).

fof(f3883,plain,
    ( spl0_330
  <=> ! [X19,X13,X2,X7] : c_in(hAPP(X19,X7),c_Set_Oimage(X19,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_bool)),X13,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f857,axiom,
    ! [X2,X19,X7,X13] : c_in(hAPP(X19,X7),c_Set_Oimage(X19,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_bool)),X13,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

fof(f3881,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f825,f3879]) ).

fof(f3879,plain,
    ( spl0_329
  <=> ! [X13,X2,X19] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Set_Oimage(X19,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f825,axiom,
    ! [X2,X19,X13] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Set_Oimage(X19,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

fof(f3877,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f747,f3875]) ).

fof(f747,axiom,
    ! [X2,X3,X9] :
      ( X3 = X9
      | ~ c_in(X9,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

fof(f3873,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f710,f3871]) ).

fof(f3871,plain,
    ( spl0_327
  <=> ! [X13,X2,X19] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Set_Ovimage(X19,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X2,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f710,axiom,
    ! [X2,X19,X13] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Set_Ovimage(X19,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X2,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

fof(f3869,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f709,f3867]) ).

fof(f3867,plain,
    ( spl0_326
  <=> ! [X4,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
        | c_lessequals(X4,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f709,axiom,
    ! [X1,X4] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
      | c_lessequals(X4,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__le_0) ).

fof(f3865,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f695,f3863]) ).

fof(f3863,plain,
    ( spl0_325
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f695,axiom,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

fof(f3861,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f648,f3859]) ).

fof(f3859,plain,
    ( spl0_324
  <=> ! [X3,X19,X13,X5,X2] :
        ( c_Fun_Oinj__on(X19,X5,X2,X13)
        | ~ c_Fun_Oinj__on(X19,c_Set_Oinsert(X3,X5,X2),X2,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f648,axiom,
    ! [X2,X3,X19,X5,X13] :
      ( c_Fun_Oinj__on(X19,X5,X2,X13)
      | ~ c_Fun_Oinj__on(X19,c_Set_Oinsert(X3,X5,X2),X2,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

fof(f3857,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f573,f3855]) ).

fof(f3855,plain,
    ( spl0_323
  <=> ! [X7,X8,X14,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(X7,X8,X2)
        | ~ c_lessequals(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f573,axiom,
    ! [X2,X8,X7,X14] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(X7,X8,X2)
      | ~ c_lessequals(X7,c_Lattices_Olower__semilattice__class_Oinf(X8,X14,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

fof(f3853,plain,
    ( spl0_322
    | ~ spl0_171
    | spl0_290 ),
    inference(avatar_split_clause,[],[f3722,f3535,f2126,f3850]) ).

fof(f3850,plain,
    ( spl0_322
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(v_G,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f2126,plain,
    ( spl0_171
  <=> ! [X2,X5] :
        ( c_Finite__Set_Ofinite(X5,X2)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f3722,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(v_G,t_a)
    | ~ spl0_171
    | spl0_290 ),
    inference(resolution,[],[f3536,f2127]) ).

fof(f2127,plain,
    ( ! [X2,X5] :
        ( c_Finite__Set_Ofinite(X5,X2)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(X5,X2) )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f2126]) ).

fof(f3536,plain,
    ( ~ c_Finite__Set_Ofinite(v_G,t_a)
    | spl0_290 ),
    inference(avatar_component_clause,[],[f3535]) ).

fof(f3848,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f572,f3846]) ).

fof(f3846,plain,
    ( spl0_321
  <=> ! [X2,X9,X7,X3] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X9,X7,X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f572,axiom,
    ! [X2,X3,X9,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X9,X7,X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

fof(f3844,plain,
    spl0_320,
    inference(avatar_split_clause,[],[f571,f3842]) ).

fof(f3842,plain,
    ( spl0_320
  <=> ! [X3,X7,X9,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X3,X7,X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f571,axiom,
    ! [X2,X3,X9,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X3,X7,X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

fof(f3840,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f570,f3838]) ).

fof(f3838,plain,
    ( spl0_319
  <=> ! [X3,X7,X9,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(X7,X9,X2)
        | ~ c_lessequals(X7,c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f570,axiom,
    ! [X2,X3,X9,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(X7,X9,X2)
      | ~ c_lessequals(X7,c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

fof(f3836,plain,
    spl0_318,
    inference(avatar_split_clause,[],[f526,f3834]) ).

fof(f3834,plain,
    ( spl0_318
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f526,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).

fof(f3832,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f525,f3830]) ).

fof(f3830,plain,
    ( spl0_317
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f525,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X9,X10,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).

fof(f3828,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f524,f3826]) ).

fof(f3826,plain,
    ( spl0_316
  <=> ! [X3,X10,X9,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f524,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).

fof(f3824,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f523,f3822]) ).

fof(f3822,plain,
    ( spl0_315
  <=> ! [X2,X9,X3,X10] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f523,axiom,
    ! [X2,X3,X10,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X9,X2),X10,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).

fof(f3820,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f476,f3818]) ).

fof(f3818,plain,
    ( spl0_314
  <=> ! [X3,X7,X9,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_HOL_Oord__class_Oless(X3,X7,X2)
        | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f476,axiom,
    ! [X2,X3,X9,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_HOL_Oord__class_Oless(X3,X7,X2)
      | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).

fof(f3816,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f475,f3814]) ).

fof(f3814,plain,
    ( spl0_313
  <=> ! [X2,X9,X7,X3] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_HOL_Oord__class_Oless(X9,X7,X2)
        | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f475,axiom,
    ! [X2,X3,X9,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_HOL_Oord__class_Oless(X9,X7,X2)
      | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X3,X9,X2),X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).

fof(f3812,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f470,f3810]) ).

fof(f3810,plain,
    ( spl0_312
  <=> ! [X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f470,axiom,
    ! [X0,X1] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).

fof(f3808,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f467,f3806]) ).

fof(f3806,plain,
    ( spl0_311
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Olinorder(X2)
        | X7 = X8
        | c_HOL_Oord__class_Oless(X7,X8,X2)
        | c_HOL_Oord__class_Oless(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f467,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Olinorder(X2)
      | X7 = X8
      | c_HOL_Oord__class_Oless(X7,X8,X2)
      | c_HOL_Oord__class_Oless(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

fof(f3804,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f430,f3802]) ).

fof(f3802,plain,
    ( spl0_310
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Oorder(X2)
        | X7 = X8
        | ~ c_lessequals(X7,X8,X2)
        | c_HOL_Oord__class_Oless(X7,X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f430,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Oorder(X2)
      | X7 = X8
      | ~ c_lessequals(X7,X8,X2)
      | c_HOL_Oord__class_Oless(X7,X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

fof(f3800,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f426,f3798]) ).

fof(f3798,plain,
    ( spl0_309
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Olinorder(X2)
        | X7 = X8
        | ~ c_lessequals(X7,X8,X2)
        | c_HOL_Oord__class_Oless(X7,X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f426,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Olinorder(X2)
      | X7 = X8
      | ~ c_lessequals(X7,X8,X2)
      | c_HOL_Oord__class_Oless(X7,X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

fof(f3796,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f412,f3794]) ).

fof(f3794,plain,
    ( spl0_308
  <=> ! [X5,X10,X6,X2] :
        ( c_in(X10,X5,X2)
        | ~ c_in(X10,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f412,axiom,
    ! [X2,X10,X6,X5] :
      ( c_in(X10,X5,X2)
      | ~ c_in(X10,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

fof(f3792,plain,
    spl0_307,
    inference(avatar_split_clause,[],[f411,f3790]) ).

fof(f3790,plain,
    ( spl0_307
  <=> ! [X5,X10,X6,X2] :
        ( c_in(X10,X6,X2)
        | ~ c_in(X10,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f411,axiom,
    ! [X2,X10,X6,X5] :
      ( c_in(X10,X6,X2)
      | ~ c_in(X10,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

fof(f3788,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f409,f3786]) ).

fof(f3786,plain,
    ( spl0_306
  <=> ! [X5,X10,X6,X2] :
        ( c_in(X10,X5,X2)
        | ~ c_in(X10,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f409,axiom,
    ! [X2,X10,X6,X5] :
      ( c_in(X10,X5,X2)
      | ~ c_in(X10,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

fof(f3784,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f408,f3782]) ).

fof(f3782,plain,
    ( spl0_305
  <=> ! [X5,X10,X6,X2] :
        ( ~ c_in(X10,X6,X2)
        | ~ c_in(X10,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f408,axiom,
    ! [X2,X10,X6,X5] :
      ( ~ c_in(X10,X6,X2)
      | ~ c_in(X10,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

fof(f3780,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f366,f3778]) ).

fof(f3778,plain,
    ( spl0_304
  <=> ! [X2,X13,X8,X19,X7] :
        ( hAPP(X19,X7) = X8
        | c_Fun_Ofun__upd(X19,X7,X8,X2,X13) != X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f366,axiom,
    ! [X2,X8,X19,X7,X13] :
      ( hAPP(X19,X7) = X8
      | c_Fun_Ofun__upd(X19,X7,X8,X2,X13) != X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

fof(f3776,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f362,f3774]) ).

fof(f3774,plain,
    ( spl0_303
  <=> ! [X5,X7,X6,X2] :
        ( hBOOL(hAPP(X5,X7))
        | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f362,axiom,
    ! [X2,X6,X7,X5] :
      ( hBOOL(hAPP(X5,X7))
      | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

fof(f3772,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f361,f3770]) ).

fof(f3770,plain,
    ( spl0_302
  <=> ! [X6,X2,X5,X7] :
        ( hBOOL(hAPP(X6,X7))
        | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f361,axiom,
    ! [X2,X6,X7,X5] :
      ( hBOOL(hAPP(X6,X7))
      | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

fof(f3768,plain,
    ( ~ spl0_301
    | ~ spl0_61
    | spl0_290 ),
    inference(avatar_split_clause,[],[f3723,f3535,f1644,f3765]) ).

fof(f3765,plain,
    ( spl0_301
  <=> class_Finite__Set_Ofinite_Ofinite(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f1644,plain,
    ( spl0_61
  <=> ! [X2,X5] :
        ( ~ class_Finite__Set_Ofinite_Ofinite(X2)
        | c_Finite__Set_Ofinite(X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f3723,plain,
    ( ~ class_Finite__Set_Ofinite_Ofinite(t_a)
    | ~ spl0_61
    | spl0_290 ),
    inference(resolution,[],[f3536,f1645]) ).

fof(f1645,plain,
    ( ! [X2,X5] :
        ( c_Finite__Set_Ofinite(X5,X2)
        | ~ class_Finite__Set_Ofinite_Ofinite(X2) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f1644]) ).

fof(f3763,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f307,f3761]) ).

fof(f3761,plain,
    ( spl0_300
  <=> ! [X6,X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Otop__class_Otop(X2) = X5
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X2) != c_Orderings_Otop__class_Otop(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f307,axiom,
    ! [X2,X6,X5] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Otop__class_Otop(X2) = X5
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X2) != c_Orderings_Otop__class_Otop(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).

fof(f3759,plain,
    spl0_299,
    inference(avatar_split_clause,[],[f306,f3757]) ).

fof(f3757,plain,
    ( spl0_299
  <=> ! [X6,X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Otop__class_Otop(X2) = X6
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X2) != c_Orderings_Otop__class_Otop(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f306,axiom,
    ! [X2,X6,X5] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Otop__class_Otop(X2) = X6
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X2) != c_Orderings_Otop__class_Otop(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).

fof(f3755,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f299,f3753]) ).

fof(f3753,plain,
    ( spl0_298
  <=> ! [X2,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f299,axiom,
    ! [X2,X3] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

fof(f3751,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f189,f3749]) ).

fof(f3749,plain,
    ( spl0_297
  <=> ! [X2,X9,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
        | c_HOL_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X9,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f189,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
      | c_HOL_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X9,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).

fof(f3747,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f188,f3745]) ).

fof(f3745,plain,
    ( spl0_296
  <=> ! [X2,X9,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X9,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f188,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X9,X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X9,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).

fof(f3743,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f183,f3741]) ).

fof(f3741,plain,
    ( spl0_295
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f183,axiom,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

fof(f3739,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f182,f3737]) ).

fof(f3737,plain,
    ( spl0_294
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f182,axiom,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

fof(f3735,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f175,f3733]) ).

fof(f3733,plain,
    ( spl0_293
  <=> ! [X6,X2,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f175,axiom,
    ! [X2,X6,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

fof(f3731,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f157,f3729]) ).

fof(f3729,plain,
    ( spl0_292
  <=> ! [X2,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f157,axiom,
    ! [X2,X3] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

fof(f3727,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f99,f3725]) ).

fof(f3725,plain,
    ( spl0_291
  <=> ! [X13,X2,X19] : c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)) = c_Set_Ovimage(X19,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_bool)),X2,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f99,axiom,
    ! [X2,X19,X13] : c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)) = c_Set_Ovimage(X19,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_bool)),X2,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).

fof(f3538,plain,
    ( ~ spl0_289
    | spl0_290
    | ~ spl0_51
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f3529,f3267,f1600,f3535,f3531]) ).

fof(f3529,plain,
    ( c_Finite__Set_Ofinite(v_G,t_a)
    | ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
    | ~ spl0_51
    | ~ spl0_277 ),
    inference(resolution,[],[f3268,f1602]) ).

fof(f3415,plain,
    ( ~ spl0_35
    | ~ spl0_288
    | ~ spl0_199
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f3172,f3018,f2376,f3412,f1520]) ).

fof(f3412,plain,
    ( spl0_288
  <=> c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f3172,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat)
    | ~ class_Orderings_Opreorder(tc_nat)
    | ~ spl0_199
    | ~ spl0_255 ),
    inference(resolution,[],[f3020,f2377]) ).

fof(f3311,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f1194,f3309]) ).

fof(f3309,plain,
    ( spl0_287
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f1194,plain,
    ! [X0,X1] :
      ( c_lessequals(X0,X1,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ),
    inference(definition_unfolding,[],[f1035,f61]) ).

fof(f1035,axiom,
    ! [X0,X1] :
      ( c_lessequals(X0,X1,tc_nat)
      | c_lessequals(c_Suc(X1),X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

fof(f3305,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f1192,f3303]) ).

fof(f3303,plain,
    ( spl0_286
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f1192,plain,
    ! [X0,X1] :
      ( c_lessequals(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f878,f61]) ).

fof(f878,axiom,
    ! [X0,X1] :
      ( c_lessequals(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

fof(f3301,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f1189,f3299]) ).

fof(f3299,plain,
    ( spl0_285
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f1189,plain,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f637,f61]) ).

fof(f637,axiom,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

fof(f3297,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f1186,f3295]) ).

fof(f1186,plain,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ),
    inference(definition_unfolding,[],[f883,f61]) ).

fof(f883,axiom,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
      | ~ c_lessequals(c_Suc(X1),X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

fof(f3293,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f1175,f3291]) ).

fof(f3291,plain,
    ( spl0_283
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f1175,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f879,f61]) ).

fof(f879,axiom,
    ! [X0,X1] :
      ( ~ c_lessequals(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

fof(f3289,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f1174,f3287]) ).

fof(f1174,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ),
    inference(definition_unfolding,[],[f1034,f61]) ).

fof(f1034,axiom,
    ! [X0,X1] :
      ( ~ c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(c_Suc(X1),X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

fof(f3285,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f1169,f3283]) ).

fof(f3283,plain,
    ( spl0_281
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f1169,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(definition_unfolding,[],[f880,f61]) ).

fof(f880,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_lessequals(c_Suc(X0),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

fof(f3281,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f1167,f3279]) ).

fof(f3279,plain,
    ( spl0_280
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f1167,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f636,f61]) ).

fof(f636,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

fof(f3277,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f1011,f3275]) ).

fof(f3275,plain,
    ( spl0_279
  <=> ! [X2,X5,X7] : c_Set_Oinsert(X7,X5,X2) = c_Set_Oinsert(X7,c_Set_Oinsert(X7,X5,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f1011,axiom,
    ! [X2,X7,X5] : c_Set_Oinsert(X7,X5,X2) = c_Set_Oinsert(X7,c_Set_Oinsert(X7,X5,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

fof(f3273,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f978,f3271]) ).

fof(f978,axiom,
    ! [X21,X4,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | ~ c_lessequals(X21,X4,tc_nat)
      | c_lessequals(X20,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).

fof(f3269,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f966,f3267]) ).

fof(f966,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(X6,X2)
      | c_Finite__Set_Ofinite(X5,X2)
      | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

fof(f3260,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f769,f3258]) ).

fof(f3258,plain,
    ( spl0_276
  <=> ! [X6,X2,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
        | c_lessequals(X5,X6,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f769,axiom,
    ! [X2,X6,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_fun(X2,tc_bool))
      | c_lessequals(X5,X6,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

fof(f3256,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f740,f3254]) ).

fof(f3254,plain,
    ( spl0_275
  <=> ! [X20,X2,X4] :
        ( ~ class_HOL_Oord(X2)
        | ~ c_lessequals(X4,X20,X2)
        | c_in(X20,c_SetInterval_Oord__class_OatLeast(X4,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f740,axiom,
    ! [X2,X4,X20] :
      ( ~ class_HOL_Oord(X2)
      | ~ c_lessequals(X4,X20,X2)
      | c_in(X20,c_SetInterval_Oord__class_OatLeast(X4,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_1) ).

fof(f3252,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f739,f3250]) ).

fof(f3250,plain,
    ( spl0_274
  <=> ! [X20,X2,X4] :
        ( ~ class_HOL_Oord(X2)
        | c_lessequals(X4,X20,X2)
        | ~ c_in(X20,c_SetInterval_Oord__class_OatLeast(X4,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f739,axiom,
    ! [X2,X4,X20] :
      ( ~ class_HOL_Oord(X2)
      | c_lessequals(X4,X20,X2)
      | ~ c_in(X20,c_SetInterval_Oord__class_OatLeast(X4,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_0) ).

fof(f3248,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f680,f3246]) ).

fof(f3246,plain,
    ( spl0_273
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f680,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

fof(f3244,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f679,f3242]) ).

fof(f679,axiom,
    ! [X0,X1] :
      ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

fof(f3240,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f675,f3238]) ).

fof(f3238,plain,
    ( spl0_271
  <=> ! [X2,X9,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X9,X3,X2),X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f675,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X9,X3,X2),X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).

fof(f3236,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f674,f3234]) ).

fof(f3234,plain,
    ( spl0_270
  <=> ! [X2,X9,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f674,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X9,X2),X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).

fof(f3231,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f664,f3229]) ).

fof(f3229,plain,
    ( spl0_269
  <=> ! [X25,X1] :
        ( ~ hBOOL(hAPP(X25,X1))
        | hBOOL(hAPP(X25,c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f664,axiom,
    ! [X1,X25] :
      ( ~ hBOOL(hAPP(X25,X1))
      | hBOOL(hAPP(X25,c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_5) ).

fof(f3226,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f663,f3224]) ).

fof(f3224,plain,
    ( spl0_268
  <=> ! [X25,X1] :
        ( hBOOL(hAPP(X25,X1))
        | ~ hBOOL(hAPP(X25,c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f663,axiom,
    ! [X1,X25] :
      ( hBOOL(hAPP(X25,X1))
      | ~ hBOOL(hAPP(X25,c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_0) ).

fof(f3222,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f568,f3220]) ).

fof(f3220,plain,
    ( spl0_267
  <=> ! [X2,X7,X8] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X8,X7,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = X8 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f568,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X8,X7,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

fof(f3218,plain,
    ( spl0_266
    | ~ spl0_52
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f2977,f2711,f1605,f3215]) ).

fof(f2711,plain,
    ( spl0_241
  <=> ! [X4,X0,X1] :
        ( c_lessequals(X4,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f2977,plain,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_52
    | ~ spl0_241 ),
    inference(resolution,[],[f2712,f1607]) ).

fof(f2712,plain,
    ( ! [X0,X1,X4] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),X1,tc_nat)
        | c_lessequals(X4,X1,tc_nat) )
    | ~ spl0_241 ),
    inference(avatar_component_clause,[],[f2711]) ).

fof(f3213,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f567,f3211]) ).

fof(f3211,plain,
    ( spl0_265
  <=> ! [X2,X8,X7] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(X7,X8,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) != X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f567,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(X7,X8,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) != X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

fof(f3209,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f566,f3207]) ).

fof(f3207,plain,
    ( spl0_264
  <=> ! [X2,X8,X7] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X7,X8,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f566,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X7,X8,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

fof(f3205,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f490,f3203]) ).

fof(f3203,plain,
    ( spl0_263
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Olinorder(X2)
        | X7 = X8
        | c_SetInterval_Oord__class_OatLeast(X7,X2) != c_SetInterval_Oord__class_OatLeast(X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f490,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Olinorder(X2)
      | X7 = X8
      | c_SetInterval_Oord__class_OatLeast(X7,X2) != c_SetInterval_Oord__class_OatLeast(X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__eq__iff_0) ).

fof(f3201,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f481,f3199]) ).

fof(f3199,plain,
    ( spl0_262
  <=> ! [X8,X7,X14] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X14,tc_nat)
        | c_Ring__and__Field_Odvd__class_Odvd(X7,X14,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f481,axiom,
    ! [X8,X7,X14] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X14,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X7,X14,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).

fof(f3197,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f360,f3195]) ).

fof(f3195,plain,
    ( spl0_261
  <=> ! [X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f360,axiom,
    ! [X2] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

fof(f3193,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f205,f3191]) ).

fof(f3191,plain,
    ( spl0_260
  <=> ! [X4,X0,X1] :
        ( X0 = X1
        | c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f205,axiom,
    ! [X0,X1,X4] :
      ( X0 = X1
      | c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

fof(f3189,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f204,f3187]) ).

fof(f3187,plain,
    ( spl0_259
  <=> ! [X8,X14,X7] :
        ( X8 = X14
        | c_HOL_Oplus__class_Oplus(X7,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X8,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f204,axiom,
    ! [X8,X7,X14] :
      ( X8 = X14
      | c_HOL_Oplus__class_Oplus(X7,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X8,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

fof(f3185,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f133,f3183]) ).

fof(f3183,plain,
    ( spl0_258
  <=> ! [X2,X0,X1] :
        ( ~ class_Nat_Osemiring__char__0(X2)
        | X0 = X1
        | c_Nat_Osemiring__1__class_Oof__nat(X0,X2) != c_Nat_Osemiring__1__class_Oof__nat(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f133,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Nat_Osemiring__char__0(X2)
      | X0 = X1
      | c_Nat_Osemiring__1__class_Oof__nat(X0,X2) != c_Nat_Osemiring__1__class_Oof__nat(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

fof(f3181,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f131,f3179]) ).

fof(f3179,plain,
    ( spl0_257
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_lessequals(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f131,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_lessequals(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).

fof(f3177,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f39,f3175]) ).

fof(f3175,plain,
    ( spl0_256
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f39,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).

fof(f3021,plain,
    ( spl0_255
    | ~ spl0_52
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f2997,f2715,f1605,f3018]) ).

fof(f2715,plain,
    ( spl0_242
  <=> ! [X4,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f2997,plain,
    ( c_lessequals(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_52
    | ~ spl0_242 ),
    inference(resolution,[],[f2716,f1607]) ).

fof(f2716,plain,
    ( ! [X0,X1,X4] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),X1,tc_nat)
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_242 ),
    inference(avatar_component_clause,[],[f2715]) ).

fof(f2916,plain,
    ( ~ spl0_36
    | ~ spl0_254
    | ~ spl0_107
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f2492,f2368,f1841,f2913,f1525]) ).

fof(f2913,plain,
    ( spl0_254
  <=> c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f1841,plain,
    ( spl0_107
  <=> c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f2492,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
    | ~ class_Orderings_Olinorder(tc_nat)
    | ~ spl0_107
    | ~ spl0_198 ),
    inference(resolution,[],[f2369,f1843]) ).

fof(f1843,plain,
    ( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f1841]) ).

fof(f2761,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f1246,f2759]) ).

fof(f2759,plain,
    ( spl0_253
  <=> ! [X20,X0] : c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X20,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f1246,plain,
    ! [X0,X20] : c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X20,tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f1143,f1139]) ).

fof(f1139,plain,
    ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
    inference(definition_unfolding,[],[f62,f61]) ).

fof(f62,axiom,
    ! [X1] : c_Suc(X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

fof(f1143,plain,
    ! [X0,X20] : c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X20,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f96,f61]) ).

fof(f96,axiom,
    ! [X0,X20] : c_HOL_Oord__class_Oless(X20,c_Suc(c_HOL_Oplus__class_Oplus(X0,X20,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

fof(f2757,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f1245,f2755]) ).

fof(f2755,plain,
    ( spl0_252
  <=> ! [X0,X7] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X7,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f1245,plain,
    ! [X0,X7] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X7,tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f1142,f1139]) ).

fof(f1142,plain,
    ! [X0,X7] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X7,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f97,f61]) ).

fof(f97,axiom,
    ! [X0,X7] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X7,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

fof(f2753,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f1145,f2751]) ).

fof(f1145,plain,
    ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f900,f61]) ).

fof(f900,axiom,
    ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

fof(f2749,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f1036,f2747]) ).

fof(f2747,plain,
    ( spl0_250
  <=> ! [X2,X5,X7,X8] :
        ( ~ hBOOL(hAPP(X5,X7))
        | hBOOL(hAPP(c_Set_Oinsert(X8,X5,X2),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f1036,axiom,
    ! [X2,X8,X7,X5] :
      ( ~ hBOOL(hAPP(X5,X7))
      | hBOOL(hAPP(c_Set_Oinsert(X8,X5,X2),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

fof(f2745,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f998,f2743]) ).

fof(f2743,plain,
    ( spl0_249
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f998,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(X1,X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).

fof(f2741,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f964,f2739]) ).

fof(f2739,plain,
    ( spl0_248
  <=> ! [X3,X9,X5,X2] :
        ( ~ c_in(X3,X5,X2)
        | c_in(X3,c_Set_Oinsert(X9,X5,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f964,axiom,
    ! [X2,X3,X9,X5] :
      ( ~ c_in(X3,X5,X2)
      | c_in(X3,c_Set_Oinsert(X9,X5,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

fof(f2737,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f907,f2735]) ).

fof(f907,axiom,
    ! [X0,X1] :
      ( ~ c_lessequals(X0,X1,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).

fof(f2733,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f906,f2731]) ).

fof(f2731,plain,
    ( spl0_246
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f906,axiom,
    ! [X0,X1] :
      ( c_lessequals(X0,X1,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).

fof(f2729,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f838,f2727]) ).

fof(f838,axiom,
    ! [X21,X1,X4] :
      ( ~ c_HOL_Oord__class_Oless(X21,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X1,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

fof(f2725,plain,
    ( spl0_244
    | ~ spl0_163
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2680,f2634,f2093,f2723]) ).

fof(f2723,plain,
    ( spl0_244
  <=> ! [X0] : v_U != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f2680,plain,
    ( ! [X0] : v_U != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
    | ~ spl0_163
    | ~ spl0_223 ),
    inference(superposition,[],[f2094,f2635]) ).

fof(f2721,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f813,f2719]) ).

fof(f2719,plain,
    ( spl0_243
  <=> ! [X7,X14,X8] :
        ( ~ c_lessequals(X7,X14,tc_nat)
        | c_lessequals(X7,c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f813,axiom,
    ! [X8,X7,X14] :
      ( ~ c_lessequals(X7,X14,tc_nat)
      | c_lessequals(X7,c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).

fof(f2717,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f812,f2715]) ).

fof(f812,axiom,
    ! [X0,X1,X4] :
      ( c_lessequals(X0,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).

fof(f2713,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f811,f2711]) ).

fof(f811,axiom,
    ! [X0,X1,X4] :
      ( c_lessequals(X4,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X4,tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).

fof(f2709,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f810,f2707]) ).

fof(f2707,plain,
    ( spl0_240
  <=> ! [X20,X21,X0] :
        ( ~ c_lessequals(X20,X21,tc_nat)
        | c_lessequals(X20,c_HOL_Oplus__class_Oplus(X21,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f810,axiom,
    ! [X21,X0,X20] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_lessequals(X20,c_HOL_Oplus__class_Oplus(X21,X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).

fof(f2705,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f792,f2703]) ).

fof(f2703,plain,
    ( spl0_239
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f792,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | ~ c_lessequals(X0,X1,tc_nat)
      | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).

fof(f2701,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f774,f2699]) ).

fof(f2699,plain,
    ( spl0_238
  <=> ! [X6,X2,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f774,axiom,
    ! [X2,X6,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

fof(f2697,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f766,f2695]) ).

fof(f2695,plain,
    ( spl0_237
  <=> ! [X6,X2,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f766,axiom,
    ! [X2,X6,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

fof(f2693,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f765,f2691]) ).

fof(f2691,plain,
    ( spl0_236
  <=> ! [X6,X2,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f765,axiom,
    ! [X2,X6,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

fof(f2689,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f712,f2687]) ).

fof(f2687,plain,
    ( spl0_235
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X1
        | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f712,axiom,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X1
      | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).

fof(f2685,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f608,f2683]) ).

fof(f2683,plain,
    ( spl0_234
  <=> ! [X2,X12,X39] :
        ( ~ c_Finite__Set_Ofinite(X12,X2)
        | c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X12,X39,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f608,axiom,
    ! [X2,X39,X12] :
      ( ~ c_Finite__Set_Ofinite(X12,X2)
      | c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X12,X39,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).

fof(f2676,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f607,f2674]) ).

fof(f2674,plain,
    ( spl0_233
  <=> ! [X2,X12,X39] :
        ( ~ c_Finite__Set_Ofinite(X39,X2)
        | c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X12,X39,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f607,axiom,
    ! [X2,X39,X12] :
      ( ~ c_Finite__Set_Ofinite(X39,X2)
      | c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X12,X39,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).

fof(f2672,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f606,f2670]) ).

fof(f2670,plain,
    ( spl0_232
  <=> ! [X6,X2,X5] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f606,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

fof(f2668,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f466,f2666]) ).

fof(f2666,plain,
    ( spl0_231
  <=> ! [X8,X7] :
        ( X7 = X8
        | c_HOL_Oord__class_Oless(X7,X8,tc_nat)
        | c_HOL_Oord__class_Oless(X8,X7,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f466,axiom,
    ! [X8,X7] :
      ( X7 = X8
      | c_HOL_Oord__class_Oless(X7,X8,tc_nat)
      | c_HOL_Oord__class_Oless(X8,X7,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

fof(f2664,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f458,f2662]) ).

fof(f2662,plain,
    ( spl0_230
  <=> ! [X8,X7] :
        ( X7 = X8
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f458,axiom,
    ! [X8,X7] :
      ( X7 = X8
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).

fof(f2660,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f342,f2658]) ).

fof(f2658,plain,
    ( spl0_229
  <=> ! [X4,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f342,axiom,
    ! [X1,X4] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).

fof(f2656,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f341,f2654]) ).

fof(f2654,plain,
    ( spl0_228
  <=> ! [X4,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f341,axiom,
    ! [X1,X4] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X1,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).

fof(f2652,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f339,f2650]) ).

fof(f2650,plain,
    ( spl0_227
  <=> ! [X2,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f339,axiom,
    ! [X2,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

fof(f2648,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f338,f2646]) ).

fof(f2646,plain,
    ( spl0_226
  <=> ! [X6,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f338,axiom,
    ! [X2,X6] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X6,tc_fun(X2,tc_bool)) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

fof(f2644,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f185,f2642]) ).

fof(f2642,plain,
    ( spl0_225
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Ozero__class_Ozero(X2) = X3
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f185,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Ozero__class_Ozero(X2) = X3
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).

fof(f2640,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f177,f2638]) ).

fof(f2638,plain,
    ( spl0_224
  <=> ! [X2,X7,X8] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = c_Lattices_Olower__semilattice__class_Oinf(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f177,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = c_Lattices_Olower__semilattice__class_Oinf(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

fof(f2636,plain,
    ( spl0_223
    | ~ spl0_149
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f2584,f2412,f2036,f2634]) ).

fof(f2036,plain,
    ( spl0_149
  <=> ! [X0] : c_in(v_pn,v_U,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f2584,plain,
    ( ! [X0] : v_U = c_Set_Oinsert(v_pn,v_U,X0)
    | ~ spl0_149
    | ~ spl0_208 ),
    inference(resolution,[],[f2413,f2037]) ).

fof(f2037,plain,
    ( ! [X0] : c_in(v_pn,v_U,X0)
    | ~ spl0_149 ),
    inference(avatar_component_clause,[],[f2036]) ).

fof(f2632,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f176,f2630]) ).

fof(f2630,plain,
    ( spl0_222
  <=> ! [X2,X7,X8] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = c_Lattices_Olower__semilattice__class_Oinf(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f176,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2) = c_Lattices_Olower__semilattice__class_Oinf(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

fof(f2628,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f152,f2626]) ).

fof(f2626,plain,
    ( spl0_221
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f152,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

fof(f2624,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f151,f2622]) ).

fof(f2622,plain,
    ( spl0_220
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f151,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

fof(f2620,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f148,f2618]) ).

fof(f2618,plain,
    ( spl0_219
  <=> ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X5,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f148,axiom,
    ! [X2,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X5,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

fof(f2616,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f147,f2614]) ).

fof(f2614,plain,
    ( spl0_218
  <=> ! [X2,X5] : c_HOL_Ominus__class_Ominus(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f147,axiom,
    ! [X2,X5] : c_HOL_Ominus__class_Ominus(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

fof(f2612,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f125,f2610]) ).

fof(f2610,plain,
    ( spl0_217
  <=> ! [X2,X9,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
        | c_HOL_Oplus__class_Oplus(X3,X9,X2) = c_HOL_Oplus__class_Oplus(X9,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f125,axiom,
    ! [X2,X3,X9] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
      | c_HOL_Oplus__class_Oplus(X3,X9,X2) = c_HOL_Oplus__class_Oplus(X9,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f2608,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f124,f2606]) ).

fof(f2606,plain,
    ( spl0_216
  <=> ! [X2,X3,X10] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(X3,X10,X2) = c_HOL_Oplus__class_Oplus(X10,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f124,axiom,
    ! [X2,X3,X10] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(X3,X10,X2) = c_HOL_Oplus__class_Oplus(X10,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(f2604,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f108,f2602]) ).

fof(f2602,plain,
    ( spl0_215
  <=> ! [X20,X21,X0] :
        ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
        | c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(X0,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f108,axiom,
    ! [X21,X0,X20] :
      ( ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(X0,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

fof(f2600,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f106,f2598]) ).

fof(f2598,plain,
    ( spl0_214
  <=> ! [X20,X4,X21] :
        ( c_HOL_Oord__class_Oless(X20,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X21,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f106,axiom,
    ! [X21,X4,X20] :
      ( c_HOL_Oord__class_Oless(X20,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X21,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

fof(f2596,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f104,f2594]) ).

fof(f2594,plain,
    ( spl0_213
  <=> ! [X8,X7,X14] :
        ( ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat)
        | c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f104,axiom,
    ! [X8,X7,X14] :
      ( ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat)
      | c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

fof(f2592,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f48,f2590]) ).

fof(f2590,plain,
    ( spl0_212
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X0
        | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f48,axiom,
    ! [X0,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X0
      | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).

fof(f2588,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f14,f2586]) ).

fof(f2586,plain,
    ( spl0_211
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(X3,X9,X2) = c_HOL_Otimes__class_Otimes(X9,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f14,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Otimes__class_Otimes(X3,X9,X2) = c_HOL_Otimes__class_Otimes(X9,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(f2538,plain,
    ( ~ spl0_209
    | ~ spl0_210
    | ~ spl0_51
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f2493,f2368,f1600,f2535,f2531]) ).

fof(f2531,plain,
    ( spl0_209
  <=> class_Orderings_Olinorder(tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f2535,plain,
    ( spl0_210
  <=> c_HOL_Oord__class_Oless(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f2493,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))
    | ~ class_Orderings_Olinorder(tc_fun(t_a,tc_bool))
    | ~ spl0_51
    | ~ spl0_198 ),
    inference(resolution,[],[f2369,f1602]) ).

fof(f2414,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f1044,f2412]) ).

fof(f1044,axiom,
    ! [X2,X3,X5] :
      ( ~ c_in(X3,X5,X2)
      | c_Set_Oinsert(X3,X5,X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

fof(f2410,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f993,f2408]) ).

fof(f993,axiom,
    ! [X2,X11,X12,X13] :
      ( ~ c_Finite__Set_Ofinite(X12,X2)
      | c_Finite__Set_Ofinite(c_Set_Oimage(X11,X12,X2,X13),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

fof(f2406,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f955,f2404]) ).

fof(f2404,plain,
    ( spl0_206
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_lessequals(X7,X8,X2)
        | c_lessequals(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f955,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_lessequals(X7,X8,X2)
      | c_lessequals(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

fof(f2402,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f819,f2400]) ).

fof(f2400,plain,
    ( spl0_205
  <=> ! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f819,axiom,
    ! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).

fof(f2398,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f789,f2396]) ).

fof(f2396,plain,
    ( spl0_204
  <=> ! [X2,X5] :
        ( c_Finite__Set_Ofinite(X5,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X5,X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f789,axiom,
    ! [X2,X5] :
      ( c_Finite__Set_Ofinite(X5,X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X5,X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_1) ).

fof(f2394,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f729,f2392]) ).

fof(f2392,plain,
    ( spl0_203
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
        | ~ c_HOL_Oord__class_Oless(X8,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f729,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
      | ~ c_HOL_Oord__class_Oless(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

fof(f2390,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f726,f2388]) ).

fof(f2388,plain,
    ( spl0_202
  <=> ! [X2,X7,X8] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(X8,X7,X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f726,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_HOL_Oord__class_Oless(X8,X7,X2)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

fof(f2386,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f725,f2384]) ).

fof(f2384,plain,
    ( spl0_201
  <=> ! [X2,X9,X3] :
        ( ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(X9,X3,X2)
        | ~ c_HOL_Oord__class_Oless(X3,X9,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f725,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X2)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

fof(f2382,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f676,f2380]) ).

fof(f2380,plain,
    ( spl0_200
  <=> ! [X16,X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X16,X7,tc_nat),X16,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f676,axiom,
    ! [X16,X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X16,X7,tc_nat),X16,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).

fof(f2378,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f565,f2376]) ).

fof(f565,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
      | ~ c_lessequals(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

fof(f2370,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f561,f2368]) ).

fof(f561,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
      | ~ c_lessequals(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

fof(f2366,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f558,f2364]) ).

fof(f558,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_HOL_Oord__class_Oless(X7,X8,X2)
      | c_lessequals(X8,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

fof(f2362,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f501,f2360]) ).

fof(f2360,plain,
    ( spl0_196
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f501,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X2),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

fof(f2358,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f495,f2356]) ).

fof(f2356,plain,
    ( spl0_195
  <=> ! [X19,X13,X2,X7] : c_Fun_Ofun__upd(X19,X7,hAPP(X19,X7),X2,X13) = X19 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f495,axiom,
    ! [X2,X19,X7,X13] : c_Fun_Ofun__upd(X19,X7,hAPP(X19,X7),X2,X13) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

fof(f2354,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f494,f2352]) ).

fof(f2352,plain,
    ( spl0_194
  <=> ! [X19,X13,X8,X2,X7] : hAPP(c_Fun_Ofun__upd(X19,X7,X8,X13,X2),X7) = X8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f494,axiom,
    ! [X2,X8,X19,X7,X13] : hAPP(c_Fun_Ofun__upd(X19,X7,X8,X13,X2),X7) = X8,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

fof(f2350,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f454,f2348]) ).

fof(f2348,plain,
    ( spl0_193
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
        | c_lessequals(X7,X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f454,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
      | c_lessequals(X7,X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

fof(f2346,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f453,f2344]) ).

fof(f2344,plain,
    ( spl0_192
  <=> ! [X2,X8,X7] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
        | c_lessequals(X7,X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f453,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X2)
      | c_lessequals(X7,X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

fof(f2342,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f344,f2340]) ).

fof(f344,axiom,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
      | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).

fof(f2338,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f335,f2336]) ).

fof(f2336,plain,
    ( spl0_190
  <=> ! [X2,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X3,c_HOL_Oone__class_Oone(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f335,axiom,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X3,c_HOL_Oone__class_Oone(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).

fof(f2334,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f320,f2332]) ).

fof(f2332,plain,
    ( spl0_189
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Omult__zero(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f320,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

fof(f2326,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f319,f2324]) ).

fof(f2324,plain,
    ( spl0_188
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Omult__zero(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f319,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

fof(f2322,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f316,f2320]) ).

fof(f2320,plain,
    ( spl0_187
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f316,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(f2318,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f315,f2316]) ).

fof(f2316,plain,
    ( spl0_186
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f315,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

fof(f2314,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f135,f2312]) ).

fof(f2312,plain,
    ( spl0_185
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f135,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

fof(f2310,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f121,f2308]) ).

fof(f2308,plain,
    ( spl0_184
  <=> ! [X2,X7] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f121,axiom,
    ! [X2,X7] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

fof(f2306,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f120,f2304]) ).

fof(f2304,plain,
    ( spl0_183
  <=> ! [X2,X7] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Obot__class_Obot(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f120,axiom,
    ! [X2,X7] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Obot__class_Obot(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

fof(f2302,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f60,f2300]) ).

fof(f2300,plain,
    ( spl0_182
  <=> ! [X2,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f60,axiom,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).

fof(f2298,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f51,f2296]) ).

fof(f2296,plain,
    ( spl0_181
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f51,axiom,
    ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

fof(f2288,plain,
    ( spl0_180
    | ~ spl0_87
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1947,f1916,f1748,f2285]) ).

fof(f2285,plain,
    ( spl0_180
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f1748,plain,
    ( spl0_87
  <=> ! [X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f1916,plain,
    ( spl0_125
  <=> ! [X7] : c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f1947,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_87
    | ~ spl0_125 ),
    inference(superposition,[],[f1917,f1749]) ).

fof(f1749,plain,
    ( ! [X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f1748]) ).

fof(f1917,plain,
    ( ! [X7] : c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f1916]) ).

fof(f2249,plain,
    ( ~ spl0_179
    | ~ spl0_87
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1945,f1912,f1748,f2246]) ).

fof(f2246,plain,
    ( spl0_179
  <=> c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f1912,plain,
    ( spl0_124
  <=> ! [X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f1945,plain,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_87
    | ~ spl0_124 ),
    inference(superposition,[],[f1913,f1749]) ).

fof(f1913,plain,
    ( ! [X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f1912]) ).

fof(f2230,plain,
    ( spl0_178
    | ~ spl0_42
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1931,f1876,f1555,f2228]) ).

fof(f2228,plain,
    ( spl0_178
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f1555,plain,
    ( spl0_42
  <=> class_Lattices_Olower__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f1876,plain,
    ( spl0_115
  <=> ! [X2,X7] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,X7,X2) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1931,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
    | ~ spl0_42
    | ~ spl0_115 ),
    inference(resolution,[],[f1877,f1557]) ).

fof(f1557,plain,
    ( class_Lattices_Olower__semilattice(tc_bool)
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f1555]) ).

fof(f1877,plain,
    ( ! [X2,X7] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,X7,X2) = X7 )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f1876]) ).

fof(f2219,plain,
    ( spl0_177
    | ~ spl0_24
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1930,f1876,f1465,f2217]) ).

fof(f2217,plain,
    ( spl0_177
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f1465,plain,
    ( spl0_24
  <=> class_Lattices_Olower__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f1930,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0
    | ~ spl0_24
    | ~ spl0_115 ),
    inference(resolution,[],[f1877,f1467]) ).

fof(f1467,plain,
    ( class_Lattices_Olower__semilattice(tc_nat)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f1465]) ).

fof(f2148,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f1273,f2146]) ).

fof(f2146,plain,
    ( spl0_176
  <=> ! [X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f1273,plain,
    ! [X1] :
      ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
    inference(forward_demodulation,[],[f1272,f378]) ).

fof(f1272,plain,
    ! [X1] :
      ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
    inference(forward_demodulation,[],[f1183,f126]) ).

fof(f1183,plain,
    ! [X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f3,f61]) ).

fof(f3,axiom,
    ! [X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

fof(f2144,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f1135,f2142]) ).

fof(f2142,plain,
    ( spl0_175
  <=> ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f1135,plain,
    ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f174,f61]) ).

fof(f174,axiom,
    ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X7),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

fof(f2140,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f1008,f2138]) ).

fof(f1008,axiom,
    ! [X2,X3,X6] : c_lessequals(X6,c_Set_Oinsert(X3,X6,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

fof(f2136,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f1007,f2134]) ).

fof(f2134,plain,
    ( spl0_173
  <=> ! [X2,X5,X3] :
        ( c_Finite__Set_Ofinite(X5,X2)
        | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X5,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f1007,axiom,
    ! [X2,X3,X5] :
      ( c_Finite__Set_Ofinite(X5,X2)
      | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X5,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

fof(f2132,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f1006,f2130]) ).

fof(f2130,plain,
    ( spl0_172
  <=> ! [X2,X5,X3] :
        ( ~ c_Finite__Set_Ofinite(X5,X2)
        | c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X5,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f1006,axiom,
    ! [X2,X3,X5] :
      ( ~ c_Finite__Set_Ofinite(X5,X2)
      | c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X5,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

fof(f2128,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f897,f2126]) ).

fof(f897,axiom,
    ! [X2,X5] :
      ( c_Finite__Set_Ofinite(X5,X2)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).

fof(f2124,plain,
    ( ~ spl0_170
    | ~ spl0_91
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1944,f1912,f1764,f2121]) ).

fof(f2121,plain,
    ( spl0_170
  <=> class_Orderings_Otop(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f1764,plain,
    ( spl0_91
  <=> ! [X2,X7] :
        ( ~ class_Orderings_Otop(X2)
        | c_lessequals(X7,c_Orderings_Otop__class_Otop(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f1944,plain,
    ( ~ class_Orderings_Otop(tc_nat)
    | ~ spl0_91
    | ~ spl0_124 ),
    inference(resolution,[],[f1913,f1765]) ).

fof(f1765,plain,
    ( ! [X2,X7] :
        ( c_lessequals(X7,c_Orderings_Otop__class_Otop(X2),X2)
        | ~ class_Orderings_Otop(X2) )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f1764]) ).

fof(f2119,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f853,f2117]) ).

fof(f2117,plain,
    ( spl0_169
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f853,axiom,
    ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

fof(f2115,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f852,f2113]) ).

fof(f2113,plain,
    ( spl0_168
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f852,axiom,
    ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

fof(f2111,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f807,f2109]) ).

fof(f2109,plain,
    ( spl0_167
  <=> ! [X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f807,axiom,
    ! [X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

fof(f2107,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f771,f2105]) ).

fof(f2105,plain,
    ( spl0_166
  <=> ! [X2,X5] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f771,axiom,
    ! [X2,X5] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

fof(f2103,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f762,f2101]) ).

fof(f2101,plain,
    ( spl0_165
  <=> ! [X2,X5] : c_lessequals(X5,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f762,axiom,
    ! [X2,X5] : c_lessequals(X5,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

fof(f2099,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f678,f2097]) ).

fof(f2097,plain,
    ( spl0_164
  <=> ! [X0] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X0
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f678,axiom,
    ! [X0] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X0
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).

fof(f2095,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f647,f2093]) ).

fof(f647,axiom,
    ! [X2,X3,X5] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X3,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

fof(f2091,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f510,f2089]) ).

fof(f2089,plain,
    ( spl0_162
  <=> ! [X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f510,axiom,
    ! [X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

fof(f2087,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f446,f2085]) ).

fof(f2085,plain,
    ( spl0_161
  <=> ! [X2,X7,X8] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f446,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

fof(f2083,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f445,f2081]) ).

fof(f2081,plain,
    ( spl0_160
  <=> ! [X2,X8,X7] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f445,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

fof(f2078,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f441,f2076]) ).

fof(f2076,plain,
    ( spl0_159
  <=> ! [X2,X8,X7] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f441,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

fof(f2074,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f440,f2072]) ).

fof(f2072,plain,
    ( spl0_158
  <=> ! [X2,X7,X8] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f440,axiom,
    ! [X2,X8,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X8,X2),X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

fof(f2070,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f383,f2068]) ).

fof(f2068,plain,
    ( spl0_157
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f383,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f2066,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f382,f2064]) ).

fof(f2064,plain,
    ( spl0_156
  <=> ! [X2,X3] :
        ( ~ class_OrderedGroup_Omonoid__add(X2)
        | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f382,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X2)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f2062,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f381,f2060]) ).

fof(f2060,plain,
    ( spl0_155
  <=> ! [X2,X3] :
        ( ~ class_OrderedGroup_Omonoid__add(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X3,X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f381,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X3,X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f2058,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f380,f2056]) ).

fof(f2056,plain,
    ( spl0_154
  <=> ! [X2,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
        | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f380,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f2054,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f375,f2052]) ).

fof(f2052,plain,
    ( spl0_153
  <=> ! [X2,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X3,X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f375,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X3,X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f2050,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f374,f2048]) ).

fof(f2048,plain,
    ( spl0_152
  <=> ! [X2,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X7,X2) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f374,axiom,
    ! [X2,X7] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X7,X2) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

fof(f2046,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f372,f2044]) ).

fof(f2044,plain,
    ( spl0_151
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f372,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).

fof(f2042,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f356,f2040]) ).

fof(f2040,plain,
    ( spl0_150
  <=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f2038,plain,
    ( spl0_149
    | ~ spl0_120
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1994,f1950,f1896,f2036]) ).

fof(f1950,plain,
    ( spl0_128
  <=> hBOOL(hAPP(v_U,v_pn)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1994,plain,
    ( ! [X0] : c_in(v_pn,v_U,X0)
    | ~ spl0_120
    | ~ spl0_128 ),
    inference(resolution,[],[f1952,f1897]) ).

fof(f1952,plain,
    ( hBOOL(hAPP(v_U,v_pn))
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1950]) ).

fof(f2034,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f337,f2032]) ).

fof(f2032,plain,
    ( spl0_148
  <=> ! [X2,X7] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X2),X7,X2) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f337,axiom,
    ! [X2,X7] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X2),X7,X2) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

fof(f2030,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f336,f2028]) ).

fof(f2028,plain,
    ( spl0_147
  <=> ! [X2,X7] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Otop__class_Otop(X2),X2) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f336,axiom,
    ! [X2,X7] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Otop__class_Otop(X2),X2) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

fof(f2026,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f330,f2024]) ).

fof(f2024,plain,
    ( spl0_146
  <=> ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f330,axiom,
    ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

fof(f2022,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f265,f2020]) ).

fof(f2020,plain,
    ( spl0_145
  <=> ! [X2,X5] : ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f265,axiom,
    ! [X2,X5] : ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

fof(f2018,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f234,f2016]) ).

fof(f2016,plain,
    ( spl0_144
  <=> ! [X25,X1] :
        ( hBOOL(hAPP(X25,X1))
        | ~ hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X25))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f234,axiom,
    ! [X1,X25] :
      ( hBOOL(hAPP(X25,X1))
      | ~ hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X25))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_full__nat__induct_1) ).

fof(f2014,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f222,f2012]) ).

fof(f2012,plain,
    ( spl0_143
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f222,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

fof(f2010,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f180,f2008]) ).

fof(f2008,plain,
    ( spl0_142
  <=> ! [X2] :
        ( ~ class_Ring__and__Field_Osemiring__1(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f180,axiom,
    ! [X2] :
      ( ~ class_Ring__and__Field_Osemiring__1(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

fof(f2006,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f126,f2004]) ).

fof(f2002,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f119,f2000]) ).

fof(f2000,plain,
    ( spl0_140
  <=> ! [X2,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X3,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f119,axiom,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X3,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).

fof(f1998,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f118,f1996]) ).

fof(f1996,plain,
    ( spl0_139
  <=> ! [X2,X3] :
        ( ~ class_Divides_Osemiring__div(X2)
        | c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f118,axiom,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X2)
      | c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).

fof(f1993,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f76,f1991]) ).

fof(f1991,plain,
    ( spl0_138
  <=> ! [X2,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X7,X2) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f76,axiom,
    ! [X2,X7] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X7,X2) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).

fof(f1989,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f73,f1987]) ).

fof(f1987,plain,
    ( spl0_137
  <=> ! [X2,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X2)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f73,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X2)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

fof(f1985,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f72,f1983]) ).

fof(f1983,plain,
    ( spl0_136
  <=> ! [X2,X3] :
        ( ~ class_OrderedGroup_Omonoid__mult(X2)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f72,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X2)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

fof(f1981,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f71,f1979]) ).

fof(f1979,plain,
    ( spl0_135
  <=> ! [X2,X3] :
        ( ~ class_OrderedGroup_Omonoid__mult(X2)
        | c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f71,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X2)
      | c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

fof(f1977,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f70,f1975]) ).

fof(f1975,plain,
    ( spl0_134
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f70,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

fof(f1973,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f67,f1971]) ).

fof(f1971,plain,
    ( spl0_133
  <=> ! [X2,X9,X4] :
        ( ~ class_Ring__and__Field_Odvd(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Otimes__class_Otimes(X9,X4,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f67,axiom,
    ! [X2,X9,X4] :
      ( ~ class_Ring__and__Field_Odvd(X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Otimes__class_Otimes(X9,X4,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).

fof(f1969,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f66,f1967]) ).

fof(f1967,plain,
    ( spl0_132
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X9,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f66,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X9,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).

fof(f1965,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f65,f1963]) ).

fof(f1963,plain,
    ( spl0_131
  <=> ! [X2,X9,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X9,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f65,axiom,
    ! [X2,X3,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X9,X3,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).

fof(f1961,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f52,f1959]) ).

fof(f1959,plain,
    ( spl0_130
  <=> ! [X2] :
        ( ~ class_Ring__and__Field_Osemiring__1(X2)
        | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X2) = c_HOL_Oone__class_Oone(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f52,axiom,
    ! [X2] :
      ( ~ class_Ring__and__Field_Osemiring__1(X2)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X2) = c_HOL_Oone__class_Oone(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).

fof(f1957,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f10,f1955]) ).

fof(f10,axiom,
    ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).

fof(f1953,plain,
    ( spl0_128
    | ~ spl0_2
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f1940,f1900,f1355,f1950]) ).

fof(f1940,plain,
    ( hBOOL(hAPP(v_U,v_pn))
    | ~ spl0_2
    | ~ spl0_121 ),
    inference(resolution,[],[f1901,f1357]) ).

fof(f1357,plain,
    ( c_in(v_pn,v_U,tc_Com_Opname)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f1355]) ).

fof(f1927,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f1249,f1925]) ).

fof(f1925,plain,
    ( spl0_127
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f1249,plain,
    ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(forward_demodulation,[],[f1248,f378]) ).

fof(f1248,plain,
    ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f1146,f1139]) ).

fof(f1146,plain,
    ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f329,f61]) ).

fof(f329,axiom,
    ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).

fof(f1923,plain,
    ( ~ spl0_126
    | ~ spl0_87
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f1846,f1824,f1748,f1920]) ).

fof(f1920,plain,
    ( spl0_126
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f1824,plain,
    ( spl0_106
  <=> ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f1846,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_87
    | ~ spl0_106 ),
    inference(superposition,[],[f1825,f1749]) ).

fof(f1825,plain,
    ( ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f1824]) ).

fof(f1918,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f1131,f1916]) ).

fof(f1131,plain,
    ! [X7] : c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f621,f61]) ).

fof(f621,axiom,
    ! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

fof(f1914,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f1130,f1912]) ).

fof(f1130,plain,
    ! [X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(definition_unfolding,[],[f987,f61]) ).

fof(f987,axiom,
    ! [X1] : ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

fof(f1910,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f1126,f1908]) ).

fof(f1908,plain,
    ( spl0_123
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1126,plain,
    ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(definition_unfolding,[],[f623,f61]) ).

fof(f623,axiom,
    ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

fof(f1906,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f1066,f1904]) ).

fof(f1904,plain,
    ( spl0_122
  <=> ! [X52,X51] :
        ( ~ class_Finite__Set_Ofinite_Ofinite(X51)
        | ~ class_Finite__Set_Ofinite_Ofinite(X52)
        | class_Finite__Set_Ofinite_Ofinite(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f1066,axiom,
    ! [X51,X52] :
      ( ~ class_Finite__Set_Ofinite_Ofinite(X51)
      | ~ class_Finite__Set_Ofinite_Ofinite(X52)
      | class_Finite__Set_Ofinite_Ofinite(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

fof(f1902,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f1021,f1900]) ).

fof(f1021,axiom,
    ! [X2,X46,X7] :
      ( ~ c_in(X7,X46,X2)
      | hBOOL(hAPP(X46,X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

fof(f1898,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f1020,f1896]) ).

fof(f1020,axiom,
    ! [X2,X46,X7] :
      ( ~ hBOOL(hAPP(X46,X7))
      | c_in(X7,X46,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

fof(f1894,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f956,f1892]) ).

fof(f1892,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f956,axiom,
    ! [X0,X1] :
      ( c_lessequals(X0,X1,tc_nat)
      | c_lessequals(X1,X0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

fof(f1890,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f847,f1888]) ).

fof(f1888,plain,
    ( spl0_118
  <=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f847,axiom,
    ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

fof(f1886,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f803,f1884]) ).

fof(f1884,plain,
    ( spl0_117
  <=> ! [X8,X7] :
        ( ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat)
        | c_lessequals(X7,X8,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f803,axiom,
    ! [X8,X7] :
      ( ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat)
      | c_lessequals(X7,X8,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

fof(f1882,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f553,f1880]) ).

fof(f1880,plain,
    ( spl0_116
  <=> ! [X2,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X5,tc_fun(X2,tc_bool)) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f553,axiom,
    ! [X2,X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X5,tc_fun(X2,tc_bool)) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

fof(f1878,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f552,f1876]) ).

fof(f552,axiom,
    ! [X2,X7] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X7,X7,X2) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

fof(f1874,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f489,f1872]) ).

fof(f1872,plain,
    ( spl0_114
  <=> ! [X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f489,axiom,
    ! [X2] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

fof(f1870,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f354,f1868]) ).

fof(f1868,plain,
    ( spl0_113
  <=> ! [X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f354,axiom,
    ! [X2] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

fof(f1866,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f322,f1864]) ).

fof(f1864,plain,
    ( spl0_112
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f322,axiom,
    ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).

fof(f1862,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f321,f1860]) ).

fof(f1860,plain,
    ( spl0_111
  <=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f321,axiom,
    ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

fof(f1858,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f314,f1856]) ).

fof(f1856,plain,
    ( spl0_110
  <=> ! [X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f314,axiom,
    ! [X2] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

fof(f1854,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f282,f1852]) ).

fof(f1852,plain,
    ( spl0_109
  <=> ! [X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f282,axiom,
    ! [X2] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X2)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

fof(f1850,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f172,f1848]) ).

fof(f1848,plain,
    ( spl0_108
  <=> ! [X13,X2,X19] : c_Fun_Oinj__on(X19,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f172,axiom,
    ! [X2,X19,X13] : c_Fun_Oinj__on(X19,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

fof(f1844,plain,
    ( spl0_107
    | ~ spl0_58
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f1837,f1816,f1631,f1841]) ).

fof(f1816,plain,
    ( spl0_104
  <=> ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f1837,plain,
    ( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
    | ~ spl0_58
    | ~ spl0_104 ),
    inference(superposition,[],[f1817,f1633]) ).

fof(f1817,plain,
    ( ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
    | ~ spl0_104 ),
    inference(avatar_component_clause,[],[f1816]) ).

fof(f1826,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f1124,f1824]) ).

fof(f1124,plain,
    ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(definition_unfolding,[],[f984,f61]) ).

fof(f984,axiom,
    ! [X1] : c_Suc(X1) != X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

fof(f1822,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f1121,f1820]) ).

fof(f1820,plain,
    ( spl0_105
  <=> ! [X2,X53,X24] :
        ( X24 = X53
        | ~ c_fequal(X24,X53,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f1121,axiom,
    ! [X2,X24,X53] :
      ( X24 = X53
      | ~ c_fequal(X24,X53,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f1818,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f1030,f1816]) ).

fof(f1030,axiom,
    ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

fof(f1814,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f1017,f1812]) ).

fof(f1812,plain,
    ( spl0_103
  <=> ! [X6,X2,X3] : c_in(X3,c_Set_Oinsert(X3,X6,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f1017,axiom,
    ! [X2,X3,X6] : c_in(X3,c_Set_Oinsert(X3,X6,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

fof(f1810,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f988,f1808]) ).

fof(f1808,plain,
    ( spl0_102
  <=> ! [X2,X5,X7] : hBOOL(hAPP(c_Set_Oinsert(X7,X5,X2),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f988,axiom,
    ! [X2,X7,X5] : hBOOL(hAPP(c_Set_Oinsert(X7,X5,X2),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

fof(f1806,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f841,f1804]) ).

fof(f1804,plain,
    ( spl0_101
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f841,axiom,
    ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

fof(f1802,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f840,f1800]) ).

fof(f1800,plain,
    ( spl0_100
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f840,axiom,
    ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

fof(f1798,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f817,f1796]) ).

fof(f1796,plain,
    ( spl0_99
  <=> ! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f817,axiom,
    ! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).

fof(f1794,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f816,f1792]) ).

fof(f1792,plain,
    ( spl0_98
  <=> ! [X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f816,axiom,
    ! [X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).

fof(f1790,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f806,f1788]) ).

fof(f1788,plain,
    ( spl0_97
  <=> ! [X0,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f806,axiom,
    ! [X0,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).

fof(f1786,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f805,f1784]) ).

fof(f1784,plain,
    ( spl0_96
  <=> ! [X0,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f805,axiom,
    ! [X0,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).

fof(f1782,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f556,f1780]) ).

fof(f1780,plain,
    ( spl0_95
  <=> ! [X2,X7] :
        ( ~ class_Orderings_Obot(X2)
        | c_lessequals(c_Orderings_Obot__class_Obot(X2),X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f556,axiom,
    ! [X2,X7] :
      ( ~ class_Orderings_Obot(X2)
      | c_lessequals(c_Orderings_Obot__class_Obot(X2),X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

fof(f1778,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f537,f1776]) ).

fof(f1776,plain,
    ( spl0_94
  <=> ! [X20,X21] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X20,tc_nat),X20,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f537,axiom,
    ! [X21,X20] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X20,tc_nat),X20,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

fof(f1774,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f536,f1772]) ).

fof(f1772,plain,
    ( spl0_93
  <=> ! [X20,X21] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X21,tc_nat),X20,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f536,axiom,
    ! [X21,X20] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X21,tc_nat),X20,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

fof(f1770,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f508,f1768]) ).

fof(f1768,plain,
    ( spl0_92
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X2),X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f508,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X2),X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).

fof(f1766,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f439,f1764]) ).

fof(f439,axiom,
    ! [X2,X7] :
      ( ~ class_Orderings_Otop(X2)
      | c_lessequals(X7,c_Orderings_Otop__class_Otop(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).

fof(f1762,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f407,f1760]) ).

fof(f1760,plain,
    ( spl0_90
  <=> ! [X2,X7] : c_in(X7,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f407,axiom,
    ! [X2,X7] : c_in(X7,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

fof(f1758,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f403,f1756]) ).

fof(f1756,plain,
    ( spl0_89
  <=> ! [X2,X7] : ~ c_in(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f403,axiom,
    ! [X2,X7] : ~ c_in(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

fof(f1754,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f378,f1752]) ).

fof(f1752,plain,
    ( spl0_88
  <=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f1750,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f377,f1748]) ).

fof(f1746,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f352,f1744]) ).

fof(f1744,plain,
    ( spl0_86
  <=> ! [X2,X7] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f352,axiom,
    ! [X2,X7] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

fof(f1742,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f326,f1740]) ).

fof(f326,axiom,
    ! [X2,X7] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

fof(f1738,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f309,f1736]) ).

fof(f1736,plain,
    ( spl0_84
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f309,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).

fof(f1734,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f289,f1732]) ).

fof(f1732,plain,
    ( spl0_83
  <=> ! [X2] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X2)
        | c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oone__class_Oone(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f289,axiom,
    ! [X2] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X2)
      | c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oone__class_Oone(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

fof(f1730,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f75,f1728]) ).

fof(f1728,plain,
    ( spl0_82
  <=> ! [X1] : c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f75,axiom,
    ! [X1] : c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).

fof(f1726,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f74,f1724]) ).

fof(f1724,plain,
    ( spl0_81
  <=> ! [X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f74,axiom,
    ! [X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).

fof(f1722,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f1072,f1720]) ).

fof(f1720,plain,
    ( spl0_80
  <=> ! [X52,X51] :
        ( ~ class_HOL_Oord(X52)
        | class_HOL_Oord(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f1072,axiom,
    ! [X51,X52] :
      ( ~ class_HOL_Oord(X52)
      | class_HOL_Oord(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

fof(f1718,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f1071,f1716]) ).

fof(f1716,plain,
    ( spl0_79
  <=> ! [X52,X51] :
        ( ~ class_Orderings_Obot(X52)
        | class_Orderings_Obot(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f1071,axiom,
    ! [X51,X52] :
      ( ~ class_Orderings_Obot(X52)
      | class_Orderings_Obot(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

fof(f1714,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f1070,f1712]) ).

fof(f1712,plain,
    ( spl0_78
  <=> ! [X52,X51] :
        ( ~ class_Orderings_Otop(X52)
        | class_Orderings_Otop(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f1070,axiom,
    ! [X51,X52] :
      ( ~ class_Orderings_Otop(X52)
      | class_Orderings_Otop(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

fof(f1710,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f1069,f1708]) ).

fof(f1069,axiom,
    ! [X51,X52] :
      ( ~ class_Orderings_Oorder(X52)
      | class_Orderings_Oorder(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f1706,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f1068,f1704]) ).

fof(f1704,plain,
    ( spl0_76
  <=> ! [X52,X51] :
        ( ~ class_Lattices_Olattice(X52)
        | class_Lattices_Olattice(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f1068,axiom,
    ! [X51,X52] :
      ( ~ class_Lattices_Olattice(X52)
      | class_Lattices_Olattice(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

fof(f1702,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f1067,f1700]) ).

fof(f1700,plain,
    ( spl0_75
  <=> ! [X52,X51] :
        ( ~ class_Orderings_Opreorder(X52)
        | class_Orderings_Opreorder(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f1067,axiom,
    ! [X51,X52] :
      ( ~ class_Orderings_Opreorder(X52)
      | class_Orderings_Opreorder(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f1698,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f1065,f1696]) ).

fof(f1696,plain,
    ( spl0_74
  <=> ! [X52,X51] :
        ( ~ class_Lattices_Obounded__lattice(X52)
        | class_Lattices_Obounded__lattice(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f1065,axiom,
    ! [X51,X52] :
      ( ~ class_Lattices_Obounded__lattice(X52)
      | class_Lattices_Obounded__lattice(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

fof(f1694,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f1064,f1692]) ).

fof(f1692,plain,
    ( spl0_73
  <=> ! [X52,X51] :
        ( ~ class_Lattices_Olattice(X52)
        | class_Lattices_Olower__semilattice(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f1064,axiom,
    ! [X51,X52] :
      ( ~ class_Lattices_Olattice(X52)
      | class_Lattices_Olower__semilattice(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

fof(f1690,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f1063,f1688]) ).

fof(f1688,plain,
    ( spl0_72
  <=> ! [X52,X51] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X52)
        | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X51,X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f1063,axiom,
    ! [X51,X52] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X52)
      | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X51,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(f1686,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f976,f1684]) ).

fof(f1684,plain,
    ( spl0_71
  <=> ! [X2,X7] : c_lessequals(X7,X7,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f976,axiom,
    ! [X2,X7] : c_lessequals(X7,X7,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

fof(f1682,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f970,f1680]) ).

fof(f1680,plain,
    ( spl0_70
  <=> ! [X2,X7] :
        ( ~ class_Orderings_Oorder(X2)
        | c_lessequals(X7,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f970,axiom,
    ! [X2,X7] :
      ( ~ class_Orderings_Oorder(X2)
      | c_lessequals(X7,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

fof(f1678,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f969,f1676]) ).

fof(f1676,plain,
    ( spl0_69
  <=> ! [X2,X7] :
        ( ~ class_Orderings_Opreorder(X2)
        | c_lessequals(X7,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f969,axiom,
    ! [X2,X7] :
      ( ~ class_Orderings_Opreorder(X2)
      | c_lessequals(X7,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

fof(f1674,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f603,f1672]) ).

fof(f1672,plain,
    ( spl0_68
  <=> ! [X2] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f603,axiom,
    ! [X2] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

fof(f1670,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f478,f1668]) ).

fof(f1668,plain,
    ( spl0_67
  <=> ! [X2,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f478,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
      | c_Ring__and__Field_Odvd__class_Odvd(X3,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).

fof(f1666,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f351,f1664]) ).

fof(f1664,plain,
    ( spl0_66
  <=> ! [X2,X7] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f351,axiom,
    ! [X2,X7] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f1662,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f350,f1660]) ).

fof(f1660,plain,
    ( spl0_65
  <=> ! [X2,X7] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f350,axiom,
    ! [X2,X7] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f1658,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f349,f1656]) ).

fof(f1656,plain,
    ( spl0_64
  <=> ! [X2,X7] :
        ( ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(X7,X7,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f349,axiom,
    ! [X2,X7] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f1654,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f346,f1652]) ).

fof(f1652,plain,
    ( spl0_63
  <=> ! [X2,X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f346,axiom,
    ! [X2,X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

fof(f1650,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f1244,f1648]) ).

fof(f1648,plain,
    ( spl0_62
  <=> ! [X4] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f1244,plain,
    ! [X4] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat),
    inference(forward_demodulation,[],[f1134,f1133]) ).

fof(f1133,plain,
    c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(definition_unfolding,[],[f154,f61]) ).

fof(f154,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).

fof(f1134,plain,
    ! [X4] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),
    inference(definition_unfolding,[],[f36,f61]) ).

fof(f36,axiom,
    ! [X4] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).

fof(f1646,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f1048,f1644]) ).

fof(f1048,axiom,
    ! [X2,X5] :
      ( ~ class_Finite__Set_Ofinite_Ofinite(X2)
      | c_Finite__Set_Ofinite(X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

fof(f1642,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f815,f1640]) ).

fof(f1640,plain,
    ( spl0_60
  <=> ! [X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f815,axiom,
    ! [X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).

fof(f1638,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f35,f1636]) ).

fof(f1636,plain,
    ( spl0_59
  <=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f35,axiom,
    ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

fof(f1634,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f1123,f1631]) ).

fof(f1123,plain,
    c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1059,f61]) ).

fof(f1059,axiom,
    c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f1629,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f1120,f1627]) ).

fof(f1627,plain,
    ( spl0_57
  <=> ! [X2,X7] : c_fequal(X7,X7,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f1120,axiom,
    ! [X2,X7] : c_fequal(X7,X7,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f1625,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f980,f1623]) ).

fof(f1623,plain,
    ( spl0_56
  <=> ! [X1] : c_lessequals(X1,X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f980,axiom,
    ! [X1] : c_lessequals(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

fof(f1621,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f479,f1619]) ).

fof(f1619,plain,
    ( spl0_55
  <=> ! [X7] : c_Ring__and__Field_Odvd__class_Odvd(X7,X7,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f479,axiom,
    ! [X7] : c_Ring__and__Field_Odvd__class_Odvd(X7,X7,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).

fof(f1617,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f347,f1615]) ).

fof(f1615,plain,
    ( spl0_54
  <=> ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f347,axiom,
    ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

fof(f1613,plain,
    ~ spl0_53,
    inference(avatar_split_clause,[],[f1062,f1610]) ).

fof(f1062,axiom,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

fof(f1608,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f1122,f1605]) ).

fof(f1122,plain,
    c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
    inference(definition_unfolding,[],[f1058,f61]) ).

fof(f1058,axiom,
    c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f1603,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f1057,f1600]) ).

fof(f1057,axiom,
    c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f1598,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f1119,f1595]) ).

fof(f1119,axiom,
    class_HOL_Oord(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

fof(f1593,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f1118,f1590]) ).

fof(f1590,plain,
    ( spl0_49
  <=> class_Orderings_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f1118,axiom,
    class_Orderings_Obot(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

fof(f1588,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f1117,f1585]) ).

fof(f1585,plain,
    ( spl0_48
  <=> class_Orderings_Otop(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1117,axiom,
    class_Orderings_Otop(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

fof(f1583,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f1116,f1580]) ).

fof(f1116,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f1578,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f1115,f1575]) ).

fof(f1575,plain,
    ( spl0_46
  <=> class_Lattices_Olattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f1115,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

fof(f1573,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f1114,f1570]) ).

fof(f1570,plain,
    ( spl0_45
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f1114,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f1568,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f1113,f1565]) ).

fof(f1565,plain,
    ( spl0_44
  <=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f1113,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

fof(f1563,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f1112,f1560]) ).

fof(f1560,plain,
    ( spl0_43
  <=> class_Lattices_Obounded__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f1112,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

fof(f1558,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f1111,f1555]) ).

fof(f1111,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

fof(f1553,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f1110,f1550]) ).

fof(f1550,plain,
    ( spl0_41
  <=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f1110,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

fof(f1548,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f1109,f1545]) ).

fof(f1545,plain,
    ( spl0_40
  <=> class_HOL_Oord(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f1109,axiom,
    class_HOL_Oord(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

fof(f1543,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f1108,f1540]) ).

fof(f1540,plain,
    ( spl0_39
  <=> class_Orderings_Obot(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f1108,axiom,
    class_Orderings_Obot(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

fof(f1538,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f1107,f1535]) ).

fof(f1535,plain,
    ( spl0_38
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1107,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f1533,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f1106,f1530]) ).

fof(f1530,plain,
    ( spl0_37
  <=> class_Lattices_Olattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f1106,axiom,
    class_Lattices_Olattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

fof(f1528,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f1105,f1525]) ).

fof(f1105,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f1523,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f1104,f1520]) ).

fof(f1104,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f1518,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f1103,f1515]) ).

fof(f1515,plain,
    ( spl0_34
  <=> class_Ring__and__Field_Odvd(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f1103,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).

fof(f1513,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f1102,f1510]) ).

fof(f1510,plain,
    ( spl0_33
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f1102,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

fof(f1508,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f1101,f1505]) ).

fof(f1505,plain,
    ( spl0_32
  <=> class_Divides_Osemiring__div(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f1101,axiom,
    class_Divides_Osemiring__div(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).

fof(f1503,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f1100,f1500]) ).

fof(f1500,plain,
    ( spl0_31
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f1100,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f1498,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f1099,f1495]) ).

fof(f1495,plain,
    ( spl0_30
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f1099,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f1493,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f1098,f1490]) ).

fof(f1490,plain,
    ( spl0_29
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f1098,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

fof(f1488,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f1097,f1485]) ).

fof(f1485,plain,
    ( spl0_28
  <=> class_Ring__and__Field_Omult__mono(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1097,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

fof(f1483,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f1096,f1480]) ).

fof(f1480,plain,
    ( spl0_27
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f1096,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

fof(f1478,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f1095,f1475]) ).

fof(f1475,plain,
    ( spl0_26
  <=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f1095,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

fof(f1473,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f1094,f1470]) ).

fof(f1470,plain,
    ( spl0_25
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f1094,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(f1468,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f1093,f1465]) ).

fof(f1093,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

fof(f1463,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f1092,f1460]) ).

fof(f1460,plain,
    ( spl0_23
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f1092,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

fof(f1458,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f1091,f1455]) ).

fof(f1455,plain,
    ( spl0_22
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f1091,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f1453,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f1090,f1450]) ).

fof(f1450,plain,
    ( spl0_21
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f1090,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f1448,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f1089,f1445]) ).

fof(f1445,plain,
    ( spl0_20
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f1089,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f1443,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f1088,f1440]) ).

fof(f1440,plain,
    ( spl0_19
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f1088,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

fof(f1438,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f1087,f1435]) ).

fof(f1435,plain,
    ( spl0_18
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f1087,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f1433,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f1086,f1430]) ).

fof(f1430,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f1086,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1428,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f1085,f1425]) ).

fof(f1425,plain,
    ( spl0_16
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f1085,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f1423,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f1084,f1420]) ).

fof(f1420,plain,
    ( spl0_15
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f1084,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

fof(f1418,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f1083,f1415]) ).

fof(f1415,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f1083,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

fof(f1413,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f1082,f1410]) ).

fof(f1410,plain,
    ( spl0_13
  <=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f1082,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

fof(f1408,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f1081,f1405]) ).

fof(f1405,plain,
    ( spl0_12
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f1081,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1403,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f1080,f1400]) ).

fof(f1400,plain,
    ( spl0_11
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f1080,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f1398,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f1079,f1395]) ).

fof(f1395,plain,
    ( spl0_10
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f1079,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f1393,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f1078,f1390]) ).

fof(f1390,plain,
    ( spl0_9
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f1078,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f1388,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f1077,f1385]) ).

fof(f1385,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f1077,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

fof(f1383,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f1076,f1380]) ).

fof(f1380,plain,
    ( spl0_7
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f1076,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

fof(f1378,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f1075,f1375]) ).

fof(f1075,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

fof(f1373,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f1074,f1370]) ).

fof(f1074,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f1368,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f1073,f1365]) ).

fof(f1073,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f1363,plain,
    ~ spl0_3,
    inference(avatar_split_clause,[],[f1061,f1360]) ).

fof(f1061,axiom,
    ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

fof(f1358,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f1060,f1355]) ).

fof(f1060,axiom,
    c_in(v_pn,v_U,tc_Com_Opname),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f1353,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f1056,f1350]) ).

fof(f1056,axiom,
    c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV884-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 20:57:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (15591)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.41  % (15595)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.42  % (15594)WARNING: value z3 for option sas not known
% 0.14/0.42  % (15592)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.42  % (15593)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.42  % (15594)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.42  % (15596)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.42  % (15597)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.42  % (15598)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)
% 0.21/0.52  TRYING [1]
% 0.21/0.53  TRYING [2]
% 2.73/0.79  TRYING [3]
% 3.35/0.87  TRYING [1]
% 3.58/0.92  TRYING [2]
% 7.15/1.41  TRYING [1]
% 7.15/1.43  TRYING [2]
% 8.77/1.65  TRYING [3]
% 12.17/2.19  % (15596)First to succeed.
% 12.17/2.21  % (15596)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15591"
% 12.17/2.22  % (15596)Refutation found. Thanks to Tanya!
% 12.17/2.22  % SZS status Unsatisfiable for theBenchmark
% 12.17/2.22  % SZS output start Proof for theBenchmark
% See solution above
% 12.97/2.24  % (15596)------------------------------
% 12.97/2.24  % (15596)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 12.97/2.24  % (15596)Termination reason: Refutation
% 12.97/2.24  
% 12.97/2.24  % (15596)Memory used [KB]: 19689
% 12.97/2.24  % (15596)Time elapsed: 1.799 s
% 12.97/2.24  % (15596)Instructions burned: 5102 (million)
% 12.97/2.24  % (15591)Success in time 1.849 s
%------------------------------------------------------------------------------