%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV242-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 16:42:38 EDT 2024

% Result   : Unsatisfiable 3.19s 0.84s
% Output   : Refutation 3.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      : 1447
% Syntax   : Number of formulae    : 2758 ( 713 unt;   0 def)
%            Number of atoms       : 6708 ( 501 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 6970 (3020   ~;3089   |;   0   &)
%                                         ( 861 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  899 ( 897 usr; 862 prp; 0-3 aty)
%            Number of functors    :  138 ( 138 usr;  24 con; 0-6 aty)
%            Number of variables   : 4394 (4394   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f10841,plain,
    $false,
    inference(avatar_sat_refutation,[],[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,f1618,f1623,f1628,f1633,f1638,f1642,f1647,f1652,f1656,f1660,f1665,f1670,f1675,f1680,f1684,f1688,f1692,f1696,f1700,f1704,f1708,f1712,f1716,f1720,f1724,f1728,f1732,f1736,f1740,f1744,f1748,f1752,f1756,f1760,f1764,f1768,f1772,f1776,f1780,f1784,f1788,f1792,f1796,f1800,f1804,f1808,f1812,f1816,f1820,f1824,f1828,f1832,f1836,f1840,f1844,f1848,f1852,f1856,f1860,f1864,f1868,f1872,f1876,f1880,f1884,f1888,f1892,f1896,f1900,f1904,f1908,f1912,f1916,f1920,f1924,f1928,f1932,f1936,f1940,f1944,f1948,f1952,f1956,f1960,f1964,f1968,f1972,f1976,f1980,f1984,f1988,f1992,f1996,f2000,f2004,f2008,f2012,f2016,f2020,f2024,f2028,f2032,f2036,f2040,f2044,f2048,f2052,f2056,f2060,f2064,f2068,f2072,f2076,f2080,f2084,f2088,f2092,f2096,f2100,f2104,f2108,f2112,f2116,f2120,f2124,f2128,f2132,f2136,f2140,f2144,f2148,f2152,f2156,f2160,f2164,f2168,f2172,f2176,f2180,f2184,f2188,f2192,f2196,f2200,f2204,f2208,f2212,f2216,f2220,f2224,f2228,f2232,f2236,f2240,f2244,f2248,f2252,f2256,f2260,f2264,f2268,f2272,f2276,f2280,f2284,f2288,f2292,f2296,f2300,f2304,f2308,f2312,f2316,f2320,f2324,f2328,f2332,f2336,f2340,f2344,f2348,f2352,f2356,f2360,f2364,f2368,f2372,f2376,f2380,f2384,f2388,f2392,f2396,f2400,f2404,f2408,f2412,f2416,f2420,f2424,f2428,f2432,f2436,f2440,f2444,f2448,f2452,f2456,f2460,f2464,f2468,f2472,f2476,f2480,f2484,f2488,f2492,f2496,f2500,f2504,f2508,f2512,f2516,f2520,f2524,f2528,f2532,f2536,f2540,f2544,f2548,f2552,f2556,f2560,f2564,f2569,f2573,f2577,f2581,f2585,f2901,f2905,f2909,f2913,f2917,f2921,f2925,f2929,f2933,f2937,f2942,f2946,f2950,f2954,f2958,f2962,f2966,f2970,f2974,f2978,f2982,f2987,f2991,f2995,f2999,f3003,f3007,f3011,f3015,f3019,f3023,f3027,f3031,f3035,f3039,f3043,f3047,f3051,f3055,f3059,f3079,f3083,f3087,f3091,f3095,f3099,f3103,f3107,f3111,f3115,f3119,f3123,f3127,f3131,f3135,f3139,f3143,f3147,f3151,f3155,f3159,f3163,f3167,f3171,f3175,f3179,f3183,f3187,f3191,f3195,f3218,f3222,f3226,f3230,f3234,f3238,f3242,f3246,f3250,f3256,f3260,f3264,f3268,f3272,f3276,f3280,f3284,f3288,f3292,f3298,f3302,f3306,f3326,f3330,f3334,f3338,f3342,f3346,f3350,f3354,f3358,f3362,f3366,f3370,f3374,f3378,f3382,f3386,f3390,f3394,f3398,f3402,f3406,f3410,f3414,f3418,f3422,f3426,f3450,f3468,f3474,f3478,f3482,f3486,f3490,f3494,f3498,f3502,f3506,f3510,f3514,f3518,f3522,f3541,f3545,f3549,f3553,f3558,f3562,f3566,f3570,f3574,f3578,f3582,f3586,f3590,f3594,f3598,f3606,f3610,f3614,f3618,f3622,f3626,f3630,f3634,f3638,f3642,f3654,f3658,f3662,f3666,f3670,f3674,f3678,f3682,f3686,f3690,f3702,f3706,f3710,f3714,f3718,f3743,f3782,f3800,f3804,f3808,f3812,f3816,f3820,f3824,f3828,f3832,f3836,f3840,f3844,f3848,f3852,f3856,f3860,f3864,f3900,f3912,f3916,f3920,f3924,f3928,f3932,f3936,f3940,f3944,f3948,f3952,f3956,f3960,f3964,f3968,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4067,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4103,f4107,f4111,f4213,f4217,f4221,f4225,f4229,f4233,f4237,f4241,f4245,f4249,f4276,f4280,f4289,f4293,f4297,f4301,f4305,f4309,f4313,f4317,f4321,f4325,f4329,f4333,f4337,f4341,f4407,f4411,f4416,f4420,f4424,f4443,f4447,f4451,f4455,f4463,f4467,f4491,f4495,f4499,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4531,f4537,f4611,f4615,f4648,f4652,f4656,f4660,f4664,f4744,f4748,f4752,f4756,f4760,f4778,f4782,f4789,f4793,f4797,f4835,f4839,f4843,f4847,f4863,f4869,f4873,f4877,f4889,f4901,f4905,f4925,f4929,f4933,f4937,f5007,f5011,f5018,f5022,f5026,f5063,f5067,f5085,f5089,f5151,f5155,f5167,f5180,f5195,f5199,f5225,f5240,f5249,f5253,f5257,f5295,f5299,f5303,f5307,f5311,f5315,f5319,f5323,f5390,f5394,f5398,f5402,f5430,f5438,f5442,f5446,f5450,f5454,f5491,f5495,f5590,f5594,f5598,f5602,f5606,f5610,f5614,f5618,f5622,f5626,f5630,f5636,f5640,f5644,f5648,f5760,f5843,f5847,f5851,f5855,f5859,f5863,f5867,f5871,f5875,f5879,f5883,f5900,f6039,f6043,f6047,f6051,f6055,f6059,f6063,f6067,f6071,f6075,f6079,f6083,f6087,f6091,f6095,f6099,f6103,f6118,f6162,f6166,f6170,f6174,f6178,f6182,f6186,f6190,f6194,f6198,f6202,f6206,f6210,f6214,f6218,f6222,f6226,f6390,f6394,f6398,f6402,f6406,f6410,f6414,f6418,f6510,f6536,f6540,f6544,f6548,f6552,f6556,f6560,f6564,f6568,f6572,f6576,f6756,f6760,f6764,f6768,f6772,f6776,f6780,f6784,f6788,f6792,f6796,f6893,f6897,f6901,f6905,f6909,f6913,f6917,f6921,f6941,f6945,f6949,f6953,f6957,f6961,f6965,f6969,f6973,f6977,f6981,f6985,f6989,f6993,f6997,f7001,f7005,f7009,f7013,f7017,f7021,f7459,f7567,f7646,f7650,f7654,f7658,f7669,f7673,f7677,f7681,f7685,f7689,f7693,f7697,f7701,f8139,f8253,f8257,f8261,f8265,f8269,f8273,f8277,f8281,f8285,f8289,f8293,f8297,f8301,f8305,f8309,f8313,f8317,f8321,f8325,f8337,f8341,f8345,f8349,f8353,f8357,f8619,f8802,f8813,f8842,f8865,f8870,f8897,f9088,f9108,f9112,f9116,f9120,f9124,f9128,f9132,f9136,f9140,f9144,f9435,f9441,f9445,f9449,f9453,f9457,f9461,f9465,f9469,f9473,f9477,f9482,f9486,f9490,f9494,f9498,f9502,f9506,f9510,f9514,f9518,f9522,f9526,f9530,f9534,f9538,f9542,f9681,f9870,f10544,f10548,f10552,f10556,f10560,f10564,f10578,f10582,f10586,f10590,f10594,f10598,f10602,f10606,f10637,f10840]) ).

fof(f10840,plain,
    ( ~ spl0_354
    | spl0_861 ),
    inference(avatar_contradiction_clause,[],[f10837]) ).

fof(f10837,plain,
    ( $false
    | ~ spl0_354
    | spl0_861 ),
    inference(resolution,[],[f10636,f3190]) ).

fof(f3190,plain,
    ( ! [X1,X12,X13] : c_lessequals(X13,c_union(X12,X13,X1),tc_set(X1))
    | ~ spl0_354 ),
    inference(avatar_component_clause,[],[f3189]) ).

fof(f3189,plain,
    ( spl0_354
  <=> ! [X13,X12,X1] : c_lessequals(X13,c_union(X12,X13,X1),tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f10636,plain,
    ( ~ c_lessequals(v_H_H,c_union(v_G_H,v_H_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
    | spl0_861 ),
    inference(avatar_component_clause,[],[f10634]) ).

fof(f10634,plain,
    ( spl0_861
  <=> c_lessequals(v_H_H,c_union(v_G_H,v_H_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f10637,plain,
    ( ~ spl0_861
    | spl0_285
    | ~ spl0_784 ),
    inference(avatar_split_clause,[],[f10565,f8283,f2894,f10634]) ).

fof(f2894,plain,
    ( spl0_285
  <=> c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f8283,plain,
    ( spl0_784
  <=> ! [X0] :
        ( c_lessequals(v_H,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(v_H_H,X0,tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f10565,plain,
    ( ~ c_lessequals(v_H_H,c_union(v_G_H,v_H_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
    | spl0_285
    | ~ spl0_784 ),
    inference(resolution,[],[f8284,f2896]) ).

fof(f2896,plain,
    ( ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
    | spl0_285 ),
    inference(avatar_component_clause,[],[f2894]) ).

fof(f8284,plain,
    ( ! [X0] :
        ( c_lessequals(v_H,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(v_H_H,X0,tc_set(tc_Message_Omsg)) )
    | ~ spl0_784 ),
    inference(avatar_component_clause,[],[f8283]) ).

fof(f10606,plain,
    ( spl0_860
    | ~ spl0_558
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f4625,f4609,f4509,f10604]) ).

fof(f10604,plain,
    ( spl0_860
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
        | ~ c_in(c_Main_ORangeE__1(X0,X1,X4,X3),X2,X3)
        | ~ c_in(X0,c_Relation_ORange(X1,X3,X4),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f4509,plain,
    ( spl0_558
  <=> ! [X5,X27,X2,X1] :
        ( ~ c_in(X27,c_Relation_ORange(X5,X2,X1),X1)
        | c_in(c_Pair(c_Main_ORangeE__1(X27,X5,X1,X2),X27,X2,X1),X5,tc_prod(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f4609,plain,
    ( spl0_565
  <=> ! [X5,X18,X12,X27,X2,X1] :
        ( ~ c_in(X18,X12,X1)
        | c_in(X27,c_Relation_OImage(X5,X12,X1,X2),X2)
        | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f4625,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
        | ~ c_in(c_Main_ORangeE__1(X0,X1,X4,X3),X2,X3)
        | ~ c_in(X0,c_Relation_ORange(X1,X3,X4),X4) )
    | ~ spl0_558
    | ~ spl0_565 ),
    inference(resolution,[],[f4610,f4510]) ).

fof(f4510,plain,
    ( ! [X2,X1,X27,X5] :
        ( c_in(c_Pair(c_Main_ORangeE__1(X27,X5,X1,X2),X27,X2,X1),X5,tc_prod(X2,X1))
        | ~ c_in(X27,c_Relation_ORange(X5,X2,X1),X1) )
    | ~ spl0_558 ),
    inference(avatar_component_clause,[],[f4509]) ).

fof(f4610,plain,
    ( ! [X2,X18,X1,X27,X5,X12] :
        ( ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2))
        | c_in(X27,c_Relation_OImage(X5,X12,X1,X2),X2)
        | ~ c_in(X18,X12,X1) )
    | ~ spl0_565 ),
    inference(avatar_component_clause,[],[f4609]) ).

fof(f10602,plain,
    ( spl0_859
    | ~ spl0_557
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f4624,f4609,f4505,f10600]) ).

fof(f10600,plain,
    ( spl0_859
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_in(c_Main_ODomainE__1(X0,X1,X2,X3),c_Relation_OImage(X1,X4,X2,X3),X3)
        | ~ c_in(X0,X4,X2)
        | ~ c_in(X0,c_Relation_ODomain(X1,X2,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f4505,plain,
    ( spl0_557
  <=> ! [X18,X5,X2,X1] :
        ( ~ c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
        | c_in(c_Pair(X18,c_Main_ODomainE__1(X18,X5,X1,X2),X1,X2),X5,tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f4624,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_in(c_Main_ODomainE__1(X0,X1,X2,X3),c_Relation_OImage(X1,X4,X2,X3),X3)
        | ~ c_in(X0,X4,X2)
        | ~ c_in(X0,c_Relation_ODomain(X1,X2,X3),X2) )
    | ~ spl0_557
    | ~ spl0_565 ),
    inference(resolution,[],[f4610,f4506]) ).

fof(f4506,plain,
    ( ! [X2,X18,X1,X5] :
        ( c_in(c_Pair(X18,c_Main_ODomainE__1(X18,X5,X1,X2),X1,X2),X5,tc_prod(X1,X2))
        | ~ c_in(X18,c_Relation_ODomain(X5,X1,X2),X1) )
    | ~ spl0_557 ),
    inference(avatar_component_clause,[],[f4505]) ).

fof(f10598,plain,
    ( spl0_858
    | ~ spl0_548
    | ~ spl0_558 ),
    inference(avatar_split_clause,[],[f4570,f4509,f4445,f10596]) ).

fof(f10596,plain,
    ( spl0_858
  <=> ! [X0,X1] :
        ( ~ c_in(c_List_Olist_ONil,c_Relation_ORange(c_List_Olistrel(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
        | c_List_Olist_ONil = c_Main_ORangeE__1(c_List_Olist_ONil,c_List_Olistrel(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).

fof(f4445,plain,
    ( spl0_548
  <=> ! [X5,X1,X23] :
        ( c_List_Olist_ONil = X23
        | ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f4570,plain,
    ( ! [X0,X1] :
        ( ~ c_in(c_List_Olist_ONil,c_Relation_ORange(c_List_Olistrel(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
        | c_List_Olist_ONil = c_Main_ORangeE__1(c_List_Olist_ONil,c_List_Olistrel(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)) )
    | ~ spl0_548
    | ~ spl0_558 ),
    inference(resolution,[],[f4510,f4446]) ).

fof(f4446,plain,
    ( ! [X1,X5,X23] :
        ( ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | c_List_Olist_ONil = X23 )
    | ~ spl0_548 ),
    inference(avatar_component_clause,[],[f4445]) ).

fof(f10594,plain,
    ( spl0_857
    | ~ spl0_547
    | ~ spl0_557 ),
    inference(avatar_split_clause,[],[f4546,f4505,f4441,f10592]) ).

fof(f10592,plain,
    ( spl0_857
  <=> ! [X0,X1] :
        ( ~ c_in(c_List_Olist_ONil,c_Relation_ODomain(c_List_Olistrel(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
        | c_List_Olist_ONil = c_Main_ODomainE__1(c_List_Olist_ONil,c_List_Olistrel(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f4441,plain,
    ( spl0_547
  <=> ! [X5,X1,X23] :
        ( c_List_Olist_ONil = X23
        | ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f4546,plain,
    ( ! [X0,X1] :
        ( ~ c_in(c_List_Olist_ONil,c_Relation_ODomain(c_List_Olistrel(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
        | c_List_Olist_ONil = c_Main_ODomainE__1(c_List_Olist_ONil,c_List_Olistrel(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)) )
    | ~ spl0_547
    | ~ spl0_557 ),
    inference(resolution,[],[f4506,f4442]) ).

fof(f4442,plain,
    ( ! [X1,X5,X23] :
        ( ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | c_List_Olist_ONil = X23 )
    | ~ spl0_547 ),
    inference(avatar_component_clause,[],[f4441]) ).

fof(f10590,plain,
    ( spl0_856
    | ~ spl0_399
    | ~ spl0_530 ),
    inference(avatar_split_clause,[],[f4364,f4295,f3408,f10588]) ).

fof(f10588,plain,
    ( spl0_856
  <=> ! [X0,X1] : c_Pair(X0,X0,X1,X1) = c_Pair(c_Main_OIdE__1(c_Pair(X0,X0,X1,X1),X1),c_Main_OIdE__1(c_Pair(X0,X0,X1,X1),X1),X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).

fof(f3408,plain,
    ( spl0_399
  <=> ! [X18,X1] : c_in(c_Pair(X18,X18,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f4295,plain,
    ( spl0_530
  <=> ! [X1,X28] :
        ( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
        | c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f4364,plain,
    ( ! [X0,X1] : c_Pair(X0,X0,X1,X1) = c_Pair(c_Main_OIdE__1(c_Pair(X0,X0,X1,X1),X1),c_Main_OIdE__1(c_Pair(X0,X0,X1,X1),X1),X1,X1)
    | ~ spl0_399
    | ~ spl0_530 ),
    inference(resolution,[],[f4296,f3409]) ).

fof(f3409,plain,
    ( ! [X18,X1] : c_in(c_Pair(X18,X18,X1,X1),c_Relation_OId,tc_prod(X1,X1))
    | ~ spl0_399 ),
    inference(avatar_component_clause,[],[f3408]) ).

fof(f4296,plain,
    ( ! [X28,X1] :
        ( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
        | c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 )
    | ~ spl0_530 ),
    inference(avatar_component_clause,[],[f4295]) ).

fof(f10586,plain,
    ( spl0_855
    | ~ spl0_422
    | ~ spl0_494 ),
    inference(avatar_split_clause,[],[f4112,f4028,f3551,f10584]) ).

fof(f10584,plain,
    ( spl0_855
  <=> ! [X2,X0,X1] :
        ( c_in(c_Main_OdiagE__1(X0,c_Main_OsubsetI__1(c_Relation_Odiag(X0,X1),X2,tc_prod(X1,X1)),X1),X0,X1)
        | c_lessequals(c_Relation_Odiag(X0,X1),X2,tc_set(tc_prod(X1,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).

fof(f3551,plain,
    ( spl0_422
  <=> ! [X13,X12,X1] :
        ( c_lessequals(X12,X13,tc_set(X1))
        | c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f4028,plain,
    ( spl0_494
  <=> ! [X12,X1,X4] :
        ( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
        | ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f4112,plain,
    ( ! [X2,X0,X1] :
        ( c_in(c_Main_OdiagE__1(X0,c_Main_OsubsetI__1(c_Relation_Odiag(X0,X1),X2,tc_prod(X1,X1)),X1),X0,X1)
        | c_lessequals(c_Relation_Odiag(X0,X1),X2,tc_set(tc_prod(X1,X1))) )
    | ~ spl0_422
    | ~ spl0_494 ),
    inference(resolution,[],[f4029,f3552]) ).

fof(f3552,plain,
    ( ! [X1,X12,X13] :
        ( c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1)
        | c_lessequals(X12,X13,tc_set(X1)) )
    | ~ spl0_422 ),
    inference(avatar_component_clause,[],[f3551]) ).

fof(f4029,plain,
    ( ! [X1,X4,X12] :
        ( ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
        | c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1) )
    | ~ spl0_494 ),
    inference(avatar_component_clause,[],[f4028]) ).

fof(f10582,plain,
    ( spl0_854
    | ~ spl0_440
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f4010,f3930,f3628,f10580]) ).

fof(f10580,plain,
    ( spl0_854
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_SetInterval_OgreaterThan(X1,tc_set(X2)),X2),X2)
        | c_less(X1,c_Main_OUnionE__1(X0,c_SetInterval_OgreaterThan(X1,tc_set(X2)),X2),tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).

fof(f3628,plain,
    ( spl0_440
  <=> ! [X50,X16,X1] :
        ( ~ class_Orderings_Oord(X1)
        | c_less(X16,X50,X1)
        | ~ c_in(X50,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f3930,plain,
    ( spl0_484
  <=> ! [X12,X32,X1] :
        ( ~ c_in(X12,c_Union(X32,X1),X1)
        | c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f4010,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_SetInterval_OgreaterThan(X1,tc_set(X2)),X2),X2)
        | c_less(X1,c_Main_OUnionE__1(X0,c_SetInterval_OgreaterThan(X1,tc_set(X2)),X2),tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_440
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3629]) ).

fof(f3629,plain,
    ( ! [X50,X1,X16] :
        ( ~ c_in(X50,c_SetInterval_OgreaterThan(X16,X1),X1)
        | c_less(X16,X50,X1)
        | ~ class_Orderings_Oord(X1) )
    | ~ spl0_440 ),
    inference(avatar_component_clause,[],[f3628]) ).

fof(f3931,plain,
    ( ! [X1,X12,X32] :
        ( c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1))
        | ~ c_in(X12,c_Union(X32,X1),X1) )
    | ~ spl0_484 ),
    inference(avatar_component_clause,[],[f3930]) ).

fof(f10578,plain,
    ( spl0_853
    | ~ spl0_434
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f4009,f3930,f3604,f10576]) ).

fof(f10576,plain,
    ( spl0_853
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_SetInterval_OatLeast(X1,tc_set(X2)),X2),X2)
        | c_lessequals(X1,c_Main_OUnionE__1(X0,c_SetInterval_OatLeast(X1,tc_set(X2)),X2),tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f3604,plain,
    ( spl0_434
  <=> ! [X50,X16,X1] :
        ( ~ class_Orderings_Oord(X1)
        | c_lessequals(X16,X50,X1)
        | ~ c_in(X50,c_SetInterval_OatLeast(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f4009,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_SetInterval_OatLeast(X1,tc_set(X2)),X2),X2)
        | c_lessequals(X1,c_Main_OUnionE__1(X0,c_SetInterval_OatLeast(X1,tc_set(X2)),X2),tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_434
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3605]) ).

fof(f3605,plain,
    ( ! [X50,X1,X16] :
        ( ~ c_in(X50,c_SetInterval_OatLeast(X16,X1),X1)
        | c_lessequals(X16,X50,X1)
        | ~ class_Orderings_Oord(X1) )
    | ~ spl0_434 ),
    inference(avatar_component_clause,[],[f3604]) ).

fof(f10564,plain,
    ( spl0_852
    | ~ spl0_443
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f4004,f3930,f3640,f10562]) ).

fof(f10562,plain,
    ( spl0_852
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_SetInterval_OlessThan(X1,tc_set(X2)),X2),X2)
        | c_less(c_Main_OUnionE__1(X0,c_SetInterval_OlessThan(X1,tc_set(X2)),X2),X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).

fof(f3640,plain,
    ( spl0_443
  <=> ! [X50,X16,X1] :
        ( ~ class_Orderings_Oord(X1)
        | c_less(X50,X16,X1)
        | ~ c_in(X50,c_SetInterval_OlessThan(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f4004,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_SetInterval_OlessThan(X1,tc_set(X2)),X2),X2)
        | c_less(c_Main_OUnionE__1(X0,c_SetInterval_OlessThan(X1,tc_set(X2)),X2),X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_443
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3641]) ).

fof(f3641,plain,
    ( ! [X50,X1,X16] :
        ( ~ c_in(X50,c_SetInterval_OlessThan(X16,X1),X1)
        | c_less(X50,X16,X1)
        | ~ class_Orderings_Oord(X1) )
    | ~ spl0_443 ),
    inference(avatar_component_clause,[],[f3640]) ).

fof(f10560,plain,
    ( spl0_851
    | ~ spl0_437
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f4003,f3930,f3616,f10558]) ).

fof(f10558,plain,
    ( spl0_851
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_SetInterval_OatMost(X1,tc_set(X2)),X2),X2)
        | c_lessequals(c_Main_OUnionE__1(X0,c_SetInterval_OatMost(X1,tc_set(X2)),X2),X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f3616,plain,
    ( spl0_437
  <=> ! [X50,X16,X1] :
        ( ~ class_Orderings_Oord(X1)
        | c_lessequals(X50,X16,X1)
        | ~ c_in(X50,c_SetInterval_OatMost(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f4003,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_SetInterval_OatMost(X1,tc_set(X2)),X2),X2)
        | c_lessequals(c_Main_OUnionE__1(X0,c_SetInterval_OatMost(X1,tc_set(X2)),X2),X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_437
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3617]) ).

fof(f3617,plain,
    ( ! [X50,X1,X16] :
        ( ~ c_in(X50,c_SetInterval_OatMost(X16,X1),X1)
        | c_lessequals(X50,X16,X1)
        | ~ class_Orderings_Oord(X1) )
    | ~ spl0_437 ),
    inference(avatar_component_clause,[],[f3616]) ).

fof(f10556,plain,
    ( spl0_850
    | ~ spl0_440
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3997,f3926,f3628,f10554]) ).

fof(f10554,plain,
    ( spl0_850
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_SetInterval_OgreaterThan(X1,tc_set(X2)),X2),X2)
        | c_less(X1,c_Main_OInterI__1(X0,c_SetInterval_OgreaterThan(X1,tc_set(X2)),X2),tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).

fof(f3926,plain,
    ( spl0_483
  <=> ! [X12,X32,X1] :
        ( c_in(X12,c_Inter(X32,X1),X1)
        | c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f3997,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_SetInterval_OgreaterThan(X1,tc_set(X2)),X2),X2)
        | c_less(X1,c_Main_OInterI__1(X0,c_SetInterval_OgreaterThan(X1,tc_set(X2)),X2),tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_440
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3629]) ).

fof(f3927,plain,
    ( ! [X1,X12,X32] :
        ( c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1))
        | c_in(X12,c_Inter(X32,X1),X1) )
    | ~ spl0_483 ),
    inference(avatar_component_clause,[],[f3926]) ).

fof(f10552,plain,
    ( spl0_849
    | ~ spl0_434
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3996,f3926,f3604,f10550]) ).

fof(f10550,plain,
    ( spl0_849
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_SetInterval_OatLeast(X1,tc_set(X2)),X2),X2)
        | c_lessequals(X1,c_Main_OInterI__1(X0,c_SetInterval_OatLeast(X1,tc_set(X2)),X2),tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).

fof(f3996,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_SetInterval_OatLeast(X1,tc_set(X2)),X2),X2)
        | c_lessequals(X1,c_Main_OInterI__1(X0,c_SetInterval_OatLeast(X1,tc_set(X2)),X2),tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_434
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3605]) ).

fof(f10548,plain,
    ( spl0_848
    | ~ spl0_443
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3991,f3926,f3640,f10546]) ).

fof(f10546,plain,
    ( spl0_848
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_SetInterval_OlessThan(X1,tc_set(X2)),X2),X2)
        | c_less(c_Main_OInterI__1(X0,c_SetInterval_OlessThan(X1,tc_set(X2)),X2),X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f3991,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_SetInterval_OlessThan(X1,tc_set(X2)),X2),X2)
        | c_less(c_Main_OInterI__1(X0,c_SetInterval_OlessThan(X1,tc_set(X2)),X2),X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_443
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3641]) ).

fof(f10544,plain,
    ( spl0_847
    | ~ spl0_437
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3990,f3926,f3616,f10542]) ).

fof(f10542,plain,
    ( spl0_847
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_SetInterval_OatMost(X1,tc_set(X2)),X2),X2)
        | c_lessequals(c_Main_OInterI__1(X0,c_SetInterval_OatMost(X1,tc_set(X2)),X2),X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).

fof(f3990,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_SetInterval_OatMost(X1,tc_set(X2)),X2),X2)
        | c_lessequals(c_Main_OInterI__1(X0,c_SetInterval_OatMost(X1,tc_set(X2)),X2),X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_437
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3617]) ).

fof(f9870,plain,
    ( spl0_846
    | ~ spl0_623
    | ~ spl0_777 ),
    inference(avatar_split_clause,[],[f8487,f8255,f5317,f9868]) ).

fof(f9868,plain,
    ( spl0_846
  <=> ! [X0] : c_lessequals(c_minus(v_G,X0,tc_set(tc_Message_Omsg)),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).

fof(f5317,plain,
    ( spl0_623
  <=> ! [X0] :
        ( ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg),v_G,tc_Message_Omsg)
        | c_lessequals(X0,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f8255,plain,
    ( spl0_777
  <=> ! [X0,X3,X2,X1] :
        ( c_in(c_Main_OsubsetI__1(c_minus(X0,X1,tc_set(X2)),X3,X2),X0,X2)
        | c_lessequals(c_minus(X0,X1,tc_set(X2)),X3,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).

fof(f8487,plain,
    ( ! [X0] : c_lessequals(c_minus(v_G,X0,tc_set(tc_Message_Omsg)),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
    | ~ spl0_623
    | ~ spl0_777 ),
    inference(duplicate_literal_removal,[],[f8400]) ).

fof(f8400,plain,
    ( ! [X0] :
        ( c_lessequals(c_minus(v_G,X0,tc_set(tc_Message_Omsg)),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
        | c_lessequals(c_minus(v_G,X0,tc_set(tc_Message_Omsg)),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) )
    | ~ spl0_623
    | ~ spl0_777 ),
    inference(resolution,[],[f8256,f5318]) ).

fof(f5318,plain,
    ( ! [X0] :
        ( ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg),v_G,tc_Message_Omsg)
        | c_lessequals(X0,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) )
    | ~ spl0_623 ),
    inference(avatar_component_clause,[],[f5317]) ).

fof(f8256,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(c_Main_OsubsetI__1(c_minus(X0,X1,tc_set(X2)),X3,X2),X0,X2)
        | c_lessequals(c_minus(X0,X1,tc_set(X2)),X3,tc_set(X2)) )
    | ~ spl0_777 ),
    inference(avatar_component_clause,[],[f8255]) ).

fof(f9681,plain,
    ( spl0_845
    | ~ spl0_417
    | ~ spl0_804 ),
    inference(avatar_split_clause,[],[f8877,f8858,f3516,f9679]) ).

fof(f9679,plain,
    ( spl0_845
  <=> ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_G),tc_Message_Omsg)
        | c_in(X0,v_G,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f3516,plain,
    ( spl0_417
  <=> ! [X53,X55] :
        ( c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg)
        | ~ c_in(X53,c_Message_Oanalz(c_Message_Oanalz(X55)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f8858,plain,
    ( spl0_804
  <=> v_G = c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).

fof(f8877,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_G),tc_Message_Omsg)
        | c_in(X0,v_G,tc_Message_Omsg) )
    | ~ spl0_417
    | ~ spl0_804 ),
    inference(superposition,[],[f3517,f8860]) ).

fof(f8860,plain,
    ( v_G = c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg))
    | ~ spl0_804 ),
    inference(avatar_component_clause,[],[f8858]) ).

fof(f3517,plain,
    ( ! [X55,X53] :
        ( ~ c_in(X53,c_Message_Oanalz(c_Message_Oanalz(X55)),tc_Message_Omsg)
        | c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg) )
    | ~ spl0_417 ),
    inference(avatar_component_clause,[],[f3516]) ).

fof(f9542,plain,
    ( spl0_844
    | ~ spl0_413
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4385,f4303,f3500,f9540]) ).

fof(f9540,plain,
    ( spl0_844
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_ORange(c_union(X1,X2,tc_prod(X3,X4)),X3,X4),X4)
        | ~ c_in(c_Pair(X5,X0,X3,X4),X2,tc_prod(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f3500,plain,
    ( spl0_413
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X13,X1)
        | c_in(X4,c_union(X12,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f4303,plain,
    ( spl0_532
  <=> ! [X5,X18,X27,X2,X1] :
        ( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
        | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f4385,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_in(X0,c_Relation_ORange(c_union(X1,X2,tc_prod(X3,X4)),X3,X4),X4)
        | ~ c_in(c_Pair(X5,X0,X3,X4),X2,tc_prod(X3,X4)) )
    | ~ spl0_413
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f3501]) ).

fof(f3501,plain,
    ( ! [X1,X4,X12,X13] :
        ( c_in(X4,c_union(X12,X13,X1),X1)
        | ~ c_in(X4,X13,X1) )
    | ~ spl0_413 ),
    inference(avatar_component_clause,[],[f3500]) ).

fof(f4304,plain,
    ( ! [X2,X18,X1,X27,X5] :
        ( ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2))
        | c_in(X27,c_Relation_ORange(X5,X1,X2),X2) )
    | ~ spl0_532 ),
    inference(avatar_component_clause,[],[f4303]) ).

fof(f9538,plain,
    ( spl0_843
    | ~ spl0_415
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4384,f4303,f3508,f9536]) ).

fof(f9536,plain,
    ( spl0_843
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_ORange(c_union(X1,X2,tc_prod(X3,X4)),X3,X4),X4)
        | ~ c_in(c_Pair(X5,X0,X3,X4),X1,tc_prod(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f3508,plain,
    ( spl0_415
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X12,X1)
        | c_in(X4,c_union(X12,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f4384,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_in(X0,c_Relation_ORange(c_union(X1,X2,tc_prod(X3,X4)),X3,X4),X4)
        | ~ c_in(c_Pair(X5,X0,X3,X4),X1,tc_prod(X3,X4)) )
    | ~ spl0_415
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f3509]) ).

fof(f3509,plain,
    ( ! [X1,X4,X12,X13] :
        ( c_in(X4,c_union(X12,X13,X1),X1)
        | ~ c_in(X4,X12,X1) )
    | ~ spl0_415 ),
    inference(avatar_component_clause,[],[f3508]) ).

fof(f9534,plain,
    ( spl0_842
    | ~ spl0_410
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4376,f4303,f3488,f9532]) ).

fof(f9532,plain,
    ( spl0_842
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_ORange(c_uminus(X1,tc_set(tc_prod(X2,X3))),X2,X3),X3)
        | c_in(c_Pair(X4,X0,X2,X3),X1,tc_prod(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f3488,plain,
    ( spl0_410
  <=> ! [X12,X1,X4] :
        ( c_in(X4,X12,X1)
        | c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f4376,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_in(X0,c_Relation_ORange(c_uminus(X1,tc_set(tc_prod(X2,X3))),X2,X3),X3)
        | c_in(c_Pair(X4,X0,X2,X3),X1,tc_prod(X2,X3)) )
    | ~ spl0_410
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f3489]) ).

fof(f3489,plain,
    ( ! [X1,X4,X12] :
        ( c_in(X4,c_uminus(X12,tc_set(X1)),X1)
        | c_in(X4,X12,X1) )
    | ~ spl0_410 ),
    inference(avatar_component_clause,[],[f3488]) ).

fof(f9530,plain,
    ( spl0_841
    | ~ spl0_416
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4374,f4303,f3512,f9528]) ).

fof(f9528,plain,
    ( spl0_841
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_ORange(c_insert(X1,X2,tc_prod(X3,X4)),X3,X4),X4)
        | ~ c_in(c_Pair(X5,X0,X3,X4),X2,tc_prod(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f3512,plain,
    ( spl0_416
  <=> ! [X18,X13,X27,X1] :
        ( ~ c_in(X18,X13,X1)
        | c_in(X18,c_insert(X27,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f4374,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_in(X0,c_Relation_ORange(c_insert(X1,X2,tc_prod(X3,X4)),X3,X4),X4)
        | ~ c_in(c_Pair(X5,X0,X3,X4),X2,tc_prod(X3,X4)) )
    | ~ spl0_416
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f3513]) ).

fof(f3513,plain,
    ( ! [X18,X1,X27,X13] :
        ( c_in(X18,c_insert(X27,X13,X1),X1)
        | ~ c_in(X18,X13,X1) )
    | ~ spl0_416 ),
    inference(avatar_component_clause,[],[f3512]) ).

fof(f9526,plain,
    ( spl0_840
    | ~ spl0_413
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4361,f4291,f3500,f9524]) ).

fof(f9524,plain,
    ( spl0_840
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_ODomain(c_union(X1,X2,tc_prod(X3,X4)),X3,X4),X3)
        | ~ c_in(c_Pair(X0,X5,X3,X4),X2,tc_prod(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f4291,plain,
    ( spl0_529
  <=> ! [X18,X5,X27,X2,X1] :
        ( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
        | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f4361,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_in(X0,c_Relation_ODomain(c_union(X1,X2,tc_prod(X3,X4)),X3,X4),X3)
        | ~ c_in(c_Pair(X0,X5,X3,X4),X2,tc_prod(X3,X4)) )
    | ~ spl0_413
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f3501]) ).

fof(f4292,plain,
    ( ! [X2,X18,X1,X27,X5] :
        ( ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2))
        | c_in(X18,c_Relation_ODomain(X5,X1,X2),X1) )
    | ~ spl0_529 ),
    inference(avatar_component_clause,[],[f4291]) ).

fof(f9522,plain,
    ( spl0_839
    | ~ spl0_415
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4360,f4291,f3508,f9520]) ).

fof(f9520,plain,
    ( spl0_839
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_ODomain(c_union(X1,X2,tc_prod(X3,X4)),X3,X4),X3)
        | ~ c_in(c_Pair(X0,X5,X3,X4),X1,tc_prod(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f4360,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_in(X0,c_Relation_ODomain(c_union(X1,X2,tc_prod(X3,X4)),X3,X4),X3)
        | ~ c_in(c_Pair(X0,X5,X3,X4),X1,tc_prod(X3,X4)) )
    | ~ spl0_415
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f3509]) ).

fof(f9518,plain,
    ( spl0_838
    | ~ spl0_410
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4352,f4291,f3488,f9516]) ).

fof(f9516,plain,
    ( spl0_838
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_ODomain(c_uminus(X1,tc_set(tc_prod(X2,X3))),X2,X3),X2)
        | c_in(c_Pair(X0,X4,X2,X3),X1,tc_prod(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).

fof(f4352,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_in(X0,c_Relation_ODomain(c_uminus(X1,tc_set(tc_prod(X2,X3))),X2,X3),X2)
        | c_in(c_Pair(X0,X4,X2,X3),X1,tc_prod(X2,X3)) )
    | ~ spl0_410
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f3489]) ).

fof(f9514,plain,
    ( spl0_837
    | ~ spl0_416
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4350,f4291,f3512,f9512]) ).

fof(f9512,plain,
    ( spl0_837
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_ODomain(c_insert(X1,X2,tc_prod(X3,X4)),X3,X4),X3)
        | ~ c_in(c_Pair(X0,X5,X3,X4),X2,tc_prod(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).

fof(f4350,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_in(X0,c_Relation_ODomain(c_insert(X1,X2,tc_prod(X3,X4)),X3,X4),X3)
        | ~ c_in(c_Pair(X0,X5,X3,X4),X2,tc_prod(X3,X4)) )
    | ~ spl0_416
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f3513]) ).

fof(f9510,plain,
    ( spl0_836
    | ~ spl0_465
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4169,f4097,f3814,f9508]) ).

fof(f9508,plain,
    ( spl0_836
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_Main_OUnionE__1(X1,X3,tc_set(X2)),X2),X2)
        | ~ c_in(X1,c_Union(X3,tc_set(X2)),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f3814,plain,
    ( spl0_465
  <=> ! [X12,X32,X1] :
        ( ~ c_in(X12,c_Union(X32,X1),X1)
        | c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f4097,plain,
    ( spl0_511
  <=> ! [X53,X12,X32,X1] :
        ( ~ c_in(X12,X53,X1)
        | ~ c_in(X53,X32,tc_set(X1))
        | c_in(X12,c_Union(X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f4169,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_Main_OUnionE__1(X1,X3,tc_set(X2)),X2),X2)
        | ~ c_in(X1,c_Union(X3,tc_set(X2)),tc_set(X2)) )
    | ~ spl0_465
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3815]) ).

fof(f3815,plain,
    ( ! [X1,X12,X32] :
        ( c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1)
        | ~ c_in(X12,c_Union(X32,X1),X1) )
    | ~ spl0_465 ),
    inference(avatar_component_clause,[],[f3814]) ).

fof(f4098,plain,
    ( ! [X1,X53,X12,X32] :
        ( ~ c_in(X53,X32,tc_set(X1))
        | ~ c_in(X12,X53,X1)
        | c_in(X12,c_Union(X32,X1),X1) )
    | ~ spl0_511 ),
    inference(avatar_component_clause,[],[f4097]) ).

fof(f9506,plain,
    ( spl0_835
    | ~ spl0_466
    | ~ spl0_507 ),
    inference(avatar_split_clause,[],[f4146,f4081,f3818,f9504]) ).

fof(f9504,plain,
    ( spl0_835
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | c_SetInterval_OlessThan(X1,X2) = c_SetInterval_OlessThan(X0,X2)
        | c_less(c_SetInterval_OlessThan(X0,X2),c_SetInterval_OlessThan(X1,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f3818,plain,
    ( spl0_466
  <=> ! [X13,X12,X1] :
        ( X12 = X13
        | ~ c_lessequals(X12,X13,tc_set(X1))
        | c_less(X12,X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f4081,plain,
    ( spl0_507
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | ~ c_lessequals(X0,X3,X1)
        | c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f4146,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | c_SetInterval_OlessThan(X1,X2) = c_SetInterval_OlessThan(X0,X2)
        | c_less(c_SetInterval_OlessThan(X0,X2),c_SetInterval_OlessThan(X1,X2),tc_set(X2)) )
    | ~ spl0_466
    | ~ spl0_507 ),
    inference(resolution,[],[f4082,f3819]) ).

fof(f3819,plain,
    ( ! [X1,X12,X13] :
        ( ~ c_lessequals(X12,X13,tc_set(X1))
        | X12 = X13
        | c_less(X12,X13,tc_set(X1)) )
    | ~ spl0_466 ),
    inference(avatar_component_clause,[],[f3818]) ).

fof(f4082,plain,
    ( ! [X3,X0,X1] :
        ( c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1))
        | ~ c_lessequals(X0,X3,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_507 ),
    inference(avatar_component_clause,[],[f4081]) ).

fof(f9502,plain,
    ( spl0_834
    | ~ spl0_469
    | ~ spl0_507 ),
    inference(avatar_split_clause,[],[f4144,f4081,f3830,f9500]) ).

fof(f9500,plain,
    ( spl0_834
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X0,X2),tc_set(X2))
        | c_SetInterval_OlessThan(X1,X2) = c_SetInterval_OlessThan(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).

fof(f3830,plain,
    ( spl0_469
  <=> ! [X13,X12,X1] :
        ( X12 = X13
        | ~ c_lessequals(X12,X13,tc_set(X1))
        | ~ c_lessequals(X13,X12,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f4144,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X0,X2),tc_set(X2))
        | c_SetInterval_OlessThan(X1,X2) = c_SetInterval_OlessThan(X0,X2) )
    | ~ spl0_469
    | ~ spl0_507 ),
    inference(resolution,[],[f4082,f3831]) ).

fof(f3831,plain,
    ( ! [X1,X12,X13] :
        ( ~ c_lessequals(X13,X12,tc_set(X1))
        | ~ c_lessequals(X12,X13,tc_set(X1))
        | X12 = X13 )
    | ~ spl0_469 ),
    inference(avatar_component_clause,[],[f3830]) ).

fof(f9498,plain,
    ( spl0_833
    | ~ spl0_466
    | ~ spl0_505 ),
    inference(avatar_split_clause,[],[f4139,f4073,f3818,f9496]) ).

fof(f9496,plain,
    ( spl0_833
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | c_SetInterval_OgreaterThan(X1,X2) = c_SetInterval_OgreaterThan(X0,X2)
        | c_less(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X0,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).

fof(f4073,plain,
    ( spl0_505
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | ~ c_lessequals(X3,X0,X1)
        | c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f4139,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | c_SetInterval_OgreaterThan(X1,X2) = c_SetInterval_OgreaterThan(X0,X2)
        | c_less(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X0,X2),tc_set(X2)) )
    | ~ spl0_466
    | ~ spl0_505 ),
    inference(resolution,[],[f4074,f3819]) ).

fof(f4074,plain,
    ( ! [X3,X0,X1] :
        ( c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
        | ~ c_lessequals(X3,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_505 ),
    inference(avatar_component_clause,[],[f4073]) ).

fof(f9494,plain,
    ( spl0_832
    | ~ spl0_469
    | ~ spl0_505 ),
    inference(avatar_split_clause,[],[f4137,f4073,f3830,f9492]) ).

fof(f9492,plain,
    ( spl0_832
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X2),c_SetInterval_OgreaterThan(X1,X2),tc_set(X2))
        | c_SetInterval_OgreaterThan(X1,X2) = c_SetInterval_OgreaterThan(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).

fof(f4137,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X2),c_SetInterval_OgreaterThan(X1,X2),tc_set(X2))
        | c_SetInterval_OgreaterThan(X1,X2) = c_SetInterval_OgreaterThan(X0,X2) )
    | ~ spl0_469
    | ~ spl0_505 ),
    inference(resolution,[],[f4074,f3831]) ).

fof(f9490,plain,
    ( spl0_831
    | ~ spl0_466
    | ~ spl0_501 ),
    inference(avatar_split_clause,[],[f4130,f4056,f3818,f9488]) ).

fof(f9488,plain,
    ( spl0_831
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_SetInterval_OatMost(X1,X2) = c_SetInterval_OatMost(X0,X2)
        | c_less(c_SetInterval_OatMost(X0,X2),c_SetInterval_OatMost(X1,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f4056,plain,
    ( spl0_501
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Oorder(X1)
        | ~ c_lessequals(X0,X3,X1)
        | c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f4130,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_SetInterval_OatMost(X1,X2) = c_SetInterval_OatMost(X0,X2)
        | c_less(c_SetInterval_OatMost(X0,X2),c_SetInterval_OatMost(X1,X2),tc_set(X2)) )
    | ~ spl0_466
    | ~ spl0_501 ),
    inference(resolution,[],[f4057,f3819]) ).

fof(f4057,plain,
    ( ! [X3,X0,X1] :
        ( c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1))
        | ~ c_lessequals(X0,X3,X1)
        | ~ class_Orderings_Oorder(X1) )
    | ~ spl0_501 ),
    inference(avatar_component_clause,[],[f4056]) ).

fof(f9486,plain,
    ( spl0_830
    | ~ spl0_469
    | ~ spl0_501 ),
    inference(avatar_split_clause,[],[f4128,f4056,f3830,f9484]) ).

fof(f9484,plain,
    ( spl0_830
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X0,X2),tc_set(X2))
        | c_SetInterval_OatMost(X1,X2) = c_SetInterval_OatMost(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).

fof(f4128,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X0,X2),tc_set(X2))
        | c_SetInterval_OatMost(X1,X2) = c_SetInterval_OatMost(X0,X2) )
    | ~ spl0_469
    | ~ spl0_501 ),
    inference(resolution,[],[f4057,f3831]) ).

fof(f9482,plain,
    ( spl0_829
    | ~ spl0_466
    | ~ spl0_499 ),
    inference(avatar_split_clause,[],[f4123,f4048,f3818,f9480]) ).

fof(f9480,plain,
    ( spl0_829
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_SetInterval_OatLeast(X1,X2) = c_SetInterval_OatLeast(X0,X2)
        | c_less(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X0,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).

fof(f4048,plain,
    ( spl0_499
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Oorder(X1)
        | ~ c_lessequals(X3,X0,X1)
        | c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f4123,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_SetInterval_OatLeast(X1,X2) = c_SetInterval_OatLeast(X0,X2)
        | c_less(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X0,X2),tc_set(X2)) )
    | ~ spl0_466
    | ~ spl0_499 ),
    inference(resolution,[],[f4049,f3819]) ).

fof(f4049,plain,
    ( ! [X3,X0,X1] :
        ( c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1))
        | ~ c_lessequals(X3,X0,X1)
        | ~ class_Orderings_Oorder(X1) )
    | ~ spl0_499 ),
    inference(avatar_component_clause,[],[f4048]) ).

fof(f9477,plain,
    ( ~ spl0_292
    | spl0_808 ),
    inference(avatar_contradiction_clause,[],[f9474]) ).

fof(f9474,plain,
    ( $false
    | ~ spl0_292
    | spl0_808 ),
    inference(resolution,[],[f9087,f2924]) ).

fof(f2924,plain,
    ( ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1))
    | ~ spl0_292 ),
    inference(avatar_component_clause,[],[f2923]) ).

fof(f2923,plain,
    ( spl0_292
  <=> ! [X12,X1] : c_lessequals(X12,X12,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f9087,plain,
    ( ~ c_lessequals(v_G,v_G,tc_set(tc_Message_Omsg))
    | spl0_808 ),
    inference(avatar_component_clause,[],[f9085]) ).

fof(f9085,plain,
    ( spl0_808
  <=> c_lessequals(v_G,v_G,tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).

fof(f9473,plain,
    ( spl0_828
    | ~ spl0_469
    | ~ spl0_499 ),
    inference(avatar_split_clause,[],[f4121,f4048,f3830,f9471]) ).

fof(f9471,plain,
    ( spl0_828
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_lessequals(c_SetInterval_OatLeast(X0,X2),c_SetInterval_OatLeast(X1,X2),tc_set(X2))
        | c_SetInterval_OatLeast(X1,X2) = c_SetInterval_OatLeast(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f4121,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_lessequals(c_SetInterval_OatLeast(X0,X2),c_SetInterval_OatLeast(X1,X2),tc_set(X2))
        | c_SetInterval_OatLeast(X1,X2) = c_SetInterval_OatLeast(X0,X2) )
    | ~ spl0_469
    | ~ spl0_499 ),
    inference(resolution,[],[f4049,f3831]) ).

fof(f9469,plain,
    ( spl0_827
    | ~ spl0_424
    | ~ spl0_486 ),
    inference(avatar_split_clause,[],[f4012,f3938,f3560,f9467]) ).

fof(f9467,plain,
    ( spl0_827
  <=> ! [X2,X0,X1] :
        ( ~ c_in(c_Main_OsubsetI__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)),X1,tc_prod(X2,X2))
        | c_lessequals(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_set(tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f3560,plain,
    ( spl0_424
  <=> ! [X13,X12,X1] :
        ( c_lessequals(X12,X13,tc_set(X1))
        | ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f3938,plain,
    ( spl0_486
  <=> ! [X5,X1,X28] :
        ( ~ c_in(X28,X5,tc_prod(X1,X1))
        | c_in(X28,c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f4012,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(c_Main_OsubsetI__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)),X1,tc_prod(X2,X2))
        | c_lessequals(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_set(tc_prod(X2,X2))) )
    | ~ spl0_424
    | ~ spl0_486 ),
    inference(resolution,[],[f3939,f3561]) ).

fof(f3561,plain,
    ( ! [X1,X12,X13] :
        ( ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1)
        | c_lessequals(X12,X13,tc_set(X1)) )
    | ~ spl0_424 ),
    inference(avatar_component_clause,[],[f3560]) ).

fof(f3939,plain,
    ( ! [X28,X1,X5] :
        ( c_in(X28,c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1))
        | ~ c_in(X28,X5,tc_prod(X1,X1)) )
    | ~ spl0_486 ),
    inference(avatar_component_clause,[],[f3938]) ).

fof(f9465,plain,
    ( spl0_826
    | ~ spl0_409
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f4002,f3930,f3484,f9463]) ).

fof(f9463,plain,
    ( spl0_826
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
        | ~ c_in(c_Main_OUnionE__1(X0,c_uminus(X1,tc_set(tc_set(X2))),X2),X1,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f3484,plain,
    ( spl0_409
  <=> ! [X12,X1,X4] :
        ( ~ c_in(X4,X12,X1)
        | ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f4002,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
        | ~ c_in(c_Main_OUnionE__1(X0,c_uminus(X1,tc_set(tc_set(X2))),X2),X1,tc_set(X2)) )
    | ~ spl0_409
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3485]) ).

fof(f3485,plain,
    ( ! [X1,X4,X12] :
        ( ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1)
        | ~ c_in(X4,X12,X1) )
    | ~ spl0_409 ),
    inference(avatar_component_clause,[],[f3484]) ).

fof(f9461,plain,
    ( spl0_825
    | ~ spl0_411
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f4001,f3930,f3492,f9459]) ).

fof(f9459,plain,
    ( spl0_825
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3)
        | c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X2,tc_set(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).

fof(f3492,plain,
    ( spl0_411
  <=> ! [X4,X13,X12,X1] :
        ( c_in(X4,X13,X1)
        | ~ c_in(X4,c_inter(X12,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f4001,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3)
        | c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X2,tc_set(X3)) )
    | ~ spl0_411
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3493]) ).

fof(f3493,plain,
    ( ! [X1,X4,X12,X13] :
        ( ~ c_in(X4,c_inter(X12,X13,X1),X1)
        | c_in(X4,X13,X1) )
    | ~ spl0_411 ),
    inference(avatar_component_clause,[],[f3492]) ).

fof(f9457,plain,
    ( spl0_824
    | ~ spl0_412
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f4000,f3930,f3496,f9455]) ).

fof(f9455,plain,
    ( spl0_824
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3)
        | c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X1,tc_set(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f3496,plain,
    ( spl0_412
  <=> ! [X4,X13,X12,X1] :
        ( c_in(X4,X12,X1)
        | ~ c_in(X4,c_inter(X12,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f4000,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3)
        | c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X1,tc_set(X3)) )
    | ~ spl0_412
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3497]) ).

fof(f3497,plain,
    ( ! [X1,X4,X12,X13] :
        ( ~ c_in(X4,c_inter(X12,X13,X1),X1)
        | c_in(X4,X12,X1) )
    | ~ spl0_412 ),
    inference(avatar_component_clause,[],[f3496]) ).

fof(f9453,plain,
    ( spl0_823
    | ~ spl0_409
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3989,f3926,f3484,f9451]) ).

fof(f9451,plain,
    ( spl0_823
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
        | ~ c_in(c_Main_OInterI__1(X0,c_uminus(X1,tc_set(tc_set(X2))),X2),X1,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).

fof(f3989,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
        | ~ c_in(c_Main_OInterI__1(X0,c_uminus(X1,tc_set(tc_set(X2))),X2),X1,tc_set(X2)) )
    | ~ spl0_409
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3485]) ).

fof(f9449,plain,
    ( spl0_822
    | ~ spl0_411
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3988,f3926,f3492,f9447]) ).

fof(f9447,plain,
    ( spl0_822
  <=> ! [X0,X3,X2,X1] :
        ( c_in(X0,c_Inter(c_inter(X1,X2,tc_set(X3)),X3),X3)
        | c_in(c_Main_OInterI__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X2,tc_set(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).

fof(f3988,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(X0,c_Inter(c_inter(X1,X2,tc_set(X3)),X3),X3)
        | c_in(c_Main_OInterI__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X2,tc_set(X3)) )
    | ~ spl0_411
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3493]) ).

fof(f9445,plain,
    ( spl0_821
    | ~ spl0_412
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3987,f3926,f3496,f9443]) ).

fof(f9443,plain,
    ( spl0_821
  <=> ! [X0,X3,X2,X1] :
        ( c_in(X0,c_Inter(c_inter(X1,X2,tc_set(X3)),X3),X3)
        | c_in(c_Main_OInterI__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X1,tc_set(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f3987,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(X0,c_Inter(c_inter(X1,X2,tc_set(X3)),X3),X3)
        | c_in(c_Main_OInterI__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X1,tc_set(X3)) )
    | ~ spl0_412
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3497]) ).

fof(f9441,plain,
    ( spl0_820
    | ~ spl0_449
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3977,f3918,f3672,f9439]) ).

fof(f9439,plain,
    ( spl0_820
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_Pow(X1,X2),tc_set(X2)),tc_List_Olist(tc_set(X2)))
        | ~ c_lessequals(c_Main_Oin__listsI__1(c_Pow(X1,X2),X0,tc_set(X2)),X1,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f3672,plain,
    ( spl0_449
  <=> ! [X13,X12,X1] :
        ( ~ c_lessequals(X12,X13,tc_set(X1))
        | c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f3918,plain,
    ( spl0_481
  <=> ! [X12,X1,X23] :
        ( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
        | c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f3977,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_Pow(X1,X2),tc_set(X2)),tc_List_Olist(tc_set(X2)))
        | ~ c_lessequals(c_Main_Oin__listsI__1(c_Pow(X1,X2),X0,tc_set(X2)),X1,tc_set(X2)) )
    | ~ spl0_449
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3673]) ).

fof(f3673,plain,
    ( ! [X1,X12,X13] :
        ( c_in(X12,c_Pow(X13,X1),tc_set(X1))
        | ~ c_lessequals(X12,X13,tc_set(X1)) )
    | ~ spl0_449 ),
    inference(avatar_component_clause,[],[f3672]) ).

fof(f3919,plain,
    ( ! [X1,X12,X23] :
        ( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
        | c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) )
    | ~ spl0_481 ),
    inference(avatar_component_clause,[],[f3918]) ).

fof(f9435,plain,
    ( ~ spl0_819
    | ~ spl0_804
    | spl0_806 ),
    inference(avatar_split_clause,[],[f8898,f8867,f8858,f9432]) ).

fof(f9432,plain,
    ( spl0_819
  <=> c_less(v_G,v_G,tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f8867,plain,
    ( spl0_806
  <=> c_less(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).

fof(f8898,plain,
    ( ~ c_less(v_G,v_G,tc_set(tc_Message_Omsg))
    | ~ spl0_804
    | spl0_806 ),
    inference(superposition,[],[f8868,f8860]) ).

fof(f8868,plain,
    ( ~ c_less(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
    | spl0_806 ),
    inference(avatar_component_clause,[],[f8867]) ).

fof(f9144,plain,
    ( spl0_818
    | ~ spl0_492
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f4804,f4787,f3962,f9142]) ).

fof(f9142,plain,
    ( spl0_818
  <=> ! [X0] :
        ( ~ c_in(X0,c_Relation_Oconverse(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
        | c_less(c_Main_OconverseE__1(c_Wellfounded__Relations_Oless__than,X0,tc_nat,tc_nat),c_Main_OconverseE__2(c_Wellfounded__Relations_Oless__than,X0,tc_nat,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f3962,plain,
    ( spl0_492
  <=> ! [X0,X3] :
        ( c_less(X0,X3,tc_nat)
        | ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f4787,plain,
    ( spl0_579
  <=> ! [X5,X29,X2,X1] :
        ( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
        | c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f4804,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Relation_Oconverse(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
        | c_less(c_Main_OconverseE__1(c_Wellfounded__Relations_Oless__than,X0,tc_nat,tc_nat),c_Main_OconverseE__2(c_Wellfounded__Relations_Oless__than,X0,tc_nat,tc_nat),tc_nat) )
    | ~ spl0_492
    | ~ spl0_579 ),
    inference(resolution,[],[f4788,f3963]) ).

fof(f3963,plain,
    ( ! [X3,X0] :
        ( ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
        | c_less(X0,X3,tc_nat) )
    | ~ spl0_492 ),
    inference(avatar_component_clause,[],[f3962]) ).

fof(f4788,plain,
    ( ! [X2,X29,X1,X5] :
        ( c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1))
        | ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) )
    | ~ spl0_579 ),
    inference(avatar_component_clause,[],[f4787]) ).

fof(f9140,plain,
    ( spl0_817
    | ~ spl0_325
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f4626,f4609,f3057,f9138]) ).

fof(f9138,plain,
    ( spl0_817
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( c_in(X0,c_Relation_OImage(c_insert(c_Pair(X1,X0,X2,X3),X4,tc_prod(X2,X3)),X5,X2,X3),X3)
        | ~ c_in(X1,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f3057,plain,
    ( spl0_325
  <=> ! [X13,X0,X1] : c_in(X0,c_insert(X0,X13,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f4626,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_in(X0,c_Relation_OImage(c_insert(c_Pair(X1,X0,X2,X3),X4,tc_prod(X2,X3)),X5,X2,X3),X3)
        | ~ c_in(X1,X5,X2) )
    | ~ spl0_325
    | ~ spl0_565 ),
    inference(resolution,[],[f4610,f3058]) ).

fof(f3058,plain,
    ( ! [X0,X1,X13] : c_in(X0,c_insert(X0,X13,X1),X1)
    | ~ spl0_325 ),
    inference(avatar_component_clause,[],[f3057]) ).

fof(f9136,plain,
    ( spl0_816
    | ~ spl0_514
    | ~ spl0_523 ),
    inference(avatar_split_clause,[],[f4264,f4243,f4109,f9134]) ).

fof(f9134,plain,
    ( spl0_816
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_set(X2))
        | ~ c_lessequals(X3,c_uminus(X1,tc_set(X2)),tc_set(X2))
        | c_lessequals(X3,c_uminus(X0,tc_set(X2)),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f4109,plain,
    ( spl0_514
  <=> ! [X13,X12,X32,X1] :
        ( ~ c_lessequals(X13,X32,tc_set(X1))
        | ~ c_lessequals(X12,X13,tc_set(X1))
        | c_lessequals(X12,X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f4243,plain,
    ( spl0_523
  <=> ! [X13,X12,X1] :
        ( ~ c_lessequals(X13,X12,tc_set(X1))
        | c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f4264,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_set(X2))
        | ~ c_lessequals(X3,c_uminus(X1,tc_set(X2)),tc_set(X2))
        | c_lessequals(X3,c_uminus(X0,tc_set(X2)),tc_set(X2)) )
    | ~ spl0_514
    | ~ spl0_523 ),
    inference(resolution,[],[f4244,f4110]) ).

fof(f4110,plain,
    ( ! [X1,X12,X32,X13] :
        ( ~ c_lessequals(X13,X32,tc_set(X1))
        | ~ c_lessequals(X12,X13,tc_set(X1))
        | c_lessequals(X12,X32,tc_set(X1)) )
    | ~ spl0_514 ),
    inference(avatar_component_clause,[],[f4109]) ).

fof(f4244,plain,
    ( ! [X1,X12,X13] :
        ( c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1))
        | ~ c_lessequals(X13,X12,tc_set(X1)) )
    | ~ spl0_523 ),
    inference(avatar_component_clause,[],[f4243]) ).

fof(f9132,plain,
    ( spl0_815
    | ~ spl0_441
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4175,f4097,f3632,f9130]) ).

fof(f9130,plain,
    ( spl0_815
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_SetInterval_OgreaterThan(X3,tc_set(X2)),X2),X2)
        | ~ c_less(X3,X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).

fof(f3632,plain,
    ( spl0_441
  <=> ! [X50,X16,X1] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_less(X16,X50,X1)
        | c_in(X50,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f4175,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_SetInterval_OgreaterThan(X3,tc_set(X2)),X2),X2)
        | ~ c_less(X3,X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_441
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3633]) ).

fof(f3633,plain,
    ( ! [X50,X1,X16] :
        ( c_in(X50,c_SetInterval_OgreaterThan(X16,X1),X1)
        | ~ c_less(X16,X50,X1)
        | ~ class_Orderings_Oord(X1) )
    | ~ spl0_441 ),
    inference(avatar_component_clause,[],[f3632]) ).

fof(f9128,plain,
    ( spl0_814
    | ~ spl0_435
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4174,f4097,f3608,f9126]) ).

fof(f9126,plain,
    ( spl0_814
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_SetInterval_OatLeast(X3,tc_set(X2)),X2),X2)
        | ~ c_lessequals(X3,X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f3608,plain,
    ( spl0_435
  <=> ! [X50,X16,X1] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_lessequals(X16,X50,X1)
        | c_in(X50,c_SetInterval_OatLeast(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f4174,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_SetInterval_OatLeast(X3,tc_set(X2)),X2),X2)
        | ~ c_lessequals(X3,X1,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_435
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3609]) ).

fof(f3609,plain,
    ( ! [X50,X1,X16] :
        ( c_in(X50,c_SetInterval_OatLeast(X16,X1),X1)
        | ~ c_lessequals(X16,X50,X1)
        | ~ class_Orderings_Oord(X1) )
    | ~ spl0_435 ),
    inference(avatar_component_clause,[],[f3608]) ).

fof(f9124,plain,
    ( spl0_813
    | ~ spl0_444
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4167,f4097,f3652,f9122]) ).

fof(f9122,plain,
    ( spl0_813
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_SetInterval_OlessThan(X3,tc_set(X2)),X2),X2)
        | ~ c_less(X1,X3,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).

fof(f3652,plain,
    ( spl0_444
  <=> ! [X50,X16,X1] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_less(X50,X16,X1)
        | c_in(X50,c_SetInterval_OlessThan(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f4167,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_SetInterval_OlessThan(X3,tc_set(X2)),X2),X2)
        | ~ c_less(X1,X3,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_444
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3653]) ).

fof(f3653,plain,
    ( ! [X50,X1,X16] :
        ( c_in(X50,c_SetInterval_OlessThan(X16,X1),X1)
        | ~ c_less(X50,X16,X1)
        | ~ class_Orderings_Oord(X1) )
    | ~ spl0_444 ),
    inference(avatar_component_clause,[],[f3652]) ).

fof(f9120,plain,
    ( spl0_812
    | ~ spl0_438
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4166,f4097,f3620,f9118]) ).

fof(f9118,plain,
    ( spl0_812
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_SetInterval_OatMost(X3,tc_set(X2)),X2),X2)
        | ~ c_lessequals(X1,X3,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).

fof(f3620,plain,
    ( spl0_438
  <=> ! [X50,X16,X1] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_lessequals(X50,X16,X1)
        | c_in(X50,c_SetInterval_OatMost(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f4166,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_SetInterval_OatMost(X3,tc_set(X2)),X2),X2)
        | ~ c_lessequals(X1,X3,tc_set(X2))
        | ~ class_Orderings_Oord(tc_set(X2)) )
    | ~ spl0_438
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3621]) ).

fof(f3621,plain,
    ( ! [X50,X1,X16] :
        ( c_in(X50,c_SetInterval_OatMost(X16,X1),X1)
        | ~ c_lessequals(X50,X16,X1)
        | ~ class_Orderings_Oord(X1) )
    | ~ spl0_438 ),
    inference(avatar_component_clause,[],[f3620]) ).

fof(f9116,plain,
    ( spl0_811
    | ~ spl0_422
    | ~ spl0_509 ),
    inference(avatar_split_clause,[],[f4154,f4089,f3551,f9114]) ).

fof(f9114,plain,
    ( spl0_811
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,tc_set(X2))
        | c_in(c_Main_OsubsetI__1(c_Inter(X1,X2),X3,X2),X0,X2)
        | c_lessequals(c_Inter(X1,X2),X3,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f4089,plain,
    ( spl0_509
  <=> ! [X53,X12,X32,X1] :
        ( c_in(X12,X53,X1)
        | ~ c_in(X53,X32,tc_set(X1))
        | ~ c_in(X12,c_Inter(X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f4154,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,X1,tc_set(X2))
        | c_in(c_Main_OsubsetI__1(c_Inter(X1,X2),X3,X2),X0,X2)
        | c_lessequals(c_Inter(X1,X2),X3,tc_set(X2)) )
    | ~ spl0_422
    | ~ spl0_509 ),
    inference(resolution,[],[f4090,f3552]) ).

fof(f4090,plain,
    ( ! [X1,X53,X12,X32] :
        ( ~ c_in(X12,c_Inter(X32,X1),X1)
        | ~ c_in(X53,X32,tc_set(X1))
        | c_in(X12,X53,X1) )
    | ~ spl0_509 ),
    inference(avatar_component_clause,[],[f4089]) ).

fof(f9112,plain,
    ( spl0_810
    | ~ spl0_406
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f4005,f3930,f3472,f9110]) ).

fof(f9110,plain,
    ( spl0_810
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_Datatype_Oo2s(X1,tc_set(X2)),X2),X2)
        | c_Datatype_Ooption_OSome(c_Main_OUnionE__1(X0,c_Datatype_Oo2s(X1,tc_set(X2)),X2),tc_set(X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).

fof(f3472,plain,
    ( spl0_406
  <=> ! [X0,X1,X40] :
        ( c_Datatype_Ooption_OSome(X0,X1) = X40
        | ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f4005,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_Datatype_Oo2s(X1,tc_set(X2)),X2),X2)
        | c_Datatype_Ooption_OSome(c_Main_OUnionE__1(X0,c_Datatype_Oo2s(X1,tc_set(X2)),X2),tc_set(X2)) = X1 )
    | ~ spl0_406
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3473]) ).

fof(f3473,plain,
    ( ! [X40,X0,X1] :
        ( ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1)
        | c_Datatype_Ooption_OSome(X0,X1) = X40 )
    | ~ spl0_406 ),
    inference(avatar_component_clause,[],[f3472]) ).

fof(f9108,plain,
    ( spl0_809
    | ~ spl0_406
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3992,f3926,f3472,f9106]) ).

fof(f9106,plain,
    ( spl0_809
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_Datatype_Oo2s(X1,tc_set(X2)),X2),X2)
        | c_Datatype_Ooption_OSome(c_Main_OInterI__1(X0,c_Datatype_Oo2s(X1,tc_set(X2)),X2),tc_set(X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).

fof(f3992,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_Datatype_Oo2s(X1,tc_set(X2)),X2),X2)
        | c_Datatype_Ooption_OSome(c_Main_OInterI__1(X0,c_Datatype_Oo2s(X1,tc_set(X2)),X2),tc_set(X2)) = X1 )
    | ~ spl0_406
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3473]) ).

fof(f9088,plain,
    ( ~ spl0_808
    | ~ spl0_804
    | spl0_805 ),
    inference(avatar_split_clause,[],[f8871,f8862,f8858,f9085]) ).

fof(f8862,plain,
    ( spl0_805
  <=> c_lessequals(c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),v_G,tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f8871,plain,
    ( ~ c_lessequals(v_G,v_G,tc_set(tc_Message_Omsg))
    | ~ spl0_804
    | spl0_805 ),
    inference(superposition,[],[f8864,f8860]) ).

fof(f8864,plain,
    ( ~ c_lessequals(c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),v_G,tc_set(tc_Message_Omsg))
    | spl0_805 ),
    inference(avatar_component_clause,[],[f8862]) ).

fof(f8897,plain,
    ( ~ spl0_807
    | spl0_285
    | ~ spl0_803 ),
    inference(avatar_split_clause,[],[f8843,f8840,f2894,f8894]) ).

fof(f8894,plain,
    ( spl0_807
  <=> c_lessequals(v_H,v_G,tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f8840,plain,
    ( spl0_803
  <=> ! [X0] :
        ( ~ c_lessequals(X0,v_G,tc_set(tc_Message_Omsg))
        | c_lessequals(X0,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f8843,plain,
    ( ~ c_lessequals(v_H,v_G,tc_set(tc_Message_Omsg))
    | spl0_285
    | ~ spl0_803 ),
    inference(resolution,[],[f8841,f2896]) ).

fof(f8841,plain,
    ( ! [X0] :
        ( c_lessequals(X0,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(X0,v_G,tc_set(tc_Message_Omsg)) )
    | ~ spl0_803 ),
    inference(avatar_component_clause,[],[f8840]) ).

fof(f8870,plain,
    ( spl0_806
    | spl0_804
    | ~ spl0_286
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f8809,f3818,f2898,f8858,f8867]) ).

fof(f2898,plain,
    ( spl0_286
  <=> c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f8809,plain,
    ( v_G = c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg))
    | c_less(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
    | ~ spl0_286
    | ~ spl0_466 ),
    inference(resolution,[],[f2899,f3819]) ).

fof(f2899,plain,
    ( c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f2898]) ).

fof(f8865,plain,
    ( spl0_804
    | ~ spl0_805
    | ~ spl0_286
    | ~ spl0_469 ),
    inference(avatar_split_clause,[],[f8807,f3830,f2898,f8862,f8858]) ).

fof(f8807,plain,
    ( ~ c_lessequals(c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),v_G,tc_set(tc_Message_Omsg))
    | v_G = c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg))
    | ~ spl0_286
    | ~ spl0_469 ),
    inference(resolution,[],[f2899,f3831]) ).

fof(f8842,plain,
    ( spl0_803
    | ~ spl0_286
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f8806,f4109,f2898,f8840]) ).

fof(f8806,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_G,tc_set(tc_Message_Omsg))
        | c_lessequals(X0,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
    | ~ spl0_286
    | ~ spl0_514 ),
    inference(resolution,[],[f2899,f4110]) ).

fof(f8813,plain,
    ( spl0_802
    | ~ spl0_286
    | ~ spl0_468 ),
    inference(avatar_split_clause,[],[f8808,f3826,f2898,f8811]) ).

fof(f8811,plain,
    ( spl0_802
  <=> ! [X0] :
        ( c_in(X0,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_Message_Omsg)
        | ~ c_in(X0,v_G,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f3826,plain,
    ( spl0_468
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X12,X1)
        | c_in(X4,X13,X1)
        | ~ c_lessequals(X12,X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f8808,plain,
    ( ! [X0] :
        ( c_in(X0,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_Message_Omsg)
        | ~ c_in(X0,v_G,tc_Message_Omsg) )
    | ~ spl0_286
    | ~ spl0_468 ),
    inference(resolution,[],[f2899,f3827]) ).

fof(f3827,plain,
    ( ! [X1,X4,X12,X13] :
        ( ~ c_lessequals(X12,X13,tc_set(X1))
        | c_in(X4,X13,X1)
        | ~ c_in(X4,X12,X1) )
    | ~ spl0_468 ),
    inference(avatar_component_clause,[],[f3826]) ).

fof(f8802,plain,
    ( ~ spl0_353
    | spl0_801 ),
    inference(avatar_contradiction_clause,[],[f8799]) ).

fof(f8799,plain,
    ( $false
    | ~ spl0_353
    | spl0_801 ),
    inference(resolution,[],[f8618,f3186]) ).

fof(f3186,plain,
    ( ! [X1,X12,X13] : c_lessequals(X12,c_union(X12,X13,X1),tc_set(X1))
    | ~ spl0_353 ),
    inference(avatar_component_clause,[],[f3185]) ).

fof(f3185,plain,
    ( spl0_353
  <=> ! [X13,X12,X1] : c_lessequals(X12,c_union(X12,X13,X1),tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f8618,plain,
    ( ~ c_lessequals(v_G_H,c_union(v_G_H,v_H_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
    | spl0_801 ),
    inference(avatar_component_clause,[],[f8616]) ).

fof(f8616,plain,
    ( spl0_801
  <=> c_lessequals(v_G_H,c_union(v_G_H,v_H_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f8619,plain,
    ( ~ spl0_801
    | spl0_286
    | ~ spl0_775 ),
    inference(avatar_split_clause,[],[f8326,f8137,f2898,f8616]) ).

fof(f8137,plain,
    ( spl0_775
  <=> ! [X0] :
        ( c_lessequals(v_G,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(v_G_H,X0,tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).

fof(f8326,plain,
    ( ~ c_lessequals(v_G_H,c_union(v_G_H,v_H_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
    | spl0_286
    | ~ spl0_775 ),
    inference(resolution,[],[f8138,f2900]) ).

fof(f2900,plain,
    ( ~ c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
    | spl0_286 ),
    inference(avatar_component_clause,[],[f2898]) ).

fof(f8138,plain,
    ( ! [X0] :
        ( c_lessequals(v_G,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(v_G_H,X0,tc_set(tc_Message_Omsg)) )
    | ~ spl0_775 ),
    inference(avatar_component_clause,[],[f8137]) ).

fof(f8357,plain,
    ( spl0_800
    | ~ spl0_476
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f4801,f4787,f3858,f8355]) ).

fof(f8355,plain,
    ( spl0_800
  <=> ! [X0,X1] :
        ( ~ c_in(X0,c_Relation_Oconverse(c_Relation_OId,X1,X1),tc_prod(X1,X1))
        | c_Main_OconverseE__1(c_Relation_OId,X0,X1,X1) = c_Main_OconverseE__2(c_Relation_OId,X0,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f3858,plain,
    ( spl0_476
  <=> ! [X18,X27,X1] :
        ( X18 = X27
        | ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f4801,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,c_Relation_Oconverse(c_Relation_OId,X1,X1),tc_prod(X1,X1))
        | c_Main_OconverseE__1(c_Relation_OId,X0,X1,X1) = c_Main_OconverseE__2(c_Relation_OId,X0,X1,X1) )
    | ~ spl0_476
    | ~ spl0_579 ),
    inference(resolution,[],[f4788,f3859]) ).

fof(f3859,plain,
    ( ! [X18,X1,X27] :
        ( ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1))
        | X18 = X27 )
    | ~ spl0_476 ),
    inference(avatar_component_clause,[],[f3858]) ).

fof(f8353,plain,
    ( spl0_799
    | ~ spl0_529
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f4800,f4787,f4291,f8351]) ).

fof(f8351,plain,
    ( spl0_799
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Relation_Oconverse(X1,X2,X3),tc_prod(X3,X2))
        | c_in(c_Main_OconverseE__1(X1,X0,X2,X3),c_Relation_ODomain(X1,X2,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f4800,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_Relation_Oconverse(X1,X2,X3),tc_prod(X3,X2))
        | c_in(c_Main_OconverseE__1(X1,X0,X2,X3),c_Relation_ODomain(X1,X2,X3),X2) )
    | ~ spl0_529
    | ~ spl0_579 ),
    inference(resolution,[],[f4788,f4292]) ).

fof(f8349,plain,
    ( spl0_798
    | ~ spl0_532
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f4799,f4787,f4303,f8347]) ).

fof(f8347,plain,
    ( spl0_798
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Relation_Oconverse(X1,X2,X3),tc_prod(X3,X2))
        | c_in(c_Main_OconverseE__2(X1,X0,X2,X3),c_Relation_ORange(X1,X2,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f4799,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_Relation_Oconverse(X1,X2,X3),tc_prod(X3,X2))
        | c_in(c_Main_OconverseE__2(X1,X0,X2,X3),c_Relation_ORange(X1,X2,X3),X3) )
    | ~ spl0_532
    | ~ spl0_579 ),
    inference(resolution,[],[f4788,f4304]) ).

fof(f8345,plain,
    ( spl0_797
    | ~ spl0_529
    | ~ spl0_571 ),
    inference(avatar_split_clause,[],[f4740,f4662,f4291,f8343]) ).

fof(f8343,plain,
    ( spl0_797
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))
        | c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(X4,X2,X3),X3,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).

fof(f4662,plain,
    ( spl0_571
  <=> ! [X18,X5,X27,X2,X1] :
        ( ~ c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
        | c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f4740,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))
        | c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(X4,X2,X3),X3,X2),X3) )
    | ~ spl0_529
    | ~ spl0_571 ),
    inference(resolution,[],[f4663,f4292]) ).

fof(f4663,plain,
    ( ! [X2,X18,X1,X27,X5] :
        ( c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
        | ~ c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1)) )
    | ~ spl0_571 ),
    inference(avatar_component_clause,[],[f4662]) ).

fof(f8341,plain,
    ( spl0_796
    | ~ spl0_532
    | ~ spl0_571 ),
    inference(avatar_split_clause,[],[f4739,f4662,f4303,f8339]) ).

fof(f8339,plain,
    ( spl0_796
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))
        | c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f4739,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))
        | c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2) )
    | ~ spl0_532
    | ~ spl0_571 ),
    inference(resolution,[],[f4663,f4304]) ).

fof(f8337,plain,
    ( spl0_795
    | ~ spl0_529
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f4707,f4654,f4291,f8335]) ).

fof(f8335,plain,
    ( spl0_795
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
        | c_in(c_Main_OImageE__1(X2,X0,X1,X3,X4),c_Relation_ODomain(X1,X3,X4),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).

fof(f4654,plain,
    ( spl0_569
  <=> ! [X12,X5,X27,X2,X1] :
        ( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
        | c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f4707,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
        | c_in(c_Main_OImageE__1(X2,X0,X1,X3,X4),c_Relation_ODomain(X1,X3,X4),X3) )
    | ~ spl0_529
    | ~ spl0_569 ),
    inference(resolution,[],[f4655,f4292]) ).

fof(f4655,plain,
    ( ! [X2,X1,X27,X5,X12] :
        ( c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1))
        | ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1) )
    | ~ spl0_569 ),
    inference(avatar_component_clause,[],[f4654]) ).

fof(f8325,plain,
    ( spl0_794
    | ~ spl0_505
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4205,f4109,f4073,f8323]) ).

fof(f8323,plain,
    ( spl0_794
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,c_SetInterval_OgreaterThan(X1,X2),tc_set(X2))
        | c_lessequals(X0,c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
        | ~ c_lessequals(X3,X1,X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).

fof(f4205,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,c_SetInterval_OgreaterThan(X1,X2),tc_set(X2))
        | c_lessequals(X0,c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
        | ~ c_lessequals(X3,X1,X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_505
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f4074]) ).

fof(f8321,plain,
    ( spl0_793
    | ~ spl0_499
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4204,f4109,f4048,f8319]) ).

fof(f8319,plain,
    ( spl0_793
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,c_SetInterval_OatLeast(X1,X2),tc_set(X2))
        | c_lessequals(X0,c_SetInterval_OatLeast(X3,X2),tc_set(X2))
        | ~ c_lessequals(X3,X1,X2)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).

fof(f4204,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,c_SetInterval_OatLeast(X1,X2),tc_set(X2))
        | c_lessequals(X0,c_SetInterval_OatLeast(X3,X2),tc_set(X2))
        | ~ c_lessequals(X3,X1,X2)
        | ~ class_Orderings_Oorder(X2) )
    | ~ spl0_499
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f4049]) ).

fof(f8317,plain,
    ( spl0_792
    | ~ spl0_507
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4200,f4109,f4081,f8315]) ).

fof(f8315,plain,
    ( spl0_792
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,c_SetInterval_OlessThan(X1,X2),tc_set(X2))
        | c_lessequals(X0,c_SetInterval_OlessThan(X3,X2),tc_set(X2))
        | ~ c_lessequals(X1,X3,X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f4200,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,c_SetInterval_OlessThan(X1,X2),tc_set(X2))
        | c_lessequals(X0,c_SetInterval_OlessThan(X3,X2),tc_set(X2))
        | ~ c_lessequals(X1,X3,X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_507
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f4082]) ).

fof(f8313,plain,
    ( spl0_791
    | ~ spl0_501
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4199,f4109,f4056,f8311]) ).

fof(f8311,plain,
    ( spl0_791
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,c_SetInterval_OatMost(X1,X2),tc_set(X2))
        | c_lessequals(X0,c_SetInterval_OatMost(X3,X2),tc_set(X2))
        | ~ c_lessequals(X1,X3,X2)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).

fof(f4199,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,c_SetInterval_OatMost(X1,X2),tc_set(X2))
        | c_lessequals(X0,c_SetInterval_OatMost(X3,X2),tc_set(X2))
        | ~ c_lessequals(X1,X3,X2)
        | ~ class_Orderings_Oorder(X2) )
    | ~ spl0_501
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f4057]) ).

fof(f8309,plain,
    ( spl0_790
    | ~ spl0_471
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4194,f4097,f3838,f8307]) ).

fof(f8307,plain,
    ( spl0_790
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Pow(X1,X2),tc_set(X2))
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_set(X2)),tc_set(X2))
        | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).

fof(f3838,plain,
    ( spl0_471
  <=> ! [X12,X1] :
        ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f4194,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Pow(X1,X2),tc_set(X2))
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_set(X2)),tc_set(X2))
        | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) )
    | ~ spl0_471
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3839]) ).

fof(f3839,plain,
    ( ! [X1,X12] :
        ( c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1)))
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) )
    | ~ spl0_471 ),
    inference(avatar_component_clause,[],[f3838]) ).

fof(f8305,plain,
    ( spl0_789
    | ~ spl0_422
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4193,f4097,f3551,f8303]) ).

fof(f8303,plain,
    ( spl0_789
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Main_OsubsetI__1(X1,X2,tc_set(X3)),X3)
        | c_in(X0,c_Union(X1,X3),X3)
        | c_lessequals(X1,X2,tc_set(tc_set(X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f4193,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_Main_OsubsetI__1(X1,X2,tc_set(X3)),X3)
        | c_in(X0,c_Union(X1,X3),X3)
        | c_lessequals(X1,X2,tc_set(tc_set(X3))) )
    | ~ spl0_422
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3552]) ).

fof(f8301,plain,
    ( spl0_788
    | ~ spl0_380
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f3999,f3930,f3332,f8299]) ).

fof(f8299,plain,
    ( spl0_788
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_insert(X1,c_emptyset,tc_set(X2)),X2),X2)
        | c_Main_OUnionE__1(X0,c_insert(X1,c_emptyset,tc_set(X2)),X2) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f3332,plain,
    ( spl0_380
  <=> ! [X18,X27,X1] :
        ( X18 = X27
        | ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f3999,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_insert(X1,c_emptyset,tc_set(X2)),X2),X2)
        | c_Main_OUnionE__1(X0,c_insert(X1,c_emptyset,tc_set(X2)),X2) = X1 )
    | ~ spl0_380
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3333]) ).

fof(f3333,plain,
    ( ! [X18,X1,X27] :
        ( ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1)
        | X18 = X27 )
    | ~ spl0_380 ),
    inference(avatar_component_clause,[],[f3332]) ).

fof(f8297,plain,
    ( spl0_787
    | ~ spl0_380
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3986,f3926,f3332,f8295]) ).

fof(f8295,plain,
    ( spl0_787
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_insert(X1,c_emptyset,tc_set(X2)),X2),X2)
        | c_Main_OInterI__1(X0,c_insert(X1,c_emptyset,tc_set(X2)),X2) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f3986,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_insert(X1,c_emptyset,tc_set(X2)),X2),X2)
        | c_Main_OInterI__1(X0,c_insert(X1,c_emptyset,tc_set(X2)),X2) = X1 )
    | ~ spl0_380
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3333]) ).

fof(f8293,plain,
    ( spl0_786
    | ~ spl0_441
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3981,f3918,f3632,f8291]) ).

fof(f8291,plain,
    ( spl0_786
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_SetInterval_OgreaterThan(X1,X2),X2),tc_List_Olist(X2))
        | ~ c_less(X1,c_Main_Oin__listsI__1(c_SetInterval_OgreaterThan(X1,X2),X0,X2),X2)
        | ~ class_Orderings_Oord(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).

fof(f3981,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_SetInterval_OgreaterThan(X1,X2),X2),tc_List_Olist(X2))
        | ~ c_less(X1,c_Main_Oin__listsI__1(c_SetInterval_OgreaterThan(X1,X2),X0,X2),X2)
        | ~ class_Orderings_Oord(X2) )
    | ~ spl0_441
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3633]) ).

fof(f8289,plain,
    ( spl0_785
    | ~ spl0_435
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3980,f3918,f3608,f8287]) ).

fof(f8287,plain,
    ( spl0_785
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_SetInterval_OatLeast(X1,X2),X2),tc_List_Olist(X2))
        | ~ c_lessequals(X1,c_Main_Oin__listsI__1(c_SetInterval_OatLeast(X1,X2),X0,X2),X2)
        | ~ class_Orderings_Oord(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f3980,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_SetInterval_OatLeast(X1,X2),X2),tc_List_Olist(X2))
        | ~ c_lessequals(X1,c_Main_Oin__listsI__1(c_SetInterval_OatLeast(X1,X2),X0,X2),X2)
        | ~ class_Orderings_Oord(X2) )
    | ~ spl0_435
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3609]) ).

fof(f8285,plain,
    ( spl0_784
    | ~ spl0_2
    | ~ spl0_727 ),
    inference(avatar_split_clause,[],[f6867,f6782,f1400,f8283]) ).

fof(f1400,plain,
    ( spl0_2
  <=> c_lessequals(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f6782,plain,
    ( spl0_727
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
        | c_lessequals(X0,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(X1,X2,tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f6867,plain,
    ( ! [X0] :
        ( c_lessequals(v_H,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(v_H_H,X0,tc_set(tc_Message_Omsg)) )
    | ~ spl0_2
    | ~ spl0_727 ),
    inference(resolution,[],[f6783,f1402]) ).

fof(f1402,plain,
    ( c_lessequals(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg))
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f1400]) ).

fof(f6783,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
        | c_lessequals(X0,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(X1,X2,tc_set(tc_Message_Omsg)) )
    | ~ spl0_727 ),
    inference(avatar_component_clause,[],[f6782]) ).

fof(f8281,plain,
    ( spl0_783
    | ~ spl0_413
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3979,f3918,f3500,f8279]) ).

fof(f8279,plain,
    ( spl0_783
  <=> ! [X0,X3,X2,X1] :
        ( c_in(X0,c_List_Olists(c_union(X1,X2,X3),X3),tc_List_Olist(X3))
        | ~ c_in(c_Main_Oin__listsI__1(c_union(X1,X2,X3),X0,X3),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f3979,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(X0,c_List_Olists(c_union(X1,X2,X3),X3),tc_List_Olist(X3))
        | ~ c_in(c_Main_Oin__listsI__1(c_union(X1,X2,X3),X0,X3),X2,X3) )
    | ~ spl0_413
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3501]) ).

fof(f8277,plain,
    ( spl0_782
    | ~ spl0_415
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3978,f3918,f3508,f8275]) ).

fof(f8275,plain,
    ( spl0_782
  <=> ! [X0,X3,X2,X1] :
        ( c_in(X0,c_List_Olists(c_union(X1,X2,X3),X3),tc_List_Olist(X3))
        | ~ c_in(c_Main_Oin__listsI__1(c_union(X1,X2,X3),X0,X3),X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f3978,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(X0,c_List_Olists(c_union(X1,X2,X3),X3),tc_List_Olist(X3))
        | ~ c_in(c_Main_Oin__listsI__1(c_union(X1,X2,X3),X0,X3),X1,X3) )
    | ~ spl0_415
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3509]) ).

fof(f8273,plain,
    ( spl0_781
    | ~ spl0_444
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3975,f3918,f3652,f8271]) ).

fof(f8271,plain,
    ( spl0_781
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_SetInterval_OlessThan(X1,X2),X2),tc_List_Olist(X2))
        | ~ c_less(c_Main_Oin__listsI__1(c_SetInterval_OlessThan(X1,X2),X0,X2),X1,X2)
        | ~ class_Orderings_Oord(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f3975,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_SetInterval_OlessThan(X1,X2),X2),tc_List_Olist(X2))
        | ~ c_less(c_Main_Oin__listsI__1(c_SetInterval_OlessThan(X1,X2),X0,X2),X1,X2)
        | ~ class_Orderings_Oord(X2) )
    | ~ spl0_444
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3653]) ).

fof(f8269,plain,
    ( spl0_780
    | ~ spl0_438
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3974,f3918,f3620,f8267]) ).

fof(f8267,plain,
    ( spl0_780
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_SetInterval_OatMost(X1,X2),X2),tc_List_Olist(X2))
        | ~ c_lessequals(c_Main_Oin__listsI__1(c_SetInterval_OatMost(X1,X2),X0,X2),X1,X2)
        | ~ class_Orderings_Oord(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).

fof(f3974,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_SetInterval_OatMost(X1,X2),X2),tc_List_Olist(X2))
        | ~ c_lessequals(c_Main_Oin__listsI__1(c_SetInterval_OatMost(X1,X2),X0,X2),X1,X2)
        | ~ class_Orderings_Oord(X2) )
    | ~ spl0_438
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3621]) ).

fof(f8265,plain,
    ( spl0_779
    | ~ spl0_410
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3973,f3918,f3488,f8263]) ).

fof(f8263,plain,
    ( spl0_779
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_uminus(X1,tc_set(X2)),X2),tc_List_Olist(X2))
        | c_in(c_Main_Oin__listsI__1(c_uminus(X1,tc_set(X2)),X0,X2),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).

fof(f3973,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_List_Olists(c_uminus(X1,tc_set(X2)),X2),tc_List_Olist(X2))
        | c_in(c_Main_Oin__listsI__1(c_uminus(X1,tc_set(X2)),X0,X2),X1,X2) )
    | ~ spl0_410
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3489]) ).

fof(f8261,plain,
    ( spl0_778
    | ~ spl0_416
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3972,f3918,f3512,f8259]) ).

fof(f8259,plain,
    ( spl0_778
  <=> ! [X0,X3,X2,X1] :
        ( c_in(X0,c_List_Olists(c_insert(X1,X2,X3),X3),tc_List_Olist(X3))
        | ~ c_in(c_Main_Oin__listsI__1(c_insert(X1,X2,X3),X0,X3),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f3972,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(X0,c_List_Olists(c_insert(X1,X2,X3),X3),tc_List_Olist(X3))
        | ~ c_in(c_Main_Oin__listsI__1(c_insert(X1,X2,X3),X0,X3),X2,X3) )
    | ~ spl0_416
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3513]) ).

fof(f8257,plain,
    ( spl0_777
    | ~ spl0_422
    | ~ spl0_447 ),
    inference(avatar_split_clause,[],[f3785,f3664,f3551,f8255]) ).

fof(f3664,plain,
    ( spl0_447
  <=> ! [X4,X13,X12,X1] :
        ( c_in(X4,X12,X1)
        | ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f3785,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(c_Main_OsubsetI__1(c_minus(X0,X1,tc_set(X2)),X3,X2),X0,X2)
        | c_lessequals(c_minus(X0,X1,tc_set(X2)),X3,tc_set(X2)) )
    | ~ spl0_422
    | ~ spl0_447 ),
    inference(resolution,[],[f3665,f3552]) ).

fof(f3665,plain,
    ( ! [X1,X4,X12,X13] :
        ( ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1)
        | c_in(X4,X12,X1) )
    | ~ spl0_447 ),
    inference(avatar_component_clause,[],[f3664]) ).

fof(f8253,plain,
    ( spl0_776
    | ~ spl0_422
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f3784,f3660,f3551,f8251]) ).

fof(f8251,plain,
    ( spl0_776
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(c_Main_OsubsetI__1(c_minus(X0,X1,tc_set(X2)),X3,X2),X1,X2)
        | c_lessequals(c_minus(X0,X1,tc_set(X2)),X3,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).

fof(f3660,plain,
    ( spl0_446
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X13,X1)
        | ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f3784,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(c_Main_OsubsetI__1(c_minus(X0,X1,tc_set(X2)),X3,X2),X1,X2)
        | c_lessequals(c_minus(X0,X1,tc_set(X2)),X3,tc_set(X2)) )
    | ~ spl0_422
    | ~ spl0_446 ),
    inference(resolution,[],[f3661,f3552]) ).

fof(f3661,plain,
    ( ! [X1,X4,X12,X13] :
        ( ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1)
        | ~ c_in(X4,X13,X1) )
    | ~ spl0_446 ),
    inference(avatar_component_clause,[],[f3660]) ).

fof(f8139,plain,
    ( spl0_775
    | ~ spl0_1
    | ~ spl0_727 ),
    inference(avatar_split_clause,[],[f6866,f6782,f1395,f8137]) ).

fof(f1395,plain,
    ( spl0_1
  <=> c_lessequals(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f6866,plain,
    ( ! [X0] :
        ( c_lessequals(v_G,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(v_G_H,X0,tc_set(tc_Message_Omsg)) )
    | ~ spl0_1
    | ~ spl0_727 ),
    inference(resolution,[],[f6783,f1397]) ).

fof(f1397,plain,
    ( c_lessequals(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f1395]) ).

fof(f7701,plain,
    ( spl0_774
    | ~ spl0_529
    | ~ spl0_566 ),
    inference(avatar_split_clause,[],[f4644,f4613,f4291,f7699]) ).

fof(f7699,plain,
    ( spl0_774
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
        | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f4613,plain,
    ( spl0_566
  <=> ! [X5,X18,X27,X1] :
        ( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
        | c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f4644,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
        | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2) )
    | ~ spl0_529
    | ~ spl0_566 ),
    inference(resolution,[],[f4614,f4292]) ).

fof(f4614,plain,
    ( ! [X18,X1,X27,X5] :
        ( c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1))
        | ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1)) )
    | ~ spl0_566 ),
    inference(avatar_component_clause,[],[f4613]) ).

fof(f7697,plain,
    ( spl0_773
    | ~ spl0_532
    | ~ spl0_566 ),
    inference(avatar_split_clause,[],[f4643,f4613,f4303,f7695]) ).

fof(f7695,plain,
    ( spl0_773
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
        | c_in(X1,c_Relation_ORange(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).

fof(f4643,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
        | c_in(X1,c_Relation_ORange(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2) )
    | ~ spl0_532
    | ~ spl0_566 ),
    inference(resolution,[],[f4614,f4304]) ).

fof(f7693,plain,
    ( spl0_772
    | ~ spl0_340
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4382,f4303,f3133,f7691]) ).

fof(f7691,plain,
    ( spl0_772
  <=> ! [X0,X3,X2,X1] : c_in(X0,c_Relation_ORange(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(c_Pair(X1,X0,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).

fof(f3133,plain,
    ( spl0_340
  <=> ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f4382,plain,
    ( ! [X2,X3,X0,X1] : c_in(X0,c_Relation_ORange(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(c_Pair(X1,X0,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X3)
    | ~ spl0_340
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f3134]) ).

fof(f3134,plain,
    ( ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1)
    | ~ spl0_340 ),
    inference(avatar_component_clause,[],[f3133]) ).

fof(f7689,plain,
    ( spl0_771
    | ~ spl0_340
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4358,f4291,f3133,f7687]) ).

fof(f7687,plain,
    ( spl0_771
  <=> ! [X0,X3,X2,X1] : c_in(X0,c_Relation_ODomain(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(c_Pair(X0,X1,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).

fof(f4358,plain,
    ( ! [X2,X3,X0,X1] : c_in(X0,c_Relation_ODomain(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(c_Pair(X0,X1,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X2)
    | ~ spl0_340
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f3134]) ).

fof(f7685,plain,
    ( spl0_770
    | ~ spl0_468
    | ~ spl0_523 ),
    inference(avatar_split_clause,[],[f4266,f4243,f3826,f7683]) ).

fof(f7683,plain,
    ( spl0_770
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_set(X2))
        | c_in(X3,c_uminus(X0,tc_set(X2)),X2)
        | ~ c_in(X3,c_uminus(X1,tc_set(X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f4266,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_set(X2))
        | c_in(X3,c_uminus(X0,tc_set(X2)),X2)
        | ~ c_in(X3,c_uminus(X1,tc_set(X2)),X2) )
    | ~ spl0_468
    | ~ spl0_523 ),
    inference(resolution,[],[f4244,f3827]) ).

fof(f7681,plain,
    ( spl0_769
    | ~ spl0_484
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4192,f4097,f3930,f7679]) ).

fof(f7679,plain,
    ( spl0_769
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Main_OUnionE__1(X1,X2,X3),X3)
        | c_in(X0,c_Union(X2,X3),X3)
        | ~ c_in(X1,c_Union(X2,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f4192,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_Main_OUnionE__1(X1,X2,X3),X3)
        | c_in(X0,c_Union(X2,X3),X3)
        | ~ c_in(X1,c_Union(X2,X3),X3) )
    | ~ spl0_484
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3931]) ).

fof(f7677,plain,
    ( spl0_768
    | ~ spl0_483
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4191,f4097,f3926,f7675]) ).

fof(f7675,plain,
    ( spl0_768
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Main_OInterI__1(X1,X2,X3),X3)
        | c_in(X0,c_Union(X2,X3),X3)
        | c_in(X1,c_Inter(X2,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).

fof(f4191,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_Main_OInterI__1(X1,X2,X3),X3)
        | c_in(X0,c_Union(X2,X3),X3)
        | c_in(X1,c_Inter(X2,X3),X3) )
    | ~ spl0_483
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3927]) ).

fof(f7673,plain,
    ( spl0_767
    | ~ spl0_413
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4173,f4097,f3500,f7671]) ).

fof(f7671,plain,
    ( spl0_767
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_union(X3,X4,tc_set(X2)),X2),X2)
        | ~ c_in(X1,X4,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).

fof(f4173,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_union(X3,X4,tc_set(X2)),X2),X2)
        | ~ c_in(X1,X4,tc_set(X2)) )
    | ~ spl0_413
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3501]) ).

fof(f7669,plain,
    ( spl0_766
    | ~ spl0_415
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4172,f4097,f3508,f7667]) ).

fof(f7667,plain,
    ( spl0_766
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_union(X3,X4,tc_set(X2)),X2),X2)
        | ~ c_in(X1,X3,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).

fof(f4172,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_union(X3,X4,tc_set(X2)),X2),X2)
        | ~ c_in(X1,X3,tc_set(X2)) )
    | ~ spl0_415
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3509]) ).

fof(f7658,plain,
    ( spl0_765
    | ~ spl0_410
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4165,f4097,f3488,f7656]) ).

fof(f7656,plain,
    ( spl0_765
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_uminus(X3,tc_set(tc_set(X2))),X2),X2)
        | c_in(X1,X3,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).

fof(f4165,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_uminus(X3,tc_set(tc_set(X2))),X2),X2)
        | c_in(X1,X3,tc_set(X2)) )
    | ~ spl0_410
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3489]) ).

fof(f7654,plain,
    ( spl0_764
    | ~ spl0_416
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4163,f4097,f3512,f7652]) ).

fof(f7652,plain,
    ( spl0_764
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_insert(X3,X4,tc_set(X2)),X2),X2)
        | ~ c_in(X1,X4,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).

fof(f4163,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_insert(X3,X4,tc_set(X2)),X2),X2)
        | ~ c_in(X1,X4,tc_set(X2)) )
    | ~ spl0_416
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3513]) ).

fof(f7650,plain,
    ( spl0_763
    | ~ spl0_424
    | ~ spl0_449 ),
    inference(avatar_split_clause,[],[f3788,f3672,f3560,f7648]) ).

fof(f7648,plain,
    ( spl0_763
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_Main_OsubsetI__1(X0,c_Pow(X1,X2),tc_set(X2)),X1,tc_set(X2))
        | c_lessequals(X0,c_Pow(X1,X2),tc_set(tc_set(X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).

fof(f3788,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_Main_OsubsetI__1(X0,c_Pow(X1,X2),tc_set(X2)),X1,tc_set(X2))
        | c_lessequals(X0,c_Pow(X1,X2),tc_set(tc_set(X2))) )
    | ~ spl0_424
    | ~ spl0_449 ),
    inference(resolution,[],[f3673,f3561]) ).

fof(f7646,plain,
    ( spl0_762
    | ~ spl0_422
    | ~ spl0_448 ),
    inference(avatar_split_clause,[],[f3786,f3668,f3551,f7644]) ).

fof(f7644,plain,
    ( spl0_762
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_Main_OsubsetI__1(c_Pow(X0,X1),X2,tc_set(X1)),X0,tc_set(X1))
        | c_lessequals(c_Pow(X0,X1),X2,tc_set(tc_set(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f3668,plain,
    ( spl0_448
  <=> ! [X13,X12,X1] :
        ( c_lessequals(X12,X13,tc_set(X1))
        | ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f3786,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_Main_OsubsetI__1(c_Pow(X0,X1),X2,tc_set(X1)),X0,tc_set(X1))
        | c_lessequals(c_Pow(X0,X1),X2,tc_set(tc_set(X1))) )
    | ~ spl0_422
    | ~ spl0_448 ),
    inference(resolution,[],[f3669,f3552]) ).

fof(f3669,plain,
    ( ! [X1,X12,X13] :
        ( ~ c_in(X12,c_Pow(X13,X1),tc_set(X1))
        | c_lessequals(X12,X13,tc_set(X1)) )
    | ~ spl0_448 ),
    inference(avatar_component_clause,[],[f3668]) ).

fof(f7567,plain,
    ( spl0_761
    | ~ spl0_623
    | ~ spl0_732 ),
    inference(avatar_split_clause,[],[f7181,f6895,f5317,f7565]) ).

fof(f7565,plain,
    ( spl0_761
  <=> ! [X0] : c_lessequals(c_inter(X0,v_G,tc_Message_Omsg),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f6895,plain,
    ( spl0_732
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2))
        | c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f7181,plain,
    ( ! [X0] : c_lessequals(c_inter(X0,v_G,tc_Message_Omsg),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
    | ~ spl0_623
    | ~ spl0_732 ),
    inference(duplicate_literal_removal,[],[f7109]) ).

fof(f7109,plain,
    ( ! [X0] :
        ( c_lessequals(c_inter(X0,v_G,tc_Message_Omsg),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
        | c_lessequals(c_inter(X0,v_G,tc_Message_Omsg),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) )
    | ~ spl0_623
    | ~ spl0_732 ),
    inference(resolution,[],[f6896,f5318]) ).

fof(f6896,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X1,X2)
        | c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2)) )
    | ~ spl0_732 ),
    inference(avatar_component_clause,[],[f6895]) ).

fof(f7459,plain,
    ( spl0_760
    | ~ spl0_623
    | ~ spl0_731 ),
    inference(avatar_split_clause,[],[f7101,f6891,f5317,f7457]) ).

fof(f7457,plain,
    ( spl0_760
  <=> ! [X0] : c_lessequals(c_inter(v_G,X0,tc_Message_Omsg),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).

fof(f6891,plain,
    ( spl0_731
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2))
        | c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f7101,plain,
    ( ! [X0] : c_lessequals(c_inter(v_G,X0,tc_Message_Omsg),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
    | ~ spl0_623
    | ~ spl0_731 ),
    inference(duplicate_literal_removal,[],[f7029]) ).

fof(f7029,plain,
    ( ! [X0] :
        ( c_lessequals(c_inter(v_G,X0,tc_Message_Omsg),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
        | c_lessequals(c_inter(v_G,X0,tc_Message_Omsg),c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) )
    | ~ spl0_623
    | ~ spl0_731 ),
    inference(resolution,[],[f6892,f5318]) ).

fof(f6892,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X0,X2)
        | c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2)) )
    | ~ spl0_731 ),
    inference(avatar_component_clause,[],[f6891]) ).

fof(f7021,plain,
    ( spl0_759
    | ~ spl0_517
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f4622,f4609,f4219,f7019]) ).

fof(f7019,plain,
    ( spl0_759
  <=> ! [X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2),X2)
        | ~ c_in(X0,X3,X2)
        | ~ c_in(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).

fof(f4219,plain,
    ( spl0_517
  <=> ! [X12,X1,X18] :
        ( ~ c_in(X18,X12,X1)
        | c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f4622,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(X0,c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2),X2)
        | ~ c_in(X0,X3,X2)
        | ~ c_in(X0,X1,X2) )
    | ~ spl0_517
    | ~ spl0_565 ),
    inference(resolution,[],[f4610,f4220]) ).

fof(f4220,plain,
    ( ! [X18,X1,X12] :
        ( c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
        | ~ c_in(X18,X12,X1) )
    | ~ spl0_517 ),
    inference(avatar_component_clause,[],[f4219]) ).

fof(f7017,plain,
    ( spl0_758
    | ~ spl0_529
    | ~ spl0_558 ),
    inference(avatar_split_clause,[],[f4568,f4509,f4291,f7015]) ).

fof(f7015,plain,
    ( spl0_758
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Relation_ORange(X1,X2,X3),X3)
        | c_in(c_Main_ORangeE__1(X0,X1,X3,X2),c_Relation_ODomain(X1,X2,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).

fof(f4568,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_Relation_ORange(X1,X2,X3),X3)
        | c_in(c_Main_ORangeE__1(X0,X1,X3,X2),c_Relation_ODomain(X1,X2,X3),X2) )
    | ~ spl0_529
    | ~ spl0_558 ),
    inference(resolution,[],[f4510,f4292]) ).

fof(f7013,plain,
    ( spl0_757
    | ~ spl0_532
    | ~ spl0_557 ),
    inference(avatar_split_clause,[],[f4543,f4505,f4303,f7011]) ).

fof(f7011,plain,
    ( spl0_757
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Relation_ODomain(X1,X2,X3),X2)
        | c_in(c_Main_ODomainE__1(X0,X1,X2,X3),c_Relation_ORange(X1,X2,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f4543,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_Relation_ODomain(X1,X2,X3),X2)
        | c_in(c_Main_ODomainE__1(X0,X1,X2,X3),c_Relation_ORange(X1,X2,X3),X3) )
    | ~ spl0_532
    | ~ spl0_557 ),
    inference(resolution,[],[f4506,f4304]) ).

fof(f7009,plain,
    ( spl0_756
    | ~ spl0_376
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f4457,f4453,f3300,f7007]) ).

fof(f7007,plain,
    ( spl0_756
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X2,X0),c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X2)),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).

fof(f3300,plain,
    ( spl0_376
  <=> ! [X53,X55] :
        ( ~ c_in(X53,X55,tc_Message_Omsg)
        | c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f4453,plain,
    ( spl0_550
  <=> ! [X53,X55,X58] :
        ( c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X58)),c_Message_Oanalz(X55),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X58,X53),c_Message_Oanalz(X55),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f4457,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X2,X0),c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X2)),X1,tc_Message_Omsg) )
    | ~ spl0_376
    | ~ spl0_550 ),
    inference(resolution,[],[f4454,f3301]) ).

fof(f3301,plain,
    ( ! [X55,X53] :
        ( c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg)
        | ~ c_in(X53,X55,tc_Message_Omsg) )
    | ~ spl0_376 ),
    inference(avatar_component_clause,[],[f3300]) ).

fof(f4454,plain,
    ( ! [X58,X55,X53] :
        ( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X58)),c_Message_Oanalz(X55),tc_Message_Omsg)
        | c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X58,X53),c_Message_Oanalz(X55),tc_Message_Omsg) )
    | ~ spl0_550 ),
    inference(avatar_component_clause,[],[f4453]) ).

fof(f7005,plain,
    ( spl0_755
    | ~ spl0_462
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4179,f4097,f3802,f7003]) ).

fof(f7003,plain,
    ( spl0_755
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_inter(X1,X2,X3),X3)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,X3),X3)
        | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f3802,plain,
    ( spl0_462
  <=> ! [X20,X1,X19] :
        ( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f4179,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_inter(X1,X2,X3),X3)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,X3),X3)
        | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) )
    | ~ spl0_462
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3803]) ).

fof(f3803,plain,
    ( ! [X1,X19,X20] :
        ( c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1)) )
    | ~ spl0_462 ),
    inference(avatar_component_clause,[],[f3802]) ).

fof(f7001,plain,
    ( spl0_754
    | ~ spl0_463
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4178,f4097,f3806,f6999]) ).

fof(f6999,plain,
    ( spl0_754
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_inter(X1,X2,X3),X3)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,X3),X3)
        | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).

fof(f3806,plain,
    ( spl0_463
  <=> ! [X20,X1,X19] :
        ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f4178,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_inter(X1,X2,X3),X3)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,X3),X3)
        | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) )
    | ~ spl0_463
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3807]) ).

fof(f3807,plain,
    ( ! [X1,X19,X20] :
        ( c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1)) )
    | ~ spl0_463 ),
    inference(avatar_component_clause,[],[f3806]) ).

fof(f6997,plain,
    ( spl0_753
    | ~ spl0_461
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4177,f4097,f3798,f6995]) ).

fof(f6995,plain,
    ( spl0_753
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,c_insert(X1,X2,X3),X3)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,X3),X3)
        | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f3798,plain,
    ( spl0_461
  <=> ! [X12,X1,X18] :
        ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f4177,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,c_insert(X1,X2,X3),X3)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,X3),X3)
        | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) )
    | ~ spl0_461
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3799]) ).

fof(f3799,plain,
    ( ! [X18,X1,X12] :
        ( c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) )
    | ~ spl0_461 ),
    inference(avatar_component_clause,[],[f3798]) ).

fof(f6993,plain,
    ( spl0_752
    | ~ spl0_468
    | ~ spl0_507 ),
    inference(avatar_split_clause,[],[f4145,f4081,f3826,f6991]) ).

fof(f6991,plain,
    ( spl0_752
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | c_in(X3,c_SetInterval_OlessThan(X1,X2),X2)
        | ~ c_in(X3,c_SetInterval_OlessThan(X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f4145,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | c_in(X3,c_SetInterval_OlessThan(X1,X2),X2)
        | ~ c_in(X3,c_SetInterval_OlessThan(X0,X2),X2) )
    | ~ spl0_468
    | ~ spl0_507 ),
    inference(resolution,[],[f4082,f3827]) ).

fof(f6989,plain,
    ( spl0_751
    | ~ spl0_468
    | ~ spl0_505 ),
    inference(avatar_split_clause,[],[f4138,f4073,f3826,f6987]) ).

fof(f6987,plain,
    ( spl0_751
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | c_in(X3,c_SetInterval_OgreaterThan(X0,X2),X2)
        | ~ c_in(X3,c_SetInterval_OgreaterThan(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f4138,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Olinorder(X2)
        | c_in(X3,c_SetInterval_OgreaterThan(X0,X2),X2)
        | ~ c_in(X3,c_SetInterval_OgreaterThan(X1,X2),X2) )
    | ~ spl0_468
    | ~ spl0_505 ),
    inference(resolution,[],[f4074,f3827]) ).

fof(f6985,plain,
    ( spl0_750
    | ~ spl0_468
    | ~ spl0_501 ),
    inference(avatar_split_clause,[],[f4129,f4056,f3826,f6983]) ).

fof(f6983,plain,
    ( spl0_750
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_in(X3,c_SetInterval_OatMost(X1,X2),X2)
        | ~ c_in(X3,c_SetInterval_OatMost(X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f4129,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_in(X3,c_SetInterval_OatMost(X1,X2),X2)
        | ~ c_in(X3,c_SetInterval_OatMost(X0,X2),X2) )
    | ~ spl0_468
    | ~ spl0_501 ),
    inference(resolution,[],[f4057,f3827]) ).

fof(f6981,plain,
    ( spl0_749
    | ~ spl0_417
    | ~ spl0_717 ),
    inference(avatar_split_clause,[],[f6922,f6566,f3516,f6979]) ).

fof(f6979,plain,
    ( spl0_749
  <=> ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_H),tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(v_H_H),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f6566,plain,
    ( spl0_717
  <=> ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_H),tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_H_H)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f6922,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_H),tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(v_H_H),tc_Message_Omsg) )
    | ~ spl0_417
    | ~ spl0_717 ),
    inference(resolution,[],[f6567,f3517]) ).

fof(f6567,plain,
    ( ! [X0] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_H_H)),tc_Message_Omsg)
        | ~ c_in(X0,c_Message_Oanalz(v_H),tc_Message_Omsg) )
    | ~ spl0_717 ),
    inference(avatar_component_clause,[],[f6566]) ).

fof(f6977,plain,
    ( spl0_748
    | ~ spl0_468
    | ~ spl0_499 ),
    inference(avatar_split_clause,[],[f4122,f4048,f3826,f6975]) ).

fof(f6975,plain,
    ( spl0_748
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_in(X3,c_SetInterval_OatLeast(X0,X2),X2)
        | ~ c_in(X3,c_SetInterval_OatLeast(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f4122,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_in(X3,c_SetInterval_OatLeast(X0,X2),X2)
        | ~ c_in(X3,c_SetInterval_OatLeast(X1,X2),X2) )
    | ~ spl0_468
    | ~ spl0_499 ),
    inference(resolution,[],[f4049,f3827]) ).

fof(f6973,plain,
    ( spl0_747
    | ~ spl0_448
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f4008,f3930,f3668,f6971]) ).

fof(f6971,plain,
    ( spl0_747
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_Pow(X1,X2),X2),X2)
        | c_lessequals(c_Main_OUnionE__1(X0,c_Pow(X1,X2),X2),X1,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f4008,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Union(c_Pow(X1,X2),X2),X2)
        | c_lessequals(c_Main_OUnionE__1(X0,c_Pow(X1,X2),X2),X1,tc_set(X2)) )
    | ~ spl0_448
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f3669]) ).

fof(f6969,plain,
    ( spl0_746
    | ~ spl0_448
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3995,f3926,f3668,f6967]) ).

fof(f6967,plain,
    ( spl0_746
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_Pow(X1,X2),X2),X2)
        | c_lessequals(c_Main_OInterI__1(X0,c_Pow(X1,X2),X2),X1,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f3995,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Inter(c_Pow(X1,X2),X2),X2)
        | c_lessequals(c_Main_OInterI__1(X0,c_Pow(X1,X2),X2),X1,tc_set(X2)) )
    | ~ spl0_448
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f3669]) ).

fof(f6965,plain,
    ( spl0_745
    | ~ spl0_424
    | ~ spl0_444 ),
    inference(avatar_split_clause,[],[f3777,f3652,f3560,f6963]) ).

fof(f6963,plain,
    ( spl0_745
  <=> ! [X2,X0,X1] :
        ( ~ c_less(c_Main_OsubsetI__1(X0,c_SetInterval_OlessThan(X1,X2),X2),X1,X2)
        | ~ class_Orderings_Oord(X2)
        | c_lessequals(X0,c_SetInterval_OlessThan(X1,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f3777,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_less(c_Main_OsubsetI__1(X0,c_SetInterval_OlessThan(X1,X2),X2),X1,X2)
        | ~ class_Orderings_Oord(X2)
        | c_lessequals(X0,c_SetInterval_OlessThan(X1,X2),tc_set(X2)) )
    | ~ spl0_424
    | ~ spl0_444 ),
    inference(resolution,[],[f3653,f3561]) ).

fof(f6961,plain,
    ( spl0_744
    | ~ spl0_422
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f3775,f3640,f3551,f6959]) ).

fof(f6959,plain,
    ( spl0_744
  <=> ! [X2,X0,X1] :
        ( c_less(c_Main_OsubsetI__1(c_SetInterval_OlessThan(X0,X1),X2,X1),X0,X1)
        | ~ class_Orderings_Oord(X1)
        | c_lessequals(c_SetInterval_OlessThan(X0,X1),X2,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f3775,plain,
    ( ! [X2,X0,X1] :
        ( c_less(c_Main_OsubsetI__1(c_SetInterval_OlessThan(X0,X1),X2,X1),X0,X1)
        | ~ class_Orderings_Oord(X1)
        | c_lessequals(c_SetInterval_OlessThan(X0,X1),X2,tc_set(X1)) )
    | ~ spl0_422
    | ~ spl0_443 ),
    inference(resolution,[],[f3641,f3552]) ).

fof(f6957,plain,
    ( spl0_743
    | ~ spl0_424
    | ~ spl0_441 ),
    inference(avatar_split_clause,[],[f3772,f3632,f3560,f6955]) ).

fof(f6955,plain,
    ( spl0_743
  <=> ! [X2,X0,X1] :
        ( ~ c_less(X0,c_Main_OsubsetI__1(X1,c_SetInterval_OgreaterThan(X0,X2),X2),X2)
        | ~ class_Orderings_Oord(X2)
        | c_lessequals(X1,c_SetInterval_OgreaterThan(X0,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f3772,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_less(X0,c_Main_OsubsetI__1(X1,c_SetInterval_OgreaterThan(X0,X2),X2),X2)
        | ~ class_Orderings_Oord(X2)
        | c_lessequals(X1,c_SetInterval_OgreaterThan(X0,X2),tc_set(X2)) )
    | ~ spl0_424
    | ~ spl0_441 ),
    inference(resolution,[],[f3633,f3561]) ).

fof(f6953,plain,
    ( spl0_742
    | ~ spl0_422
    | ~ spl0_440 ),
    inference(avatar_split_clause,[],[f3770,f3628,f3551,f6951]) ).

fof(f6951,plain,
    ( spl0_742
  <=> ! [X2,X0,X1] :
        ( c_less(X0,c_Main_OsubsetI__1(c_SetInterval_OgreaterThan(X0,X1),X2,X1),X1)
        | ~ class_Orderings_Oord(X1)
        | c_lessequals(c_SetInterval_OgreaterThan(X0,X1),X2,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f3770,plain,
    ( ! [X2,X0,X1] :
        ( c_less(X0,c_Main_OsubsetI__1(c_SetInterval_OgreaterThan(X0,X1),X2,X1),X1)
        | ~ class_Orderings_Oord(X1)
        | c_lessequals(c_SetInterval_OgreaterThan(X0,X1),X2,tc_set(X1)) )
    | ~ spl0_422
    | ~ spl0_440 ),
    inference(resolution,[],[f3629,f3552]) ).

fof(f6949,plain,
    ( spl0_741
    | ~ spl0_424
    | ~ spl0_438 ),
    inference(avatar_split_clause,[],[f3767,f3620,f3560,f6947]) ).

fof(f6947,plain,
    ( spl0_741
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_Main_OsubsetI__1(X0,c_SetInterval_OatMost(X1,X2),X2),X1,X2)
        | ~ class_Orderings_Oord(X2)
        | c_lessequals(X0,c_SetInterval_OatMost(X1,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f3767,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_Main_OsubsetI__1(X0,c_SetInterval_OatMost(X1,X2),X2),X1,X2)
        | ~ class_Orderings_Oord(X2)
        | c_lessequals(X0,c_SetInterval_OatMost(X1,X2),tc_set(X2)) )
    | ~ spl0_424
    | ~ spl0_438 ),
    inference(resolution,[],[f3621,f3561]) ).

fof(f6945,plain,
    ( spl0_740
    | ~ spl0_422
    | ~ spl0_437 ),
    inference(avatar_split_clause,[],[f3765,f3616,f3551,f6943]) ).

fof(f6943,plain,
    ( spl0_740
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_Main_OsubsetI__1(c_SetInterval_OatMost(X0,X1),X2,X1),X0,X1)
        | ~ class_Orderings_Oord(X1)
        | c_lessequals(c_SetInterval_OatMost(X0,X1),X2,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f3765,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_Main_OsubsetI__1(c_SetInterval_OatMost(X0,X1),X2,X1),X0,X1)
        | ~ class_Orderings_Oord(X1)
        | c_lessequals(c_SetInterval_OatMost(X0,X1),X2,tc_set(X1)) )
    | ~ spl0_422
    | ~ spl0_437 ),
    inference(resolution,[],[f3617,f3552]) ).

fof(f6941,plain,
    ( spl0_739
    | ~ spl0_424
    | ~ spl0_435 ),
    inference(avatar_split_clause,[],[f3762,f3608,f3560,f6939]) ).

fof(f6939,plain,
    ( spl0_739
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Main_OsubsetI__1(X1,c_SetInterval_OatLeast(X0,X2),X2),X2)
        | ~ class_Orderings_Oord(X2)
        | c_lessequals(X1,c_SetInterval_OatLeast(X0,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f3762,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Main_OsubsetI__1(X1,c_SetInterval_OatLeast(X0,X2),X2),X2)
        | ~ class_Orderings_Oord(X2)
        | c_lessequals(X1,c_SetInterval_OatLeast(X0,X2),tc_set(X2)) )
    | ~ spl0_424
    | ~ spl0_435 ),
    inference(resolution,[],[f3609,f3561]) ).

fof(f6921,plain,
    ( spl0_738
    | ~ spl0_422
    | ~ spl0_434 ),
    inference(avatar_split_clause,[],[f3760,f3604,f3551,f6919]) ).

fof(f6919,plain,
    ( spl0_738
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,c_Main_OsubsetI__1(c_SetInterval_OatLeast(X0,X1),X2,X1),X1)
        | ~ class_Orderings_Oord(X1)
        | c_lessequals(c_SetInterval_OatLeast(X0,X1),X2,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f3760,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,c_Main_OsubsetI__1(c_SetInterval_OatLeast(X0,X1),X2,X1),X1)
        | ~ class_Orderings_Oord(X1)
        | c_lessequals(c_SetInterval_OatLeast(X0,X1),X2,tc_set(X1)) )
    | ~ spl0_422
    | ~ spl0_434 ),
    inference(resolution,[],[f3605,f3552]) ).

fof(f6917,plain,
    ( spl0_737
    | ~ spl0_413
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f3736,f3560,f3500,f6915]) ).

fof(f6915,plain,
    ( spl0_737
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f3736,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X2,X3) )
    | ~ spl0_413
    | ~ spl0_424 ),
    inference(resolution,[],[f3561,f3501]) ).

fof(f6913,plain,
    ( spl0_736
    | ~ spl0_415
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f3735,f3560,f3508,f6911]) ).

fof(f6911,plain,
    ( spl0_736
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f3735,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X1,X3) )
    | ~ spl0_415
    | ~ spl0_424 ),
    inference(resolution,[],[f3561,f3509]) ).

fof(f6909,plain,
    ( spl0_735
    | ~ spl0_410
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f3733,f3560,f3488,f6907]) ).

fof(f6907,plain,
    ( spl0_735
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,c_uminus(X1,tc_set(X2)),tc_set(X2))
        | c_in(c_Main_OsubsetI__1(X0,c_uminus(X1,tc_set(X2)),X2),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f3733,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,c_uminus(X1,tc_set(X2)),tc_set(X2))
        | c_in(c_Main_OsubsetI__1(X0,c_uminus(X1,tc_set(X2)),X2),X1,X2) )
    | ~ spl0_410
    | ~ spl0_424 ),
    inference(resolution,[],[f3561,f3489]) ).

fof(f6905,plain,
    ( spl0_734
    | ~ spl0_416
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f3732,f3560,f3512,f6903]) ).

fof(f6903,plain,
    ( spl0_734
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X0,c_insert(X1,X2,X3),tc_set(X3))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_insert(X1,X2,X3),X3),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f3732,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,c_insert(X1,X2,X3),tc_set(X3))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_insert(X1,X2,X3),X3),X2,X3) )
    | ~ spl0_416
    | ~ spl0_424 ),
    inference(resolution,[],[f3561,f3513]) ).

fof(f6901,plain,
    ( spl0_733
    | ~ spl0_409
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f3726,f3551,f3484,f6899]) ).

fof(f6899,plain,
    ( spl0_733
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_uminus(X0,tc_set(X1)),X2,tc_set(X1))
        | ~ c_in(c_Main_OsubsetI__1(c_uminus(X0,tc_set(X1)),X2,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f3726,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_uminus(X0,tc_set(X1)),X2,tc_set(X1))
        | ~ c_in(c_Main_OsubsetI__1(c_uminus(X0,tc_set(X1)),X2,X1),X0,X1) )
    | ~ spl0_409
    | ~ spl0_422 ),
    inference(resolution,[],[f3552,f3485]) ).

fof(f6897,plain,
    ( spl0_732
    | ~ spl0_411
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f3725,f3551,f3492,f6895]) ).

fof(f3725,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2))
        | c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X1,X2) )
    | ~ spl0_411
    | ~ spl0_422 ),
    inference(resolution,[],[f3552,f3493]) ).

fof(f6893,plain,
    ( spl0_731
    | ~ spl0_412
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f3724,f3551,f3496,f6891]) ).

fof(f3724,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2))
        | c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X0,X2) )
    | ~ spl0_412
    | ~ spl0_422 ),
    inference(resolution,[],[f3552,f3497]) ).

fof(f6796,plain,
    ( spl0_730
    | ~ spl0_492
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f4704,f4654,f3962,f6794]) ).

fof(f6794,plain,
    ( spl0_730
  <=> ! [X0,X1] :
        ( ~ c_in(X0,c_Relation_OImage(c_Wellfounded__Relations_Oless__than,X1,tc_nat,tc_nat),tc_nat)
        | c_less(c_Main_OImageE__1(X1,X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f4704,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,c_Relation_OImage(c_Wellfounded__Relations_Oless__than,X1,tc_nat,tc_nat),tc_nat)
        | c_less(c_Main_OImageE__1(X1,X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),X0,tc_nat) )
    | ~ spl0_492
    | ~ spl0_569 ),
    inference(resolution,[],[f4655,f3963]) ).

fof(f6792,plain,
    ( spl0_729
    | ~ spl0_377
    | ~ spl0_546 ),
    inference(avatar_split_clause,[],[f4436,f4422,f3304,f6790]) ).

fof(f6790,plain,
    ( spl0_729
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
        | c_in(X0,c_Message_Oparts(X2),tc_Message_Omsg)
        | ~ c_in(X0,c_union(X2,X1,tc_Message_Omsg),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f3304,plain,
    ( spl0_377
  <=> ! [X53,X55] :
        ( ~ c_in(X53,X55,tc_Message_Omsg)
        | c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f4422,plain,
    ( spl0_546
  <=> ! [X20,X55,X4] :
        ( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
        | c_in(X4,c_Message_Oparts(X55),tc_Message_Omsg)
        | ~ c_in(X4,c_Message_Oparts(c_union(X20,X55,tc_Message_Omsg)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f4436,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
        | c_in(X0,c_Message_Oparts(X2),tc_Message_Omsg)
        | ~ c_in(X0,c_union(X2,X1,tc_Message_Omsg),tc_Message_Omsg) )
    | ~ spl0_377
    | ~ spl0_546 ),
    inference(resolution,[],[f4423,f3305]) ).

fof(f3305,plain,
    ( ! [X55,X53] :
        ( c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg)
        | ~ c_in(X53,X55,tc_Message_Omsg) )
    | ~ spl0_377 ),
    inference(avatar_component_clause,[],[f3304]) ).

fof(f4423,plain,
    ( ! [X55,X4,X20] :
        ( ~ c_in(X4,c_Message_Oparts(c_union(X20,X55,tc_Message_Omsg)),tc_Message_Omsg)
        | c_in(X4,c_Message_Oparts(X55),tc_Message_Omsg)
        | c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg) )
    | ~ spl0_546 ),
    inference(avatar_component_clause,[],[f4422]) ).

fof(f6788,plain,
    ( spl0_728
    | ~ spl0_417
    | ~ spl0_708 ),
    inference(avatar_split_clause,[],[f6715,f6508,f3516,f6786]) ).

fof(f6786,plain,
    ( spl0_728
  <=> ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_G),tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f6508,plain,
    ( spl0_708
  <=> ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_G),tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_G_H)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f6715,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_G),tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg) )
    | ~ spl0_417
    | ~ spl0_708 ),
    inference(resolution,[],[f6509,f3517]) ).

fof(f6509,plain,
    ( ! [X0] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(X0,c_Message_Oanalz(v_G),tc_Message_Omsg) )
    | ~ spl0_708 ),
    inference(avatar_component_clause,[],[f6508]) ).

fof(f6784,plain,
    ( spl0_727
    | ~ spl0_457
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4208,f4109,f3712,f6782]) ).

fof(f3712,plain,
    ( spl0_457
  <=> ! [X20,X55] :
        ( ~ c_lessequals(X20,X55,tc_set(tc_Message_Omsg))
        | c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X55),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f4208,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
        | c_lessequals(X0,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(X1,X2,tc_set(tc_Message_Omsg)) )
    | ~ spl0_457
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f3713]) ).

fof(f3713,plain,
    ( ! [X55,X20] :
        ( c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X55),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(X20,X55,tc_set(tc_Message_Omsg)) )
    | ~ spl0_457 ),
    inference(avatar_component_clause,[],[f3712]) ).

fof(f6780,plain,
    ( spl0_726
    | ~ spl0_449
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4171,f4097,f3672,f6778]) ).

fof(f6778,plain,
    ( spl0_726
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_Pow(X3,X2),X2),X2)
        | ~ c_lessequals(X1,X3,tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f4171,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_Pow(X3,X2),X2),X2)
        | ~ c_lessequals(X1,X3,tc_set(X2)) )
    | ~ spl0_449
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3673]) ).

fof(f6776,plain,
    ( spl0_725
    | ~ spl0_457
    | ~ spl0_469 ),
    inference(avatar_split_clause,[],[f3894,f3830,f3712,f6774]) ).

fof(f6774,plain,
    ( spl0_725
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_Message_Oanalz(X0),c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
        | c_Message_Oanalz(X1) = c_Message_Oanalz(X0)
        | ~ c_lessequals(X1,X0,tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f3894,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_Message_Oanalz(X0),c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
        | c_Message_Oanalz(X1) = c_Message_Oanalz(X0)
        | ~ c_lessequals(X1,X0,tc_set(tc_Message_Omsg)) )
    | ~ spl0_457
    | ~ spl0_469 ),
    inference(resolution,[],[f3831,f3713]) ).

fof(f6772,plain,
    ( spl0_724
    | ~ spl0_457
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f3874,f3818,f3712,f6770]) ).

fof(f6770,plain,
    ( spl0_724
  <=> ! [X0,X1] :
        ( c_Message_Oanalz(X1) = c_Message_Oanalz(X0)
        | c_less(c_Message_Oanalz(X0),c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(X0,X1,tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f3874,plain,
    ( ! [X0,X1] :
        ( c_Message_Oanalz(X1) = c_Message_Oanalz(X0)
        | c_less(c_Message_Oanalz(X0),c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(X0,X1,tc_set(tc_Message_Omsg)) )
    | ~ spl0_457
    | ~ spl0_466 ),
    inference(resolution,[],[f3819,f3713]) ).

fof(f6768,plain,
    ( spl0_723
    | ~ spl0_418
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f3730,f3551,f3520,f6766]) ).

fof(f6766,plain,
    ( spl0_723
  <=> ! [X0,X1] :
        ( c_lessequals(c_Message_Oparts(c_Message_Oparts(X0)),X1,tc_set(tc_Message_Omsg))
        | c_in(c_Main_OsubsetI__1(c_Message_Oparts(c_Message_Oparts(X0)),X1,tc_Message_Omsg),c_Message_Oparts(X0),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f3520,plain,
    ( spl0_418
  <=> ! [X53,X55] :
        ( c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg)
        | ~ c_in(X53,c_Message_Oparts(c_Message_Oparts(X55)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f3730,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_Message_Oparts(c_Message_Oparts(X0)),X1,tc_set(tc_Message_Omsg))
        | c_in(c_Main_OsubsetI__1(c_Message_Oparts(c_Message_Oparts(X0)),X1,tc_Message_Omsg),c_Message_Oparts(X0),tc_Message_Omsg) )
    | ~ spl0_418
    | ~ spl0_422 ),
    inference(resolution,[],[f3552,f3521]) ).

fof(f3521,plain,
    ( ! [X55,X53] :
        ( ~ c_in(X53,c_Message_Oparts(c_Message_Oparts(X55)),tc_Message_Omsg)
        | c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg) )
    | ~ spl0_418 ),
    inference(avatar_component_clause,[],[f3520]) ).

fof(f6764,plain,
    ( spl0_722
    | ~ spl0_417
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f3728,f3551,f3516,f6762]) ).

fof(f6762,plain,
    ( spl0_722
  <=> ! [X0,X1] :
        ( c_lessequals(c_Message_Oanalz(c_Message_Oanalz(X0)),X1,tc_set(tc_Message_Omsg))
        | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(X0)),X1,tc_Message_Omsg),c_Message_Oanalz(X0),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f3728,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_Message_Oanalz(c_Message_Oanalz(X0)),X1,tc_set(tc_Message_Omsg))
        | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(X0)),X1,tc_Message_Omsg),c_Message_Oanalz(X0),tc_Message_Omsg) )
    | ~ spl0_417
    | ~ spl0_422 ),
    inference(resolution,[],[f3552,f3517]) ).

fof(f6760,plain,
    ( spl0_721
    | ~ spl0_406
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f3727,f3551,f3472,f6758]) ).

fof(f6758,plain,
    ( spl0_721
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_Datatype_Oo2s(X0,X1),X2,tc_set(X1))
        | c_Datatype_Ooption_OSome(c_Main_OsubsetI__1(c_Datatype_Oo2s(X0,X1),X2,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f3727,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_Datatype_Oo2s(X0,X1),X2,tc_set(X1))
        | c_Datatype_Ooption_OSome(c_Main_OsubsetI__1(c_Datatype_Oo2s(X0,X1),X2,X1),X1) = X0 )
    | ~ spl0_406
    | ~ spl0_422 ),
    inference(resolution,[],[f3552,f3473]) ).

fof(f6756,plain,
    ( spl0_720
    | ~ spl0_380
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f3723,f3551,f3332,f6754]) ).

fof(f6754,plain,
    ( spl0_720
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_insert(X0,c_emptyset,X1),X2,tc_set(X1))
        | c_Main_OsubsetI__1(c_insert(X0,c_emptyset,X1),X2,X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f3723,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_insert(X0,c_emptyset,X1),X2,tc_set(X1))
        | c_Main_OsubsetI__1(c_insert(X0,c_emptyset,X1),X2,X1) = X0 )
    | ~ spl0_380
    | ~ spl0_422 ),
    inference(resolution,[],[f3552,f3333]) ).

fof(f6576,plain,
    ( spl0_719
    | ~ spl0_282
    | ~ spl0_605 ),
    inference(avatar_split_clause,[],[f5126,f5087,f2575,f6574]) ).

fof(f6574,plain,
    ( spl0_719
  <=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Datatype__Universe_Odprod(c_emptyset,X1,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f2575,plain,
    ( spl0_282
  <=> ! [X18,X1] : ~ c_in(X18,c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f5087,plain,
    ( spl0_605
  <=> ! [X5,X4,X6,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__3(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f5126,plain,
    ( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Datatype__Universe_Odprod(c_emptyset,X1,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ spl0_282
    | ~ spl0_605 ),
    inference(resolution,[],[f5088,f2576]) ).

fof(f2576,plain,
    ( ! [X18,X1] : ~ c_in(X18,c_emptyset,X1)
    | ~ spl0_282 ),
    inference(avatar_component_clause,[],[f2575]) ).

fof(f5088,plain,
    ( ! [X2,X1,X6,X4,X5] :
        ( c_in(c_Pair(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__3(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) )
    | ~ spl0_605 ),
    inference(avatar_component_clause,[],[f5087]) ).

fof(f6572,plain,
    ( spl0_718
    | ~ spl0_282
    | ~ spl0_604 ),
    inference(avatar_split_clause,[],[f5097,f5083,f2575,f6570]) ).

fof(f6570,plain,
    ( spl0_718
  <=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Datatype__Universe_Odprod(X1,c_emptyset,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f5083,plain,
    ( spl0_604
  <=> ! [X5,X4,X6,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Main_OdprodE__2(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f5097,plain,
    ( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Datatype__Universe_Odprod(X1,c_emptyset,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ spl0_282
    | ~ spl0_604 ),
    inference(resolution,[],[f5084,f2576]) ).

fof(f5084,plain,
    ( ! [X2,X1,X6,X4,X5] :
        ( c_in(c_Pair(c_Main_OdprodE__2(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) )
    | ~ spl0_604 ),
    inference(avatar_component_clause,[],[f5083]) ).

fof(f6568,plain,
    ( spl0_717
    | ~ spl0_2
    | ~ spl0_700 ),
    inference(avatar_split_clause,[],[f6438,f6388,f1400,f6566]) ).

fof(f6388,plain,
    ( spl0_700
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(X0,c_Message_Oanalz(X2),tc_Message_Omsg)
        | ~ c_lessequals(X2,X1,tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f6438,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_H),tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_H_H)),tc_Message_Omsg) )
    | ~ spl0_2
    | ~ spl0_700 ),
    inference(resolution,[],[f6389,f1402]) ).

fof(f6389,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X2,X1,tc_set(tc_Message_Omsg))
        | ~ c_in(X0,c_Message_Oanalz(X2),tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg) )
    | ~ spl0_700 ),
    inference(avatar_component_clause,[],[f6388]) ).

fof(f6564,plain,
    ( spl0_716
    | ~ spl0_476
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f4703,f4654,f3858,f6562]) ).

fof(f6562,plain,
    ( spl0_716
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Relation_OImage(c_Relation_OId,X1,X2,X2),X2)
        | c_Main_OImageE__1(X1,X0,c_Relation_OId,X2,X2) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f4703,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Relation_OImage(c_Relation_OId,X1,X2,X2),X2)
        | c_Main_OImageE__1(X1,X0,c_Relation_OId,X2,X2) = X0 )
    | ~ spl0_476
    | ~ spl0_569 ),
    inference(resolution,[],[f4655,f3859]) ).

fof(f6560,plain,
    ( spl0_715
    | ~ spl0_493
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f4623,f4609,f3966,f6558]) ).

fof(f6558,plain,
    ( spl0_715
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Relation_OImage(c_Wellfounded__Relations_Oless__than,X1,tc_nat,tc_nat),tc_nat)
        | ~ c_in(X2,X1,tc_nat)
        | ~ c_less(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f3966,plain,
    ( spl0_493
  <=> ! [X0,X3] :
        ( ~ c_less(X0,X3,tc_nat)
        | c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f4623,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Relation_OImage(c_Wellfounded__Relations_Oless__than,X1,tc_nat,tc_nat),tc_nat)
        | ~ c_in(X2,X1,tc_nat)
        | ~ c_less(X2,X0,tc_nat) )
    | ~ spl0_493
    | ~ spl0_565 ),
    inference(resolution,[],[f4610,f3967]) ).

fof(f3967,plain,
    ( ! [X3,X0] :
        ( c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
        | ~ c_less(X0,X3,tc_nat) )
    | ~ spl0_493 ),
    inference(avatar_component_clause,[],[f3966]) ).

fof(f6556,plain,
    ( spl0_714
    | ~ spl0_318
    | ~ spl0_537 ),
    inference(avatar_split_clause,[],[f4392,f4323,f3029,f6554]) ).

fof(f6554,plain,
    ( spl0_714
  <=> ! [X0,X1] :
        ( ~ c_Divides_Oop_Advd(c_0,X0,tc_nat)
        | ~ c_Divides_Oop_Advd(c_0,X1,tc_nat)
        | c_0 = c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f3029,plain,
    ( spl0_318
  <=> ! [X15] :
        ( c_0 = X15
        | ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f4323,plain,
    ( spl0_537
  <=> ! [X21,X16,X15] :
        ( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
        | ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
        | c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f4392,plain,
    ( ! [X0,X1] :
        ( ~ c_Divides_Oop_Advd(c_0,X0,tc_nat)
        | ~ c_Divides_Oop_Advd(c_0,X1,tc_nat)
        | c_0 = c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)) )
    | ~ spl0_318
    | ~ spl0_537 ),
    inference(resolution,[],[f4324,f3030]) ).

fof(f3030,plain,
    ( ! [X15] :
        ( ~ c_Divides_Oop_Advd(c_0,X15,tc_nat)
        | c_0 = X15 )
    | ~ spl0_318 ),
    inference(avatar_component_clause,[],[f3029]) ).

fof(f4324,plain,
    ( ! [X21,X16,X15] :
        ( c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat)
        | ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
        | ~ c_Divides_Oop_Advd(X16,X21,tc_nat) )
    | ~ spl0_537 ),
    inference(avatar_component_clause,[],[f4323]) ).

fof(f6552,plain,
    ( spl0_713
    | ~ spl0_325
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4373,f4303,f3057,f6550]) ).

fof(f6550,plain,
    ( spl0_713
  <=> ! [X4,X0,X3,X2,X1] : c_in(X0,c_Relation_ORange(c_insert(c_Pair(X1,X0,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f4373,plain,
    ( ! [X2,X3,X0,X1,X4] : c_in(X0,c_Relation_ORange(c_insert(c_Pair(X1,X0,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X3)
    | ~ spl0_325
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f3058]) ).

fof(f6548,plain,
    ( spl0_712
    | ~ spl0_325
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4349,f4291,f3057,f6546]) ).

fof(f6546,plain,
    ( spl0_712
  <=> ! [X4,X0,X3,X2,X1] : c_in(X0,c_Relation_ODomain(c_insert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f4349,plain,
    ( ! [X2,X3,X0,X1,X4] : c_in(X0,c_Relation_ODomain(c_insert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X2)
    | ~ spl0_325
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f3058]) ).

fof(f6544,plain,
    ( spl0_711
    | ~ spl0_340
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4170,f4097,f3133,f6542]) ).

fof(f6542,plain,
    ( spl0_711
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,tc_set(X2)),tc_set(X2)),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f4170,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,tc_set(X2)),tc_set(X2)),X2),X2) )
    | ~ spl0_340
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3134]) ).

fof(f6540,plain,
    ( spl0_710
    | ~ spl0_377
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3984,f3918,f3304,f6538]) ).

fof(f6538,plain,
    ( spl0_710
  <=> ! [X0,X1] :
        ( c_in(X0,c_List_Olists(c_Message_Oparts(X1),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg))
        | ~ c_in(c_Main_Oin__listsI__1(c_Message_Oparts(X1),X0,tc_Message_Omsg),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f3984,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_List_Olists(c_Message_Oparts(X1),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg))
        | ~ c_in(c_Main_Oin__listsI__1(c_Message_Oparts(X1),X0,tc_Message_Omsg),X1,tc_Message_Omsg) )
    | ~ spl0_377
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3305]) ).

fof(f6536,plain,
    ( spl0_709
    | ~ spl0_376
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3982,f3918,f3300,f6534]) ).

fof(f6534,plain,
    ( spl0_709
  <=> ! [X0,X1] :
        ( c_in(X0,c_List_Olists(c_Message_Oanalz(X1),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg))
        | ~ c_in(c_Main_Oin__listsI__1(c_Message_Oanalz(X1),X0,tc_Message_Omsg),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f3982,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_List_Olists(c_Message_Oanalz(X1),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg))
        | ~ c_in(c_Main_Oin__listsI__1(c_Message_Oanalz(X1),X0,tc_Message_Omsg),X1,tc_Message_Omsg) )
    | ~ spl0_376
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f3301]) ).

fof(f6510,plain,
    ( spl0_708
    | ~ spl0_1
    | ~ spl0_700 ),
    inference(avatar_split_clause,[],[f6437,f6388,f1395,f6508]) ).

fof(f6437,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Message_Oanalz(v_G),tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_G_H)),tc_Message_Omsg) )
    | ~ spl0_1
    | ~ spl0_700 ),
    inference(resolution,[],[f6389,f1397]) ).

fof(f6418,plain,
    ( spl0_707
    | ~ spl0_532
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f4706,f4654,f4303,f6416]) ).

fof(f6416,plain,
    ( spl0_707
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
        | c_in(X0,c_Relation_ORange(X1,X3,X4),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f4706,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
        | c_in(X0,c_Relation_ORange(X1,X3,X4),X4) )
    | ~ spl0_532
    | ~ spl0_569 ),
    inference(resolution,[],[f4655,f4304]) ).

fof(f6414,plain,
    ( spl0_706
    | ~ spl0_492
    | ~ spl0_558 ),
    inference(avatar_split_clause,[],[f4566,f4509,f3962,f6412]) ).

fof(f6412,plain,
    ( spl0_706
  <=> ! [X0] :
        ( ~ c_in(X0,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
        | c_less(c_Main_ORangeE__1(X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f4566,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
        | c_less(c_Main_ORangeE__1(X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),X0,tc_nat) )
    | ~ spl0_492
    | ~ spl0_558 ),
    inference(resolution,[],[f4510,f3963]) ).

fof(f6410,plain,
    ( spl0_705
    | ~ spl0_492
    | ~ spl0_557 ),
    inference(avatar_split_clause,[],[f4542,f4505,f3962,f6408]) ).

fof(f6408,plain,
    ( spl0_705
  <=> ! [X0] :
        ( ~ c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
        | c_less(X0,c_Main_ODomainE__1(X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f4542,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
        | c_less(X0,c_Main_ODomainE__1(X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat) )
    | ~ spl0_492
    | ~ spl0_557 ),
    inference(resolution,[],[f4506,f3963]) ).

fof(f6406,plain,
    ( spl0_704
    | ~ spl0_305
    | ~ spl0_545 ),
    inference(avatar_split_clause,[],[f4433,f4418,f2976,f6404]) ).

fof(f6404,plain,
    ( spl0_704
  <=> ! [X0,X3,X2,X1] :
        ( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) != c_append(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
        | X0 = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f2976,plain,
    ( spl0_305
  <=> ! [X25,X1] : c_append(c_List_Olist_ONil,X25,X1) = X25 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f4418,plain,
    ( spl0_545
  <=> ! [X23,X0,X3,X25,X1] :
        ( X0 = X3
        | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f4433,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) != c_append(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
        | X0 = X3 )
    | ~ spl0_305
    | ~ spl0_545 ),
    inference(superposition,[],[f4419,f2977]) ).

fof(f2977,plain,
    ( ! [X1,X25] : c_append(c_List_Olist_ONil,X25,X1) = X25
    | ~ spl0_305 ),
    inference(avatar_component_clause,[],[f2976]) ).

fof(f4419,plain,
    ( ! [X3,X0,X1,X25,X23] :
        ( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
        | X0 = X3 )
    | ~ spl0_545 ),
    inference(avatar_component_clause,[],[f4418]) ).

fof(f6402,plain,
    ( spl0_703
    | ~ spl0_305
    | ~ spl0_543 ),
    inference(avatar_split_clause,[],[f4430,f4409,f2976,f6400]) ).

fof(f6400,plain,
    ( spl0_703
  <=> ! [X0,X3,X2,X1] :
        ( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) != c_append(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
        | c_List_Olist_ONil = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f4409,plain,
    ( spl0_543
  <=> ! [X3,X0,X23,X25,X1] :
        ( X23 = X25
        | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f4430,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) != c_append(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
        | c_List_Olist_ONil = X2 )
    | ~ spl0_305
    | ~ spl0_543 ),
    inference(superposition,[],[f4410,f2977]) ).

fof(f4410,plain,
    ( ! [X3,X0,X1,X25,X23] :
        ( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
        | X23 = X25 )
    | ~ spl0_543 ),
    inference(avatar_component_clause,[],[f4409]) ).

fof(f6398,plain,
    ( spl0_702
    | ~ spl0_478
    | ~ spl0_644 ),
    inference(avatar_split_clause,[],[f5784,f5616,f3898,f6396]) ).

fof(f6396,plain,
    ( spl0_702
  <=> ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X1,X0),v_G,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f3898,plain,
    ( spl0_478
  <=> ! [X0] :
        ( c_in(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg)
        | ~ c_in(X0,v_G,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f5616,plain,
    ( spl0_644
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X2,X0),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f5784,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X1,X0),v_G,tc_Message_Omsg) )
    | ~ spl0_478
    | ~ spl0_644 ),
    inference(resolution,[],[f5617,f3899]) ).

fof(f3899,plain,
    ( ! [X0] :
        ( c_in(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg)
        | ~ c_in(X0,v_G,tc_Message_Omsg) )
    | ~ spl0_478 ),
    inference(avatar_component_clause,[],[f3898]) ).

fof(f5617,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(c_Message_Omsg_OCrypt(X2,X0),X1,tc_Message_Omsg)
        | c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg) )
    | ~ spl0_644 ),
    inference(avatar_component_clause,[],[f5616]) ).

fof(f6394,plain,
    ( spl0_701
    | ~ spl0_494
    | ~ spl0_517 ),
    inference(avatar_split_clause,[],[f4254,f4219,f4028,f6392]) ).

fof(f6392,plain,
    ( spl0_701
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(c_Main_OdiagE__1(X1,c_Pair(X0,X0,X2,X2),X2),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f4254,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(c_Main_OdiagE__1(X1,c_Pair(X0,X0,X2,X2),X2),X1,X2) )
    | ~ spl0_494
    | ~ spl0_517 ),
    inference(resolution,[],[f4220,f4029]) ).

fof(f6390,plain,
    ( spl0_700
    | ~ spl0_457
    | ~ spl0_468 ),
    inference(avatar_split_clause,[],[f3884,f3826,f3712,f6388]) ).

fof(f3884,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(X0,c_Message_Oanalz(X2),tc_Message_Omsg)
        | ~ c_lessequals(X2,X1,tc_set(tc_Message_Omsg)) )
    | ~ spl0_457
    | ~ spl0_468 ),
    inference(resolution,[],[f3827,f3713]) ).

fof(f6226,plain,
    ( spl0_699
    | ~ spl0_425
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f4621,f4609,f3564,f6224]) ).

fof(f6224,plain,
    ( spl0_699
  <=> ! [X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2,X2),X2)
        | ~ c_in(X0,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f3564,plain,
    ( spl0_425
  <=> ! [X18,X5,X1] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f4621,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2,X2),X2)
        | ~ c_in(X0,X3,X2) )
    | ~ spl0_425
    | ~ spl0_565 ),
    inference(resolution,[],[f4610,f3565]) ).

fof(f3565,plain,
    ( ! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1))
    | ~ spl0_425 ),
    inference(avatar_component_clause,[],[f3564]) ).

fof(f6222,plain,
    ( spl0_698
    | ~ spl0_476
    | ~ spl0_558 ),
    inference(avatar_split_clause,[],[f4565,f4509,f3858,f6220]) ).

fof(f6220,plain,
    ( spl0_698
  <=> ! [X0,X1] :
        ( ~ c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1)
        | c_Main_ORangeE__1(X0,c_Relation_OId,X1,X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f4565,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1)
        | c_Main_ORangeE__1(X0,c_Relation_OId,X1,X1) = X0 )
    | ~ spl0_476
    | ~ spl0_558 ),
    inference(resolution,[],[f4510,f3859]) ).

fof(f6218,plain,
    ( spl0_697
    | ~ spl0_476
    | ~ spl0_557 ),
    inference(avatar_split_clause,[],[f4541,f4505,f3858,f6216]) ).

fof(f6216,plain,
    ( spl0_697
  <=> ! [X0,X1] :
        ( ~ c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1)
        | c_Main_ODomainE__1(X0,c_Relation_OId,X1,X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f4541,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1)
        | c_Main_ODomainE__1(X0,c_Relation_OId,X1,X1) = X0 )
    | ~ spl0_476
    | ~ spl0_557 ),
    inference(resolution,[],[f4506,f3859]) ).

fof(f6214,plain,
    ( spl0_696
    | ~ spl0_485
    | ~ spl0_643 ),
    inference(avatar_split_clause,[],[f5755,f5612,f3934,f6212]) ).

fof(f6212,plain,
    ( spl0_696
  <=> ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_H_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_H,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f3934,plain,
    ( spl0_485
  <=> ! [X0] :
        ( c_in(X0,c_Message_Oanalz(v_H_H),tc_Message_Omsg)
        | ~ c_in(X0,v_H,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f5612,plain,
    ( spl0_643
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X2),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f5755,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_H_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_H,tc_Message_Omsg) )
    | ~ spl0_485
    | ~ spl0_643 ),
    inference(resolution,[],[f5613,f3935]) ).

fof(f3935,plain,
    ( ! [X0] :
        ( c_in(X0,c_Message_Oanalz(v_H_H),tc_Message_Omsg)
        | ~ c_in(X0,v_H,tc_Message_Omsg) )
    | ~ spl0_485 ),
    inference(avatar_component_clause,[],[f3934]) ).

fof(f5613,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X2),X1,tc_Message_Omsg)
        | c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg) )
    | ~ spl0_643 ),
    inference(avatar_component_clause,[],[f5612]) ).

fof(f6210,plain,
    ( spl0_695
    | ~ spl0_325
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4162,f4097,f3057,f6208]) ).

fof(f6208,plain,
    ( spl0_695
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_insert(X1,X3,tc_set(X2)),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f4162,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_insert(X1,X3,tc_set(X2)),X2),X2) )
    | ~ spl0_325
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3058]) ).

fof(f6206,plain,
    ( spl0_694
    | ~ spl0_322
    | ~ spl0_497 ),
    inference(avatar_split_clause,[],[f4115,f4040,f3045,f6204]) ).

fof(f6204,plain,
    ( spl0_694
  <=> ! [X0,X1] :
        ( c_less(c_0,X0,tc_nat)
        | c_less(c_0,X1,tc_nat)
        | c_0 = c_plus(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f3045,plain,
    ( spl0_322
  <=> ! [X21] :
        ( c_0 = X21
        | c_less(c_0,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f4040,plain,
    ( spl0_497
  <=> ! [X21,X15] :
        ( c_less(c_0,X15,tc_nat)
        | c_less(c_0,X21,tc_nat)
        | ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f4115,plain,
    ( ! [X0,X1] :
        ( c_less(c_0,X0,tc_nat)
        | c_less(c_0,X1,tc_nat)
        | c_0 = c_plus(X1,X0,tc_nat) )
    | ~ spl0_322
    | ~ spl0_497 ),
    inference(resolution,[],[f4041,f3046]) ).

fof(f3046,plain,
    ( ! [X21] :
        ( c_less(c_0,X21,tc_nat)
        | c_0 = X21 )
    | ~ spl0_322 ),
    inference(avatar_component_clause,[],[f3045]) ).

fof(f4041,plain,
    ( ! [X21,X15] :
        ( ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat)
        | c_less(c_0,X21,tc_nat)
        | c_less(c_0,X15,tc_nat) )
    | ~ spl0_497 ),
    inference(avatar_component_clause,[],[f4040]) ).

fof(f6202,plain,
    ( spl0_693
    | ~ spl0_357
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f3907,f3854,f3220,f6200]) ).

fof(f6200,plain,
    ( spl0_693
  <=> ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X0,c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),tc_nat,tc_nat)),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f3220,plain,
    ( spl0_357
  <=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f3854,plain,
    ( spl0_475
  <=> ! [X21,X16,X15] :
        ( c_Divides_Oop_Advd(X16,X21,tc_nat)
        | ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f3907,plain,
    ( ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X0,c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),tc_nat,tc_nat)),X2,tc_nat)
    | ~ spl0_357
    | ~ spl0_475 ),
    inference(resolution,[],[f3855,f3221]) ).

fof(f3221,plain,
    ( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat)
    | ~ spl0_357 ),
    inference(avatar_component_clause,[],[f3220]) ).

fof(f3855,plain,
    ( ! [X21,X16,X15] :
        ( ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat)
        | c_Divides_Oop_Advd(X16,X21,tc_nat) )
    | ~ spl0_475 ),
    inference(avatar_component_clause,[],[f3854]) ).

fof(f6198,plain,
    ( spl0_692
    | ~ spl0_356
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f3906,f3854,f3216,f6196]) ).

fof(f6196,plain,
    ( spl0_692
  <=> ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)),X2,tc_nat,tc_nat)),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f3216,plain,
    ( spl0_356
  <=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f3906,plain,
    ( ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)),X2,tc_nat,tc_nat)),X1,tc_nat)
    | ~ spl0_356
    | ~ spl0_475 ),
    inference(resolution,[],[f3855,f3217]) ).

fof(f3217,plain,
    ( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat)
    | ~ spl0_356 ),
    inference(avatar_component_clause,[],[f3216]) ).

fof(f6194,plain,
    ( spl0_691
    | ~ spl0_357
    | ~ spl0_474 ),
    inference(avatar_split_clause,[],[f3904,f3850,f3220,f6192]) ).

fof(f6192,plain,
    ( spl0_691
  <=> ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X0,c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),tc_nat,tc_nat)),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f3850,plain,
    ( spl0_474
  <=> ! [X16,X21,X15] :
        ( c_Divides_Oop_Advd(X16,X15,tc_nat)
        | ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f3904,plain,
    ( ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X0,c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),tc_nat,tc_nat)),X1,tc_nat)
    | ~ spl0_357
    | ~ spl0_474 ),
    inference(resolution,[],[f3851,f3221]) ).

fof(f3851,plain,
    ( ! [X21,X16,X15] :
        ( ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat)
        | c_Divides_Oop_Advd(X16,X15,tc_nat) )
    | ~ spl0_474 ),
    inference(avatar_component_clause,[],[f3850]) ).

fof(f6190,plain,
    ( spl0_690
    | ~ spl0_356
    | ~ spl0_474 ),
    inference(avatar_split_clause,[],[f3903,f3850,f3216,f6188]) ).

fof(f6188,plain,
    ( spl0_690
  <=> ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)),X2,tc_nat,tc_nat)),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f3903,plain,
    ( ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)),X2,tc_nat,tc_nat)),X0,tc_nat)
    | ~ spl0_356
    | ~ spl0_474 ),
    inference(resolution,[],[f3851,f3217]) ).

fof(f6186,plain,
    ( spl0_689
    | ~ spl0_354
    | ~ spl0_469 ),
    inference(avatar_split_clause,[],[f3891,f3830,f3189,f6184]) ).

fof(f6184,plain,
    ( spl0_689
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_union(X0,X1,X2),X1,tc_set(X2))
        | c_union(X0,X1,X2) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f3891,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_union(X0,X1,X2),X1,tc_set(X2))
        | c_union(X0,X1,X2) = X1 )
    | ~ spl0_354
    | ~ spl0_469 ),
    inference(resolution,[],[f3831,f3190]) ).

fof(f6182,plain,
    ( spl0_688
    | ~ spl0_353
    | ~ spl0_469 ),
    inference(avatar_split_clause,[],[f3890,f3830,f3185,f6180]) ).

fof(f6180,plain,
    ( spl0_688
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_union(X0,X1,X2),X0,tc_set(X2))
        | c_union(X0,X1,X2) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f3890,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_union(X0,X1,X2),X0,tc_set(X2))
        | c_union(X0,X1,X2) = X0 )
    | ~ spl0_353
    | ~ spl0_469 ),
    inference(resolution,[],[f3831,f3186]) ).

fof(f6178,plain,
    ( spl0_687
    | ~ spl0_354
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f3871,f3818,f3189,f6176]) ).

fof(f6176,plain,
    ( spl0_687
  <=> ! [X2,X0,X1] :
        ( c_union(X1,X0,X2) = X0
        | c_less(X0,c_union(X1,X0,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f3871,plain,
    ( ! [X2,X0,X1] :
        ( c_union(X1,X0,X2) = X0
        | c_less(X0,c_union(X1,X0,X2),tc_set(X2)) )
    | ~ spl0_354
    | ~ spl0_466 ),
    inference(resolution,[],[f3819,f3190]) ).

fof(f6174,plain,
    ( spl0_686
    | ~ spl0_353
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f3870,f3818,f3185,f6172]) ).

fof(f6172,plain,
    ( spl0_686
  <=> ! [X2,X0,X1] :
        ( c_union(X0,X1,X2) = X0
        | c_less(X0,c_union(X0,X1,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f3870,plain,
    ( ! [X2,X0,X1] :
        ( c_union(X0,X1,X2) = X0
        | c_less(X0,c_union(X0,X1,X2),tc_set(X2)) )
    | ~ spl0_353
    | ~ spl0_466 ),
    inference(resolution,[],[f3819,f3186]) ).

fof(f6170,plain,
    ( spl0_685
    | ~ spl0_478
    | ~ spl0_643 ),
    inference(avatar_split_clause,[],[f5754,f5612,f3898,f6168]) ).

fof(f6168,plain,
    ( spl0_685
  <=> ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_G,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f5754,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_G,tc_Message_Omsg) )
    | ~ spl0_478
    | ~ spl0_643 ),
    inference(resolution,[],[f5613,f3899]) ).

fof(f6166,plain,
    ( spl0_684
    | ~ spl0_377
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f3738,f3560,f3304,f6164]) ).

fof(f6164,plain,
    ( spl0_684
  <=> ! [X0,X1] :
        ( c_lessequals(X0,c_Message_Oparts(X1),tc_set(tc_Message_Omsg))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oparts(X1),tc_Message_Omsg),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f3738,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,c_Message_Oparts(X1),tc_set(tc_Message_Omsg))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oparts(X1),tc_Message_Omsg),X1,tc_Message_Omsg) )
    | ~ spl0_377
    | ~ spl0_424 ),
    inference(resolution,[],[f3561,f3305]) ).

fof(f6162,plain,
    ( spl0_683
    | ~ spl0_376
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f3737,f3560,f3300,f6160]) ).

fof(f6160,plain,
    ( spl0_683
  <=> ! [X0,X1] :
        ( c_lessequals(X0,c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oanalz(X1),tc_Message_Omsg),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f3737,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
        | ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oanalz(X1),tc_Message_Omsg),X1,tc_Message_Omsg) )
    | ~ spl0_376
    | ~ spl0_424 ),
    inference(resolution,[],[f3561,f3301]) ).

fof(f6118,plain,
    ( spl0_682
    | ~ spl0_485
    | ~ spl0_642 ),
    inference(avatar_split_clause,[],[f5729,f5608,f3934,f6116]) ).

fof(f6116,plain,
    ( spl0_682
  <=> ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_H_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X1,X0),v_H,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f5608,plain,
    ( spl0_642
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X2,X0),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f5729,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_H_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X1,X0),v_H,tc_Message_Omsg) )
    | ~ spl0_485
    | ~ spl0_642 ),
    inference(resolution,[],[f5609,f3935]) ).

fof(f5609,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X2,X0),X1,tc_Message_Omsg)
        | c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg) )
    | ~ spl0_642 ),
    inference(avatar_component_clause,[],[f5608]) ).

fof(f6103,plain,
    ( spl0_681
    | ~ spl0_518
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f4708,f4654,f4223,f6101]) ).

fof(f6101,plain,
    ( spl0_681
  <=> ! [X2,X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_OImage(c_List_Olex(X0,X1),X2,tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f4223,plain,
    ( spl0_518
  <=> ! [X5,X1,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f4708,plain,
    ( ! [X2,X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_OImage(c_List_Olex(X0,X1),X2,tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
    | ~ spl0_518
    | ~ spl0_569 ),
    inference(resolution,[],[f4655,f4224]) ).

fof(f4224,plain,
    ( ! [X1,X5,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
    | ~ spl0_518 ),
    inference(avatar_component_clause,[],[f4223]) ).

fof(f6099,plain,
    ( spl0_680
    | ~ spl0_517
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4371,f4303,f4219,f6097]) ).

fof(f6097,plain,
    ( spl0_680
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Relation_ORange(c_Relation_Odiag(X1,X2),X2,X2),X2)
        | ~ c_in(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f4371,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Relation_ORange(c_Relation_Odiag(X1,X2),X2,X2),X2)
        | ~ c_in(X0,X1,X2) )
    | ~ spl0_517
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f4220]) ).

fof(f6095,plain,
    ( spl0_679
    | ~ spl0_517
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4347,f4291,f4219,f6093]) ).

fof(f6093,plain,
    ( spl0_679
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Relation_ODomain(c_Relation_Odiag(X1,X2),X2,X2),X2)
        | ~ c_in(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f4347,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Relation_ODomain(c_Relation_Odiag(X1,X2),X2,X2),X2)
        | ~ c_in(X0,X1,X2) )
    | ~ spl0_517
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f4220]) ).

fof(f6091,plain,
    ( spl0_678
    | ~ spl0_478
    | ~ spl0_642 ),
    inference(avatar_split_clause,[],[f5728,f5608,f3898,f6089]) ).

fof(f6089,plain,
    ( spl0_678
  <=> ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X1,X0),v_G,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f5728,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Message_Oparts(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X1,X0),v_G,tc_Message_Omsg) )
    | ~ spl0_478
    | ~ spl0_642 ),
    inference(resolution,[],[f5609,f3899]) ).

fof(f6087,plain,
    ( spl0_677
    | ~ spl0_354
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4203,f4109,f3189,f6085]) ).

fof(f6085,plain,
    ( spl0_677
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_set(X2))
        | c_lessequals(X0,c_union(X3,X1,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f4203,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_set(X2))
        | c_lessequals(X0,c_union(X3,X1,X2),tc_set(X2)) )
    | ~ spl0_354
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f3190]) ).

fof(f6083,plain,
    ( spl0_676
    | ~ spl0_353
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4202,f4109,f3185,f6081]) ).

fof(f6081,plain,
    ( spl0_676
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_set(X2))
        | c_lessequals(X0,c_union(X1,X3,X2),tc_set(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f4202,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_set(X2))
        | c_lessequals(X0,c_union(X1,X3,X2),tc_set(X2)) )
    | ~ spl0_353
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f3186]) ).

fof(f6079,plain,
    ( spl0_675
    | ~ spl0_335
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4189,f4097,f3113,f6077]) ).

fof(f6077,plain,
    ( spl0_675
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f3113,plain,
    ( spl0_335
  <=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f4189,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_335
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3114]) ).

fof(f3114,plain,
    ( ! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint))
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f3113]) ).

fof(f6075,plain,
    ( spl0_674
    | ~ spl0_334
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4188,f4097,f3109,f6073]) ).

fof(f6073,plain,
    ( spl0_674
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f3109,plain,
    ( spl0_334
  <=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f4188,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
    | ~ spl0_334
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3110]) ).

fof(f3110,plain,
    ( ! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f3109]) ).

fof(f6071,plain,
    ( spl0_673
    | ~ spl0_333
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4187,f4097,f3105,f6069]) ).

fof(f6069,plain,
    ( spl0_673
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f3105,plain,
    ( spl0_333
  <=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f4187,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_333
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3106]) ).

fof(f3106,plain,
    ( ! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint))
    | ~ spl0_333 ),
    inference(avatar_component_clause,[],[f3105]) ).

fof(f6067,plain,
    ( spl0_672
    | ~ spl0_332
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4186,f4097,f3101,f6065]) ).

fof(f6065,plain,
    ( spl0_672
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f3101,plain,
    ( spl0_332
  <=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f4186,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
    | ~ spl0_332
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3102]) ).

fof(f3102,plain,
    ( ! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
    | ~ spl0_332 ),
    inference(avatar_component_clause,[],[f3101]) ).

fof(f6063,plain,
    ( spl0_671
    | ~ spl0_331
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4184,f4097,f3097,f6061]) ).

fof(f6061,plain,
    ( spl0_671
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f3097,plain,
    ( spl0_331
  <=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f4184,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_331
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3098]) ).

fof(f3098,plain,
    ( ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint))
    | ~ spl0_331 ),
    inference(avatar_component_clause,[],[f3097]) ).

fof(f6059,plain,
    ( spl0_670
    | ~ spl0_330
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4183,f4097,f3093,f6057]) ).

fof(f6057,plain,
    ( spl0_670
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f3093,plain,
    ( spl0_330
  <=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f4183,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
    | ~ spl0_330
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3094]) ).

fof(f3094,plain,
    ( ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
    | ~ spl0_330 ),
    inference(avatar_component_clause,[],[f3093]) ).

fof(f6055,plain,
    ( spl0_669
    | ~ spl0_329
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4182,f4097,f3089,f6053]) ).

fof(f6053,plain,
    ( spl0_669
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f3089,plain,
    ( spl0_329
  <=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f4182,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_329
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3090]) ).

fof(f3090,plain,
    ( ! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint))
    | ~ spl0_329 ),
    inference(avatar_component_clause,[],[f3089]) ).

fof(f6051,plain,
    ( spl0_668
    | ~ spl0_328
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4181,f4097,f3085,f6049]) ).

fof(f6049,plain,
    ( spl0_668
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f3085,plain,
    ( spl0_328
  <=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f4181,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
    | ~ spl0_328
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3086]) ).

fof(f3086,plain,
    ( ! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
    | ~ spl0_328 ),
    inference(avatar_component_clause,[],[f3085]) ).

fof(f6047,plain,
    ( spl0_667
    | ~ spl0_485
    | ~ spl0_641 ),
    inference(avatar_split_clause,[],[f5703,f5604,f3934,f6045]) ).

fof(f6045,plain,
    ( spl0_667
  <=> ! [X0,X1] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_H_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_H,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f5604,plain,
    ( spl0_641
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X2),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f5703,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_H_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_H,tc_Message_Omsg) )
    | ~ spl0_485
    | ~ spl0_641 ),
    inference(resolution,[],[f5605,f3935]) ).

fof(f5605,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X2),X1,tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg) )
    | ~ spl0_641 ),
    inference(avatar_component_clause,[],[f5604]) ).

fof(f6043,plain,
    ( spl0_666
    | ~ spl0_382
    | ~ spl0_383 ),
    inference(avatar_split_clause,[],[f3433,f3344,f3340,f6041]) ).

fof(f6041,plain,
    ( spl0_666
  <=> ! [X2,X0,X1] :
        ( c_Datatype_Ooption_OSome(X2,X1) != X0
        | c_Main_Onot__Some__eq__iff1__1(X0,X1) = X2
        | c_Datatype_Ooption_ONone = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f3340,plain,
    ( spl0_382
  <=> ! [X0,X1] :
        ( c_Datatype_Ooption_ONone = X0
        | c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X0,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f3344,plain,
    ( spl0_383
  <=> ! [X41,X1,X18] :
        ( X18 = X41
        | c_Datatype_Ooption_OSome(X41,X1) != c_Datatype_Ooption_OSome(X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f3433,plain,
    ( ! [X2,X0,X1] :
        ( c_Datatype_Ooption_OSome(X2,X1) != X0
        | c_Main_Onot__Some__eq__iff1__1(X0,X1) = X2
        | c_Datatype_Ooption_ONone = X0 )
    | ~ spl0_382
    | ~ spl0_383 ),
    inference(superposition,[],[f3345,f3341]) ).

fof(f3341,plain,
    ( ! [X0,X1] :
        ( c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X0,X1),X1) = X0
        | c_Datatype_Ooption_ONone = X0 )
    | ~ spl0_382 ),
    inference(avatar_component_clause,[],[f3340]) ).

fof(f3345,plain,
    ( ! [X41,X1,X18] :
        ( c_Datatype_Ooption_OSome(X41,X1) != c_Datatype_Ooption_OSome(X18,X1)
        | X18 = X41 )
    | ~ spl0_383 ),
    inference(avatar_component_clause,[],[f3344]) ).

fof(f6039,plain,
    ( spl0_665
    | ~ spl0_381
    | ~ spl0_383 ),
    inference(avatar_split_clause,[],[f3432,f3344,f3336,f6037]) ).

fof(f6037,plain,
    ( spl0_665
  <=> ! [X2,X0,X1] :
        ( c_Datatype_Ooption_OSome(X2,X1) != X0
        | c_Main_Onot__None__eq__iff1__1(X0,X1) = X2
        | c_Datatype_Ooption_ONone = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f3336,plain,
    ( spl0_381
  <=> ! [X0,X1] :
        ( c_Datatype_Ooption_ONone = X0
        | c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X0,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f3432,plain,
    ( ! [X2,X0,X1] :
        ( c_Datatype_Ooption_OSome(X2,X1) != X0
        | c_Main_Onot__None__eq__iff1__1(X0,X1) = X2
        | c_Datatype_Ooption_ONone = X0 )
    | ~ spl0_381
    | ~ spl0_383 ),
    inference(superposition,[],[f3345,f3337]) ).

fof(f3337,plain,
    ( ! [X0,X1] :
        ( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X0,X1),X1) = X0
        | c_Datatype_Ooption_ONone = X0 )
    | ~ spl0_381 ),
    inference(avatar_component_clause,[],[f3336]) ).

fof(f5900,plain,
    ( spl0_664
    | ~ spl0_478
    | ~ spl0_641 ),
    inference(avatar_split_clause,[],[f5702,f5604,f3898,f5898]) ).

fof(f5898,plain,
    ( spl0_664
  <=> ! [X0,X1] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_G,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f5702,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_G,tc_Message_Omsg) )
    | ~ spl0_478
    | ~ spl0_641 ),
    inference(resolution,[],[f5605,f3899]) ).

fof(f5883,plain,
    ( spl0_663
    | ~ spl0_64
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f4633,f4609,f1702,f5881]) ).

fof(f5881,plain,
    ( spl0_663
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_in(X0,c_Relation_OImage(c_UNIV,X1,X2,X3),X3)
        | ~ c_in(X4,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f1702,plain,
    ( spl0_64
  <=> ! [X0,X1] : c_in(X0,c_UNIV,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f4633,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_in(X0,c_Relation_OImage(c_UNIV,X1,X2,X3),X3)
        | ~ c_in(X4,X1,X2) )
    | ~ spl0_64
    | ~ spl0_565 ),
    inference(resolution,[],[f4610,f1703]) ).

fof(f1703,plain,
    ( ! [X0,X1] : c_in(X0,c_UNIV,X1)
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f1702]) ).

fof(f5879,plain,
    ( spl0_662
    | ~ spl0_399
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f4620,f4609,f3408,f5877]) ).

fof(f5877,plain,
    ( spl0_662
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Relation_OImage(c_Relation_OId,X1,X2,X2),X2)
        | ~ c_in(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f4620,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Relation_OImage(c_Relation_OId,X1,X2,X2),X2)
        | ~ c_in(X0,X1,X2) )
    | ~ spl0_399
    | ~ spl0_565 ),
    inference(resolution,[],[f4610,f3409]) ).

fof(f5875,plain,
    ( spl0_661
    | ~ spl0_518
    | ~ spl0_558 ),
    inference(avatar_split_clause,[],[f4569,f4509,f4223,f5873]) ).

fof(f5873,plain,
    ( spl0_661
  <=> ! [X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_ORange(c_List_Olex(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f4569,plain,
    ( ! [X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_ORange(c_List_Olex(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
    | ~ spl0_518
    | ~ spl0_558 ),
    inference(resolution,[],[f4510,f4224]) ).

fof(f5871,plain,
    ( spl0_660
    | ~ spl0_519
    | ~ spl0_557 ),
    inference(avatar_split_clause,[],[f4545,f4505,f4227,f5869]) ).

fof(f5869,plain,
    ( spl0_660
  <=> ! [X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_ODomain(c_List_Olex(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f4227,plain,
    ( spl0_519
  <=> ! [X25,X5,X1] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f4545,plain,
    ( ! [X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_ODomain(c_List_Olex(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
    | ~ spl0_519
    | ~ spl0_557 ),
    inference(resolution,[],[f4506,f4228]) ).

fof(f4228,plain,
    ( ! [X1,X5,X25] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
    | ~ spl0_519 ),
    inference(avatar_component_clause,[],[f4227]) ).

fof(f5867,plain,
    ( spl0_659
    | ~ spl0_292
    | ~ spl0_540 ),
    inference(avatar_split_clause,[],[f4399,f4335,f2923,f5865]) ).

fof(f5865,plain,
    ( spl0_659
  <=> ! [X0,X1] : c_insert(X0,c_emptyset,X1) = c_insert(X0,c_insert(X0,c_emptyset,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f4335,plain,
    ( spl0_540
  <=> ! [X12,X0,X1] :
        ( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
        | c_insert(X0,c_emptyset,X1) = c_insert(X0,X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f4399,plain,
    ( ! [X0,X1] : c_insert(X0,c_emptyset,X1) = c_insert(X0,c_insert(X0,c_emptyset,X1),X1)
    | ~ spl0_292
    | ~ spl0_540 ),
    inference(resolution,[],[f4336,f2924]) ).

fof(f4336,plain,
    ( ! [X0,X1,X12] :
        ( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
        | c_insert(X0,c_emptyset,X1) = c_insert(X0,X12,X1) )
    | ~ spl0_540 ),
    inference(avatar_component_clause,[],[f4335]) ).

fof(f5863,plain,
    ( spl0_658
    | ~ spl0_317
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4190,f4097,f3025,f5861]) ).

fof(f5861,plain,
    ( spl0_658
  <=> ! [X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OlessThan(X1,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f3025,plain,
    ( spl0_317
  <=> ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f4190,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OlessThan(X1,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
    | ~ spl0_317
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3026]) ).

fof(f3026,plain,
    ( ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
    | ~ spl0_317 ),
    inference(avatar_component_clause,[],[f3025]) ).

fof(f5859,plain,
    ( spl0_657
    | ~ spl0_316
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4185,f4097,f3021,f5857]) ).

fof(f5857,plain,
    ( spl0_657
  <=> ! [X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatMost(X1,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f3021,plain,
    ( spl0_316
  <=> ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f4185,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,c_SetInterval_OatMost(X1,tc_nat),tc_nat)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
    | ~ spl0_316
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3022]) ).

fof(f3022,plain,
    ( ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
    | ~ spl0_316 ),
    inference(avatar_component_clause,[],[f3021]) ).

fof(f5855,plain,
    ( spl0_656
    | ~ spl0_314
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4180,f4097,f3013,f5853]) ).

fof(f5853,plain,
    ( spl0_656
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,c_List_Oset(X1,X2),X2)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f3013,plain,
    ( spl0_314
  <=> ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f4180,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_List_Oset(X1,X2),X2)
        | c_in(X0,c_Union(c_Finite__Set_OFinites,X2),X2) )
    | ~ spl0_314
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f3014]) ).

fof(f3014,plain,
    ( ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1))
    | ~ spl0_314 ),
    inference(avatar_component_clause,[],[f3013]) ).

fof(f5851,plain,
    ( spl0_655
    | ~ spl0_485
    | ~ spl0_640 ),
    inference(avatar_split_clause,[],[f5677,f5600,f3934,f5849]) ).

fof(f5849,plain,
    ( spl0_655
  <=> ! [X0,X1] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_H_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X1,X0),v_H,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f5600,plain,
    ( spl0_640
  <=> ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X2,X0),X1,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f5677,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_H_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X1,X0),v_H,tc_Message_Omsg) )
    | ~ spl0_485
    | ~ spl0_640 ),
    inference(resolution,[],[f5601,f3935]) ).

fof(f5601,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X2,X0),X1,tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg) )
    | ~ spl0_640 ),
    inference(avatar_component_clause,[],[f5600]) ).

fof(f5847,plain,
    ( spl0_654
    | ~ spl0_387
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f3445,f3372,f3360,f5845]) ).

fof(f5845,plain,
    ( spl0_654
  <=> ! [X0,X1] :
        ( ~ c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f3360,plain,
    ( spl0_387
  <=> ! [X11,X42] :
        ( c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint)
        | ~ c_Divides_Oop_Advd(X42,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f3372,plain,
    ( spl0_390
  <=> ! [X11,X42] :
        ( ~ c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint)
        | c_Divides_Oop_Advd(c_uminus(X42,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f3445,plain,
    ( ! [X0,X1] :
        ( ~ c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) )
    | ~ spl0_387
    | ~ spl0_390 ),
    inference(resolution,[],[f3373,f3361]) ).

fof(f3361,plain,
    ( ! [X11,X42] :
        ( ~ c_Divides_Oop_Advd(X42,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint) )
    | ~ spl0_387 ),
    inference(avatar_component_clause,[],[f3360]) ).

fof(f3373,plain,
    ( ! [X11,X42] :
        ( c_Divides_Oop_Advd(c_uminus(X42,tc_IntDef_Oint),X11,tc_IntDef_Oint)
        | ~ c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint) )
    | ~ spl0_390 ),
    inference(avatar_component_clause,[],[f3372]) ).

fof(f5843,plain,
    ( spl0_653
    | ~ spl0_388
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f3443,f3368,f3364,f5841]) ).

fof(f5841,plain,
    ( spl0_653
  <=> ! [X0,X1] :
        ( c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f3364,plain,
    ( spl0_388
  <=> ! [X11,X42] :
        ( ~ c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint)
        | c_Divides_Oop_Advd(X42,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f3368,plain,
    ( spl0_389
  <=> ! [X11,X42] :
        ( c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint)
        | ~ c_Divides_Oop_Advd(c_uminus(X42,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f3443,plain,
    ( ! [X0,X1] :
        ( c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) )
    | ~ spl0_388
    | ~ spl0_389 ),
    inference(resolution,[],[f3369,f3365]) ).

fof(f3365,plain,
    ( ! [X11,X42] :
        ( c_Divides_Oop_Advd(X42,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint) )
    | ~ spl0_388 ),
    inference(avatar_component_clause,[],[f3364]) ).

fof(f3369,plain,
    ( ! [X11,X42] :
        ( ~ c_Divides_Oop_Advd(c_uminus(X42,tc_IntDef_Oint),X11,tc_IntDef_Oint)
        | c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint) )
    | ~ spl0_389 ),
    inference(avatar_component_clause,[],[f3368]) ).

fof(f5760,plain,
    ( spl0_652
    | ~ spl0_478
    | ~ spl0_640 ),
    inference(avatar_split_clause,[],[f5676,f5600,f3898,f5758]) ).

fof(f5758,plain,
    ( spl0_652
  <=> ! [X0,X1] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X1,X0),v_G,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f5676,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Message_Oanalz(c_Message_Oanalz(v_G_H)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X1,X0),v_G,tc_Message_Omsg) )
    | ~ spl0_478
    | ~ spl0_640 ),
    inference(resolution,[],[f5601,f3899]) ).

fof(f5648,plain,
    ( spl0_651
    | ~ spl0_282
    | ~ spl0_596 ),
    inference(avatar_split_clause,[],[f4982,f4935,f2575,f5646]) ).

fof(f5646,plain,
    ( spl0_651
  <=> ! [X4,X0,X3,X2,X1] : ~ c_in(X0,c_Relation_Orel__comp(X1,c_emptyset,X2,X3,X4),tc_prod(X4,X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f4935,plain,
    ( spl0_596
  <=> ! [X5,X31,X30,X6,X2,X1] :
        ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
        | c_in(c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),X1,X31),X6,tc_prod(X1,X31)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f4982,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_in(X0,c_Relation_Orel__comp(X1,c_emptyset,X2,X3,X4),tc_prod(X4,X3))
    | ~ spl0_282
    | ~ spl0_596 ),
    inference(resolution,[],[f4936,f2576]) ).

fof(f4936,plain,
    ( ! [X31,X2,X1,X6,X5,X30] :
        ( c_in(c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),X1,X31),X6,tc_prod(X1,X31))
        | ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2)) )
    | ~ spl0_596 ),
    inference(avatar_component_clause,[],[f4935]) ).

fof(f5644,plain,
    ( spl0_650
    | ~ spl0_282
    | ~ spl0_594 ),
    inference(avatar_split_clause,[],[f4953,f4927,f2575,f5642]) ).

fof(f5642,plain,
    ( spl0_650
  <=> ! [X4,X0,X3,X2,X1] : ~ c_in(X0,c_Relation_Orel__comp(c_emptyset,X1,X2,X3,X4),tc_prod(X4,X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f4927,plain,
    ( spl0_594
  <=> ! [X5,X31,X30,X6,X2,X1] :
        ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
        | c_in(c_Pair(c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X31,X2),X5,tc_prod(X31,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f4953,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_in(X0,c_Relation_Orel__comp(c_emptyset,X1,X2,X3,X4),tc_prod(X4,X3))
    | ~ spl0_282
    | ~ spl0_594 ),
    inference(resolution,[],[f4928,f2576]) ).

fof(f4928,plain,
    ( ! [X31,X2,X1,X6,X5,X30] :
        ( c_in(c_Pair(c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X31,X2),X5,tc_prod(X31,X2))
        | ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2)) )
    | ~ spl0_594 ),
    inference(avatar_component_clause,[],[f4927]) ).

fof(f5640,plain,
    ( spl0_649
    | ~ spl0_282
    | ~ spl0_568 ),
    inference(avatar_split_clause,[],[f4685,f4650,f2575,f5638]) ).

fof(f5638,plain,
    ( spl0_649
  <=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Datatype__Universe_Ouprod(c_emptyset,X1,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f4650,plain,
    ( spl0_568
  <=> ! [X4,X13,X12,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OuprodE__1(X12,X13,X4,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f4685,plain,
    ( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Datatype__Universe_Ouprod(c_emptyset,X1,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ spl0_282
    | ~ spl0_568 ),
    inference(resolution,[],[f4651,f2576]) ).

fof(f4651,plain,
    ( ! [X2,X1,X4,X12,X13] :
        ( c_in(c_Main_OuprodE__1(X12,X13,X4,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) )
    | ~ spl0_568 ),
    inference(avatar_component_clause,[],[f4650]) ).

fof(f5636,plain,
    ( spl0_648
    | ~ spl0_282
    | ~ spl0_567 ),
    inference(avatar_split_clause,[],[f4666,f4646,f2575,f5634]) ).

fof(f5634,plain,
    ( spl0_648
  <=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Datatype__Universe_Ouprod(X1,c_emptyset,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f4646,plain,
    ( spl0_567
  <=> ! [X4,X13,X12,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OuprodE__2(X12,X13,X4,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f4666,plain,
    ( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Datatype__Universe_Ouprod(X1,c_emptyset,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ spl0_282
    | ~ spl0_567 ),
    inference(resolution,[],[f4647,f2576]) ).

fof(f4647,plain,
    ( ! [X2,X1,X4,X12,X13] :
        ( c_in(c_Main_OuprodE__2(X12,X13,X4,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) )
    | ~ spl0_567 ),
    inference(avatar_component_clause,[],[f4646]) ).

fof(f5630,plain,
    ( spl0_647
    | ~ spl0_493
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4372,f4303,f3966,f5628]) ).

fof(f5628,plain,
    ( spl0_647
  <=> ! [X0,X1] :
        ( c_in(X0,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
        | ~ c_less(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f4372,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
        | ~ c_less(X1,X0,tc_nat) )
    | ~ spl0_493
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f3967]) ).

fof(f5626,plain,
    ( spl0_646
    | ~ spl0_493
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4348,f4291,f3966,f5624]) ).

fof(f5624,plain,
    ( spl0_646
  <=> ! [X0,X1] :
        ( c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
        | ~ c_less(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f4348,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
        | ~ c_less(X0,X1,tc_nat) )
    | ~ spl0_493
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f3967]) ).

fof(f5622,plain,
    ( spl0_645
    | ~ spl0_297
    | ~ spl0_305
    | ~ spl0_521 ),
    inference(avatar_split_clause,[],[f4260,f4235,f2976,f2944,f5620]) ).

fof(f5620,plain,
    ( spl0_645
  <=> ! [X0,X1] : c_List_Olist_OCons(X1,c_List_Olist_ONil,X0) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f2944,plain,
    ( spl0_297
  <=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f4235,plain,
    ( spl0_521
  <=> ! [X25,X1,X3] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f4260,plain,
    ( ! [X0,X1] : c_List_Olist_OCons(X1,c_List_Olist_ONil,X0) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),X0)
    | ~ spl0_297
    | ~ spl0_305
    | ~ spl0_521 ),
    inference(forward_demodulation,[],[f4255,f2977]) ).

fof(f4255,plain,
    ( ! [X0,X1] : c_List_Olist_OCons(X1,c_List_Olist_ONil,X0) = c_List_Orev(c_append(c_List_Olist_ONil,c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),X0),X0)
    | ~ spl0_297
    | ~ spl0_521 ),
    inference(superposition,[],[f4236,f2945]) ).

fof(f2945,plain,
    ( ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1)
    | ~ spl0_297 ),
    inference(avatar_component_clause,[],[f2944]) ).

fof(f4236,plain,
    ( ! [X3,X1,X25] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1)
    | ~ spl0_521 ),
    inference(avatar_component_clause,[],[f4235]) ).

fof(f5618,plain,
    ( spl0_644
    | ~ spl0_377
    | ~ spl0_458 ),
    inference(avatar_split_clause,[],[f3796,f3716,f3304,f5616]) ).

fof(f3716,plain,
    ( spl0_458
  <=> ! [X53,X55,X58] :
        ( c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X58,X53),c_Message_Oparts(X55),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f3796,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X2,X0),X1,tc_Message_Omsg) )
    | ~ spl0_377
    | ~ spl0_458 ),
    inference(resolution,[],[f3717,f3305]) ).

fof(f3717,plain,
    ( ! [X58,X55,X53] :
        ( ~ c_in(c_Message_Omsg_OCrypt(X58,X53),c_Message_Oparts(X55),tc_Message_Omsg)
        | c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg) )
    | ~ spl0_458 ),
    inference(avatar_component_clause,[],[f3716]) ).

fof(f5614,plain,
    ( spl0_643
    | ~ spl0_377
    | ~ spl0_456 ),
    inference(avatar_split_clause,[],[f3795,f3708,f3304,f5612]) ).

fof(f3708,plain,
    ( spl0_456
  <=> ! [X54,X53,X55] :
        ( c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oparts(X55),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f3795,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X2),X1,tc_Message_Omsg) )
    | ~ spl0_377
    | ~ spl0_456 ),
    inference(resolution,[],[f3709,f3305]) ).

fof(f3709,plain,
    ( ! [X54,X55,X53] :
        ( ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oparts(X55),tc_Message_Omsg)
        | c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg) )
    | ~ spl0_456 ),
    inference(avatar_component_clause,[],[f3708]) ).

fof(f5610,plain,
    ( spl0_642
    | ~ spl0_377
    | ~ spl0_455 ),
    inference(avatar_split_clause,[],[f3794,f3704,f3304,f5608]) ).

fof(f3704,plain,
    ( spl0_455
  <=> ! [X54,X53,X55] :
        ( c_in(X54,c_Message_Oparts(X55),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oparts(X55),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f3794,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X2,X0),X1,tc_Message_Omsg) )
    | ~ spl0_377
    | ~ spl0_455 ),
    inference(resolution,[],[f3705,f3305]) ).

fof(f3705,plain,
    ( ! [X54,X55,X53] :
        ( ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oparts(X55),tc_Message_Omsg)
        | c_in(X54,c_Message_Oparts(X55),tc_Message_Omsg) )
    | ~ spl0_455 ),
    inference(avatar_component_clause,[],[f3704]) ).

fof(f5606,plain,
    ( spl0_641
    | ~ spl0_376
    | ~ spl0_454 ),
    inference(avatar_split_clause,[],[f3793,f3700,f3300,f5604]) ).

fof(f3700,plain,
    ( spl0_454
  <=> ! [X54,X53,X55] :
        ( c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oanalz(X55),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f3793,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X0,X2),X1,tc_Message_Omsg) )
    | ~ spl0_376
    | ~ spl0_454 ),
    inference(resolution,[],[f3701,f3301]) ).

fof(f3701,plain,
    ( ! [X54,X55,X53] :
        ( ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oanalz(X55),tc_Message_Omsg)
        | c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg) )
    | ~ spl0_454 ),
    inference(avatar_component_clause,[],[f3700]) ).

fof(f5602,plain,
    ( spl0_640
    | ~ spl0_376
    | ~ spl0_453 ),
    inference(avatar_split_clause,[],[f3792,f3688,f3300,f5600]) ).

fof(f3688,plain,
    ( spl0_453
  <=> ! [X54,X53,X55] :
        ( c_in(X54,c_Message_Oanalz(X55),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oanalz(X55),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f3792,plain,
    ( ! [X2,X0,X1] :
        ( c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X2,X0),X1,tc_Message_Omsg) )
    | ~ spl0_376
    | ~ spl0_453 ),
    inference(resolution,[],[f3689,f3301]) ).

fof(f3689,plain,
    ( ! [X54,X55,X53] :
        ( ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oanalz(X55),tc_Message_Omsg)
        | c_in(X54,c_Message_Oanalz(X55),tc_Message_Omsg) )
    | ~ spl0_453 ),
    inference(avatar_component_clause,[],[f3688]) ).

fof(f5598,plain,
    ( spl0_639
    | ~ spl0_340
    | ~ spl0_382 ),
    inference(avatar_split_clause,[],[f3430,f3340,f3133,f5596]) ).

fof(f5596,plain,
    ( spl0_639
  <=> ! [X0,X1] :
        ( c_in(c_Main_Onot__Some__eq__iff1__1(X0,X1),c_Datatype_Oo2s(X0,X1),X1)
        | c_Datatype_Ooption_ONone = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f3430,plain,
    ( ! [X0,X1] :
        ( c_in(c_Main_Onot__Some__eq__iff1__1(X0,X1),c_Datatype_Oo2s(X0,X1),X1)
        | c_Datatype_Ooption_ONone = X0 )
    | ~ spl0_340
    | ~ spl0_382 ),
    inference(superposition,[],[f3134,f3341]) ).

fof(f5594,plain,
    ( spl0_638
    | ~ spl0_340
    | ~ spl0_381 ),
    inference(avatar_split_clause,[],[f3428,f3336,f3133,f5592]) ).

fof(f5592,plain,
    ( spl0_638
  <=> ! [X0,X1] :
        ( c_in(c_Main_Onot__None__eq__iff1__1(X0,X1),c_Datatype_Oo2s(X0,X1),X1)
        | c_Datatype_Ooption_ONone = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f3428,plain,
    ( ! [X0,X1] :
        ( c_in(c_Main_Onot__None__eq__iff1__1(X0,X1),c_Datatype_Oo2s(X0,X1),X1)
        | c_Datatype_Ooption_ONone = X0 )
    | ~ spl0_340
    | ~ spl0_381 ),
    inference(superposition,[],[f3134,f3337]) ).

fof(f5590,plain,
    ( spl0_637
    | ~ spl0_468
    | ~ spl0_564 ),
    inference(avatar_split_clause,[],[f4732,f4535,f3826,f5588]) ).

fof(f5588,plain,
    ( spl0_637
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,v_H,tc_set(tc_Message_Omsg))
        | c_in(X1,c_Message_Oanalz(v_H_H),tc_Message_Omsg)
        | ~ c_in(X1,X0,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f4535,plain,
    ( spl0_564
  <=> ! [X0] :
        ( ~ c_lessequals(X0,v_H,tc_set(tc_Message_Omsg))
        | c_lessequals(X0,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f4732,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,v_H,tc_set(tc_Message_Omsg))
        | c_in(X1,c_Message_Oanalz(v_H_H),tc_Message_Omsg)
        | ~ c_in(X1,X0,tc_Message_Omsg) )
    | ~ spl0_468
    | ~ spl0_564 ),
    inference(resolution,[],[f4536,f3827]) ).

fof(f4536,plain,
    ( ! [X0] :
        ( c_lessequals(X0,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(X0,v_H,tc_set(tc_Message_Omsg)) )
    | ~ spl0_564 ),
    inference(avatar_component_clause,[],[f4535]) ).

fof(f5495,plain,
    ( spl0_636
    | ~ spl0_291
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4197,f4109,f2919,f5493]) ).

fof(f5493,plain,
    ( spl0_636
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
        | c_lessequals(X0,X2,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f2919,plain,
    ( spl0_291
  <=> ! [X12,X1] : c_lessequals(c_emptyset,X12,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f4197,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
        | c_lessequals(X0,X2,tc_set(X1)) )
    | ~ spl0_291
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f2920]) ).

fof(f2920,plain,
    ( ! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1))
    | ~ spl0_291 ),
    inference(avatar_component_clause,[],[f2919]) ).

fof(f5491,plain,
    ( spl0_635
    | ~ spl0_64
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f4168,f4097,f1702,f5489]) ).

fof(f5489,plain,
    ( spl0_635
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_UNIV,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f4168,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,X1,X2)
        | c_in(X0,c_Union(c_UNIV,X2),X2) )
    | ~ spl0_64
    | ~ spl0_511 ),
    inference(resolution,[],[f4098,f1703]) ).

fof(f5454,plain,
    ( spl0_634
    | ~ spl0_282
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f4805,f4787,f2575,f5452]) ).

fof(f5452,plain,
    ( spl0_634
  <=> ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f4805,plain,
    ( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1))
    | ~ spl0_282
    | ~ spl0_579 ),
    inference(resolution,[],[f4788,f2576]) ).

fof(f5450,plain,
    ( spl0_633
    | ~ spl0_468
    | ~ spl0_555 ),
    inference(avatar_split_clause,[],[f4618,f4497,f3826,f5448]) ).

fof(f5448,plain,
    ( spl0_633
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,v_G,tc_set(tc_Message_Omsg))
        | c_in(X1,c_Message_Oanalz(v_G_H),tc_Message_Omsg)
        | ~ c_in(X1,X0,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f4497,plain,
    ( spl0_555
  <=> ! [X0] :
        ( ~ c_lessequals(X0,v_G,tc_set(tc_Message_Omsg))
        | c_lessequals(X0,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f4618,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,v_G,tc_set(tc_Message_Omsg))
        | c_in(X1,c_Message_Oanalz(v_G_H),tc_Message_Omsg)
        | ~ c_in(X1,X0,tc_Message_Omsg) )
    | ~ spl0_468
    | ~ spl0_555 ),
    inference(resolution,[],[f4498,f3827]) ).

fof(f4498,plain,
    ( ! [X0] :
        ( c_lessequals(X0,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(X0,v_G,tc_set(tc_Message_Omsg)) )
    | ~ spl0_555 ),
    inference(avatar_component_clause,[],[f4497]) ).

fof(f5446,plain,
    ( spl0_632
    | ~ spl0_425
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4370,f4303,f3564,f5444]) ).

fof(f5444,plain,
    ( spl0_632
  <=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f4370,plain,
    ( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2)
    | ~ spl0_425
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f3565]) ).

fof(f5442,plain,
    ( spl0_631
    | ~ spl0_425
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4346,f4291,f3564,f5440]) ).

fof(f5440,plain,
    ( spl0_631
  <=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f4346,plain,
    ( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2)
    | ~ spl0_425
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f3565]) ).

fof(f5438,plain,
    ( spl0_630
    | ~ spl0_481
    | ~ spl0_516 ),
    inference(avatar_split_clause,[],[f4253,f4215,f3918,f5436]) ).

fof(f5436,plain,
    ( spl0_630
  <=> ! [X0,X1] : c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f4215,plain,
    ( spl0_516
  <=> ! [X12,X1,X23] :
        ( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f4253,plain,
    ( ! [X0,X1] : c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1))
    | ~ spl0_481
    | ~ spl0_516 ),
    inference(duplicate_literal_removal,[],[f4250]) ).

fof(f4250,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1))
        | c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1)) )
    | ~ spl0_481
    | ~ spl0_516 ),
    inference(resolution,[],[f4216,f3919]) ).

fof(f4216,plain,
    ( ! [X1,X12,X23] :
        ( c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1)
        | c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) )
    | ~ spl0_516 ),
    inference(avatar_component_clause,[],[f4215]) ).

fof(f5430,plain,
    ( spl0_629
    | ~ spl0_305
    | ~ spl0_432 ),
    inference(avatar_split_clause,[],[f3754,f3592,f2976,f5428]) ).

fof(f5428,plain,
    ( spl0_629
  <=> ! [X2,X0,X1] :
        ( c_append(c_List_Olist_ONil,X2,X1) != X0
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f3592,plain,
    ( spl0_432
  <=> ! [X43,X23,X25,X1] :
        ( X25 = X43
        | c_append(X23,X25,X1) != c_append(X23,X43,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f3754,plain,
    ( ! [X2,X0,X1] :
        ( c_append(c_List_Olist_ONil,X2,X1) != X0
        | X0 = X2 )
    | ~ spl0_305
    | ~ spl0_432 ),
    inference(superposition,[],[f3593,f2977]) ).

fof(f3593,plain,
    ( ! [X1,X25,X23,X43] :
        ( c_append(X23,X25,X1) != c_append(X23,X43,X1)
        | X25 = X43 )
    | ~ spl0_432 ),
    inference(avatar_component_clause,[],[f3592]) ).

fof(f5402,plain,
    ( spl0_628
    | ~ spl0_282
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f4710,f4654,f2575,f5400]) ).

fof(f5400,plain,
    ( spl0_628
  <=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f4710,plain,
    ( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3)
    | ~ spl0_282
    | ~ spl0_569 ),
    inference(resolution,[],[f4655,f2576]) ).

fof(f5398,plain,
    ( spl0_627
    | ~ spl0_424
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f4023,f3934,f3560,f5396]) ).

fof(f5396,plain,
    ( spl0_627
  <=> ! [X0] :
        ( ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oanalz(v_H_H),tc_Message_Omsg),v_H,tc_Message_Omsg)
        | c_lessequals(X0,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f4023,plain,
    ( ! [X0] :
        ( ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oanalz(v_H_H),tc_Message_Omsg),v_H,tc_Message_Omsg)
        | c_lessequals(X0,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)) )
    | ~ spl0_424
    | ~ spl0_485 ),
    inference(resolution,[],[f3935,f3561]) ).

fof(f5394,plain,
    ( spl0_626
    | ~ spl0_291
    | ~ spl0_469 ),
    inference(avatar_split_clause,[],[f3887,f3830,f2919,f5392]) ).

fof(f5392,plain,
    ( spl0_626
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
        | c_emptyset = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f3887,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
        | c_emptyset = X0 )
    | ~ spl0_291
    | ~ spl0_469 ),
    inference(resolution,[],[f3831,f2920]) ).

fof(f5390,plain,
    ( spl0_625
    | ~ spl0_291
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f3867,f3818,f2919,f5388]) ).

fof(f5388,plain,
    ( spl0_625
  <=> ! [X0,X1] :
        ( c_emptyset = X0
        | c_less(c_emptyset,X0,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f3867,plain,
    ( ! [X0,X1] :
        ( c_emptyset = X0
        | c_less(c_emptyset,X0,tc_set(X1)) )
    | ~ spl0_291
    | ~ spl0_466 ),
    inference(resolution,[],[f3819,f2920]) ).

fof(f5323,plain,
    ( spl0_624
    | ~ spl0_282
    | ~ spl0_558 ),
    inference(avatar_split_clause,[],[f4571,f4509,f2575,f5321]) ).

fof(f5321,plain,
    ( spl0_624
  <=> ! [X2,X0,X1] : ~ c_in(X0,c_Relation_ORange(c_emptyset,X1,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f4571,plain,
    ( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_ORange(c_emptyset,X1,X2),X2)
    | ~ spl0_282
    | ~ spl0_558 ),
    inference(resolution,[],[f4510,f2576]) ).

fof(f5319,plain,
    ( spl0_623
    | ~ spl0_424
    | ~ spl0_478 ),
    inference(avatar_split_clause,[],[f3969,f3898,f3560,f5317]) ).

fof(f3969,plain,
    ( ! [X0] :
        ( ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg),v_G,tc_Message_Omsg)
        | c_lessequals(X0,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) )
    | ~ spl0_424
    | ~ spl0_478 ),
    inference(resolution,[],[f3899,f3561]) ).

fof(f5315,plain,
    ( spl0_622
    | ~ spl0_282
    | ~ spl0_557 ),
    inference(avatar_split_clause,[],[f4547,f4505,f2575,f5313]) ).

fof(f5313,plain,
    ( spl0_622
  <=> ! [X2,X0,X1] : ~ c_in(X0,c_Relation_ODomain(c_emptyset,X1,X2),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f4547,plain,
    ( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_ODomain(c_emptyset,X1,X2),X1)
    | ~ spl0_282
    | ~ spl0_557 ),
    inference(resolution,[],[f4506,f2576]) ).

fof(f5311,plain,
    ( spl0_621
    | ~ spl0_64
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4379,f4303,f1702,f5309]) ).

fof(f5309,plain,
    ( spl0_621
  <=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f4379,plain,
    ( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2)
    | ~ spl0_64
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f1703]) ).

fof(f5307,plain,
    ( spl0_620
    | ~ spl0_399
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f4369,f4303,f3408,f5305]) ).

fof(f5305,plain,
    ( spl0_620
  <=> ! [X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f4369,plain,
    ( ! [X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1)
    | ~ spl0_399
    | ~ spl0_532 ),
    inference(resolution,[],[f4304,f3409]) ).

fof(f5303,plain,
    ( spl0_619
    | ~ spl0_64
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4355,f4291,f1702,f5301]) ).

fof(f5301,plain,
    ( spl0_619
  <=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f4355,plain,
    ( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1)
    | ~ spl0_64
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f1703]) ).

fof(f5299,plain,
    ( spl0_618
    | ~ spl0_399
    | ~ spl0_529 ),
    inference(avatar_split_clause,[],[f4345,f4291,f3408,f5297]) ).

fof(f5297,plain,
    ( spl0_618
  <=> ! [X0,X1] : c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f4345,plain,
    ( ! [X0,X1] : c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1)
    | ~ spl0_399
    | ~ spl0_529 ),
    inference(resolution,[],[f4292,f3409]) ).

fof(f5295,plain,
    ( spl0_617
    | ~ spl0_64
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3976,f3918,f1702,f5293]) ).

fof(f5293,plain,
    ( spl0_617
  <=> ! [X0,X1] : c_in(X0,c_List_Olists(c_UNIV,X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f3976,plain,
    ( ! [X0,X1] : c_in(X0,c_List_Olists(c_UNIV,X1),tc_List_Olist(X1))
    | ~ spl0_64
    | ~ spl0_481 ),
    inference(resolution,[],[f3919,f1703]) ).

fof(f5257,plain,
    ( spl0_616
    | ~ spl0_292
    | ~ spl0_504 ),
    inference(avatar_split_clause,[],[f4132,f4069,f2923,f5255]) ).

fof(f5255,plain,
    ( spl0_616
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f4069,plain,
    ( spl0_504
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_lessequals(X3,X0,X1)
        | ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f4132,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_292
    | ~ spl0_504 ),
    inference(resolution,[],[f4070,f2924]) ).

fof(f4070,plain,
    ( ! [X3,X0,X1] :
        ( ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
        | c_lessequals(X3,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_504 ),
    inference(avatar_component_clause,[],[f4069]) ).

fof(f5253,plain,
    ( spl0_615
    | ~ spl0_282
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f3998,f3930,f2575,f5251]) ).

fof(f5251,plain,
    ( spl0_615
  <=> ! [X0,X1] : ~ c_in(X0,c_Union(c_emptyset,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f3998,plain,
    ( ! [X0,X1] : ~ c_in(X0,c_Union(c_emptyset,X1),X1)
    | ~ spl0_282
    | ~ spl0_484 ),
    inference(resolution,[],[f3931,f2576]) ).

fof(f5249,plain,
    ( spl0_614
    | ~ spl0_282
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3985,f3926,f2575,f5247]) ).

fof(f5247,plain,
    ( spl0_614
  <=> ! [X0,X1] : c_in(X0,c_Inter(c_emptyset,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f3985,plain,
    ( ! [X0,X1] : c_in(X0,c_Inter(c_emptyset,X1),X1)
    | ~ spl0_282
    | ~ spl0_483 ),
    inference(resolution,[],[f3927,f2576]) ).

fof(f5240,plain,
    spl0_613,
    inference(avatar_split_clause,[],[f6,f5238]) ).

fof(f5238,plain,
    ( spl0_613
  <=> ! [X5,X10,X9,X7,X8,X6,X2,X1] :
        ( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_OScons(X10,X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f6,axiom,
    ! [X2,X10,X1,X8,X6,X9,X7,X5] :
      ( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_OScons(X10,X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

fof(f5225,plain,
    spl0_612,
    inference(avatar_split_clause,[],[f10,f5223]) ).

fof(f5223,plain,
    ( spl0_612
  <=> ! [X5,X11,X6,X2,X1] :
        ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f10,axiom,
    ! [X2,X11,X1,X6,X5] :
      ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).

fof(f5199,plain,
    spl0_611,
    inference(avatar_split_clause,[],[f9,f5197]) ).

fof(f5197,plain,
    ( spl0_611
  <=> ! [X5,X11,X6,X2,X1] :
        ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
        | c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f9,axiom,
    ! [X2,X11,X1,X6,X5] :
      ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
      | c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).

fof(f5195,plain,
    spl0_610,
    inference(avatar_split_clause,[],[f8,f5193]) ).

fof(f5193,plain,
    ( spl0_610
  <=> ! [X5,X11,X6,X2,X1] :
        ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
        | c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f8,axiom,
    ! [X2,X11,X1,X6,X5] :
      ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
      | c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).

fof(f5180,plain,
    spl0_609,
    inference(avatar_split_clause,[],[f7,f5178]) ).

fof(f5178,plain,
    ( spl0_609
  <=> ! [X5,X11,X6,X2,X1] :
        ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
        | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f7,axiom,
    ! [X2,X11,X1,X6,X5] :
      ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
      | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).

fof(f5167,plain,
    spl0_608,
    inference(avatar_split_clause,[],[f3,f5165]) ).

fof(f5165,plain,
    ( spl0_608
  <=> ! [X5,X4,X6,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__2(X4,X5,X6,X1,X2),X1,X2),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f3,axiom,
    ! [X2,X1,X6,X4,X5] :
      ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__2(X4,X5,X6,X1,X2),X1,X2),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

fof(f5155,plain,
    spl0_607,
    inference(avatar_split_clause,[],[f12,f5153]) ).

fof(f5153,plain,
    ( spl0_607
  <=> ! [X5,X7,X8,X6,X2,X1] :
        ( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_OIn1(X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f12,axiom,
    ! [X2,X1,X8,X6,X7,X5] :
      ( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_OIn1(X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

fof(f5151,plain,
    spl0_606,
    inference(avatar_split_clause,[],[f11,f5149]) ).

fof(f5149,plain,
    ( spl0_606
  <=> ! [X6,X9,X10,X5,X2,X1] :
        ( ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_OIn0(X10,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f11,axiom,
    ! [X2,X10,X1,X6,X9,X5] :
      ( ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_OIn0(X10,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

fof(f5089,plain,
    spl0_605,
    inference(avatar_split_clause,[],[f5,f5087]) ).

fof(f5,axiom,
    ! [X2,X1,X6,X4,X5] :
      ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__3(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

fof(f5085,plain,
    spl0_604,
    inference(avatar_split_clause,[],[f4,f5083]) ).

fof(f4,axiom,
    ! [X2,X1,X6,X4,X5] :
      ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Main_OdprodE__2(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

fof(f5067,plain,
    spl0_603,
    inference(avatar_split_clause,[],[f54,f5065]) ).

fof(f5065,plain,
    ( spl0_603
  <=> ! [X3,X23,X5,X25,X1] :
        ( ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f54,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).

fof(f5063,plain,
    spl0_602,
    inference(avatar_split_clause,[],[f51,f5061]) ).

fof(f5061,plain,
    ( spl0_602
  <=> ! [X3,X23,X5,X25,X1] :
        ( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | c_in(c_Pair(X25,c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f51,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
      | c_in(c_Pair(X25,c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).

fof(f5026,plain,
    spl0_601,
    inference(avatar_split_clause,[],[f85,f5024]) ).

fof(f5024,plain,
    ( spl0_601
  <=> ! [X31,X4,X18,X6,X5,X27,X2,X1] :
        ( ~ c_in(c_Pair(X27,X4,X2,X31),X5,tc_prod(X2,X31))
        | ~ c_in(c_Pair(X18,X27,X1,X2),X6,tc_prod(X1,X2))
        | c_in(c_Pair(X18,X4,X1,X31),c_Relation_Orel__comp(X5,X6,X2,X31,X1),tc_prod(X1,X31)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f85,axiom,
    ! [X2,X31,X18,X1,X6,X27,X4,X5] :
      ( ~ c_in(c_Pair(X27,X4,X2,X31),X5,tc_prod(X2,X31))
      | ~ c_in(c_Pair(X18,X27,X1,X2),X6,tc_prod(X1,X2))
      | c_in(c_Pair(X18,X4,X1,X31),c_Relation_Orel__comp(X5,X6,X2,X31,X1),tc_prod(X1,X31)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

fof(f5022,plain,
    spl0_600,
    inference(avatar_split_clause,[],[f53,f5020]) ).

fof(f5020,plain,
    ( spl0_600
  <=> ! [X5,X3,X23,X25,X1] :
        ( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X1) = X23
        | ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f53,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X1) = X23
      | ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).

fof(f5018,plain,
    spl0_599,
    inference(avatar_split_clause,[],[f50,f5016]) ).

fof(f5016,plain,
    ( spl0_599
  <=> ! [X5,X3,X23,X25,X1] :
        ( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),X1) = X23
        | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f50,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),X1) = X23
      | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).

fof(f5011,plain,
    spl0_598,
    inference(avatar_split_clause,[],[f55,f5009]) ).

fof(f5009,plain,
    ( spl0_598
  <=> ! [X3,X23,X5,X25,X1] :
        ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),X3,X1,X1),X5,tc_prod(X1,X1))
        | ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f55,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),X3,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).

fof(f5007,plain,
    spl0_597,
    inference(avatar_split_clause,[],[f52,f5005]) ).

fof(f5005,plain,
    ( spl0_597
  <=> ! [X3,X23,X5,X25,X1] :
        ( c_in(c_Pair(X3,c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),X1,X1),X5,tc_prod(X1,X1))
        | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f52,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( c_in(c_Pair(X3,c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),X1,X1),X5,tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).

fof(f4937,plain,
    spl0_596,
    inference(avatar_split_clause,[],[f83,f4935]) ).

fof(f83,axiom,
    ! [X31,X2,X1,X6,X5,X30] :
      ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
      | c_in(c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),X1,X31),X6,tc_prod(X1,X31)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

fof(f4933,plain,
    ( spl0_595
    | ~ spl0_453
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f4025,f3934,f3688,f4931]) ).

fof(f4931,plain,
    ( spl0_595
  <=> ! [X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_H,tc_Message_Omsg)
        | c_in(X1,c_Message_Oanalz(v_H_H),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f4025,plain,
    ( ! [X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_H,tc_Message_Omsg)
        | c_in(X1,c_Message_Oanalz(v_H_H),tc_Message_Omsg) )
    | ~ spl0_453
    | ~ spl0_485 ),
    inference(resolution,[],[f3935,f3689]) ).

fof(f4929,plain,
    spl0_594,
    inference(avatar_split_clause,[],[f82,f4927]) ).

fof(f82,axiom,
    ! [X31,X2,X1,X6,X5,X30] :
      ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
      | c_in(c_Pair(c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X31,X2),X5,tc_prod(X31,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

fof(f4925,plain,
    spl0_593,
    inference(avatar_split_clause,[],[f20,f4923]) ).

fof(f4923,plain,
    ( spl0_593
  <=> ! [X13,X14,X12,X2,X1] :
        ( ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f20,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).

fof(f4905,plain,
    spl0_592,
    inference(avatar_split_clause,[],[f19,f4903]) ).

fof(f4903,plain,
    ( spl0_592
  <=> ! [X13,X14,X12,X2,X1] :
        ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
        | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f19,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
      | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).

fof(f4901,plain,
    spl0_591,
    inference(avatar_split_clause,[],[f18,f4899]) ).

fof(f4899,plain,
    ( spl0_591
  <=> ! [X14,X13,X12,X2,X1] :
        ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
        | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f18,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
      | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).

fof(f4889,plain,
    spl0_590,
    inference(avatar_split_clause,[],[f17,f4887]) ).

fof(f4887,plain,
    ( spl0_590
  <=> ! [X13,X14,X12,X2,X1] :
        ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
        | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
        | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f17,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
      | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
      | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).

fof(f4877,plain,
    ( spl0_589
    | ~ spl0_454
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f4024,f3934,f3700,f4875]) ).

fof(f4875,plain,
    ( spl0_589
  <=> ! [X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_H,tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(v_H_H),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f4024,plain,
    ( ! [X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_H,tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(v_H_H),tc_Message_Omsg) )
    | ~ spl0_454
    | ~ spl0_485 ),
    inference(resolution,[],[f3935,f3701]) ).

fof(f4873,plain,
    spl0_588,
    inference(avatar_split_clause,[],[f115,f4871]) ).

fof(f4871,plain,
    ( spl0_588
  <=> ! [X13,X14,X12,X2,X1] :
        ( ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
        | c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14
        | c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f115,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
      | c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14
      | c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

fof(f4869,plain,
    spl0_587,
    inference(avatar_split_clause,[],[f84,f4867]) ).

fof(f4867,plain,
    ( spl0_587
  <=> ! [X5,X31,X30,X6,X2,X1] :
        ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
        | c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X1,X2) = X30 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f84,axiom,
    ! [X31,X2,X1,X6,X5,X30] :
      ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
      | c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X1,X2) = X30 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

fof(f4863,plain,
    spl0_586,
    inference(avatar_split_clause,[],[f16,f4861]) ).

fof(f4861,plain,
    ( spl0_586
  <=> ! [X9,X13,X7,X12,X2,X1] :
        ( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f16,axiom,
    ! [X2,X1,X9,X7,X12,X13] :
      ( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

fof(f4847,plain,
    spl0_585,
    inference(avatar_split_clause,[],[f117,f4845]) ).

fof(f4845,plain,
    ( spl0_585
  <=> ! [X2,X14,X13,X12,X1] :
        ( c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
        | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
        | c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f117,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
      | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
      | c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

fof(f4843,plain,
    spl0_584,
    inference(avatar_split_clause,[],[f116,f4841]) ).

fof(f4841,plain,
    ( spl0_584
  <=> ! [X13,X14,X12,X2,X1] :
        ( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
        | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
        | c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f116,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
      | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
      | c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

fof(f4839,plain,
    spl0_583,
    inference(avatar_split_clause,[],[f13,f4837]) ).

fof(f4837,plain,
    ( spl0_583
  <=> ! [X4,X13,X12,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_Datatype__Universe_OScons(c_Main_OuprodE__1(X12,X13,X4,X1,X2),c_Main_OuprodE__2(X12,X13,X4,X1,X2),X1,X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f13,axiom,
    ! [X2,X1,X4,X12,X13] :
      ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_Datatype__Universe_OScons(c_Main_OuprodE__1(X12,X13,X4,X1,X2),c_Main_OuprodE__2(X12,X13,X4,X1,X2),X1,X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

fof(f4835,plain,
    ( spl0_582
    | ~ spl0_453
    | ~ spl0_478 ),
    inference(avatar_split_clause,[],[f3971,f3898,f3688,f4833]) ).

fof(f4833,plain,
    ( spl0_582
  <=> ! [X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_G,tc_Message_Omsg)
        | c_in(X1,c_Message_Oanalz(v_G_H),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f3971,plain,
    ( ! [X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_G,tc_Message_Omsg)
        | c_in(X1,c_Message_Oanalz(v_G_H),tc_Message_Omsg) )
    | ~ spl0_453
    | ~ spl0_478 ),
    inference(resolution,[],[f3899,f3689]) ).

fof(f4797,plain,
    spl0_581,
    inference(avatar_split_clause,[],[f1355,f4795]) ).

fof(f4795,plain,
    ( spl0_581
  <=> ! [X3,X0,X5,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
        | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
        | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f1355,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
      | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

fof(f4793,plain,
    spl0_580,
    inference(avatar_split_clause,[],[f1352,f4791]) ).

fof(f4791,plain,
    ( spl0_580
  <=> ! [X3,X0,X5,X1] :
        ( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
        | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
        | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f1352,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
      | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

fof(f4789,plain,
    spl0_579,
    inference(avatar_split_clause,[],[f77,f4787]) ).

fof(f77,axiom,
    ! [X2,X29,X1,X5] :
      ( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
      | c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

fof(f4782,plain,
    spl0_578,
    inference(avatar_split_clause,[],[f118,f4780]) ).

fof(f4780,plain,
    ( spl0_578
  <=> ! [X13,X14,X12,X2,X1] :
        ( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
        | c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
        | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f118,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
      | c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
      | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

fof(f4778,plain,
    ( spl0_577
    | ~ spl0_454
    | ~ spl0_478 ),
    inference(avatar_split_clause,[],[f3970,f3898,f3700,f4776]) ).

fof(f4776,plain,
    ( spl0_577
  <=> ! [X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_G,tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f3970,plain,
    ( ! [X0,X1] :
        ( ~ c_in(c_Message_Omsg_OMPair(X0,X1),v_G,tc_Message_Omsg)
        | c_in(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg) )
    | ~ spl0_454
    | ~ spl0_478 ),
    inference(resolution,[],[f3899,f3701]) ).

fof(f4760,plain,
    spl0_576,
    inference(avatar_split_clause,[],[f1354,f4758]) ).

fof(f4758,plain,
    ( spl0_576
  <=> ! [X3,X0,X5,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
        | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f1354,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

fof(f4756,plain,
    spl0_575,
    inference(avatar_split_clause,[],[f1351,f4754]) ).

fof(f4754,plain,
    ( spl0_575
  <=> ! [X3,X0,X5,X1] :
        ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
        | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f1351,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

fof(f4752,plain,
    spl0_574,
    inference(avatar_split_clause,[],[f1221,f4750]) ).

fof(f4750,plain,
    ( spl0_574
  <=> ! [X23,X12,X25,X1] :
        ( ~ c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f1221,axiom,
    ! [X1,X25,X12,X23] :
      ( ~ c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).

fof(f4748,plain,
    spl0_573,
    inference(avatar_split_clause,[],[f122,f4746]) ).

fof(f4746,plain,
    ( spl0_573
  <=> ! [X5,X18,X27,X1] :
        ( ~ c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1))
        | c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f122,axiom,
    ! [X18,X1,X27,X5] :
      ( ~ c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1))
      | c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

fof(f4744,plain,
    spl0_572,
    inference(avatar_split_clause,[],[f78,f4742]) ).

fof(f4742,plain,
    ( spl0_572
  <=> ! [X5,X29,X2,X1] :
        ( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
        | c_Pair(c_Main_OconverseE__2(X5,X29,X2,X1),c_Main_OconverseE__1(X5,X29,X2,X1),X1,X2) = X29 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f78,axiom,
    ! [X2,X29,X1,X5] :
      ( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
      | c_Pair(c_Main_OconverseE__2(X5,X29,X2,X1),c_Main_OconverseE__1(X5,X29,X2,X1),X1,X2) = X29 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

fof(f4664,plain,
    spl0_571,
    inference(avatar_split_clause,[],[f1289,f4662]) ).

fof(f1289,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( ~ c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
      | c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).

fof(f4660,plain,
    spl0_570,
    inference(avatar_split_clause,[],[f1288,f4658]) ).

fof(f4658,plain,
    ( spl0_570
  <=> ! [X18,X5,X27,X2,X1] :
        ( c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
        | ~ c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f1288,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
      | ~ c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).

fof(f4656,plain,
    spl0_569,
    inference(avatar_split_clause,[],[f73,f4654]) ).

fof(f73,axiom,
    ! [X2,X1,X27,X5,X12] :
      ( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
      | c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

fof(f4652,plain,
    spl0_568,
    inference(avatar_split_clause,[],[f15,f4650]) ).

fof(f15,axiom,
    ! [X2,X1,X4,X12,X13] :
      ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OuprodE__1(X12,X13,X4,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

fof(f4648,plain,
    spl0_567,
    inference(avatar_split_clause,[],[f14,f4646]) ).

fof(f14,axiom,
    ! [X2,X1,X4,X12,X13] :
      ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OuprodE__2(X12,X13,X4,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

fof(f4615,plain,
    spl0_566,
    inference(avatar_split_clause,[],[f121,f4613]) ).

fof(f121,axiom,
    ! [X18,X1,X27,X5] :
      ( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
      | c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

fof(f4611,plain,
    spl0_565,
    inference(avatar_split_clause,[],[f74,f4609]) ).

fof(f74,axiom,
    ! [X2,X18,X1,X27,X5,X12] :
      ( ~ c_in(X18,X12,X1)
      | c_in(X27,c_Relation_OImage(X5,X12,X1,X2),X2)
      | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

fof(f4537,plain,
    ( spl0_564
    | ~ spl0_2
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4207,f4109,f1400,f4535]) ).

fof(f4207,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_H,tc_set(tc_Message_Omsg))
        | c_lessequals(X0,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)) )
    | ~ spl0_2
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f1402]) ).

fof(f4531,plain,
    spl0_563,
    inference(avatar_split_clause,[],[f1287,f4529]) ).

fof(f4529,plain,
    ( spl0_563
  <=> ! [X5,X18,X27,X2,X1] :
        ( ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
        | c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f1287,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
      | c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).

fof(f4527,plain,
    spl0_562,
    inference(avatar_split_clause,[],[f1286,f4525]) ).

fof(f4525,plain,
    ( spl0_562
  <=> ! [X5,X18,X27,X2,X1] :
        ( c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
        | ~ c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f1286,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
      | ~ c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).

fof(f4523,plain,
    spl0_561,
    inference(avatar_split_clause,[],[f1191,f4521]) ).

fof(f4521,plain,
    ( spl0_561
  <=> ! [X18,X13,X12,X1] :
        ( ~ c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f1191,axiom,
    ! [X1,X18,X12,X13] :
      ( ~ c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

fof(f4519,plain,
    spl0_560,
    inference(avatar_split_clause,[],[f1190,f4517]) ).

fof(f4517,plain,
    ( spl0_560
  <=> ! [X18,X13,X12,X1] :
        ( c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f1190,axiom,
    ! [X1,X18,X12,X13] :
      ( c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

fof(f4515,plain,
    spl0_559,
    inference(avatar_split_clause,[],[f79,f4513]) ).

fof(f4513,plain,
    ( spl0_559
  <=> ! [X12,X1,X4] :
        ( ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
        | c_Pair(c_Main_OdiagE__1(X12,X4,X1),c_Main_OdiagE__1(X12,X4,X1),X1,X1) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f79,axiom,
    ! [X1,X4,X12] :
      ( ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
      | c_Pair(c_Main_OdiagE__1(X12,X4,X1),c_Main_OdiagE__1(X12,X4,X1),X1,X1) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

fof(f4511,plain,
    spl0_558,
    inference(avatar_split_clause,[],[f75,f4509]) ).

fof(f75,axiom,
    ! [X2,X1,X27,X5] :
      ( ~ c_in(X27,c_Relation_ORange(X5,X2,X1),X1)
      | c_in(c_Pair(c_Main_ORangeE__1(X27,X5,X1,X2),X27,X2,X1),X5,tc_prod(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

fof(f4507,plain,
    spl0_557,
    inference(avatar_split_clause,[],[f69,f4505]) ).

fof(f69,axiom,
    ! [X2,X18,X1,X5] :
      ( ~ c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
      | c_in(c_Pair(X18,c_Main_ODomainE__1(X18,X5,X1,X2),X1,X2),X5,tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

fof(f4503,plain,
    spl0_556,
    inference(avatar_split_clause,[],[f60,f4501]) ).

fof(f4501,plain,
    ( spl0_556
  <=> ! [X18,X12,X1,X26] :
        ( ~ c_in(X18,X12,X1)
        | ~ c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | c_in(c_List_Olist_OCons(X18,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f60,axiom,
    ! [X18,X1,X26,X12] :
      ( ~ c_in(X18,X12,X1)
      | ~ c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | c_in(c_List_Olist_OCons(X18,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

fof(f4499,plain,
    ( spl0_555
    | ~ spl0_1
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f4206,f4109,f1395,f4497]) ).

fof(f4206,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_G,tc_set(tc_Message_Omsg))
        | c_lessequals(X0,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) )
    | ~ spl0_1
    | ~ spl0_514 ),
    inference(resolution,[],[f4110,f1397]) ).

fof(f4495,plain,
    spl0_554,
    inference(avatar_split_clause,[],[f22,f4493]) ).

fof(f4493,plain,
    ( spl0_554
  <=> ! [X13,X7,X12,X2,X1] :
        ( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f22,axiom,
    ! [X2,X1,X7,X12,X13] :
      ( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).

fof(f4491,plain,
    spl0_553,
    inference(avatar_split_clause,[],[f21,f4489]) ).

fof(f4489,plain,
    ( spl0_553
  <=> ! [X13,X12,X9,X2,X1] :
        ( ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f21,axiom,
    ! [X2,X1,X9,X12,X13] :
      ( ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).

fof(f4467,plain,
    spl0_552,
    inference(avatar_split_clause,[],[f33,f4465]) ).

fof(f4465,plain,
    ( spl0_552
  <=> ! [X12,X1] :
        ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
        | ~ c_in(c_Main_Ofinite__Union__1(X12,X1),c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f33,axiom,
    ! [X1,X12] :
      ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
      | ~ c_in(c_Main_Ofinite__Union__1(X12,X1),c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

fof(f4463,plain,
    spl0_551,
    inference(avatar_split_clause,[],[f32,f4461]) ).

fof(f4461,plain,
    ( spl0_551
  <=> ! [X12,X1] :
        ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
        | c_in(c_Main_Ofinite__Union__1(X12,X1),X12,tc_set(X1))
        | c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f32,axiom,
    ! [X1,X12] :
      ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
      | c_in(c_Main_Ofinite__Union__1(X12,X1),X12,tc_set(X1))
      | c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

fof(f4455,plain,
    spl0_550,
    inference(avatar_split_clause,[],[f1369,f4453]) ).

fof(f1369,axiom,
    ! [X58,X55,X53] :
      ( c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X58)),c_Message_Oanalz(X55),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(X58,X53),c_Message_Oanalz(X55),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).

fof(f4451,plain,
    spl0_549,
    inference(avatar_split_clause,[],[f1242,f4449]) ).

fof(f4449,plain,
    ( spl0_549
  <=> ! [X3,X23,X25,X1] :
        ( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
        | c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f1242,axiom,
    ! [X3,X1,X25,X23] :
      ( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
      | c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff1_0) ).

fof(f4447,plain,
    spl0_548,
    inference(avatar_split_clause,[],[f57,f4445]) ).

fof(f57,axiom,
    ! [X1,X5,X23] :
      ( c_List_Olist_ONil = X23
      | ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

fof(f4443,plain,
    spl0_547,
    inference(avatar_split_clause,[],[f56,f4441]) ).

fof(f56,axiom,
    ! [X1,X5,X23] :
      ( c_List_Olist_ONil = X23
      | ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

fof(f4424,plain,
    spl0_546,
    inference(avatar_split_clause,[],[f1373,f4422]) ).

fof(f1373,axiom,
    ! [X55,X4,X20] :
      ( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
      | c_in(X4,c_Message_Oparts(X55),tc_Message_Omsg)
      | ~ c_in(X4,c_Message_Oparts(c_union(X20,X55,tc_Message_Omsg)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).

fof(f4420,plain,
    spl0_545,
    inference(avatar_split_clause,[],[f1218,f4418]) ).

fof(f1218,axiom,
    ! [X3,X0,X1,X25,X23] :
      ( X0 = X3
      | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).

fof(f4416,plain,
    ( ~ spl0_544
    | ~ spl0_378
    | ~ spl0_527 ),
    inference(avatar_split_clause,[],[f4389,f4282,f3324,f4413]) ).

fof(f4413,plain,
    ( spl0_544
  <=> c_lessequals(c_Message_Oanalz(v_H_H),v_H,tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f3324,plain,
    ( spl0_378
  <=> ! [X13,X12,X1] :
        ( ~ c_less(X12,X13,tc_set(X1))
        | ~ c_lessequals(X13,X12,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f4282,plain,
    ( spl0_527
  <=> c_less(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f4389,plain,
    ( ~ c_lessequals(c_Message_Oanalz(v_H_H),v_H,tc_set(tc_Message_Omsg))
    | ~ spl0_378
    | ~ spl0_527 ),
    inference(resolution,[],[f4284,f3325]) ).

fof(f3325,plain,
    ( ! [X1,X12,X13] :
        ( ~ c_less(X12,X13,tc_set(X1))
        | ~ c_lessequals(X13,X12,tc_set(X1)) )
    | ~ spl0_378 ),
    inference(avatar_component_clause,[],[f3324]) ).

fof(f4284,plain,
    ( c_less(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg))
    | ~ spl0_527 ),
    inference(avatar_component_clause,[],[f4282]) ).

fof(f4411,plain,
    spl0_543,
    inference(avatar_split_clause,[],[f1217,f4409]) ).

fof(f1217,axiom,
    ! [X3,X0,X1,X25,X23] :
      ( X23 = X25
      | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).

fof(f4407,plain,
    spl0_542,
    inference(avatar_split_clause,[],[f1196,f4405]) ).

fof(f4405,plain,
    ( spl0_542
  <=> ! [X20,X1,X19] :
        ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f1196,axiom,
    ! [X1,X19,X20] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).

fof(f4341,plain,
    spl0_541,
    inference(avatar_split_clause,[],[f1342,f4339]) ).

fof(f4339,plain,
    ( spl0_541
  <=> ! [X12,X27,X1,X18] :
        ( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
        | c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f1342,axiom,
    ! [X1,X18,X27,X12] :
      ( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
      | c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

fof(f4337,plain,
    spl0_540,
    inference(avatar_split_clause,[],[f1340,f4335]) ).

fof(f1340,axiom,
    ! [X0,X1,X12] :
      ( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
      | c_insert(X0,c_emptyset,X1) = c_insert(X0,X12,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

fof(f4333,plain,
    spl0_539,
    inference(avatar_split_clause,[],[f1220,f4331]) ).

fof(f4331,plain,
    ( spl0_539
  <=> ! [X12,X1,X23,X25] :
        ( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f1220,axiom,
    ! [X1,X25,X12,X23] :
      ( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).

fof(f4329,plain,
    spl0_538,
    inference(avatar_split_clause,[],[f1219,f4327]) ).

fof(f4327,plain,
    ( spl0_538
  <=> ! [X23,X12,X25,X1] :
        ( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f1219,axiom,
    ! [X1,X12,X23,X25] :
      ( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).

fof(f4325,plain,
    spl0_537,
    inference(avatar_split_clause,[],[f1201,f4323]) ).

fof(f1201,axiom,
    ! [X21,X16,X15] :
      ( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
      | ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
      | c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff2_0) ).

fof(f4321,plain,
    spl0_536,
    inference(avatar_split_clause,[],[f1198,f4319]) ).

fof(f4319,plain,
    ( spl0_536
  <=> ! [X2,X5,X1] :
        ( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
        | c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f1198,axiom,
    ! [X2,X1,X5] :
      ( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
      | c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).

fof(f4317,plain,
    spl0_535,
    inference(avatar_split_clause,[],[f1197,f4315]) ).

fof(f4315,plain,
    ( spl0_535
  <=> ! [X2,X5,X1] :
        ( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
        | ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f1197,axiom,
    ! [X2,X1,X5] :
      ( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
      | ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).

fof(f4313,plain,
    spl0_534,
    inference(avatar_split_clause,[],[f114,f4311]) ).

fof(f4311,plain,
    ( spl0_534
  <=> ! [X13,X12,X27,X2,X1] :
        ( ~ c_in(X27,X13,X1)
        | c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f114,axiom,
    ! [X2,X1,X27,X12,X13] :
      ( ~ c_in(X27,X13,X1)
      | c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

fof(f4309,plain,
    spl0_533,
    inference(avatar_split_clause,[],[f113,f4307]) ).

fof(f4307,plain,
    ( spl0_533
  <=> ! [X18,X13,X12,X2,X1] :
        ( ~ c_in(X18,X12,X1)
        | c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f113,axiom,
    ! [X2,X18,X1,X12,X13] :
      ( ~ c_in(X18,X12,X1)
      | c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

fof(f4305,plain,
    spl0_532,
    inference(avatar_split_clause,[],[f76,f4303]) ).

fof(f76,axiom,
    ! [X2,X1,X18,X27,X5] :
      ( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
      | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

fof(f4301,plain,
    spl0_531,
    inference(avatar_split_clause,[],[f72,f4299]) ).

fof(f4299,plain,
    ( spl0_531
  <=> ! [X12,X5,X27,X2,X1] :
        ( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
        | c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f72,axiom,
    ! [X2,X1,X27,X5,X12] :
      ( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
      | c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

fof(f4297,plain,
    spl0_530,
    inference(avatar_split_clause,[],[f71,f4295]) ).

fof(f71,axiom,
    ! [X28,X1] :
      ( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
      | c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

fof(f4293,plain,
    spl0_529,
    inference(avatar_split_clause,[],[f70,f4291]) ).

fof(f70,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
      | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

fof(f4289,plain,
    ( spl0_527
    | spl0_528
    | ~ spl0_2
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f3873,f3818,f1400,f4286,f4282]) ).

fof(f4286,plain,
    ( spl0_528
  <=> v_H = c_Message_Oanalz(v_H_H) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f3873,plain,
    ( v_H = c_Message_Oanalz(v_H_H)
    | c_less(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg))
    | ~ spl0_2
    | ~ spl0_466 ),
    inference(resolution,[],[f3819,f1402]) ).

fof(f4280,plain,
    spl0_526,
    inference(avatar_split_clause,[],[f58,f4278]) ).

fof(f4278,plain,
    ( spl0_526
  <=> ! [X12,X0,X1,X26] :
        ( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f58,axiom,
    ! [X0,X1,X26,X12] :
      ( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

fof(f4276,plain,
    spl0_525,
    inference(avatar_split_clause,[],[f46,f4274]) ).

fof(f4274,plain,
    ( spl0_525
  <=> ! [X24,X23,X12,X1] :
        ( c_in(X24,X12,X1)
        | ~ c_in(X24,c_List_Oset(X23,X1),X1)
        | ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f46,axiom,
    ! [X1,X24,X12,X23] :
      ( c_in(X24,X12,X1)
      | ~ c_in(X24,c_List_Oset(X23,X1),X1)
      | ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

fof(f4249,plain,
    spl0_524,
    inference(avatar_split_clause,[],[f1318,f4247]) ).

fof(f4247,plain,
    ( spl0_524
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X12,X1)
        | c_in(X4,X13,X1)
        | c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f1318,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X12,X1)
      | c_in(X4,X13,X1)
      | c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

fof(f4245,plain,
    spl0_523,
    inference(avatar_split_clause,[],[f1315,f4243]) ).

fof(f1315,axiom,
    ! [X1,X12,X13] :
      ( ~ c_lessequals(X13,X12,tc_set(X1))
      | c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).

fof(f4241,plain,
    spl0_522,
    inference(avatar_split_clause,[],[f1314,f4239]) ).

fof(f4239,plain,
    ( spl0_522
  <=> ! [X13,X12,X1] :
        ( c_lessequals(X13,X12,tc_set(X1))
        | ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f1314,axiom,
    ! [X1,X12,X13] :
      ( c_lessequals(X13,X12,tc_set(X1))
      | ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).

fof(f4237,plain,
    spl0_521,
    inference(avatar_split_clause,[],[f1243,f4235]) ).

fof(f1243,axiom,
    ! [X3,X1,X25] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff2_0) ).

fof(f4233,plain,
    spl0_520,
    inference(avatar_split_clause,[],[f1236,f4231]) ).

fof(f4231,plain,
    ( spl0_520
  <=> ! [X1,X23] :
        ( c_List_Oremdups(X23,X1) = X23
        | c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f1236,axiom,
    ! [X1,X23] :
      ( c_List_Oremdups(X23,X1) = X23
      | c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).

fof(f4229,plain,
    spl0_519,
    inference(avatar_split_clause,[],[f1216,f4227]) ).

fof(f1216,axiom,
    ! [X1,X5,X25] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).

fof(f4225,plain,
    spl0_518,
    inference(avatar_split_clause,[],[f1210,f4223]) ).

fof(f1210,axiom,
    ! [X1,X5,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).

fof(f4221,plain,
    spl0_517,
    inference(avatar_split_clause,[],[f81,f4219]) ).

fof(f81,axiom,
    ! [X18,X1,X12] :
      ( ~ c_in(X18,X12,X1)
      | c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

fof(f4217,plain,
    spl0_516,
    inference(avatar_split_clause,[],[f47,f4215]) ).

fof(f47,axiom,
    ! [X1,X12,X23] :
      ( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

fof(f4213,plain,
    ( ~ spl0_515
    | ~ spl0_378
    | ~ spl0_502 ),
    inference(avatar_split_clause,[],[f4135,f4060,f3324,f4210]) ).

fof(f4210,plain,
    ( spl0_515
  <=> c_lessequals(c_Message_Oanalz(v_G_H),v_G,tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f4060,plain,
    ( spl0_502
  <=> c_less(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f4135,plain,
    ( ~ c_lessequals(c_Message_Oanalz(v_G_H),v_G,tc_set(tc_Message_Omsg))
    | ~ spl0_378
    | ~ spl0_502 ),
    inference(resolution,[],[f4062,f3325]) ).

fof(f4062,plain,
    ( c_less(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
    | ~ spl0_502 ),
    inference(avatar_component_clause,[],[f4060]) ).

fof(f4111,plain,
    spl0_514,
    inference(avatar_split_clause,[],[f1389,f4109]) ).

fof(f1389,axiom,
    ! [X1,X12,X32,X13] :
      ( ~ c_lessequals(X13,X32,tc_set(X1))
      | ~ c_lessequals(X12,X13,tc_set(X1))
      | c_lessequals(X12,X32,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).

fof(f4107,plain,
    spl0_513,
    inference(avatar_split_clause,[],[f1353,f4105]) ).

fof(f4105,plain,
    ( spl0_513
  <=> ! [X5,X1,X0,X3] :
        ( c_Wellfounded__Recursion_Owf(X5,X1)
        | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f1353,axiom,
    ! [X3,X0,X1,X5] :
      ( c_Wellfounded__Recursion_Owf(X5,X1)
      | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

fof(f4103,plain,
    spl0_512,
    inference(avatar_split_clause,[],[f1350,f4101]) ).

fof(f4101,plain,
    ( spl0_512
  <=> ! [X5,X1,X0,X3] :
        ( c_Wellfounded__Recursion_Oacyclic(X5,X1)
        | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f1350,axiom,
    ! [X3,X0,X1,X5] :
      ( c_Wellfounded__Recursion_Oacyclic(X5,X1)
      | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

fof(f4099,plain,
    spl0_511,
    inference(avatar_split_clause,[],[f1332,f4097]) ).

fof(f1332,axiom,
    ! [X1,X53,X12,X32] :
      ( ~ c_in(X12,X53,X1)
      | ~ c_in(X53,X32,tc_set(X1))
      | c_in(X12,c_Union(X32,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).

fof(f4095,plain,
    spl0_510,
    inference(avatar_split_clause,[],[f1328,f4093]) ).

fof(f4093,plain,
    ( spl0_510
  <=> ! [X4,X13,X12,X1] :
        ( c_in(X4,X12,X1)
        | c_in(X4,X13,X1)
        | ~ c_in(X4,c_union(X12,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f1328,axiom,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X12,X1)
      | c_in(X4,X13,X1)
      | ~ c_in(X4,c_union(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

fof(f4091,plain,
    spl0_509,
    inference(avatar_split_clause,[],[f1322,f4089]) ).

fof(f1322,axiom,
    ! [X1,X53,X12,X32] :
      ( c_in(X12,X53,X1)
      | ~ c_in(X53,X32,tc_set(X1))
      | ~ c_in(X12,c_Inter(X32,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).

fof(f4087,plain,
    spl0_508,
    inference(avatar_split_clause,[],[f1321,f4085]) ).

fof(f4085,plain,
    ( spl0_508
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X13,X1)
        | ~ c_in(X4,X12,X1)
        | c_in(X4,c_inter(X12,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f1321,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X13,X1)
      | ~ c_in(X4,X12,X1)
      | c_in(X4,c_inter(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).

fof(f4083,plain,
    spl0_507,
    inference(avatar_split_clause,[],[f1310,f4081]) ).

fof(f1310,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | ~ c_lessequals(X0,X3,X1)
      | c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).

fof(f4079,plain,
    spl0_506,
    inference(avatar_split_clause,[],[f1309,f4077]) ).

fof(f4077,plain,
    ( spl0_506
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_lessequals(X0,X3,X1)
        | ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f1309,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_lessequals(X0,X3,X1)
      | ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).

fof(f4075,plain,
    spl0_505,
    inference(avatar_split_clause,[],[f1305,f4073]) ).

fof(f1305,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | ~ c_lessequals(X3,X0,X1)
      | c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).

fof(f4071,plain,
    spl0_504,
    inference(avatar_split_clause,[],[f1304,f4069]) ).

fof(f1304,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_lessequals(X3,X0,X1)
      | ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).

fof(f4067,plain,
    ( spl0_502
    | spl0_503
    | ~ spl0_1
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f3872,f3818,f1395,f4064,f4060]) ).

fof(f4064,plain,
    ( spl0_503
  <=> v_G = c_Message_Oanalz(v_G_H) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f3872,plain,
    ( v_G = c_Message_Oanalz(v_G_H)
    | c_less(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg))
    | ~ spl0_1
    | ~ spl0_466 ),
    inference(resolution,[],[f3819,f1397]) ).

fof(f4058,plain,
    spl0_501,
    inference(avatar_split_clause,[],[f1300,f4056]) ).

fof(f1300,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | ~ c_lessequals(X0,X3,X1)
      | c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).

fof(f4054,plain,
    spl0_500,
    inference(avatar_split_clause,[],[f1299,f4052]) ).

fof(f4052,plain,
    ( spl0_500
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Oorder(X1)
        | c_lessequals(X0,X3,X1)
        | ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f1299,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | c_lessequals(X0,X3,X1)
      | ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).

fof(f4050,plain,
    spl0_499,
    inference(avatar_split_clause,[],[f1295,f4048]) ).

fof(f1295,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | ~ c_lessequals(X3,X0,X1)
      | c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).

fof(f4046,plain,
    spl0_498,
    inference(avatar_split_clause,[],[f1294,f4044]) ).

fof(f4044,plain,
    ( spl0_498
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Oorder(X1)
        | c_lessequals(X3,X0,X1)
        | ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f1294,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | c_lessequals(X3,X0,X1)
      | ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).

fof(f4042,plain,
    spl0_497,
    inference(avatar_split_clause,[],[f1263,f4040]) ).

fof(f1263,axiom,
    ! [X21,X15] :
      ( c_less(c_0,X15,tc_nat)
      | c_less(c_0,X21,tc_nat)
      | ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).

fof(f4038,plain,
    spl0_496,
    inference(avatar_split_clause,[],[f127,f4036]) ).

fof(f4036,plain,
    ( spl0_496
  <=> ! [X35,X36,X2,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(X35,X2)
        | ~ c_Wellfounded__Recursion_Owf(X36,X1)
        | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f127,axiom,
    ! [X2,X36,X1,X35] :
      ( ~ c_Wellfounded__Recursion_Owf(X35,X2)
      | ~ c_Wellfounded__Recursion_Owf(X36,X1)
      | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).

fof(f4034,plain,
    spl0_495,
    inference(avatar_split_clause,[],[f125,f4032]) ).

fof(f4032,plain,
    ( spl0_495
  <=> ! [X34,X33,X2,X1] :
        ( ~ c_Relation_Otrans(X33,X2)
        | ~ c_Relation_Otrans(X34,X1)
        | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f125,axiom,
    ! [X2,X1,X34,X33] :
      ( ~ c_Relation_Otrans(X33,X2)
      | ~ c_Relation_Otrans(X34,X1)
      | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).

fof(f4030,plain,
    spl0_494,
    inference(avatar_split_clause,[],[f80,f4028]) ).

fof(f80,axiom,
    ! [X1,X4,X12] :
      ( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
      | ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

fof(f3968,plain,
    spl0_493,
    inference(avatar_split_clause,[],[f1357,f3966]) ).

fof(f1357,axiom,
    ! [X3,X0] :
      ( ~ c_less(X0,X3,tc_nat)
      | c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).

fof(f3964,plain,
    spl0_492,
    inference(avatar_split_clause,[],[f1356,f3962]) ).

fof(f1356,axiom,
    ! [X3,X0] :
      ( c_less(X0,X3,tc_nat)
      | ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).

fof(f3960,plain,
    spl0_491,
    inference(avatar_split_clause,[],[f1336,f3958]) ).

fof(f3958,plain,
    ( spl0_491
  <=> ! [X18,X12,X27,X1] :
        ( X18 = X27
        | c_in(X18,X12,X1)
        | ~ c_in(X18,c_insert(X27,X12,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f1336,axiom,
    ! [X18,X1,X27,X12] :
      ( X18 = X27
      | c_in(X18,X12,X1)
      | ~ c_in(X18,c_insert(X27,X12,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

fof(f3956,plain,
    spl0_490,
    inference(avatar_split_clause,[],[f1284,f3954]) ).

fof(f3954,plain,
    ( spl0_490
  <=> ! [X2,X41,X18,X27,X52,X1] :
        ( X27 = X52
        | c_Pair(X18,X27,X1,X2) != c_Pair(X41,X52,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f1284,axiom,
    ! [X2,X41,X18,X1,X27,X52] :
      ( X27 = X52
      | c_Pair(X18,X27,X1,X2) != c_Pair(X41,X52,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).

fof(f3952,plain,
    spl0_489,
    inference(avatar_split_clause,[],[f1283,f3950]) ).

fof(f3950,plain,
    ( spl0_489
  <=> ! [X52,X41,X18,X27,X2,X1] :
        ( X18 = X41
        | c_Pair(X18,X27,X1,X2) != c_Pair(X41,X52,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f1283,axiom,
    ! [X2,X41,X18,X1,X27,X52] :
      ( X18 = X41
      | c_Pair(X18,X27,X1,X2) != c_Pair(X41,X52,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).

fof(f3948,plain,
    spl0_488,
    inference(avatar_split_clause,[],[f1178,f3946]) ).

fof(f3946,plain,
    ( spl0_488
  <=> ! [X9,X7,X8,X10,X2,X1] :
        ( X7 = X8
        | c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f1178,axiom,
    ! [X2,X10,X1,X8,X9,X7] :
      ( X7 = X8
      | c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

fof(f3944,plain,
    spl0_487,
    inference(avatar_split_clause,[],[f1177,f3942]) ).

fof(f3942,plain,
    ( spl0_487
  <=> ! [X7,X10,X8,X9,X2,X1] :
        ( X9 = X10
        | c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f1177,axiom,
    ! [X2,X10,X1,X8,X9,X7] :
      ( X9 = X10
      | c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

fof(f3940,plain,
    spl0_486,
    inference(avatar_split_clause,[],[f119,f3938]) ).

fof(f119,axiom,
    ! [X28,X1,X5] :
      ( ~ c_in(X28,X5,tc_prod(X1,X1))
      | c_in(X28,c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

fof(f3936,plain,
    ( spl0_485
    | ~ spl0_2
    | ~ spl0_468 ),
    inference(avatar_split_clause,[],[f3883,f3826,f1400,f3934]) ).

fof(f3883,plain,
    ( ! [X0] :
        ( c_in(X0,c_Message_Oanalz(v_H_H),tc_Message_Omsg)
        | ~ c_in(X0,v_H,tc_Message_Omsg) )
    | ~ spl0_2
    | ~ spl0_468 ),
    inference(resolution,[],[f3827,f1402]) ).

fof(f3932,plain,
    spl0_484,
    inference(avatar_split_clause,[],[f99,f3930]) ).

fof(f99,axiom,
    ! [X1,X12,X32] :
      ( ~ c_in(X12,c_Union(X32,X1),X1)
      | c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).

fof(f3928,plain,
    spl0_483,
    inference(avatar_split_clause,[],[f96,f3926]) ).

fof(f96,axiom,
    ! [X1,X12,X32] :
      ( c_in(X12,c_Inter(X32,X1),X1)
      | c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).

fof(f3924,plain,
    spl0_482,
    inference(avatar_split_clause,[],[f59,f3922]) ).

fof(f3922,plain,
    ( spl0_482
  <=> ! [X0,X12,X1,X26] :
        ( c_in(X0,X12,X1)
        | ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f59,axiom,
    ! [X0,X1,X26,X12] :
      ( c_in(X0,X12,X1)
      | ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

fof(f3920,plain,
    spl0_481,
    inference(avatar_split_clause,[],[f48,f3918]) ).

fof(f48,axiom,
    ! [X1,X12,X23] :
      ( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
      | c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

fof(f3916,plain,
    spl0_480,
    inference(avatar_split_clause,[],[f43,f3914]) ).

fof(f3914,plain,
    ( spl0_480
  <=> ! [X17,X15] :
        ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
        | c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f43,axiom,
    ! [X17,X15] :
      ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
      | c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

fof(f3912,plain,
    spl0_479,
    inference(avatar_split_clause,[],[f27,f3910]) ).

fof(f3910,plain,
    ( spl0_479
  <=> ! [X17,X15] :
        ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
        | c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f27,axiom,
    ! [X17,X15] :
      ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
      | c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).

fof(f3900,plain,
    ( spl0_478
    | ~ spl0_1
    | ~ spl0_468 ),
    inference(avatar_split_clause,[],[f3882,f3826,f1395,f3898]) ).

fof(f3882,plain,
    ( ! [X0] :
        ( c_in(X0,c_Message_Oanalz(v_G_H),tc_Message_Omsg)
        | ~ c_in(X0,v_G,tc_Message_Omsg) )
    | ~ spl0_1
    | ~ spl0_468 ),
    inference(resolution,[],[f3827,f1397]) ).

fof(f3864,plain,
    ( spl0_477
    | ~ spl0_306
    | ~ spl0_429 ),
    inference(avatar_split_clause,[],[f3748,f3580,f2980,f3862]) ).

fof(f3862,plain,
    ( spl0_477
  <=> ! [X2,X0,X1] :
        ( c_append(X2,c_List_Olist_ONil,X1) != X0
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f2980,plain,
    ( spl0_306
  <=> ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f3580,plain,
    ( spl0_429
  <=> ! [X43,X23,X25,X1] :
        ( X25 = X43
        | c_append(X25,X23,X1) != c_append(X43,X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f3748,plain,
    ( ! [X2,X0,X1] :
        ( c_append(X2,c_List_Olist_ONil,X1) != X0
        | X0 = X2 )
    | ~ spl0_306
    | ~ spl0_429 ),
    inference(superposition,[],[f3581,f2981]) ).

fof(f2981,plain,
    ( ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23
    | ~ spl0_306 ),
    inference(avatar_component_clause,[],[f2980]) ).

fof(f3581,plain,
    ( ! [X1,X25,X23,X43] :
        ( c_append(X25,X23,X1) != c_append(X43,X23,X1)
        | X25 = X43 )
    | ~ spl0_429 ),
    inference(avatar_component_clause,[],[f3580]) ).

fof(f3860,plain,
    spl0_476,
    inference(avatar_split_clause,[],[f1290,f3858]) ).

fof(f1290,axiom,
    ! [X18,X1,X27] :
      ( X18 = X27
      | ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).

fof(f3856,plain,
    spl0_475,
    inference(avatar_split_clause,[],[f1200,f3854]) ).

fof(f1200,axiom,
    ! [X21,X16,X15] :
      ( c_Divides_Oop_Advd(X16,X21,tc_nat)
      | ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).

fof(f3852,plain,
    spl0_474,
    inference(avatar_split_clause,[],[f1199,f3850]) ).

fof(f1199,axiom,
    ! [X21,X16,X15] :
      ( c_Divides_Oop_Advd(X16,X15,tc_nat)
      | ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).

fof(f3848,plain,
    spl0_473,
    inference(avatar_split_clause,[],[f1195,f3846]) ).

fof(f3846,plain,
    ( spl0_473
  <=> ! [X20,X1,X19] :
        ( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f1195,axiom,
    ! [X1,X19,X20] :
      ( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).

fof(f3844,plain,
    spl0_472,
    inference(avatar_split_clause,[],[f1194,f3842]) ).

fof(f3842,plain,
    ( spl0_472
  <=> ! [X20,X1,X19] :
        ( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f1194,axiom,
    ! [X1,X19,X20] :
      ( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).

fof(f3840,plain,
    spl0_471,
    inference(avatar_split_clause,[],[f1193,f3838]) ).

fof(f1193,axiom,
    ! [X1,X12] :
      ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

fof(f3836,plain,
    spl0_470,
    inference(avatar_split_clause,[],[f1192,f3834]) ).

fof(f3834,plain,
    ( spl0_470
  <=> ! [X12,X1] :
        ( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f1192,axiom,
    ! [X1,X12] :
      ( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

fof(f3832,plain,
    spl0_469,
    inference(avatar_split_clause,[],[f111,f3830]) ).

fof(f111,axiom,
    ! [X1,X12,X13] :
      ( X12 = X13
      | ~ c_lessequals(X12,X13,tc_set(X1))
      | ~ c_lessequals(X13,X12,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

fof(f3828,plain,
    spl0_468,
    inference(avatar_split_clause,[],[f108,f3826]) ).

fof(f108,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X12,X1)
      | c_in(X4,X13,X1)
      | ~ c_lessequals(X12,X13,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

fof(f3824,plain,
    ( spl0_467
    | ~ spl0_303
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f3721,f3547,f2968,f3822]) ).

fof(f3822,plain,
    ( spl0_467
  <=> ! [X0] : c_lessequals(c_Nat_Osize(c_List_Oremdups(c_List_Olist_ONil,X0),tc_List_Olist(X0)),c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f2968,plain,
    ( spl0_303
  <=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f3547,plain,
    ( spl0_421
  <=> ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f3721,plain,
    ( ! [X0] : c_lessequals(c_Nat_Osize(c_List_Oremdups(c_List_Olist_ONil,X0),tc_List_Olist(X0)),c_0,tc_nat)
    | ~ spl0_303
    | ~ spl0_421 ),
    inference(superposition,[],[f3548,f2969]) ).

fof(f2969,plain,
    ( ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1))
    | ~ spl0_303 ),
    inference(avatar_component_clause,[],[f2968]) ).

fof(f3548,plain,
    ( ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
    | ~ spl0_421 ),
    inference(avatar_component_clause,[],[f3547]) ).

fof(f3820,plain,
    spl0_466,
    inference(avatar_split_clause,[],[f104,f3818]) ).

fof(f104,axiom,
    ! [X1,X12,X13] :
      ( X12 = X13
      | ~ c_lessequals(X12,X13,tc_set(X1))
      | c_less(X12,X13,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

fof(f3816,plain,
    spl0_465,
    inference(avatar_split_clause,[],[f100,f3814]) ).

fof(f100,axiom,
    ! [X1,X12,X32] :
      ( ~ c_in(X12,c_Union(X32,X1),X1)
      | c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

fof(f3812,plain,
    spl0_464,
    inference(avatar_split_clause,[],[f97,f3810]) ).

fof(f3810,plain,
    ( spl0_464
  <=> ! [X12,X32,X1] :
        ( c_in(X12,c_Inter(X32,X1),X1)
        | ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f97,axiom,
    ! [X1,X12,X32] :
      ( c_in(X12,c_Inter(X32,X1),X1)
      | ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).

fof(f3808,plain,
    spl0_463,
    inference(avatar_split_clause,[],[f31,f3806]) ).

fof(f31,axiom,
    ! [X1,X19,X20] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

fof(f3804,plain,
    spl0_462,
    inference(avatar_split_clause,[],[f30,f3802]) ).

fof(f30,axiom,
    ! [X1,X19,X20] :
      ( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

fof(f3800,plain,
    spl0_461,
    inference(avatar_split_clause,[],[f29,f3798]) ).

fof(f29,axiom,
    ! [X1,X18,X12] :
      ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

fof(f3782,plain,
    ( spl0_460
    | ~ spl0_300
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f3729,f3551,f2956,f3780]) ).

fof(f3780,plain,
    ( spl0_460
  <=> ! [X0] : c_lessequals(c_Message_Oparts(c_emptyset),X0,tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f2956,plain,
    ( spl0_300
  <=> ! [X53] : ~ c_in(X53,c_Message_Oparts(c_emptyset),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f3729,plain,
    ( ! [X0] : c_lessequals(c_Message_Oparts(c_emptyset),X0,tc_set(tc_Message_Omsg))
    | ~ spl0_300
    | ~ spl0_422 ),
    inference(resolution,[],[f3552,f2957]) ).

fof(f2957,plain,
    ( ! [X53] : ~ c_in(X53,c_Message_Oparts(c_emptyset),tc_Message_Omsg)
    | ~ spl0_300 ),
    inference(avatar_component_clause,[],[f2956]) ).

fof(f3743,plain,
    ( spl0_459
    | ~ spl0_64
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f3734,f3560,f1702,f3741]) ).

fof(f3741,plain,
    ( spl0_459
  <=> ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f3734,plain,
    ( ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1))
    | ~ spl0_64
    | ~ spl0_424 ),
    inference(resolution,[],[f3561,f1703]) ).

fof(f3718,plain,
    spl0_458,
    inference(avatar_split_clause,[],[f1383,f3716]) ).

fof(f1383,axiom,
    ! [X58,X55,X53] :
      ( c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(X58,X53),c_Message_Oparts(X55),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).

fof(f3714,plain,
    spl0_457,
    inference(avatar_split_clause,[],[f1372,f3712]) ).

fof(f1372,axiom,
    ! [X55,X20] :
      ( ~ c_lessequals(X20,X55,tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X55),tc_set(tc_Message_Omsg)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).

fof(f3710,plain,
    spl0_456,
    inference(avatar_split_clause,[],[f1361,f3708]) ).

fof(f1361,axiom,
    ! [X54,X55,X53] :
      ( c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oparts(X55),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).

fof(f3706,plain,
    spl0_455,
    inference(avatar_split_clause,[],[f1360,f3704]) ).

fof(f1360,axiom,
    ! [X54,X55,X53] :
      ( c_in(X54,c_Message_Oparts(X55),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oparts(X55),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).

fof(f3702,plain,
    spl0_454,
    inference(avatar_split_clause,[],[f1359,f3700]) ).

fof(f1359,axiom,
    ! [X54,X55,X53] :
      ( c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oanalz(X55),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).

fof(f3690,plain,
    spl0_453,
    inference(avatar_split_clause,[],[f1358,f3688]) ).

fof(f1358,axiom,
    ! [X54,X55,X53] :
      ( c_in(X54,c_Message_Oanalz(X55),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X53,X54),c_Message_Oanalz(X55),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).

fof(f3686,plain,
    spl0_452,
    inference(avatar_split_clause,[],[f1346,f3684]) ).

fof(f3684,plain,
    ( spl0_452
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X3
        | c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f1346,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X3
      | c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).

fof(f3682,plain,
    spl0_451,
    inference(avatar_split_clause,[],[f1344,f3680]) ).

fof(f3680,plain,
    ( spl0_451
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X3
        | c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f1344,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X3
      | c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).

fof(f3678,plain,
    spl0_450,
    inference(avatar_split_clause,[],[f1338,f3676]) ).

fof(f3676,plain,
    ( spl0_450
  <=> ! [X18,X12,X27,X1] :
        ( X18 = X27
        | c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f1338,axiom,
    ! [X18,X1,X27,X12] :
      ( X18 = X27
      | c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

fof(f3674,plain,
    spl0_449,
    inference(avatar_split_clause,[],[f1324,f3672]) ).

fof(f1324,axiom,
    ! [X1,X12,X13] :
      ( ~ c_lessequals(X12,X13,tc_set(X1))
      | c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).

fof(f3670,plain,
    spl0_448,
    inference(avatar_split_clause,[],[f1323,f3668]) ).

fof(f1323,axiom,
    ! [X1,X12,X13] :
      ( c_lessequals(X12,X13,tc_set(X1))
      | ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).

fof(f3666,plain,
    spl0_447,
    inference(avatar_split_clause,[],[f1317,f3664]) ).

fof(f1317,axiom,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X12,X1)
      | ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).

fof(f3662,plain,
    spl0_446,
    inference(avatar_split_clause,[],[f1316,f3660]) ).

fof(f1316,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X13,X1)
      | ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).

fof(f3658,plain,
    spl0_445,
    inference(avatar_split_clause,[],[f1313,f3656]) ).

fof(f3656,plain,
    ( spl0_445
  <=> ! [X13,X12,X1] :
        ( X12 = X13
        | c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f1313,axiom,
    ! [X1,X12,X13] :
      ( X12 = X13
      | c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).

fof(f3654,plain,
    spl0_444,
    inference(avatar_split_clause,[],[f1308,f3652]) ).

fof(f1308,axiom,
    ! [X50,X1,X16] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_less(X50,X16,X1)
      | c_in(X50,c_SetInterval_OlessThan(X16,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).

fof(f3642,plain,
    spl0_443,
    inference(avatar_split_clause,[],[f1307,f3640]) ).

fof(f1307,axiom,
    ! [X50,X1,X16] :
      ( ~ class_Orderings_Oord(X1)
      | c_less(X50,X16,X1)
      | ~ c_in(X50,c_SetInterval_OlessThan(X16,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).

fof(f3638,plain,
    spl0_442,
    inference(avatar_split_clause,[],[f1306,f3636]) ).

fof(f3636,plain,
    ( spl0_442
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | X0 = X3
        | c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f1306,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | X0 = X3
      | c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).

fof(f3634,plain,
    spl0_441,
    inference(avatar_split_clause,[],[f1303,f3632]) ).

fof(f1303,axiom,
    ! [X50,X1,X16] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_less(X16,X50,X1)
      | c_in(X50,c_SetInterval_OgreaterThan(X16,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).

fof(f3630,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f1302,f3628]) ).

fof(f1302,axiom,
    ! [X50,X1,X16] :
      ( ~ class_Orderings_Oord(X1)
      | c_less(X16,X50,X1)
      | ~ c_in(X50,c_SetInterval_OgreaterThan(X16,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).

fof(f3626,plain,
    spl0_439,
    inference(avatar_split_clause,[],[f1301,f3624]) ).

fof(f3624,plain,
    ( spl0_439
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | X0 = X3
        | c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f1301,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | X0 = X3
      | c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).

fof(f3622,plain,
    spl0_438,
    inference(avatar_split_clause,[],[f1298,f3620]) ).

fof(f1298,axiom,
    ! [X50,X1,X16] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_lessequals(X50,X16,X1)
      | c_in(X50,c_SetInterval_OatMost(X16,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).

fof(f3618,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f1297,f3616]) ).

fof(f1297,axiom,
    ! [X50,X1,X16] :
      ( ~ class_Orderings_Oord(X1)
      | c_lessequals(X50,X16,X1)
      | ~ c_in(X50,c_SetInterval_OatMost(X16,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).

fof(f3614,plain,
    spl0_436,
    inference(avatar_split_clause,[],[f1296,f3612]) ).

fof(f3612,plain,
    ( spl0_436
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | X0 = X3
        | c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f1296,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | X0 = X3
      | c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).

fof(f3610,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f1293,f3608]) ).

fof(f1293,axiom,
    ! [X50,X1,X16] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_lessequals(X16,X50,X1)
      | c_in(X50,c_SetInterval_OatLeast(X16,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).

fof(f3606,plain,
    spl0_434,
    inference(avatar_split_clause,[],[f1292,f3604]) ).

fof(f1292,axiom,
    ! [X50,X1,X16] :
      ( ~ class_Orderings_Oord(X1)
      | c_lessequals(X16,X50,X1)
      | ~ c_in(X50,c_SetInterval_OatLeast(X16,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).

fof(f3598,plain,
    spl0_433,
    inference(avatar_split_clause,[],[f1291,f3596]) ).

fof(f3596,plain,
    ( spl0_433
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | X0 = X3
        | c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f1291,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | X0 = X3
      | c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).

fof(f3594,plain,
    spl0_432,
    inference(avatar_split_clause,[],[f1247,f3592]) ).

fof(f1247,axiom,
    ! [X1,X25,X23,X43] :
      ( X25 = X43
      | c_append(X23,X25,X1) != c_append(X23,X43,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).

fof(f3590,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f1241,f3588]) ).

fof(f3588,plain,
    ( spl0_431
  <=> ! [X18,X41,X49,X48,X1] :
        ( X48 = X49
        | c_List_Olist_OCons(X41,X48,X1) != c_List_Olist_OCons(X18,X49,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f1241,axiom,
    ! [X41,X48,X49,X1,X18] :
      ( X48 = X49
      | c_List_Olist_OCons(X41,X48,X1) != c_List_Olist_OCons(X18,X49,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).

fof(f3586,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f1240,f3584]) ).

fof(f3584,plain,
    ( spl0_430
  <=> ! [X41,X18,X49,X48,X1] :
        ( X18 = X41
        | c_List_Olist_OCons(X41,X48,X1) != c_List_Olist_OCons(X18,X49,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f1240,axiom,
    ! [X41,X48,X49,X18,X1] :
      ( X18 = X41
      | c_List_Olist_OCons(X41,X48,X1) != c_List_Olist_OCons(X18,X49,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).

fof(f3582,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f1225,f3580]) ).

fof(f1225,axiom,
    ! [X1,X25,X23,X43] :
      ( X25 = X43
      | c_append(X25,X23,X1) != c_append(X43,X23,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).

fof(f3578,plain,
    spl0_428,
    inference(avatar_split_clause,[],[f1171,f3576]) ).

fof(f3576,plain,
    ( spl0_428
  <=> ! [X7,X9,X2,X1] :
        ( X7 = X9
        | c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f1171,axiom,
    ! [X2,X1,X9,X7] :
      ( X7 = X9
      | c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

fof(f3574,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f1169,f3572]) ).

fof(f3572,plain,
    ( spl0_427
  <=> ! [X7,X9,X2,X1] :
        ( X7 = X9
        | c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f1169,axiom,
    ! [X2,X1,X9,X7] :
      ( X7 = X9
      | c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

fof(f3570,plain,
    spl0_426,
    inference(avatar_split_clause,[],[f1167,f3568]) ).

fof(f3568,plain,
    ( spl0_426
  <=> ! [X2,X18,X27,X1] :
        ( X18 = X27
        | c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f1167,axiom,
    ! [X2,X18,X1,X27] :
      ( X18 = X27
      | c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq__iff1_0) ).

fof(f3566,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f120,f3564]) ).

fof(f120,axiom,
    ! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

fof(f3562,plain,
    spl0_424,
    inference(avatar_split_clause,[],[f110,f3560]) ).

fof(f110,axiom,
    ! [X1,X12,X13] :
      ( c_lessequals(X12,X13,tc_set(X1))
      | ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

fof(f3558,plain,
    ( spl0_423
    | ~ spl0_60
    | ~ spl0_404 ),
    inference(avatar_split_clause,[],[f3527,f3448,f1686,f3555]) ).

fof(f3555,plain,
    ( spl0_423
  <=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f1686,plain,
    ( spl0_60
  <=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f3448,plain,
    ( spl0_404
  <=> ! [X0] :
        ( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
        | c_0 = c_uminus(X0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f3527,plain,
    ( c_0 = c_uminus(c_0,tc_IntDef_Oint)
    | ~ spl0_60
    | ~ spl0_404 ),
    inference(resolution,[],[f3449,f1687]) ).

fof(f1687,plain,
    ( ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint)
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f1686]) ).

fof(f3449,plain,
    ( ! [X0] :
        ( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
        | c_0 = c_uminus(X0,tc_IntDef_Oint) )
    | ~ spl0_404 ),
    inference(avatar_component_clause,[],[f3448]) ).

fof(f3553,plain,
    spl0_422,
    inference(avatar_split_clause,[],[f109,f3551]) ).

fof(f109,axiom,
    ! [X1,X12,X13] :
      ( c_lessequals(X12,X13,tc_set(X1))
      | c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

fof(f3549,plain,
    spl0_421,
    inference(avatar_split_clause,[],[f49,f3547]) ).

fof(f49,axiom,
    ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).

fof(f3545,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f2,f3543]) ).

fof(f3543,plain,
    ( spl0_420
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X3
        | c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X3
      | c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).

fof(f3541,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f1,f3539]) ).

fof(f3539,plain,
    ( spl0_419
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X3
        | c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X3
      | c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).

fof(f3522,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f1386,f3520]) ).

fof(f1386,axiom,
    ! [X55,X53] :
      ( c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg)
      | ~ c_in(X53,c_Message_Oparts(c_Message_Oparts(X55)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).

fof(f3518,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f1371,f3516]) ).

fof(f1371,axiom,
    ! [X55,X53] :
      ( c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg)
      | ~ c_in(X53,c_Message_Oanalz(c_Message_Oanalz(X55)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).

fof(f3514,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f1334,f3512]) ).

fof(f1334,axiom,
    ! [X18,X1,X27,X13] :
      ( ~ c_in(X18,X13,X1)
      | c_in(X18,c_insert(X27,X13,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

fof(f3510,plain,
    spl0_415,
    inference(avatar_split_clause,[],[f1327,f3508]) ).

fof(f1327,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X12,X1)
      | c_in(X4,c_union(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).

fof(f3506,plain,
    ( spl0_414
    | ~ spl0_313
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f3442,f3368,f3009,f3504]) ).

fof(f3504,plain,
    ( spl0_414
  <=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f3009,plain,
    ( spl0_313
  <=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f3442,plain,
    ( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_313
    | ~ spl0_389 ),
    inference(resolution,[],[f3369,f3010]) ).

fof(f3010,plain,
    ( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_313 ),
    inference(avatar_component_clause,[],[f3009]) ).

fof(f3502,plain,
    spl0_413,
    inference(avatar_split_clause,[],[f1326,f3500]) ).

fof(f1326,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X13,X1)
      | c_in(X4,c_union(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

fof(f3498,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f1320,f3496]) ).

fof(f1320,axiom,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X12,X1)
      | ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).

fof(f3494,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f1319,f3492]) ).

fof(f1319,axiom,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X13,X1)
      | ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).

fof(f3490,plain,
    spl0_410,
    inference(avatar_split_clause,[],[f1312,f3488]) ).

fof(f1312,axiom,
    ! [X1,X4,X12] :
      ( c_in(X4,X12,X1)
      | c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).

fof(f3486,plain,
    spl0_409,
    inference(avatar_split_clause,[],[f1311,f3484]) ).

fof(f1311,axiom,
    ! [X1,X4,X12] :
      ( ~ c_in(X4,X12,X1)
      | ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).

fof(f3482,plain,
    spl0_408,
    inference(avatar_split_clause,[],[f1265,f3480]) ).

fof(f3480,plain,
    ( spl0_408
  <=> ! [X21,X15] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f1265,axiom,
    ! [X21,X15] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).

fof(f3478,plain,
    spl0_407,
    inference(avatar_split_clause,[],[f1264,f3476]) ).

fof(f3476,plain,
    ( spl0_407
  <=> ! [X21,X15] :
        ( ~ c_less(c_0,X15,tc_nat)
        | c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f1264,axiom,
    ! [X21,X15] :
      ( ~ c_less(c_0,X15,tc_nat)
      | c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).

fof(f3474,plain,
    spl0_406,
    inference(avatar_split_clause,[],[f1160,f3472]) ).

fof(f1160,axiom,
    ! [X40,X0,X1] :
      ( c_Datatype_Ooption_OSome(X0,X1) = X40
      | ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).

fof(f3468,plain,
    ( spl0_405
    | ~ spl0_312
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f3441,f3368,f3005,f3466]) ).

fof(f3466,plain,
    ( spl0_405
  <=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f3005,plain,
    ( spl0_312
  <=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f3441,plain,
    ( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_312
    | ~ spl0_389 ),
    inference(resolution,[],[f3369,f3006]) ).

fof(f3006,plain,
    ( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_312 ),
    inference(avatar_component_clause,[],[f3005]) ).

fof(f3450,plain,
    ( spl0_404
    | ~ spl0_319
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f3438,f3364,f3033,f3448]) ).

fof(f3033,plain,
    ( spl0_319
  <=> ! [X15] :
        ( c_0 = X15
        | ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f3438,plain,
    ( ! [X0] :
        ( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
        | c_0 = c_uminus(X0,tc_IntDef_Oint) )
    | ~ spl0_319
    | ~ spl0_388 ),
    inference(resolution,[],[f3365,f3034]) ).

fof(f3034,plain,
    ( ! [X15] :
        ( ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint)
        | c_0 = X15 )
    | ~ spl0_319 ),
    inference(avatar_component_clause,[],[f3033]) ).

fof(f3426,plain,
    spl0_403,
    inference(avatar_split_clause,[],[f1382,f3424]) ).

fof(f3424,plain,
    ( spl0_403
  <=> ! [X61,X57,X56,X62] :
        ( X61 = X62
        | c_Message_Omsg_OCrypt(X57,X61) != c_Message_Omsg_OCrypt(X56,X62) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f1382,axiom,
    ! [X56,X57,X62,X61] :
      ( X61 = X62
      | c_Message_Omsg_OCrypt(X57,X61) != c_Message_Omsg_OCrypt(X56,X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).

fof(f3422,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f1381,f3420]) ).

fof(f3420,plain,
    ( spl0_402
  <=> ! [X61,X57,X56,X62] :
        ( X56 = X57
        | c_Message_Omsg_OCrypt(X57,X61) != c_Message_Omsg_OCrypt(X56,X62) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f1381,axiom,
    ! [X56,X57,X62,X61] :
      ( X56 = X57
      | c_Message_Omsg_OCrypt(X57,X61) != c_Message_Omsg_OCrypt(X56,X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).

fof(f3418,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f1380,f3416]) ).

fof(f3416,plain,
    ( spl0_401
  <=> ! [X66,X64,X65,X63] :
        ( X64 = X66
        | c_Message_Omsg_OMPair(X63,X64) != c_Message_Omsg_OMPair(X65,X66) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f1380,axiom,
    ! [X65,X63,X66,X64] :
      ( X64 = X66
      | c_Message_Omsg_OMPair(X63,X64) != c_Message_Omsg_OMPair(X65,X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).

fof(f3414,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f1379,f3412]) ).

fof(f3412,plain,
    ( spl0_400
  <=> ! [X65,X64,X63,X66] :
        ( X63 = X65
        | c_Message_Omsg_OMPair(X63,X64) != c_Message_Omsg_OMPair(X65,X66) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f1379,axiom,
    ! [X65,X63,X66,X64] :
      ( X63 = X65
      | c_Message_Omsg_OMPair(X63,X64) != c_Message_Omsg_OMPair(X65,X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).

fof(f3410,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f1285,f3408]) ).

fof(f1285,axiom,
    ! [X18,X1] : c_in(c_Pair(X18,X18,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).

fof(f3406,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f1260,f3404]) ).

fof(f3404,plain,
    ( spl0_398
  <=> ! [X21,X15] :
        ( ~ c_less(X15,X21,tc_nat)
        | c_less(c_Suc(X15),c_Suc(X21),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f1260,axiom,
    ! [X21,X15] :
      ( ~ c_less(X15,X21,tc_nat)
      | c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).

fof(f3402,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f1259,f3400]) ).

fof(f3400,plain,
    ( spl0_397
  <=> ! [X21,X15] :
        ( c_less(X15,X21,tc_nat)
        | ~ c_less(c_Suc(X15),c_Suc(X21),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f1259,axiom,
    ! [X21,X15] :
      ( c_less(X15,X21,tc_nat)
      | ~ c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).

fof(f3398,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f1258,f3396]) ).

fof(f3396,plain,
    ( spl0_396
  <=> ! [X21,X15] :
        ( ~ c_lessequals(X21,X15,tc_nat)
        | c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f1258,axiom,
    ! [X21,X15] :
      ( ~ c_lessequals(X21,X15,tc_nat)
      | c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).

fof(f3394,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f1257,f3392]) ).

fof(f3392,plain,
    ( spl0_395
  <=> ! [X21,X15] :
        ( c_lessequals(X21,X15,tc_nat)
        | ~ c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f1257,axiom,
    ! [X21,X15] :
      ( c_lessequals(X21,X15,tc_nat)
      | ~ c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).

fof(f3390,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f1246,f3388]) ).

fof(f3388,plain,
    ( spl0_394
  <=> ! [X25,X1,X23] :
        ( X23 = X25
        | c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f1246,axiom,
    ! [X1,X25,X23] :
      ( X23 = X25
      | c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv__iff1_0) ).

fof(f3386,plain,
    spl0_393,
    inference(avatar_split_clause,[],[f1235,f3384]) ).

fof(f3384,plain,
    ( spl0_393
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f1235,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).

fof(f3382,plain,
    spl0_392,
    inference(avatar_split_clause,[],[f1231,f3380]) ).

fof(f3380,plain,
    ( spl0_392
  <=> ! [X45,X44,X46,X47] :
        ( X45 = X47
        | c_List_Ochar_OChar(X44,X45) != c_List_Ochar_OChar(X46,X47) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f1231,axiom,
    ! [X46,X47,X44,X45] :
      ( X45 = X47
      | c_List_Ochar_OChar(X44,X45) != c_List_Ochar_OChar(X46,X47) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_1) ).

fof(f3378,plain,
    spl0_391,
    inference(avatar_split_clause,[],[f1230,f3376]) ).

fof(f3376,plain,
    ( spl0_391
  <=> ! [X44,X47,X46,X45] :
        ( X44 = X46
        | c_List_Ochar_OChar(X44,X45) != c_List_Ochar_OChar(X46,X47) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f1230,axiom,
    ! [X46,X47,X44,X45] :
      ( X44 = X46
      | c_List_Ochar_OChar(X44,X45) != c_List_Ochar_OChar(X46,X47) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_0) ).

fof(f3374,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f1209,f3372]) ).

fof(f1209,axiom,
    ! [X11,X42] :
      ( ~ c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(c_uminus(X42,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).

fof(f3370,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f1208,f3368]) ).

fof(f1208,axiom,
    ! [X11,X42] :
      ( c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint)
      | ~ c_Divides_Oop_Advd(c_uminus(X42,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).

fof(f3366,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f1205,f3364]) ).

fof(f1205,axiom,
    ! [X11,X42] :
      ( ~ c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X42,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).

fof(f3362,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f1204,f3360]) ).

fof(f1204,axiom,
    ! [X11,X42] :
      ( c_Divides_Oop_Advd(X42,X11,tc_IntDef_Oint)
      | ~ c_Divides_Oop_Advd(X42,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).

fof(f3358,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f1181,f3356]) ).

fof(f3356,plain,
    ( spl0_386
  <=> ! [X9,X7,X16,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f1181,axiom,
    ! [X2,X1,X9,X7,X16] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb__iff1_0) ).

fof(f3354,plain,
    spl0_385,
    inference(avatar_split_clause,[],[f1179,f3352]) ).

fof(f3352,plain,
    ( spl0_385
  <=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f1179,axiom,
    ! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom__iff1_0) ).

fof(f3350,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f1174,f3348]) ).

fof(f3348,plain,
    ( spl0_384
  <=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f1174,axiom,
    ! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons__iff1_0) ).

fof(f3346,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f1166,f3344]) ).

fof(f1166,axiom,
    ! [X41,X18,X1] :
      ( X18 = X41
      | c_Datatype_Ooption_OSome(X41,X1) != c_Datatype_Ooption_OSome(X18,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).

fof(f3342,plain,
    spl0_382,
    inference(avatar_split_clause,[],[f1163,f3340]) ).

fof(f1163,axiom,
    ! [X0,X1] :
      ( c_Datatype_Ooption_ONone = X0
      | c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X0,X1),X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq__iff1_0) ).

fof(f3338,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f1162,f3336]) ).

fof(f1162,axiom,
    ! [X0,X1] :
      ( c_Datatype_Ooption_ONone = X0
      | c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X0,X1),X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq__iff1_0) ).

fof(f3334,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f105,f3332]) ).

fof(f105,axiom,
    ! [X18,X1,X27] :
      ( X18 = X27
      | ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

fof(f3330,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f103,f3328]) ).

fof(f3328,plain,
    ( spl0_379
  <=> ! [X13,X12,X1] :
        ( ~ c_less(X12,X13,tc_set(X1))
        | c_lessequals(X12,X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f103,axiom,
    ! [X1,X12,X13] :
      ( ~ c_less(X12,X13,tc_set(X1))
      | c_lessequals(X12,X13,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

fof(f3326,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f102,f3324]) ).

fof(f102,axiom,
    ! [X1,X12,X13] :
      ( ~ c_less(X12,X13,tc_set(X1))
      | ~ c_lessequals(X13,X12,tc_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

fof(f3306,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f1384,f3304]) ).

fof(f1384,axiom,
    ! [X55,X53] :
      ( ~ c_in(X53,X55,tc_Message_Omsg)
      | c_in(X53,c_Message_Oparts(X55),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).

fof(f3302,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f1370,f3300]) ).

fof(f1370,axiom,
    ! [X55,X53] :
      ( ~ c_in(X53,X55,tc_Message_Omsg)
      | c_in(X53,c_Message_Oanalz(X55),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).

fof(f3298,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f1349,f3296]) ).

fof(f3296,plain,
    ( spl0_375
  <=> ! [X5,X1] :
        ( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
        | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f1349,axiom,
    ! [X1,X5] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
      | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

fof(f3292,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f1348,f3290]) ).

fof(f3290,plain,
    ( spl0_374
  <=> ! [X5,X1] :
        ( c_Wellfounded__Recursion_Oacyclic(X5,X1)
        | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f1348,axiom,
    ! [X1,X5] :
      ( c_Wellfounded__Recursion_Oacyclic(X5,X1)
      | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

fof(f3288,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f1345,f3286]) ).

fof(f3286,plain,
    ( spl0_373
  <=> ! [X2,X27,X1,X18] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f1345,axiom,
    ! [X2,X18,X1,X27] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

fof(f3284,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f1330,f3282]) ).

fof(f3282,plain,
    ( spl0_372
  <=> ! [X13,X12,X1] :
        ( c_emptyset = X13
        | c_emptyset != c_union(X12,X13,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f1330,axiom,
    ! [X1,X12,X13] :
      ( c_emptyset = X13
      | c_emptyset != c_union(X12,X13,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).

fof(f3280,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f1329,f3278]) ).

fof(f3278,plain,
    ( spl0_371
  <=> ! [X13,X12,X1] :
        ( c_emptyset = X12
        | c_emptyset != c_union(X12,X13,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f1329,axiom,
    ! [X1,X12,X13] :
      ( c_emptyset = X12
      | c_emptyset != c_union(X12,X13,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).

fof(f3276,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f1267,f3274]) ).

fof(f3274,plain,
    ( spl0_370
  <=> ! [X21,X15] :
        ( c_0 = X21
        | c_0 != c_plus(X15,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f1267,axiom,
    ! [X21,X15] :
      ( c_0 = X21
      | c_0 != c_plus(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).

fof(f3272,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f1266,f3270]) ).

fof(f3270,plain,
    ( spl0_369
  <=> ! [X21,X15] :
        ( c_0 = X15
        | c_0 != c_plus(X15,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f1266,axiom,
    ! [X21,X15] :
      ( c_0 = X15
      | c_0 != c_plus(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).

fof(f3268,plain,
    spl0_368,
    inference(avatar_split_clause,[],[f1232,f3266]) ).

fof(f3266,plain,
    ( spl0_368
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f1232,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).

fof(f3264,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f1228,f3262]) ).

fof(f3262,plain,
    ( spl0_367
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X25
        | c_append(X23,X25,X1) != X23 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f1228,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X25
      | c_append(X23,X25,X1) != X23 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).

fof(f3260,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f1226,f3258]) ).

fof(f3258,plain,
    ( spl0_366
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_append(X23,X25,X1) != X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f1226,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X23
      | c_append(X23,X25,X1) != X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).

fof(f3256,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f1212,f3254]) ).

fof(f3254,plain,
    ( spl0_365
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X25
        | c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f1212,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X25
      | c_List_Olist_ONil != c_append(X23,X25,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).

fof(f3250,plain,
    spl0_364,
    inference(avatar_split_clause,[],[f1211,f3248]) ).

fof(f3248,plain,
    ( spl0_364
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f1211,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Olist_ONil != c_append(X23,X25,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).

fof(f3246,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f1184,f3244]) ).

fof(f3244,plain,
    ( spl0_363
  <=> ! [X5,X12,X1] :
        ( c_emptyset = X12
        | c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f1184,axiom,
    ! [X1,X5,X12] :
      ( c_emptyset = X12
      | c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff1_0) ).

fof(f3242,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f1173,f3240]) ).

fof(f3240,plain,
    ( spl0_362
  <=> ! [X2,X16,X1,X18] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f1173,axiom,
    ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb__iff1_0) ).

fof(f3238,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f1172,f3236]) ).

fof(f3236,plain,
    ( spl0_361
  <=> ! [X2,X1,X7,X9] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f1172,axiom,
    ! [X2,X1,X9,X7] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

fof(f3234,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f63,f3232]) ).

fof(f3232,plain,
    ( spl0_360
  <=> ! [X5,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
        | c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f63,axiom,
    ! [X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
      | c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

fof(f3230,plain,
    spl0_359,
    inference(avatar_split_clause,[],[f62,f3228]) ).

fof(f3228,plain,
    ( spl0_359
  <=> ! [X5,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
        | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f62,axiom,
    ! [X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
      | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).

fof(f3226,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f38,f3224]) ).

fof(f3224,plain,
    ( spl0_358
  <=> ! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f38,axiom,
    ! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).

fof(f3222,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f35,f3220]) ).

fof(f35,axiom,
    ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).

fof(f3218,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f34,f3216]) ).

fof(f34,axiom,
    ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).

fof(f3195,plain,
    ( spl0_355
    | ~ spl0_313
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3066,f3033,f3009,f3193]) ).

fof(f3193,plain,
    ( spl0_355
  <=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f3066,plain,
    ( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
    | ~ spl0_313
    | ~ spl0_319 ),
    inference(resolution,[],[f3034,f3010]) ).

fof(f3191,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f1388,f3189]) ).

fof(f1388,axiom,
    ! [X1,X12,X13] : c_lessequals(X13,c_union(X12,X13,X1),tc_set(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__upper2_0) ).

fof(f3187,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f1387,f3185]) ).

fof(f1387,axiom,
    ! [X1,X12,X13] : c_lessequals(X12,c_union(X12,X13,X1),tc_set(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__upper1_0) ).

fof(f3183,plain,
    spl0_352,
    inference(avatar_split_clause,[],[f1378,f3181]) ).

fof(f3181,plain,
    ( spl0_352
  <=> ! [X61,X62] :
        ( X61 = X62
        | c_Message_Omsg_OHash(X61) != c_Message_Omsg_OHash(X62) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f1378,axiom,
    ! [X62,X61] :
      ( X61 = X62
      | c_Message_Omsg_OHash(X61) != c_Message_Omsg_OHash(X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5__iff1_0) ).

fof(f3179,plain,
    spl0_351,
    inference(avatar_split_clause,[],[f1377,f3177]) ).

fof(f3177,plain,
    ( spl0_351
  <=> ! [X57,X56] :
        ( X56 = X57
        | c_Message_Omsg_OKey(X57) != c_Message_Omsg_OKey(X56) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f1377,axiom,
    ! [X56,X57] :
      ( X56 = X57
      | c_Message_Omsg_OKey(X57) != c_Message_Omsg_OKey(X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4__iff1_0) ).

fof(f3175,plain,
    spl0_350,
    inference(avatar_split_clause,[],[f1376,f3173]) ).

fof(f3173,plain,
    ( spl0_350
  <=> ! [X57,X56] :
        ( X56 = X57
        | c_Message_Omsg_ONonce(X57) != c_Message_Omsg_ONonce(X56) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f1376,axiom,
    ! [X56,X57] :
      ( X56 = X57
      | c_Message_Omsg_ONonce(X57) != c_Message_Omsg_ONonce(X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3__iff1_0) ).

fof(f3171,plain,
    ( spl0_349
    | ~ spl0_312
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3065,f3033,f3005,f3169]) ).

fof(f3169,plain,
    ( spl0_349
  <=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f3065,plain,
    ( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
    | ~ spl0_312
    | ~ spl0_319 ),
    inference(resolution,[],[f3034,f3006]) ).

fof(f3167,plain,
    spl0_348,
    inference(avatar_split_clause,[],[f1375,f3165]) ).

fof(f3165,plain,
    ( spl0_348
  <=> ! [X57,X56] :
        ( X56 = X57
        | c_Message_Omsg_ONumber(X57) != c_Message_Omsg_ONumber(X56) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f1375,axiom,
    ! [X56,X57] :
      ( X56 = X57
      | c_Message_Omsg_ONumber(X57) != c_Message_Omsg_ONumber(X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2__iff1_0) ).

fof(f3163,plain,
    spl0_347,
    inference(avatar_split_clause,[],[f1374,f3161]) ).

fof(f3161,plain,
    ( spl0_347
  <=> ! [X60,X59] :
        ( X59 = X60
        | c_Message_Omsg_OAgent(X59) != c_Message_Omsg_OAgent(X60) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f1374,axiom,
    ! [X59,X60] :
      ( X59 = X60
      | c_Message_Omsg_OAgent(X59) != c_Message_Omsg_OAgent(X60) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1__iff1_0) ).

fof(f3159,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f1368,f3157]) ).

fof(f3157,plain,
    ( spl0_346
  <=> ! [X57,X56] :
        ( X56 = X57
        | c_Message_Oagent_OFriend(X56) != c_Message_Oagent_OFriend(X57) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f1368,axiom,
    ! [X56,X57] :
      ( X56 = X57
      | c_Message_Oagent_OFriend(X56) != c_Message_Oagent_OFriend(X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject__iff1_0) ).

fof(f3155,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f1271,f3153]) ).

fof(f3153,plain,
    ( spl0_345
  <=> ! [X21] :
        ( c_0 = X21
        | ~ c_less(X21,c_Suc(c_0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f1271,axiom,
    ! [X21] :
      ( c_0 = X21
      | ~ c_less(X21,c_Suc(c_0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).

fof(f3151,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f1256,f3149]) ).

fof(f3149,plain,
    ( spl0_344
  <=> ! [X21,X15] :
        ( X15 = X21
        | c_Suc(X21) != c_Suc(X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f1256,axiom,
    ! [X21,X15] :
      ( X15 = X21
      | c_Suc(X21) != c_Suc(X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).

fof(f3147,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f1254,f3145]) ).

fof(f3145,plain,
    ( spl0_343
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_emptyset != c_List_Oset(X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f1254,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_emptyset != c_List_Oset(X23,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).

fof(f3143,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f1214,f3141]) ).

fof(f3141,plain,
    ( spl0_342
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Olist_ONil != c_List_Orev(X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f1214,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Olist_ONil != c_List_Orev(X23,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff1_0) ).

fof(f3139,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f1203,f3137]) ).

fof(f3137,plain,
    ( spl0_341
  <=> ! [X21,X15] :
        ( X15 = X21
        | c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f1203,axiom,
    ! [X21,X15] :
      ( X15 = X21
      | c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).

fof(f3135,plain,
    spl0_340,
    inference(avatar_split_clause,[],[f1161,f3133]) ).

fof(f1161,axiom,
    ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).

fof(f3131,plain,
    spl0_339,
    inference(avatar_split_clause,[],[f252,f3129]) ).

fof(f3129,plain,
    ( spl0_339
  <=> ! [X38,X37] :
        ( ~ class_Finite__Set_Ofinite(X38)
        | ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_sum(X38,X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f252,axiom,
    ! [X38,X37] :
      ( ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_sum(X38,X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).

fof(f3127,plain,
    ( spl0_338
    | ~ spl0_311
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3063,f3029,f3001,f3125]) ).

fof(f3125,plain,
    ( spl0_338
  <=> ! [X0] : c_0 = c_times(X0,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f3001,plain,
    ( spl0_311
  <=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f3063,plain,
    ( ! [X0] : c_0 = c_times(X0,c_0,tc_nat)
    | ~ spl0_311
    | ~ spl0_318 ),
    inference(resolution,[],[f3030,f3002]) ).

fof(f3002,plain,
    ( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat)
    | ~ spl0_311 ),
    inference(avatar_component_clause,[],[f3001]) ).

fof(f3123,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f246,f3121]) ).

fof(f3121,plain,
    ( spl0_337
  <=> ! [X38,X37] :
        ( ~ class_Finite__Set_Ofinite(X38)
        | ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_prod(X38,X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f246,axiom,
    ! [X38,X37] :
      ( ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_prod(X38,X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).

fof(f3119,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f196,f3117]) ).

fof(f3117,plain,
    ( spl0_336
  <=> ! [X38,X37] :
        ( ~ class_Finite__Set_Ofinite(X38)
        | ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_fun(X38,X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f196,axiom,
    ! [X38,X37] :
      ( ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_fun(X38,X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).

fof(f3115,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f94,f3113]) ).

fof(f94,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

fof(f3111,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f93,f3109]) ).

fof(f93,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

fof(f3107,plain,
    spl0_333,
    inference(avatar_split_clause,[],[f92,f3105]) ).

fof(f92,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

fof(f3103,plain,
    spl0_332,
    inference(avatar_split_clause,[],[f91,f3101]) ).

fof(f91,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

fof(f3099,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f89,f3097]) ).

fof(f89,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

fof(f3095,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f88,f3093]) ).

fof(f88,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

fof(f3091,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f87,f3089]) ).

fof(f87,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

fof(f3087,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f86,f3085]) ).

fof(f86,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

fof(f3083,plain,
    ( spl0_327
    | ~ spl0_310
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3062,f3029,f2997,f3081]) ).

fof(f3081,plain,
    ( spl0_327
  <=> ! [X0] : c_0 = c_times(c_0,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f2997,plain,
    ( spl0_310
  <=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f3062,plain,
    ( ! [X0] : c_0 = c_times(c_0,X0,tc_nat)
    | ~ spl0_310
    | ~ spl0_318 ),
    inference(resolution,[],[f3030,f2998]) ).

fof(f2998,plain,
    ( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat)
    | ~ spl0_310 ),
    inference(avatar_component_clause,[],[f2997]) ).

fof(f3079,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f37,f3077]) ).

fof(f3077,plain,
    ( spl0_326
  <=> ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f37,axiom,
    ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).

fof(f3059,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f1335,f3057]) ).

fof(f1335,axiom,
    ! [X0,X1,X13] : c_in(X0,c_insert(X0,X13,X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

fof(f3055,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f1278,f3053]) ).

fof(f3053,plain,
    ( spl0_324
  <=> ! [X50,X51] : ~ c_less(c_plus(X51,X50,tc_nat),X50,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f1278,axiom,
    ! [X50,X51] : ~ c_less(c_plus(X51,X50,tc_nat),X50,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).

fof(f3051,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f1277,f3049]) ).

fof(f3049,plain,
    ( spl0_323
  <=> ! [X50,X51] : ~ c_less(c_plus(X50,X51,tc_nat),X50,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f1277,axiom,
    ! [X50,X51] : ~ c_less(c_plus(X50,X51,tc_nat),X50,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).

fof(f3047,plain,
    spl0_322,
    inference(avatar_split_clause,[],[f1275,f3045]) ).

fof(f1275,axiom,
    ! [X21] :
      ( c_0 = X21
      | c_less(c_0,X21,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).

fof(f3043,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f1273,f3041]) ).

fof(f3041,plain,
    ( spl0_321
  <=> ! [X21] :
        ( c_0 = X21
        | ~ c_less(X21,c_1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f1273,axiom,
    ! [X21] :
      ( c_0 = X21
      | ~ c_less(X21,c_1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).

fof(f3039,plain,
    spl0_320,
    inference(avatar_split_clause,[],[f1269,f3037]) ).

fof(f3037,plain,
    ( spl0_320
  <=> ! [X50] :
        ( c_0 = X50
        | ~ c_lessequals(X50,c_0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f1269,axiom,
    ! [X50] :
      ( c_0 = X50
      | ~ c_lessequals(X50,c_0,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).

fof(f3035,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f1206,f3033]) ).

fof(f1206,axiom,
    ! [X15] :
      ( c_0 = X15
      | ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).

fof(f3031,plain,
    spl0_318,
    inference(avatar_split_clause,[],[f1182,f3029]) ).

fof(f1182,axiom,
    ! [X15] :
      ( c_0 = X15
      | ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).

fof(f3027,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f95,f3025]) ).

fof(f95,axiom,
    ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).

fof(f3023,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f90,f3021]) ).

fof(f90,axiom,
    ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).

fof(f3019,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f61,f3017]) ).

fof(f3017,plain,
    ( spl0_315
  <=> ! [X12,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f61,axiom,
    ! [X1,X12] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

fof(f3015,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f45,f3013]) ).

fof(f45,axiom,
    ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

fof(f3011,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f42,f3009]) ).

fof(f42,axiom,
    ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).

fof(f3007,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f41,f3005]) ).

fof(f41,axiom,
    ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).

fof(f3003,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f26,f3001]) ).

fof(f26,axiom,
    ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).

fof(f2999,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f25,f2997]) ).

fof(f25,axiom,
    ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).

fof(f2995,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f1331,f2993]) ).

fof(f2993,plain,
    ( spl0_309
  <=> ! [X1] : c_emptyset = c_union(c_emptyset,c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f1331,axiom,
    ! [X1] : c_emptyset = c_union(c_emptyset,c_emptyset,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).

fof(f2991,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f1282,f2989]) ).

fof(f2989,plain,
    ( spl0_308
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X1)
        | ~ c_less(X0,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f1282,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | ~ c_less(X0,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).

fof(f2987,plain,
    spl0_307,
    inference(avatar_split_clause,[],[f1268,f2984]) ).

fof(f2984,plain,
    ( spl0_307
  <=> c_0 = c_plus(c_0,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f1268,axiom,
    c_0 = c_plus(c_0,c_0,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).

fof(f2982,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f1251,f2980]) ).

fof(f1251,axiom,
    ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).

fof(f2978,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f1249,f2976]) ).

fof(f1249,axiom,
    ! [X1,X25] : c_append(c_List_Olist_ONil,X25,X1) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).

fof(f2974,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f1238,f2972]) ).

fof(f2972,plain,
    ( spl0_304
  <=> ! [X41,X48,X1] : c_List_Olist_ONil != c_List_Olist_OCons(X41,X48,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f1238,axiom,
    ! [X41,X48,X1] : c_List_Olist_ONil != c_List_Olist_OCons(X41,X48,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).

fof(f2970,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f1233,f2968]) ).

fof(f1233,axiom,
    ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).

fof(f2966,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f1187,f2964]) ).

fof(f2964,plain,
    ( spl0_302
  <=> ! [X5,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f1187,axiom,
    ! [X1,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff2_0) ).

fof(f2962,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f68,f2960]) ).

fof(f2960,plain,
    ( spl0_301
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X1)
        | c_lessequals(X0,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f68,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | c_lessequals(X0,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

fof(f2958,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f1385,f2956]) ).

fof(f1385,axiom,
    ! [X53] : ~ c_in(X53,c_Message_Oparts(c_emptyset),tc_Message_Omsg),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).

fof(f2954,plain,
    spl0_299,
    inference(avatar_split_clause,[],[f1337,f2952]) ).

fof(f2952,plain,
    ( spl0_299
  <=> ! [X12,X1] : ~ c_less(X12,c_emptyset,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f1337,axiom,
    ! [X1,X12] : ~ c_less(X12,c_emptyset,tc_set(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).

fof(f2950,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f1253,f2948]) ).

fof(f2948,plain,
    ( spl0_298
  <=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f1253,axiom,
    ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).

fof(f2946,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f1215,f2944]) ).

fof(f1215,axiom,
    ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff2_0) ).

fof(f2942,plain,
    ~ spl0_296,
    inference(avatar_split_clause,[],[f1202,f2939]) ).

fof(f2939,plain,
    ( spl0_296
  <=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f1202,axiom,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).

fof(f2937,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f1165,f2935]) ).

fof(f2935,plain,
    ( spl0_295
  <=> ! [X41,X1] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X41,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f1165,axiom,
    ! [X41,X1] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X41,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2__iff1_0) ).

fof(f2933,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f250,f2931]) ).

fof(f2931,plain,
    ( spl0_294
  <=> ! [X37] :
        ( ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_set(X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f250,axiom,
    ! [X37] :
      ( ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_set(X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).

fof(f2929,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f128,f2927]) ).

fof(f2927,plain,
    ( spl0_293
  <=> ! [X37] :
        ( ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f128,axiom,
    ! [X37] :
      ( ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).

fof(f2925,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f112,f2923]) ).

fof(f112,axiom,
    ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

fof(f2921,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f101,f2919]) ).

fof(f101,axiom,
    ! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

fof(f2917,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f67,f2915]) ).

fof(f2915,plain,
    ( spl0_290
  <=> ! [X21] : c_less(c_0,c_Suc(X21),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f67,axiom,
    ! [X21] : c_less(c_0,c_Suc(X21),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).

fof(f2913,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f65,f2911]) ).

fof(f2911,plain,
    ( spl0_289
  <=> ! [X21] : c_less(X21,c_Suc(X21),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f65,axiom,
    ! [X21] : c_less(X21,c_Suc(X21),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

fof(f2909,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f28,f2907]) ).

fof(f2907,plain,
    ( spl0_288
  <=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f28,axiom,
    ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

fof(f2905,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f24,f2903]) ).

fof(f2903,plain,
    ( spl0_287
  <=> ! [X16] : c_Divides_Oop_Advd(c_Suc(c_0),X16,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f24,axiom,
    ! [X16] : c_Divides_Oop_Advd(c_Suc(c_0),X16,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).

fof(f2901,plain,
    ( ~ spl0_285
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f1392,f2898,f2894]) ).

fof(f1392,axiom,
    ( ~ c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f2585,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f1366,f2583]) ).

fof(f2583,plain,
    ( spl0_284
  <=> ! [X57] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X57) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f1366,axiom,
    ! [X57] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5__iff1_0) ).

fof(f2581,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f1363,f2579]) ).

fof(f2579,plain,
    ( spl0_283
  <=> ! [X56] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X56) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f1363,axiom,
    ! [X56] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X56),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2__iff1_0) ).

fof(f2577,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f1333,f2575]) ).

fof(f1333,axiom,
    ! [X18,X1] : ~ c_in(X18,c_emptyset,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

fof(f2573,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f1279,f2571]) ).

fof(f2571,plain,
    ( spl0_281
  <=> ! [X21] : ~ c_less(X21,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f1279,axiom,
    ! [X21] : ~ c_less(X21,c_0,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).

fof(f2569,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f1274,f2566]) ).

fof(f2566,plain,
    ( spl0_280
  <=> c_less(c_0,c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f1274,axiom,
    c_less(c_0,c_1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).

fof(f2564,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f1262,f2562]) ).

fof(f2562,plain,
    ( spl0_279
  <=> ! [X15] : c_0 != c_Suc(X15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f1262,axiom,
    ! [X15] : c_0 != c_Suc(X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).

fof(f2560,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f1159,f2558]) ).

fof(f2558,plain,
    ( spl0_278
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f1159,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).

fof(f2556,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f1158,f2554]) ).

fof(f2554,plain,
    ( spl0_277
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f1158,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).

fof(f2552,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f1157,f2550]) ).

fof(f2550,plain,
    ( spl0_276
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f1157,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).

fof(f2548,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f1156,f2546]) ).

fof(f2546,plain,
    ( spl0_275
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f1156,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).

fof(f2544,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f1155,f2542]) ).

fof(f2542,plain,
    ( spl0_274
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f1155,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).

fof(f2540,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f1154,f2538]) ).

fof(f2538,plain,
    ( spl0_273
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f1154,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).

fof(f2536,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f1067,f2534]) ).

fof(f2534,plain,
    ( spl0_272
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f1067,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).

fof(f2532,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f1059,f2530]) ).

fof(f2530,plain,
    ( spl0_271
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f1059,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).

fof(f2528,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f1058,f2526]) ).

fof(f2526,plain,
    ( spl0_270
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f1058,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).

fof(f2524,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f1048,f2522]) ).

fof(f2522,plain,
    ( spl0_269
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f1048,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).

fof(f2520,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f1047,f2518]) ).

fof(f2518,plain,
    ( spl0_268
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f1047,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).

fof(f2516,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f1046,f2514]) ).

fof(f2514,plain,
    ( spl0_267
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f1046,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).

fof(f2512,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f1044,f2510]) ).

fof(f2510,plain,
    ( spl0_266
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f1044,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).

fof(f2508,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f1043,f2506]) ).

fof(f2506,plain,
    ( spl0_265
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f1043,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).

fof(f2504,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f1042,f2502]) ).

fof(f2502,plain,
    ( spl0_264
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f1042,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).

fof(f2500,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f1041,f2498]) ).

fof(f2498,plain,
    ( spl0_263
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f1041,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).

fof(f2496,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f1040,f2494]) ).

fof(f2494,plain,
    ( spl0_262
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f1040,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).

fof(f2492,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f1024,f2490]) ).

fof(f2490,plain,
    ( spl0_261
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f1024,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

fof(f2488,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f1023,f2486]) ).

fof(f2486,plain,
    ( spl0_260
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f1023,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).

fof(f2484,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f1022,f2482]) ).

fof(f2482,plain,
    ( spl0_259
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f1022,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

fof(f2480,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f1021,f2478]) ).

fof(f2478,plain,
    ( spl0_258
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f1021,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).

fof(f2476,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f989,f2474]) ).

fof(f2474,plain,
    ( spl0_257
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f989,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).

fof(f2472,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f980,f2470]) ).

fof(f2470,plain,
    ( spl0_256
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f980,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).

fof(f2468,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f979,f2466]) ).

fof(f2466,plain,
    ( spl0_255
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f979,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

fof(f2464,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f976,f2462]) ).

fof(f2462,plain,
    ( spl0_254
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f976,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

fof(f2460,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f966,f2458]) ).

fof(f2458,plain,
    ( spl0_253
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f966,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).

fof(f2456,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f965,f2454]) ).

fof(f2454,plain,
    ( spl0_252
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f965,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).

fof(f2452,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f962,f2450]) ).

fof(f2450,plain,
    ( spl0_251
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f962,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).

fof(f2448,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f961,f2446]) ).

fof(f2446,plain,
    ( spl0_250
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f961,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).

fof(f2444,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f957,f2442]) ).

fof(f2442,plain,
    ( spl0_249
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f957,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).

fof(f2440,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f955,f2438]) ).

fof(f2438,plain,
    ( spl0_248
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f955,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Opordered__comm__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).

fof(f2436,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f954,f2434]) ).

fof(f2434,plain,
    ( spl0_247
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f954,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).

fof(f2432,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f947,f2430]) ).

fof(f2430,plain,
    ( spl0_246
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f947,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).

fof(f2428,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f946,f2426]) ).

fof(f2426,plain,
    ( spl0_245
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f946,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).

fof(f2424,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f941,f2422]) ).

fof(f2422,plain,
    ( spl0_244
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f941,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).

fof(f2420,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f940,f2418]) ).

fof(f2418,plain,
    ( spl0_243
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f940,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).

fof(f2416,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f939,f2414]) ).

fof(f2414,plain,
    ( spl0_242
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f939,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).

fof(f2412,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f938,f2410]) ).

fof(f2410,plain,
    ( spl0_241
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f938,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).

fof(f2408,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f937,f2406]) ).

fof(f2406,plain,
    ( spl0_240
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f937,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).

fof(f2404,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f936,f2402]) ).

fof(f2402,plain,
    ( spl0_239
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f936,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).

fof(f2400,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f935,f2398]) ).

fof(f2398,plain,
    ( spl0_238
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f935,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).

fof(f2396,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f934,f2394]) ).

fof(f2394,plain,
    ( spl0_237
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f934,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).

fof(f2392,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f933,f2390]) ).

fof(f2390,plain,
    ( spl0_236
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f933,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).

fof(f2388,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f924,f2386]) ).

fof(f2386,plain,
    ( spl0_235
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f924,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).

fof(f2384,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f923,f2382]) ).

fof(f2382,plain,
    ( spl0_234
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f923,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).

fof(f2380,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f922,f2378]) ).

fof(f2378,plain,
    ( spl0_233
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f922,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).

fof(f2376,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f921,f2374]) ).

fof(f2374,plain,
    ( spl0_232
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f921,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).

fof(f2372,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f920,f2370]) ).

fof(f2370,plain,
    ( spl0_231
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f920,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Opordered__comm__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).

fof(f2368,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f919,f2366]) ).

fof(f2366,plain,
    ( spl0_230
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f919,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).

fof(f2364,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f918,f2362]) ).

fof(f2362,plain,
    ( spl0_229
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f918,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).

fof(f2360,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f917,f2358]) ).

fof(f2358,plain,
    ( spl0_228
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f917,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).

fof(f2356,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f916,f2354]) ).

fof(f2354,plain,
    ( spl0_227
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f916,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).

fof(f2352,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f915,f2350]) ).

fof(f2350,plain,
    ( spl0_226
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f915,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).

fof(f2348,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f913,f2346]) ).

fof(f2346,plain,
    ( spl0_225
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f913,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).

fof(f2344,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f912,f2342]) ).

fof(f2342,plain,
    ( spl0_224
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f912,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).

fof(f2340,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f911,f2338]) ).

fof(f2338,plain,
    ( spl0_223
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f911,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).

fof(f2336,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f910,f2334]) ).

fof(f2334,plain,
    ( spl0_222
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f910,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).

fof(f2332,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f909,f2330]) ).

fof(f2330,plain,
    ( spl0_221
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f909,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Oordered__semiring__strict(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).

fof(f2328,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f908,f2326]) ).

fof(f2326,plain,
    ( spl0_220
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f908,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).

fof(f2324,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f883,f2322]) ).

fof(f2322,plain,
    ( spl0_219
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f883,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Olordered__ab__group__join(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).

fof(f2320,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f882,f2318]) ).

fof(f2318,plain,
    ( spl0_218
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f882,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Olordered__ab__group__meet(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).

fof(f2316,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f881,f2314]) ).

fof(f2314,plain,
    ( spl0_217
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f881,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Olordered__ab__group__abs(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).

fof(f2312,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f880,f2310]) ).

fof(f2310,plain,
    ( spl0_216
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Opordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f880,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Opordered__ring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).

fof(f2308,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f879,f2306]) ).

fof(f2306,plain,
    ( spl0_215
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Olordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f879,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Olordered__ring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).

fof(f2304,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f878,f2302]) ).

fof(f2302,plain,
    ( spl0_214
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f878,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).

fof(f2300,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f876,f2298]) ).

fof(f2298,plain,
    ( spl0_213
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f876,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).

fof(f2296,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f875,f2294]) ).

fof(f2294,plain,
    ( spl0_212
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f875,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Oaxclass__abs__if(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).

fof(f2292,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f874,f2290]) ).

fof(f2290,plain,
    ( spl0_211
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f874,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).

fof(f2288,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f873,f2286]) ).

fof(f2286,plain,
    ( spl0_210
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f873,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).

fof(f2284,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f872,f2282]) ).

fof(f2282,plain,
    ( spl0_209
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f872,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).

fof(f2280,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f871,f2278]) ).

fof(f2278,plain,
    ( spl0_208
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f871,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).

fof(f2276,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f870,f2274]) ).

fof(f2274,plain,
    ( spl0_207
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f870,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).

fof(f2272,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f869,f2270]) ).

fof(f2270,plain,
    ( spl0_206
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f869,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).

fof(f2268,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f868,f2266]) ).

fof(f2266,plain,
    ( spl0_205
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f868,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).

fof(f2264,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f867,f2262]) ).

fof(f2262,plain,
    ( spl0_204
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f867,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).

fof(f2260,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f865,f2258]) ).

fof(f2258,plain,
    ( spl0_203
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f865,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).

fof(f2256,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f864,f2254]) ).

fof(f2254,plain,
    ( spl0_202
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f864,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).

fof(f2252,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f863,f2250]) ).

fof(f2250,plain,
    ( spl0_201
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f863,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).

fof(f2248,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f862,f2246]) ).

fof(f2246,plain,
    ( spl0_200
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f862,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).

fof(f2244,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f861,f2242]) ).

fof(f2242,plain,
    ( spl0_199
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f861,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Oordered__semiring__strict(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).

fof(f2240,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f847,f2238]) ).

fof(f2238,plain,
    ( spl0_198
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oordered__semidom(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f847,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oordered__semidom(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).

fof(f2236,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f846,f2234]) ).

fof(f2234,plain,
    ( spl0_197
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f846,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).

fof(f2232,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f845,f2230]) ).

fof(f2230,plain,
    ( spl0_196
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f845,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).

fof(f2228,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f844,f2226]) ).

fof(f2226,plain,
    ( spl0_195
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f844,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Olordered__ab__group__join(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).

fof(f2224,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f843,f2222]) ).

fof(f2222,plain,
    ( spl0_194
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f843,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Olordered__ab__group__meet(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).

fof(f2220,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f842,f2218]) ).

fof(f2218,plain,
    ( spl0_193
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f842,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Olordered__ab__group__abs(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

fof(f2216,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f840,f2214]) ).

fof(f2214,plain,
    ( spl0_192
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f840,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__ring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).

fof(f2212,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f839,f2210]) ).

fof(f2210,plain,
    ( spl0_191
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Olordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f839,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Olordered__ring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).

fof(f2208,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f838,f2206]) ).

fof(f2206,plain,
    ( spl0_190
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f838,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oordered__ring__strict(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).

fof(f2204,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f837,f2202]) ).

fof(f2202,plain,
    ( spl0_189
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f837,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oaxclass__abs__if(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).

fof(f2200,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f836,f2198]) ).

fof(f2198,plain,
    ( spl0_188
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f836,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).

fof(f2196,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f835,f2194]) ).

fof(f2194,plain,
    ( spl0_187
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f835,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).

fof(f2192,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f834,f2190]) ).

fof(f2190,plain,
    ( spl0_186
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f834,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).

fof(f2188,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f833,f2186]) ).

fof(f2186,plain,
    ( spl0_185
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f833,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

fof(f2184,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f832,f2182]) ).

fof(f2182,plain,
    ( spl0_184
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f832,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__comm__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).

fof(f2180,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f831,f2178]) ).

fof(f2178,plain,
    ( spl0_183
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f831,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

fof(f2176,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f829,f2174]) ).

fof(f2174,plain,
    ( spl0_182
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f829,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).

fof(f2172,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f828,f2170]) ).

fof(f2170,plain,
    ( spl0_181
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f828,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).

fof(f2168,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f827,f2166]) ).

fof(f2166,plain,
    ( spl0_180
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f827,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).

fof(f2164,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f826,f2162]) ).

fof(f2162,plain,
    ( spl0_179
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f826,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).

fof(f2160,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f825,f2158]) ).

fof(f2158,plain,
    ( spl0_178
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f825,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

fof(f2156,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f824,f2154]) ).

fof(f2154,plain,
    ( spl0_177
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f824,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).

fof(f2152,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f823,f2150]) ).

fof(f2150,plain,
    ( spl0_176
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f823,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

fof(f2148,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f822,f2146]) ).

fof(f2146,plain,
    ( spl0_175
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f822,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).

fof(f2144,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f821,f2142]) ).

fof(f2142,plain,
    ( spl0_174
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f821,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oordered__semiring__strict(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).

fof(f2140,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f820,f2138]) ).

fof(f2138,plain,
    ( spl0_173
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f820,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).

fof(f2136,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f727,f2134]) ).

fof(f2134,plain,
    ( spl0_172
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f727,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__comm__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).

fof(f2132,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f726,f2130]) ).

fof(f2130,plain,
    ( spl0_171
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f726,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).

fof(f2128,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f725,f2126]) ).

fof(f2126,plain,
    ( spl0_170
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f725,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).

fof(f2124,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f723,f2122]) ).

fof(f2122,plain,
    ( spl0_169
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f723,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).

fof(f2120,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f722,f2118]) ).

fof(f2118,plain,
    ( spl0_168
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f722,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Oordered__semiring__strict(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).

fof(f2116,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f719,f2114]) ).

fof(f2114,plain,
    ( spl0_167
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f719,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).

fof(f2112,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f718,f2110]) ).

fof(f2110,plain,
    ( spl0_166
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f718,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).

fof(f2108,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f716,f2106]) ).

fof(f2106,plain,
    ( spl0_165
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f716,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).

fof(f2104,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f715,f2102]) ).

fof(f2102,plain,
    ( spl0_164
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f715,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).

fof(f2100,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f714,f2098]) ).

fof(f2098,plain,
    ( spl0_163
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f714,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).

fof(f2096,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f713,f2094]) ).

fof(f2094,plain,
    ( spl0_162
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f713,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).

fof(f2092,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f712,f2090]) ).

fof(f2090,plain,
    ( spl0_161
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f712,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).

fof(f2088,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f711,f2086]) ).

fof(f2086,plain,
    ( spl0_160
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f711,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).

fof(f2084,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f710,f2082]) ).

fof(f2082,plain,
    ( spl0_159
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f710,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).

fof(f2080,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f709,f2078]) ).

fof(f2078,plain,
    ( spl0_158
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f709,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).

fof(f2076,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f704,f2074]) ).

fof(f2074,plain,
    ( spl0_157
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f704,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).

fof(f2072,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f703,f2070]) ).

fof(f2070,plain,
    ( spl0_156
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f703,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).

fof(f2068,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f702,f2066]) ).

fof(f2066,plain,
    ( spl0_155
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f702,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).

fof(f2064,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f701,f2062]) ).

fof(f2062,plain,
    ( spl0_154
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f701,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).

fof(f2060,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f700,f2058]) ).

fof(f2058,plain,
    ( spl0_153
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f700,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).

fof(f2056,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f698,f2054]) ).

fof(f2054,plain,
    ( spl0_152
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f698,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Olordered__ab__group__join(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).

fof(f2052,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f696,f2050]) ).

fof(f2050,plain,
    ( spl0_151
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f696,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Olordered__ab__group__meet(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).

fof(f2048,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f695,f2046]) ).

fof(f2046,plain,
    ( spl0_150
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f695,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).

fof(f2044,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f694,f2042]) ).

fof(f2042,plain,
    ( spl0_149
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f694,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).

fof(f2040,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f693,f2038]) ).

fof(f2038,plain,
    ( spl0_148
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f693,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).

fof(f2036,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f692,f2034]) ).

fof(f2034,plain,
    ( spl0_147
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f692,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).

fof(f2032,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f691,f2030]) ).

fof(f2030,plain,
    ( spl0_146
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f691,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Olordered__ab__group__abs(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).

fof(f2028,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f686,f2026]) ).

fof(f2026,plain,
    ( spl0_145
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f686,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).

fof(f2024,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f677,f2022]) ).

fof(f2022,plain,
    ( spl0_144
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f677,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).

fof(f2020,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f676,f2018]) ).

fof(f2018,plain,
    ( spl0_143
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f676,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).

fof(f2016,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f674,f2014]) ).

fof(f2014,plain,
    ( spl0_142
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Opordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f674,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Opordered__ring(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).

fof(f2012,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f483,f2010]) ).

fof(f2010,plain,
    ( spl0_141
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f483,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).

fof(f2008,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f454,f2006]) ).

fof(f2006,plain,
    ( spl0_140
  <=> ! [X39] :
        ( ~ class_Orderings_Oorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f454,axiom,
    ! [X39] :
      ( ~ class_Orderings_Oorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

fof(f2004,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f453,f2002]) ).

fof(f2002,plain,
    ( spl0_139
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f453,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

fof(f2000,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f452,f1998]) ).

fof(f1998,plain,
    ( spl0_138
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f452,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

fof(f1996,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f451,f1994]) ).

fof(f1994,plain,
    ( spl0_137
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f451,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).

fof(f1992,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f450,f1990]) ).

fof(f1990,plain,
    ( spl0_136
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f450,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).

fof(f1988,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f449,f1986]) ).

fof(f1986,plain,
    ( spl0_135
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f449,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).

fof(f1984,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f441,f1982]) ).

fof(f1982,plain,
    ( spl0_134
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f441,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).

fof(f1980,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f440,f1978]) ).

fof(f1978,plain,
    ( spl0_133
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f440,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

fof(f1976,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f439,f1974]) ).

fof(f1974,plain,
    ( spl0_132
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f439,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).

fof(f1972,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f433,f1970]) ).

fof(f1970,plain,
    ( spl0_131
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f433,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).

fof(f1968,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f432,f1966]) ).

fof(f1966,plain,
    ( spl0_130
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f432,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).

fof(f1964,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f431,f1962]) ).

fof(f1962,plain,
    ( spl0_129
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f431,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).

fof(f1960,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f430,f1958]) ).

fof(f1958,plain,
    ( spl0_128
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f430,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).

fof(f1956,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f426,f1954]) ).

fof(f1954,plain,
    ( spl0_127
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f426,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).

fof(f1952,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f425,f1950]) ).

fof(f1950,plain,
    ( spl0_126
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f425,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).

fof(f1948,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f424,f1946]) ).

fof(f1946,plain,
    ( spl0_125
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f424,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).

fof(f1944,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f416,f1942]) ).

fof(f1942,plain,
    ( spl0_124
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f416,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).

fof(f1940,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f415,f1938]) ).

fof(f1938,plain,
    ( spl0_123
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f415,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).

fof(f1936,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f414,f1934]) ).

fof(f1934,plain,
    ( spl0_122
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f414,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).

fof(f1932,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f413,f1930]) ).

fof(f1930,plain,
    ( spl0_121
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f413,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).

fof(f1928,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f410,f1926]) ).

fof(f1926,plain,
    ( spl0_120
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f410,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).

fof(f1924,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f404,f1922]) ).

fof(f1922,plain,
    ( spl0_119
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f404,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).

fof(f1920,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f403,f1918]) ).

fof(f1918,plain,
    ( spl0_118
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f403,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

fof(f1916,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f402,f1914]) ).

fof(f1914,plain,
    ( spl0_117
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f402,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).

fof(f1912,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f401,f1910]) ).

fof(f1910,plain,
    ( spl0_116
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f401,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

fof(f1908,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f400,f1906]) ).

fof(f1906,plain,
    ( spl0_115
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f400,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

fof(f1904,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f399,f1902]) ).

fof(f1902,plain,
    ( spl0_114
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f399,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

fof(f1900,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f398,f1898]) ).

fof(f1898,plain,
    ( spl0_113
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f398,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).

fof(f1896,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f397,f1894]) ).

fof(f1894,plain,
    ( spl0_112
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f397,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

fof(f1892,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f393,f1890]) ).

fof(f1890,plain,
    ( spl0_111
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f393,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).

fof(f1888,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f392,f1886]) ).

fof(f1886,plain,
    ( spl0_110
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f392,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).

fof(f1884,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f391,f1882]) ).

fof(f1882,plain,
    ( spl0_109
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f391,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).

fof(f1880,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f390,f1878]) ).

fof(f1878,plain,
    ( spl0_108
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f390,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).

fof(f1876,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f389,f1874]) ).

fof(f1874,plain,
    ( spl0_107
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f389,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).

fof(f1872,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f385,f1870]) ).

fof(f1870,plain,
    ( spl0_106
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f385,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).

fof(f1868,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f384,f1866]) ).

fof(f1866,plain,
    ( spl0_105
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f384,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).

fof(f1864,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f383,f1862]) ).

fof(f1862,plain,
    ( spl0_104
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f383,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).

fof(f1860,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f382,f1858]) ).

fof(f1858,plain,
    ( spl0_103
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f382,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).

fof(f1856,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f375,f1854]) ).

fof(f1854,plain,
    ( spl0_102
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f375,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).

fof(f1852,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f374,f1850]) ).

fof(f1850,plain,
    ( spl0_101
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f374,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).

fof(f1848,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f373,f1846]) ).

fof(f1846,plain,
    ( spl0_100
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f373,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).

fof(f1844,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f372,f1842]) ).

fof(f1842,plain,
    ( spl0_99
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f372,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).

fof(f1840,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f371,f1838]) ).

fof(f1838,plain,
    ( spl0_98
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f371,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).

fof(f1836,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f370,f1834]) ).

fof(f1834,plain,
    ( spl0_97
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f370,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).

fof(f1832,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f366,f1830]) ).

fof(f1830,plain,
    ( spl0_96
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f366,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).

fof(f1828,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f365,f1826]) ).

fof(f1826,plain,
    ( spl0_95
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f365,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).

fof(f1824,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f364,f1822]) ).

fof(f1822,plain,
    ( spl0_94
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f364,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).

fof(f1820,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f363,f1818]) ).

fof(f1818,plain,
    ( spl0_93
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f363,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).

fof(f1816,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f356,f1814]) ).

fof(f1814,plain,
    ( spl0_92
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f356,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).

fof(f1812,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f354,f1810]) ).

fof(f1810,plain,
    ( spl0_91
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f354,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).

fof(f1808,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f353,f1806]) ).

fof(f1806,plain,
    ( spl0_90
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f353,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).

fof(f1804,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f352,f1802]) ).

fof(f1802,plain,
    ( spl0_89
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f352,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

fof(f1800,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f347,f1798]) ).

fof(f1798,plain,
    ( spl0_88
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f347,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).

fof(f1796,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f346,f1794]) ).

fof(f1794,plain,
    ( spl0_87
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f346,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

fof(f1792,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f345,f1790]) ).

fof(f1790,plain,
    ( spl0_86
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f345,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).

fof(f1788,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f344,f1786]) ).

fof(f1786,plain,
    ( spl0_85
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f344,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

fof(f1784,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f343,f1782]) ).

fof(f1782,plain,
    ( spl0_84
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f343,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).

fof(f1780,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f338,f1778]) ).

fof(f1778,plain,
    ( spl0_83
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f338,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

fof(f1776,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f337,f1774]) ).

fof(f1774,plain,
    ( spl0_82
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f337,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).

fof(f1772,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f336,f1770]) ).

fof(f1770,plain,
    ( spl0_81
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f336,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).

fof(f1768,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f335,f1766]) ).

fof(f1766,plain,
    ( spl0_80
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f335,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).

fof(f1764,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f334,f1762]) ).

fof(f1762,plain,
    ( spl0_79
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f334,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).

fof(f1760,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f333,f1758]) ).

fof(f1758,plain,
    ( spl0_78
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f333,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).

fof(f1756,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f332,f1754]) ).

fof(f1754,plain,
    ( spl0_77
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f332,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).

fof(f1752,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f328,f1750]) ).

fof(f1750,plain,
    ( spl0_76
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f328,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).

fof(f1748,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f327,f1746]) ).

fof(f1746,plain,
    ( spl0_75
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f327,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).

fof(f1744,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f326,f1742]) ).

fof(f1742,plain,
    ( spl0_74
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f326,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).

fof(f1740,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f319,f1738]) ).

fof(f1738,plain,
    ( spl0_73
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f319,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).

fof(f1736,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f260,f1734]) ).

fof(f1734,plain,
    ( spl0_72
  <=> ! [X39] :
        ( ~ class_LOrder_Omeet__semilorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f260,axiom,
    ! [X39] :
      ( ~ class_LOrder_Omeet__semilorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).

fof(f1732,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f259,f1730]) ).

fof(f1730,plain,
    ( spl0_71
  <=> ! [X39] :
        ( ~ class_LOrder_Omeet__semilorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f259,axiom,
    ! [X39] :
      ( ~ class_LOrder_Omeet__semilorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).

fof(f1728,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f258,f1726]) ).

fof(f1726,plain,
    ( spl0_70
  <=> ! [X39] :
        ( ~ class_LOrder_Olorder(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f258,axiom,
    ! [X39] :
      ( ~ class_LOrder_Olorder(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).

fof(f1724,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f257,f1722]) ).

fof(f1722,plain,
    ( spl0_69
  <=> ! [X39] :
        ( ~ class_LOrder_Olorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f257,axiom,
    ! [X39] :
      ( ~ class_LOrder_Olorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).

fof(f1720,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f256,f1718]) ).

fof(f1718,plain,
    ( spl0_68
  <=> ! [X39] :
        ( ~ class_LOrder_Olorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f256,axiom,
    ! [X39] :
      ( ~ class_LOrder_Olorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).

fof(f1716,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f255,f1714]) ).

fof(f1714,plain,
    ( spl0_67
  <=> ! [X39] :
        ( ~ class_LOrder_Olorder(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f255,axiom,
    ! [X39] :
      ( ~ class_LOrder_Olorder(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).

fof(f1712,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f254,f1710]) ).

fof(f1710,plain,
    ( spl0_66
  <=> ! [X39] :
        ( ~ class_LOrder_Ojoin__semilorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f254,axiom,
    ! [X39] :
      ( ~ class_LOrder_Ojoin__semilorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

fof(f1708,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f253,f1706]) ).

fof(f1706,plain,
    ( spl0_65
  <=> ! [X39] :
        ( ~ class_LOrder_Ojoin__semilorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f253,axiom,
    ! [X39] :
      ( ~ class_LOrder_Ojoin__semilorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).

fof(f1704,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f98,f1702]) ).

fof(f98,axiom,
    ! [X0,X1] : c_in(X0,c_UNIV,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

fof(f1700,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f66,f1698]) ).

fof(f1698,plain,
    ( spl0_63
  <=> ! [X21] : ~ c_less(X21,X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f66,axiom,
    ! [X21] : ~ c_less(X21,X21,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

fof(f1696,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f64,f1694]) ).

fof(f1694,plain,
    ( spl0_62
  <=> ! [X21] : c_lessequals(c_0,X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f64,axiom,
    ! [X21] : c_lessequals(c_0,X21,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

fof(f1692,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f40,f1690]) ).

fof(f1690,plain,
    ( spl0_61
  <=> ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f40,axiom,
    ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).

fof(f1688,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f39,f1686]) ).

fof(f39,axiom,
    ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

fof(f1684,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f23,f1682]) ).

fof(f1682,plain,
    ( spl0_59
  <=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f23,axiom,
    ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

fof(f1680,plain,
    ~ spl0_58,
    inference(avatar_split_clause,[],[f1364,f1677]) ).

fof(f1677,plain,
    ( spl0_58
  <=> c_Message_Oagent_OServer = c_Message_Oagent_OSpy ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f1364,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).

fof(f1675,plain,
    ~ spl0_57,
    inference(avatar_split_clause,[],[f1325,f1672]) ).

fof(f1672,plain,
    ( spl0_57
  <=> c_emptyset = c_UNIV ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f1325,axiom,
    c_emptyset != c_UNIV,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

fof(f1670,plain,
    ~ spl0_56,
    inference(avatar_split_clause,[],[f1280,f1667]) ).

fof(f1667,plain,
    ( spl0_56
  <=> c_Numeral_Obit_OB0 = c_Numeral_Obit_OB1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f1280,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1__iff1_0) ).

fof(f1665,plain,
    ~ spl0_55,
    inference(avatar_split_clause,[],[f1188,f1662]) ).

fof(f1662,plain,
    ( spl0_55
  <=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f1188,axiom,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1__iff1_0) ).

fof(f1660,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f249,f1658]) ).

fof(f1658,plain,
    ( spl0_54
  <=> ! [X37] : class_Orderings_Oorder(tc_set(X37)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f249,axiom,
    ! [X37] : class_Orderings_Oorder(tc_set(X37)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).

fof(f1656,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f248,f1654]) ).

fof(f1654,plain,
    ( spl0_53
  <=> ! [X37] : class_Orderings_Oord(tc_set(X37)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f248,axiom,
    ! [X37] : class_Orderings_Oord(tc_set(X37)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).

fof(f1652,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f126,f1649]) ).

fof(f1649,plain,
    ( spl0_52
  <=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f126,axiom,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).

fof(f1647,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f124,f1644]) ).

fof(f1644,plain,
    ( spl0_51
  <=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f124,axiom,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).

fof(f1642,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f123,f1640]) ).

fof(f1640,plain,
    ( spl0_50
  <=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f123,axiom,
    ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

fof(f1638,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f244,f1635]) ).

fof(f1635,plain,
    ( spl0_49
  <=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f244,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).

fof(f1633,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f243,f1630]) ).

fof(f1630,plain,
    ( spl0_48
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f243,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).

fof(f1628,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f242,f1625]) ).

fof(f1625,plain,
    ( spl0_47
  <=> class_LOrder_Olorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f242,axiom,
    class_LOrder_Olorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).

fof(f1623,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f241,f1620]) ).

fof(f1620,plain,
    ( spl0_46
  <=> class_LOrder_Ojoin__semilorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f241,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).

fof(f1618,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f236,f1615]) ).

fof(f1615,plain,
    ( spl0_45
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f236,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).

fof(f1613,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f235,f1610]) ).

fof(f1610,plain,
    ( spl0_44
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f235,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).

fof(f1608,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f234,f1605]) ).

fof(f1605,plain,
    ( spl0_43
  <=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f234,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).

fof(f1603,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f233,f1600]) ).

fof(f1600,plain,
    ( spl0_42
  <=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f233,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).

fof(f1598,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f232,f1595]) ).

fof(f1595,plain,
    ( spl0_41
  <=> class_LOrder_Omeet__semilorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f232,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).

fof(f1593,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f231,f1590]) ).

fof(f1590,plain,
    ( spl0_40
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f231,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).

fof(f1588,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f230,f1585]) ).

fof(f1585,plain,
    ( spl0_39
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f230,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).

fof(f1583,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f229,f1580]) ).

fof(f1580,plain,
    ( spl0_38
  <=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f229,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).

fof(f1578,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f228,f1575]) ).

fof(f1575,plain,
    ( spl0_37
  <=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f228,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).

fof(f1573,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f227,f1570]) ).

fof(f1570,plain,
    ( spl0_36
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f227,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).

fof(f1568,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f226,f1565]) ).

fof(f1565,plain,
    ( spl0_35
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f226,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).

fof(f1563,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f225,f1560]) ).

fof(f1560,plain,
    ( spl0_34
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f225,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).

fof(f1558,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f221,f1555]) ).

fof(f1555,plain,
    ( spl0_33
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f221,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).

fof(f1553,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f210,f1550]) ).

fof(f1550,plain,
    ( spl0_32
  <=> class_Orderings_Oord(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f210,axiom,
    class_Orderings_Oord(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).

fof(f1548,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f195,f1545]) ).

fof(f1545,plain,
    ( spl0_31
  <=> class_Finite__Set_Ofinite(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f195,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).

fof(f1543,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f194,f1540]) ).

fof(f1540,plain,
    ( spl0_30
  <=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f194,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).

fof(f1538,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f183,f1535]) ).

fof(f1535,plain,
    ( spl0_29
  <=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f183,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).

fof(f1533,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f181,f1530]) ).

fof(f1530,plain,
    ( spl0_28
  <=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f181,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).

fof(f1528,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f180,f1525]) ).

fof(f1525,plain,
    ( spl0_27
  <=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f180,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).

fof(f1523,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f178,f1520]) ).

fof(f1520,plain,
    ( spl0_26
  <=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f178,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).

fof(f1518,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f177,f1515]) ).

fof(f1515,plain,
    ( spl0_25
  <=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f177,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).

fof(f1513,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f176,f1510]) ).

fof(f1510,plain,
    ( spl0_24
  <=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f176,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).

fof(f1508,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f175,f1505]) ).

fof(f1505,plain,
    ( spl0_23
  <=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f175,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).

fof(f1503,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f174,f1500]) ).

fof(f1500,plain,
    ( spl0_22
  <=> class_Orderings_Oord(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f174,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

fof(f1498,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f173,f1495]) ).

fof(f1495,plain,
    ( spl0_21
  <=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f173,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).

fof(f1493,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f172,f1490]) ).

fof(f1490,plain,
    ( spl0_20
  <=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f172,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).

fof(f1488,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f171,f1485]) ).

fof(f1485,plain,
    ( spl0_19
  <=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f171,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).

fof(f1483,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f170,f1480]) ).

fof(f1480,plain,
    ( spl0_18
  <=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f170,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).

fof(f1478,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f169,f1475]) ).

fof(f1475,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f169,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).

fof(f1473,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f168,f1470]) ).

fof(f1470,plain,
    ( spl0_16
  <=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f168,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).

fof(f1468,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f167,f1465]) ).

fof(f1465,plain,
    ( spl0_15
  <=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f167,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).

fof(f1463,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f166,f1460]) ).

fof(f1460,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f166,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).

fof(f1458,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f165,f1455]) ).

fof(f1455,plain,
    ( spl0_13
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f165,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).

fof(f1453,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f164,f1450]) ).

fof(f1450,plain,
    ( spl0_12
  <=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f164,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).

fof(f1448,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f162,f1445]) ).

fof(f1445,plain,
    ( spl0_11
  <=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f162,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).

fof(f1443,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f161,f1440]) ).

fof(f1440,plain,
    ( spl0_10
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f161,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).

fof(f1438,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f160,f1435]) ).

fof(f1435,plain,
    ( spl0_9
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f160,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).

fof(f1433,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f159,f1430]) ).

fof(f1430,plain,
    ( spl0_8
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f159,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).

fof(f1428,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f158,f1425]) ).

fof(f1425,plain,
    ( spl0_7
  <=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f158,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

fof(f1423,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f157,f1420]) ).

fof(f1420,plain,
    ( spl0_6
  <=> class_LOrder_Olorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f157,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).

fof(f1418,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f156,f1415]) ).

fof(f1415,plain,
    ( spl0_5
  <=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f156,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).

fof(f1413,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f155,f1410]) ).

fof(f1410,plain,
    ( spl0_4
  <=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f155,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).

fof(f1408,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f154,f1405]) ).

fof(f1405,plain,
    ( spl0_3
  <=> class_Orderings_Oorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f154,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

fof(f1403,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f1391,f1400]) ).

fof(f1391,axiom,
    c_lessequals(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f1398,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f1390,f1395]) ).

fof(f1390,axiom,
    c_lessequals(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWV242-1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 04:28:19 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (17255)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40  % (17258)WARNING: value z3 for option sas not known
% 0.21/0.40  % (17258)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)
% 0.21/0.40  % (17257)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.41  % (17260)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)
% 0.21/0.41  % (17261)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)
% 0.21/0.41  % (17256)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.41  % (17259)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.41  % (17262)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)
% 0.21/0.46  TRYING [1]
% 0.21/0.48  TRYING [2]
% 1.31/0.57  TRYING [3]
% 2.12/0.70  TRYING [1]
% 2.12/0.73  TRYING [2]
% 2.63/0.76  TRYING [1]
% 2.78/0.77  TRYING [2]
% 2.78/0.81  % (17260)First to succeed.
% 3.19/0.83  TRYING [3]
% 3.19/0.84  % (17260)Refutation found. Thanks to Tanya!
% 3.19/0.84  % SZS status Unsatisfiable for theBenchmark
% 3.19/0.84  % SZS output start Proof for theBenchmark
% See solution above
% 3.34/0.85  % (17260)------------------------------
% 3.34/0.85  % (17260)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 3.34/0.85  % (17260)Termination reason: Refutation
% 3.34/0.85  
% 3.34/0.85  % (17260)Memory used [KB]: 8132
% 3.34/0.85  % (17260)Time elapsed: 0.433 s
% 3.34/0.85  % (17260)Instructions burned: 1119 (million)
% 3.34/0.85  % (17260)------------------------------
% 3.34/0.85  % (17260)------------------------------
% 3.34/0.85  % (17255)Success in time 0.481 s
%------------------------------------------------------------------------------